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http://www4.ncsu.edu/unity/lockers/users/f/felder/public/tutorials/excel1.html | 1,443,977,984,000,000,000 | text/html | crawl-data/CC-MAIN-2015-40/segments/1443736675795.7/warc/CC-MAIN-20151001215755-00232-ip-10-137-6-227.ec2.internal.warc.gz | 1,166,356,722 | 13,251 | I. FUNDAMENTALS, FORMULAS, AND FUNCTIONS
Richard M. Felder
Department of Chemical Engineering
North Carolina State University
(Revised by E.M. Wilcox, August, 1998)
A spreadsheet is a matrix of information, organized by rows and columns. Each cell of the spreadsheet may contain a number, a character string, or a mathematical formula. An illustrative spreadsheet is shown below.
A B C D 1 Personal Budget Sheet: September 1998 2 3 Actual 4 Budget Expense Saving 5 6 Entertainment \$50.00 \$60.00 (\$10.00) 7 Books \$20.00 \$0.00 \$20.00 8 Groceries \$150.00 \$120.00 \$30.00 9 Rent \$150.00 \$150.00 \$0.00 10 Stationery \$10.00 \$0.00 \$10.00 11 Transportation \$20.00 \$10.00 \$10.00 12 Utilities \$30.00 \$30.00 \$0.00 13 14 Total \$430.00 \$370.00 \$60.00
The spreadsheet has 14 rows and four columns (A-D).
In preparing this spreadsheet, the user will have typed in labels (text) or numbers for the cells in Rows 1-12, Columns A-C, such as
Expense in Cell [C4] (Column C, Row 4)
150.00 in Cell [B8]
In other cells the user will have placed formulas to be used to calculate the cell contents. For instance, the formula in Cell D6 would be
=B6-C6 (entered in Cell D6)
which means, subtract the number in Cell C6 from the number in Cell B6 and put the result in Cell D6. (All formulas begin with equal signs.) The formula in Cell B14 might be
=SUM(B6:B12) (entered in Cell B14)
which means add the numbers in Cells B6 through B12 and put the result in Cell B14.
Once input values and formulas have been entered in their respective cells, the spreadsheet program executes all the formulas and inserts the results in the corresponding cells of the spreadsheet. If some of the cell values are then changed, the formulas are automatically recalculated to reflect the new input values. Once the spreadsheet has been prepared it can be printed out and used to generate plots and tables to be included in a report.
RUNNING EXCEL ON UNITY/EOS WORKSTATIONS
Excel is Microsoft's (and the world's) most popular spreadsheet program. It runs on Windows machines (like the Windows NT workstations in the basement of the laundry building) and on Macintoshes. It can also run on UNIX machines (like the SPARCstations in Riddick 118), but only under a Windows emulator like SoftWindows or WABI, both of which can be accessed from the SPARCstations. Running on a Windows machine rather than a Windows emulator is invariably faster.
IMPORTANT COMMANDS
Before taking you through an introductory tutorial, we list several important commands for easy reference. If you want to quit a session or if you get in trouble, check this list.
• Entering Excel.
1. UNIX Workstations. To start an Excel session on EOS on a workstation that runs under UNIX (like the SPARCstations in 118 Riddick), move the pointer outside any existing windows, hold down the middle mouse button until the Application Menu appears, drag the pointer down to MS-Window Emulation and to the right and down to Soft Windows or WABI, and release. It may take few minutes for Windows to start. A Windows 3.1 window will eventually open.
Under Program Manager, double-click on MS Office and then on Excel. Excel will open in a new window. If you have never used Excel before, you may want to take a few minutes to work through the "Getting Started" tutorial. Click on "Return to Microsoft Excel" to begin using Excel.
2. Windows NT Workstations. (Instructions still to follow.)
To recover a spreadsheet that you previously stored, choose the File menu and select Open. Alternatively, click the "Open File" icon (which looks like a yellow file folder being opened) at the far left of the Excel tool bar. In the dialog window that opens, point to the name of the desired spreadsheet file under "File Name" (scroll to it if necessary) and then double-click the left mouse button. The stored spreadsheet will appear in the worksheet window and its name will appear in the header. If you do not see any files, make sure that under "List Files of Type" it says Microsoft Excel Files (*.xl*) or alternatively All Files (*.*).
• Saving.
To store (save) the worksheet you have been working on, choose the File menu and select Save, or click the ``Save File'' icon (which looks like a floppy disk with an arrow pointing into it on the Excel tool bar). Name the spreadsheet in the dialog window that opens, or click on OK to save under the previous name. The file name may be anything you like, but the file type should be .xls (e.g. budget.xls).
Save frequently while you are working!
• Getting on-line help.
If you have never done so, explore the on-line Help facility (use the Help menu button at the upper right of the Excel window) to get an idea of the kind of information available there. If you don't explore the facility first, you may not think of using it when you need it.
• Quitting.
To quit Excel, choose the File menu and select Exit, or double click on the horizontal bar in the upper left-hand corner. To exit the windows emulator, go to the Program Manager window and exit as you did in Excel.
TUTORIAL
Getting Started
Log on and open Excel, following the procedure given previously for the type of workstation you are running (Windows or UNIX). The Excel window that opens has the following components (find them on the screen as we describe them):
• Sheet (or Worksheet:) The large grid with columns labeled A,B,C,... and rows labeled 1,2,3,... You enter values (sometimes numbers, sometimes alphanumeric text) in some of the cells of the worksheet (e.g. Cell [C3], located in Column C and Row 3) and enter formulas in other cells. You can build a spreadsheet with many more rows and columns than are shown on the screen at the moment; you just can't display all of it at once.
For large programs it is often convenient to work on more than one sheet. To create or switch to a different sheet, you would click on the number of the sheet you wish to change to at the bottom of the Excel window. (Don't do it now.) The Workbook is the set of worksheets that comprise a complete file.
• Title bar. The bar at the top of the window frame with "Microsoft Excel - Book 1" in it. As soon as you save a current spreadsheet or load a new one, the spreadsheet file name will appear in the title bar.
• Standard toolbar. This toolbar contains buttons that provide convenient shortcuts for some of the more commonly used operations, such as opening and saving files, printing the spreadsheet, formatting cells, cutting and pasting, and creating graphs.
• Menu bar. You select items for each of the menus shown by holding down the left mouse button on the desired menu button (e.g. File or Format or Tools), dragging the pointer down to the desired menu selection, and releasing the mouse button.
• Formatting toolbar. The formatting toolbar displays the font used for text and numbers (Arial is default), the font size (10 is default), buttons to make selected text boldface (B), italicized (I), or underlined (U), buttons to make text left-adjusted, centered, or right-adjusted within a cell, and several others.
• Formula bar. The line just above the worksheet column headings (A B C...) contains a narrow window (the address window) and a wide window (the edit line).
• The address window should now contain [A1], indicating that the cell cursor is at Column A, Row 1. (The cursor location is the cell with the darkened border on the worksheet.) Type a number now, but don't hit the return key.
• As soon as you entered information in the cell, an X, a check mark, and an = or an fx (depending on which type of machine you're on) were displayed to the right of the edit line if they weren't already there. If you click on the X, the previous value in the cell will remain unchanged. If you click on the check mark or hit [Return], what you typed will be entered. (Don't worry about the other button for now.) Try it.
• When you click on a cell, whatever is in the cell will be displayed on the edit line. As soon as you type anything, whatever you type will appear on the edit line, replacing the former cell contents.
Some of our descriptions may not exactly match what you seen on your screen. The reason is that two different versions of Excel are installed on the Windows NT and UNIX file servers.
We will explain the other features of the Excel window in the exercises that follow. The symbol [Return] henceforth denotes the Return or Enter key.
Moving around the worksheet
1. Move the cursor around the worksheet using the mouse. Move the pointer to different cells of the worksheet and click the left mouse button. Note that the cell cursor jumps to the cell on which you click and the cell address of its new location is shown on the control/status line.
2. Move the cursor with the arrow keys. Use the four arrow keys toward the lower right of the keyboard to move the cell cursor up, down, left, and right.
3. Go directly to a named cell. Using the mouse, choose the Edit menu (move the pointer to it and press and hold the left mouse button) and select Go to... (drag the pointer down to that item and release the button). In the Selection window of the dialog box that appears, type D5 [Return]. The cursor should now be in Cell D5.
4. Return the cursor to Cell A1. Press [Control][Home]. (The control key is toward the lower left of the keyboard and the home key is in the second group of keys from the right.)
5. Shift the worksheet. Hold the right arrow down to push the cursor past the rightmost column showing on the screen. Notice that you are bringing additional columns into view on the right and pushing others off to the left. Keep going past Column Z and observe how the adjacent columns are labeled (AA, AB, AC,...). Now move down to higher numbered rows at the bottom with the down arrow, pushing upper rows out of view at the top.
• Enter a number in a cell. Send the cursor to Cell AV61. (Use the Go To command under the Edit menu.) Type 27 [Return]. The number you typed should appear in Cell AV61.
Scrolling the worksheet.
• Scroll horizontally one column at a time. Look at the bar just below the last visible row of the worksheet. On the left are some arrow buttons (for scrolling from one sheet to another) and sheet numbers, and on the right is the horizontal scroll bar, a window with a button or bar inside it and arrow buttons on either side. Point to the small arrow button at the left of the scroll bar and click. The worksheet shifts left by one column. Do it once more. Now scroll back to the right, with the arrow at the right of the scroll bar, until the 27 reappears at the lower right.
• Scroll horizontally with the slider bar. Move the pointer to the slider bar (the button within the scroll bar). Hold the left mouse button down and move the pointer left and then right to scroll the worksheet horizontally.
• Scroll vertically. Use the vertical scroll bar to the right of the worksheet to scroll up and down a row at a time (click on arrows) or continuously (drag the slider bar with the pointer).
• Return to the upper left of the worksheet. Press [Control][Home]. Cell [A1] should appear at the upper left corner of the worksheet with the cursor in it.
In the remainder of this tutorial, you will produce a spreadsheet that appears as follows:
Trial Worksheet: M= 3 Run X Y M(X-Y) 1 2 4 -6 2 3 4 -3 3 6 2 12 TOTAL 11 10 3
You will enter the first row, the column titles, the entries for the Columns headed RUN, X, and Y, and the word TOTAL, and you will then enter formulas that Excel will use to calculate the values of M(X-Y) and the column totals.
Entering labels and numbers in cells
A cell can contain:
• a number
• a label--any string of characters, like RUN, X, and TOTAL
• a formula, like =(2.0+B5)/C5 (two plus the number in Cell B5 divided by the number in Cell C5). Formulas always begin with equal signs.
We will show you how to enter labels and numbers in the next series of instructions, and we will eventually get to formulas.
Note: Throughout the remainder of the exercise we will tell you to type things enclosed in angled brackets (< >) followed by [Return]: for example, type < 26.3 > [Return]. (Don't type it now.) When you see instructions like this, type what is in the brackets but not the brackets themselves and then hit the Return key.
11. Enter a label in a cell.
• Move the cursor to Cell [A1] if it is not already there.
• Type < Trial Wormsheet: M = >. For the moment, don't follow it with [CR]. (Don't type the brackets, and really type ``Wormsheet"). What you typed should appear on the edit line.
Whenever text is displayed on the edit line, you can edit it using the mouse, arrow keys, and delete key, just as though you were editing a text file in a text editor or word processing program.
• Now hit the [Return] key to insert the text in Cell A1. The text has gone over the width of Column A, but since nothing will be entered in Cell B1 this is not a problem.
Instead of hitting the [Return] key to enter what you typed into Cell [A1], you could have clicked on the check symbol. In either case the cursor would remain on Cell [A1]. You could also have hit the down arrow key to move the cursor down to Cell [A2] or the right arrow to move the cursor right to Cell [B1] after the entry had been made in Cell [A1]. If you had wanted to cancel the editing without changing the content of Cell [A1], you could have clicked on the X symbol.
12. Move the cursor to Cell C1 (point at it and click the left mouse button). Type < 3 >.
Don't type [Return] yet. (If you did, type another 3.) As soon as you typed the number, it appeared on the edit line preceded by an =. If you had wanted the 3 to be considered a label, you would have preceded it with an apostrophe ('3).
13. Type [Return] to enter the 3 in Cell C1.
14. Move the cursor to Cell A3. Type RUN[Return].
Notice that the text appears at the left of the cell (i.e., it is left-justified in the column). Excel does this automatically when you enter anything but a number or formula.
15. Justify and center labels.
You can position a label in a cell using the justification buttons on the formatting tool bar. These buttons have icons consisting of left justified, centered, and right justified lines. Clicking on these buttons will adjust the positioning of the text in a highlighted region or in the current cell if no region is highlighted. Try it in Cell C3, ending by right-justifying the label.
16. Enter a number and move the cursor down one cell.
Move the cursor to Cell A5 and type 1. Then hit the down-arrow key to enter the number and move the cursor down to the next cell. Notice that numbers are automatically right justified.
17. Enter 2 and 3 respectively in Cells A6 and A7, moving down with each entry.
• Enter < TOTAL >[Return] in Cell A9, and then right-justify it.
• Move the cursor to Cell B3. (Point and click.)
• Enter < X > [Return] and right-justify it.
• Enter 5, 3, and 6 in Cells B5, B6, and B7.
• Move the cursor to Cell C3 and enter < Y >(right justified).
• Enter 4, 4, and 2 in Cells C5, C6, and C7.
At this point the worksheet should appear as follows (with slightly different spacing):
Trial Wormsheet: M = RUN X Y 1 5 4 2 3 4 3 6 2 TOTAL
Not shown but still part of the worksheet is the 27 in Cell AV61.
Erasing and editing cell contents
18. Erase the contents of a cell. Let's now get rid of that 27.
• Move the cursor to Cell AV61 (use the Go To command under the View menu).
• Choose the Edit menu and select Clear then All. Alternatively, you can just hit the delete or backspace button. The 27 should disappear from Cell AV61.
• Send the cursor back to Cell A1. ([Control][Home])
19. Edit (revise) the contents of a cell.
We now observe that the word Wormsheet in Cell A1 should really be Worksheet. Move the pointer next to the offending m in the edit line. Hold down the left mouse button and drag the pointer over the m, so that it (and only it) is highlighted. Type k [Return]. The corrected text should appear in Cell A1.
Naming and saving a worksheet
Choose the File menu and select Save As... After a few seconds a dialog window will come up with your current directory name in the Selection window. Click on the file name and type [mod1.xls]. The file worksheet has now been stored under the name mod1.xls and the file name appears at the top of the spreadsheet window. A convenient shortcut for saving the spreadsheet is the Save button on the tool bar, which appears as a floppy disk icon.
You can give a stored spreadsheet file any name you want. However, for normal applications the type should always be .xls.
Selecting a range of cells (highlighting a region of the worksheet)
20. Select a range with the mouse.
Move the pointer to Cell A5. Hold down the left mouse button, drag the pointer to Cell [C7], and release.
The black rectangular region defined by your starting point (Cell A5) and finishing point (Cell C7) has been selected. Once you have selected a region, you may do a variety of things with it (don't do any of them now):
• Erase the contents of the selected cells (using the Clear command under the Edit menu).
• Copy the contents to another region of the worksheet, having them also remain where they are (using the Copy command under the Edit menu).
• Cut them from their current location and Paste them somewhere else (using the Cut and Paste commands under the Edit menu).
• Format the selected cells (using the Cells command under the Format menu) so that whatever numbers appear in them now and subsequently are written as decimals with a specified number of digits past the decimal point (fixed format), or in scientific notation, e.g. 4.1e-03 (scientific format), or with dollar signs, etc.
21. Deselect.
Click the left mouse button anywhere in the worksheet outside the highlighted region. The highlighting disappears.
22. Select a range using the Select command.
• Choose the Edit menu and select the Go To command. A dialog window should come up with a cursor blinking in the selection box.
• Type [ a5:b7 ] [Return]. The highlight box should cover the designated region (a5 at the upper left to b7 at the lower right). (This is a convenient way to select a range that goes beyond the visible portion of the worksheet.)
• Deselect. (Point and click anywhere in the worksheet area.)
23. Select an entire column, an entire row, or the complete worksheet..
• Click the left mouse button on the letter at the top of any column. The entire column is selected. You can select an entire row by clicking on its number to the left of the worksheet, or select the entire worksheet area by clicking the button at the top left corner of the worksheet (above 1 and to the left of A). Try it.
• Deselect in the usual way.
Copying Cells
• Select the range you wish to copy. Select range A3:B7 by pointing at Cell A3, holding down the left button, dragging to Cell B7, and releasing.
• Copy the selected range. Right click on the highlighted cells, and select copy. Point to Cell D3 (the upper left cell of the region in which you want the selected range to be copied) and click the right mouse button and select paste. The range should be duplicated, with the upper left cell in the location you clicked on (Cell D3). You could have done the same thing by choosing Copy from the Edit menu and then clicking on Cell D3and choosing Paste from the Edit menu. There are also copy and paste buttons on the toolbar.
• Erase the cell values just inserted. Select range D3:E7 by pressing the left mouse button and dragging the pointer. Choose the Edit menu and select Clear - All. The cells should now be blank. Alternatively, you can undo the copy by selecting Edit - Undo, or by clicking the counterclockwise arrow icon on the tool bar.
Saving the revised worksheet.
24. Choose the File menu and select Save. Alternatively, click the disk icon on the tool bar. The current version of the spreadsheet will be saved under the same file name (mod1.xls).
You should never work for more than three minutes without saving. If the system crashes while you are working, you will lose everything you have done since the last save.
Quitting Excel
25. Choose the File menu and select Exit.
You can now log off and take a break or proceed directly to Step 26 to continue the exercise. Before you log off, be sure to close the windows emulator.
* * * * *
Recalling stored worksheets
If you logged off before, bring up Excel again. (On a UNIX workstation, press the middle mouse button to bring up the Applications Menu and select MS-Windows Emulators - Soft Windows; under Program manager double click on MS Office; double click on Excel.)
26. Open the previously saved file.
Choose the File menu and select Open. When the dialog window comes up, point to the name of the desired file (mod1.xls), first scrolling to it or changing the drive if necessary, and then double-click with the left mouse button. The worksheet generated previously should appear on the screen. If it does not, recreate it.
Entering Formulas
Enter M(X-Y) in Cell D3 and right-justify it (i.e., enter M(X-Y) [Return] and right-justify it (button on the formatting toolbar).
28. Enter a formula in a cell.
• Move the cursor to Cell D5.
• Type < =\$C\$1 * (B5-C5) >[Return]. (Don't omit the = sign.)
You have just entered the formula D5 = C1*(B5-C5). The value in Cell D5 will be that in Cell C1 (3) times the difference between the value in Cell B5 (5) minus that in Cell C5 (4). The formula appears on the edit line and the calculated value (3) appears in the cell on the worksheet. (We will explain the dollar signs in front of the column and row labels of Cell C1 when we talk about copying formulas.)
Note the following points about formulas:
• When you begin an entry with an equal sign (=), Excel understands that what follows is either a number or a formula (as opposed to a label). (To enter a label, which begins with an equal sign, you must prefix the label with a left quote mark (').)
• Any component of a cell entry consisting of one or two letters followed by one or two numbers (e.g. B6, D16, AM27) is taken to be a cell address, and the number in that cell will be substituted in the formula.
• The arithmetic operators that can go in formulas are +, -, * (multiplication), / (division), and ^ (exponentiation). For example, D6^2 signifies the square of the value in Cell D6.
• If a formula contains a string of operations, e.g. 5^2 + 3/4 * 6, all exponentiations will be done first, then all multiplications and divisions from left to right, and finally all additions and subtractions from left to right. To change this order, use parentheses.
29. Enter a formula by pointing and clicking on component cells.
Keeping the cursor on Cell D5,
• Type < =\$C\$1 * ( >( (no [Return] yet)
• Point to Cell B5 and click. Notice that the cell address appears in the formula on the edit line.
• Type < - >
• Click on Cell C5. Observe the result on the edit line.
• Type < ) >[Return].
The same formula has now been entered in Cell D5, with the same result.
In short, you can insert a cell address in a formula by typing it in or by pointing at the cell and clicking the left mouse button.
30. Change the value of a cell that appears in a formula.
Change the value in Cell B5 to 2 (click on Cell B5 and type 2 [Return]). Notice that the value in Cell D5 immediately changes (to -6), reflecting the new value in B5.
Copying a Formula
We now want to copy the formula in Cell D5 into Cells D6 and D7, but not to copy it exactly. We want each cell in Column D to contain the difference between the values in the same row of Column B (X) and Column C (Y) multiplied by the value in C1. Thus, the formula in Cell D6 should be D6 = C1*(B6-C6), and that in Cell D7 should be D7 = C1*(B7-C7). This task turns out to be very easy to accomplish with Excel. Excel will automatically change the cell names when a formula is copied.
31. Copy a formula in one cell into selected adjacent cells.
• Select the cell containing the formula to be copied. Point to Cell D5 and click on it.
• Copy the formula by clicking and dragging over the desired target range. Point to the little black square at the lower right corner of Cell D5, press and hold the left mouse button, drag the cursor down to Cell D7, and release.
The formula has now been copied, with the appropriate changes in cell addresses having been made automatically. (Check this: click on Cell D6 and look at the formula in the edit line, and then do the same for Cell D7.)
How did Excel know which cell addresses should go in the copied formulas? The answer follows.
Relative and Fixed Cell Addresses in Formulas
• When you enter cell addresses such as B5 and C5 in formulas they are relative addresses. Suppose the formula cell is the cell containing the formula (D5). To Excel, the formula (B5-C5) in Cell D5 means the value two cells to the left of the formula cell (B5) minus the value one cell to the left of the formula cell (C5).
• When you copy a formula from one cell (D5) to another (D6), the same addresses relative to the new formula cell are used. If the formula in Cell D5 involves B5, then the copied formula in Cell D6 will instead involve B6 (as before, the cell two columns to the left of the formula cell).
• Sometimes you may want to refer to a fixed cell address in a formula, i.e., a cell address that should not change when you copy the formula to a new cell. For example, we did not want Cell C1 in our formula to change to C2, C3, etc., when we copied to lower formula cells. To keep a cell address fixed, we precede the row and column identifiers of the fixed address in the formula with dollar signs. Thus, \$C\$1 in a formula will always be Cell C1, regardless of where on the worksheet the formula is copied. (\$C1 would fix the column but would let the row vary.)
Excel Functions
32. Move to Cell B9. Type < =SUM(B5:B7) >[Return].
You have just used an Excel function called SUM, which calculates the sum of the cell values in its argument (in this case, Cells B5 through B7).
Excel has a variety of built-in mathematical functions (ABS, EXP, LN, SIN, etc.), statistical functions (AVERAGE, MAX, MIN), financial functions, and others. Some of these functions are listed at the end of this tutorial.
33. Copy the formula in Cell B9 into Cells C9 and D9.
• Click on Cell B9.
• Point to the square at the lower right of Cell B9, drag over C9:D9, and release.
You copied the formula in Cell B9 into Cells C9 and D9, changing the cell addresses appropriately. Verify that the formulas (edit line) and the values (worksheet) in Cells C9 and D9 are correct.
The worksheet should now appear like the one shown at the beginning of this exercise.
34. Save.
35. Change a cell value and recalculate the spreadsheet.
Change the value in Cell B6 to 5. Notice that all cells affected by this change (B9, D6, and D9) instantly assume their new values.
36. Print the worksheet.
Choose the File menu and select Print. Alternatively, click the printer icon on the tool bar. In the dialogue box that comes up, choose "Selected sheet" and click on OK.
If you only wanted to print a portion of the spreadsheet you would select the desired range and then click on "Selection" in the dialogue box. If you have a number of sheets and want to print all of them, you would choose "Entire Workbook."
37. Exit from Excel. Choose the File menu and select Exit.
APPENDIX: EXCEL FUNCTIONS
Listed below are some (but not all) of the built-in functions provided by Excel. Arguments may be numbers, cell addresses, or cell ranges [e.g. EXP(4.5), SUM(A2,A4), AVERAGE(C6:C15)].
If a function has multiple arguments, the argument values or the addresses of the cells containing these values may be listed as ranges (C3:C9), or as individual cell addresses and/or numbers separated by commas (A4,C5,17.3), or a combination (A5,B4:B8,C3). To get a complete list of functions and more information about them, use the on-line help facility.
ABS(X) Absolute value of X COS(X) Cosine of X (X in radians) EXP(X) ex INT(X) Integer value of X LN(X) ln X LOG(X) log X RADIANS(X) 3.14159 X/180 RAND() Returns a random number uniform on the interval [0,1]. SIN(X) Sine of X (X in radians) SQRT(X) Square root of X TAN(X) Tangent of X (X in radians) AVERAGE(X:Y) Average of the arguments RSQ(R1,R2) Pearson's product-moment correlation coefficient for he paired data in Ranges R1 and R2 COUNT(X:Y) Count of non-blank arguments MAX(X:Y) Maximum of the arguments, not counting blank cells and cells containing text strings MIN(X:Y) Minimum of the arguments SUMSQ(X:Y) Sum of squares of the arguments STDEV(X:Y) Sample standard deviation of the arguments (N-1 weighting) SUM(X:Y) Sum of the arguments VARS(X:Y) Sample variance (N-1 weighting) of the arguments MDETERM(M) Determinant of the square matrix specified by Range M MINVERSE(M) Inverse of square matrix M MMUL(M1,M2) Product of multiplication of matrix M2 by matrix M1 TRANSPOSE(M) Transpose of matrix | 6,849 | 29,084 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2015-40 | longest | en | 0.832285 |
https://www.extendoffice.com/excel/functions/excel-pearson-function.html | 1,718,901,541,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861957.99/warc/CC-MAIN-20240620141245-20240620171245-00855.warc.gz | 648,575,633 | 39,336 | ## Excel PEARSON Function
The PEARSON function returns the Pearson product-moment correlation coefficient (r) for two supplied sets of values.
#### Syntax
=PEARSON(array1, array2)
#### Arguments
• array1 (required): A set of independent values.
• array2 (required): A set of dependent values.
#### Return Value
The PEARSON function returns a numeric value.
#### Function Notes
• Arguments can be either of the following:
• Numbers;
• Names, arrays, or references that contain numbers.
• Logical values and other values that can be converted to numbers that you type directly into the list of arguments will be counted.
• If text or empty cells are referenced as either of the arguments, the values will be ignored.
• PEARSON returns the #N/A error if the number of values that are directly supplied as array1 and array2 is different.
• PEARSON returns the #DIV/0! error if:
• array1 and/or array2 are empty;
• array1 and/or array2 have only one data point;
• The standard deviation of the values in one or both of the supplied arrays equals to zero.
• The equation for the Pearson product moment correlation coefficient (r) is:
Where x and y are the sample means of the two arrays of values.
#### Example
Take the table below as an example. To get the Pearson product-moment correlation coefficient for two supplied sets of values listed in the table, please copy or enter the formula below in the result cell, and press Enter to get the result.
=PEARSON(B6:B12,C6:C12)
#### Related functions
Excel RSQ Function
The RSQ function returns the square of the Pearson product-moment correlation coefficient (r2) for two supplied sets of values.
Excel CORREL Function
The CORREL function returns the correlation coefficient of two cell ranges, which can be used to determine the relationship between two properties.
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• Brings Efficient Tabs to Office (include Excel), Just Like Chrome, Edge and Firefox. | 932 | 3,838 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.15625 | 3 | CC-MAIN-2024-26 | longest | en | 0.658841 |
http://www.caraudio.com/forums/amplifiers/395354-fuse-rating-vs-rms-question.html | 1,448,620,311,000,000,000 | text/html | crawl-data/CC-MAIN-2015-48/segments/1448398448506.69/warc/CC-MAIN-20151124205408-00103-ip-10-71-132-137.ec2.internal.warc.gz | 336,549,180 | 14,266 | 1. ## Fuse rating vs. RMS question
Is it true that if a amp has two 30 amp fuses it can only put out 600 watts rms?
2x40 amp fuses = 800 wrms max ect ect...
2. ## Re: Fuse rating vs. RMS question
roughly. its about 10a per 100w
3. ## Re: Fuse rating vs. RMS question
that is just in general, for every 100 clean rms you need 10a of current.
some amps,as an example, are 80%efficent and some are 60%. so it will vary from amp to amp.
4. ## Re: Fuse rating vs. RMS question
so 2x40 amp fuses can do 800wrms at 100% efficiency but it cant possibly do more right?
5. ## Re: Fuse rating vs. RMS question
Originally Posted by BamBam28
so 2x40 amp fuses can do 800wrms at 100% efficiency but it cant possibly do more right?
at 100% yes but there arnt any 100%efficient amps that i know of. it wont do more than 800 clean rms though.
6. ## Re: Fuse rating vs. RMS question
Originally Posted by skmfkr
roughly. its about 10a per 100w
according to wat
7. ## Re: Fuse rating vs. RMS question
the amps ive seen. my aq 2200d was 200a my 3250 is 300a. someone posted a jl 1000/1 and said the manual said 100a. so yeh its seems that its about 10a per 100w.
8. ## Re: Fuse rating vs. RMS question
if you think so..
9. ## Re: Fuse rating vs. RMS question
at 12v, you can calculate the approximate max (clean) rms by multiplying 12*fuse rating. So an amp with a 10a fuse would give you 120 watts @ 12v. Now consider that it is likely 80% efficient or so depending on what kind of amp/quality/etc...and you end up with a little under 100 watts.
Yes, guessing that an amp will do 10 times it's fuse rating in power is generally a good estimate. You will not find an amp that needs a 50 amp fuse making 1000 watts at 12-14v without serious distortion and blowing that fuse if not damaging the amp
10. ## Re: Fuse rating vs. RMS question
Originally Posted by skmfkr
the amps ive seen. my aq 2200d was 200a my 3250 is 300a. someone posted a jl 1000/1 and said the manual said 100a. so yeh its seems that its about 10a per 100w.
If you are referring to the Slash series from JL Audio, then you are wrong. It doesn't have fuses.
11. ## Re: Fuse rating vs. RMS question
Originally Posted by Ferendon
If you are referring to the Slash series from JL Audio, then you are wrong. It doesn't have fuses.
no ****, he was asking what size inline fuse for it.
12. ## Re: Fuse rating vs. RMS question
totally wrong there is plenty of amps out there that have 2 40 amp fuses and are rated @1200rms and do 1400ish clamped. reason it takes 200% of fuse rating to blow over a 3sec period.
13. ## Re: Fuse rating vs. RMS question
Thats my general rule of thumb. It's not accurate, but it's good enough for a guesstimate. There's usually a pretty good correlation.
14. ## Re: Fuse rating vs. RMS question
Originally Posted by SPLaudio
totally wrong there is plenty of amps out there that have 2 40 amp fuses and are rated @1200rms and do 1400ish clamped. reason it takes 200% of fuse rating to blow over a 3sec period.
true but i bet its not clean power.
and your saying that an 80a fuse will need to see 240a for 3 seconds to blow?
15. ## Re: Fuse rating vs. RMS question
Fuse rating also depends on if your amp is High Voltage/High Impedance versus High Current/Low Impedance. I have an amp that does 400 watts RMS @ 8 ohms with a tiny *** 25 amp fuse! Of course the rail voltages inside of that amplifier are high enough to pack a serious wallop to them!
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Apr17 awarded Popular Question Feb13 comment Is there a size of rectangle that retains its ratio when it's folded in half? This article covers exactly your question. Feb3 comment How to find the point of intersection of four parametric equations Generally, setting these equations equal should give you where they intersect. You would also presumably have to define a period which this solution would be valid. Jan26 answered Axis of revolution Jan26 comment How to integrate $(x^2 - y^2) / (x^2 + y^2)^2$ OP is asking specifically for a method of solution that does NOT require the fundamental theorem of calculus. Dec21 accepted How can I determine the bounds for this inequality? Dec21 revised How can I determine the bounds for this inequality? Rewrote to account for some forgotten terms. Dec21 suggested approved edit on How can I determine the bounds for this inequality? Dec21 awarded Constituent Dec21 asked How can I determine the bounds for this inequality? Dec9 awarded Caucus Sep30 awarded Explainer Jul2 awarded Curious Jun3 awarded Popular Question May30 awarded Popular Question May24 accepted Is this computation erroneous? May24 comment Is this computation erroneous? By the time that $n=100$ such that we are not dealing with purely fractional exponentiation in the function $2^{n/100}$, $n^{100}$ is already $100^{100}$ which is clearly bigger than $2^1$. May24 comment Is this computation erroneous? How is that true? At $n=1$, $2^{n/100}$ is the 100th root of 2, which is slightly over 1; $n^{100}$ is 1. At $n=2$ $2^{n/100}$ is the 50th root of 2, which is also slightly over 1; $n^{100}$ is enormous. May24 asked Is this computation erroneous? Feb19 awarded Yearling | 417 | 1,768 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2015-18 | longest | en | 0.937556 |
https://www.physicsforums.com/threads/diagonal-lines.242094/ | 1,606,846,551,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141681209.60/warc/CC-MAIN-20201201170219-20201201200219-00301.warc.gz | 827,333,793 | 20,430 | # Diagonal Lines
climbhi
Alright, I have a question that I know is very dumb, but despite my best efforts I've been unable to come up with an answer that satisfies me. Here it is:
We know the shortest distance b/n two points is a straight line. So, if we have a right triangle with legs of unit length, the shortest distance between the endpoints is the hypotenuse (which will have length $$\sqrt{2}$$).
Okay, now let's walk the distance b/n the two points in several different ways:
1.) Walk 1 unit East, then 1 unit North. Total distance = 1 + 1 = 2.
2.) Walk 1/2 unit East, then 1/2 unit North, then 1/2 unit East, then 1/2 unit North. Total Distance = 1/2 + 1/2 + 1/2 + 1/2 = 2.
3.) Walk 1/3 unit East, then 1/3 unit North, 1/3 unit East, then 1/3 unit North, 1/3 unit East, then 1/3 unit North. Total distance = 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3 = 2.
I'm sure you see where I'm going by now. So, my question is, why doesn't the sum of this "stair step" method approach $$\sqrt{2}$$ as your step size approaches 0? Is there something fundamentally different about a diagonal line? I just can't see what the difference is b/n a "stair step" of infinitesimal step size and a diagonal line...
This has been bugging me for a while, so someone please set me straight (pun intended).
What do you mean "why"? As you have pointed out, the total distance traveled remains 2. For a "stair", if you look at horizontal segments alone, you clearly see that they add up to the horizontal distance between the two bases, independently of how many segments (or stairs, same number) there are. Same goes with the vertical segments.
climbhi
What do you mean "why"? As you have pointed out, the total distance traveled remains 2. For a "stair", if you look at horizontal segments alone, you clearly see that they add up to the horizontal distance between the two bases, independently of how many segments (or stairs, same number) there are. Same goes with the vertical segments.
Yes, of course I see that, but it doesn't answer my actual question: What is the difference b/n a stair step of infinitesimally small step size and an actual diagonal line? So, to apply the question to the example at hand: Why would a stair step of infinitesimally small step size from start to end yield a total distance of 2, whereas a diagonal line would yield a total distance of $$\sqrt{2}$$?
climbhi
http://www.mathpages.com/home/kmath063.htm
Thanks for the great article. It's nice to realize that I'm not the only one to have been confused by this. I was actually getting a little depressed (I just commented to my wife that I felt like I needed to return my recently-earned physics degree...)
But, despite the great points in the article, it doesn't really satisfy me. Basically, it just says that you have to be careful not to assume that because some limiting case has some of the properties of entity it's approaching that it has all the same properties. That's a great point, but it doesn't actually get into the why of things.
So, why does this limiting scenario (the stair step) not possess all the properties of the entity it's approaching (the diagonal line)? I'm not seeing, fundamentally, what the difference is.
Yes, of course I see that, but it doesn't answer my actual question: What is the difference b/n a stair step of infinitesimally small step size and an actual diagonal line? So, to apply the question to the example at hand: Why would a stair step of infinitesimally small step size from start to end yield a total distance of 2, whereas a diagonal line would yield a total distance of $$\sqrt{2}$$?
It seems as though the source of your questions stems from your concept of "infinitely small". The "infinitely small" is a nebulous notion, no longer regarded as meaningful by modern mathematicians. One must speak of the passage to the limit (2), which has a clear definition, instead of obstructing the matter with unclear terms (i.e. "infinitely small step sizes).
Hurkyl
Staff Emeritus
Gold Member
That's a great point, but it doesn't actually get into the why of things.
You made an assumption about how things behave -- that it didn't matter in which order you applied the steps "compute the length" and "take the limit". You looked at an actual example. The example demonstrated your assumption was flawed. I'm not sure what you find unsatisfactory about this state of affairs.
Maybe simply restating what you have shown will help? In whatever topological space you're using to make sense of that limit, you've proven that the following cannot both be true:
(1) That sequence of stairsteps converges to that line segment
(2) The length function is continuous
In particular, your work says (almost literally) that if (1) holds, then that line segment is a discontinuity of the length function.
Last edited:
If you draw a picture of your stairs, and make the step size really small, the picture will "look like" a diagonal line, but it is not! Take just one of your stair "steps" and pake the picture bigger - you will see that the diagonal length is still the hypotenuse and its length is still sqrt(x^2 + y^2). No matter how small the step size, this picture of just one step is always the same. When you add up all those little hypotenuses, you get sqrt(2); you do not get 1+1 = 2.
Does that help?
Alright, I have a question that I know is very dumb, but despite my best efforts I've been unable to come up with an answer that satisfies me.
Here it is: .....
Climbhi,
Progress, progress, progress. Thanks to the generous people on this forum (generous with their time), you know know that your question is very very far from being a dumb question.
(Somehow, "You want 'an answer that satisfies you.'" seems like a more natural way to put that last sentence.)
That's not a criteria that anybody can really work to in a logical manner except you. (More accurately, in a "deductive" manner.)
I applaud you for holding out for an answer that satisfies your criteria.
Here's my contribution to the mix.
Let f:[0,1]->[0,1] be the function defined by f(x) = x. the derivative of f(x) is one (f'(x)=1).
Let f_n be the nth staircase function as you describe it.
Then, for f_n converges uniformly to f (as n-->infinity).
("Converges uniformly" means converges pointwise AND for every epsilon in the delta-epsilon definition of a limit, the same N_0 works for all points in the unit interval [1,1].)
(f_n converges pointwise to f as n goes to infinity) iff (for all real numbers x)(for all epsilon greater than zero)(there exists a natural number N_0 such that)(n>N_0 ==> |f_n(x)-f(x)|<epsilon).
However, the limit as n-->infinity of the derivatives of f_n (f_n') do not converge to any function. In fact, loosely speaking, the sequence f_n'(x) is equal to zero an infinite number of times and it is equal to infinity an infinite number of times.
BTW, a question that I have forgotten the answer to, and maybe one of you gurus know off the top of your head is, is the following statement true when (f and f_n are differentiable functions mapping R into R)?
If f_n -> f uniformly and f_n'->g pointwise as n-->infinity, then f = g?
If not, what if f and f_n are continuously differentiable?
What if f_n'->g uniformly?
Are there other cases that are interesting?
DJ
Last edited:
HallsofIvy
Homework Helper
Yes, if fn goes to f uniformly then it also goes to f pointwise and the limit is unique.
Yes, if fn goes to f uniformly then it also goes to f pointwise and the limit is unique.
Thanks, HallsOfIvy! DJ
This is an interesting problem, intuitively I would imagine that one can draw a stair case with a blunt pencil, there is a limit where the thickness of the line would cause the staircase to look like a diagonal. This is the point at which definitions of length would be ambiguous because they are the same order of magnitude as the width of the line drawn. No matter how the pencil is sharpened, this point will always be reached. This would indicate that there is not a gradual approximation from a staircase to a diagonal and that the two are fundamentally different objects when viewed at the appropriate resolution. Not too sure how that translates into mathematical terms though.
HallsofIvy | 1,996 | 8,232 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.34375 | 4 | CC-MAIN-2020-50 | latest | en | 0.936968 |
http://mt4indicators.com/uz/levels-indicator/ | 1,601,283,765,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600401598891.71/warc/CC-MAIN-20200928073028-20200928103028-00656.warc.gz | 94,701,673 | 18,982 | Levels – ko'rsatkich
# Levels – ko'rsatkich
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ulushi
Author: ug
The indicator uses the construction method described by Vladislav Antonov (you can see his session reviews at Viak or Alpari). I failed to find such an indicator in the internet, so I decided to create it by myself. Below is a short extract from his description:
I shouldn’t explain you what support and resistance are. There are many methods to detect price levels. ammo, I apply my own calculations. The dynamic support/resistance lines are determined by MA lines, whereas the static ones are calculated on the basis of a larger timeframe.
1. To calculate intraday levels for one hour, you should take High, Low and Close values from the preceding one-hour candlestick.
2. To calculate intraday levels for one day, you should take High, Low and Close values from the preceding one-day candlestick.
3. To calculate intraday levels for one week, you should take High, Low and Close values from the preceding one-week candlestick.
In my review, I calculate the price levels of support/resistance on the basis of the one-day candlestick of the preceding day. Shunday qilib, the price levels will be valid all day long, but we should recalculate them the next day. Masalan, if we take a one-day candlestick 02.11.06: High = 1.2786 Low = 1.2736 Close = 1.2780 and obtain the levels for the current day and use them on all charts for the timeframes smaller than one-day timeframe. On the next day, we will have to calculate the new levels.
Bu yerda 3 calculation methods according to the size of the preceding candlestick:
Reduced – support/resistance levels for a weak market. If the market was closed with a large candlestick of more than 200 ball, it is better to use this method, since a correction is expected, so the market will be flat.
Normal – support/resistance levels for a market with average volatility. Daily candlesticks range from 100 uchun 200 ball. Normal method is good in use when a stable growth or sinking is being observed, candlesticks being approximately of the same size.
Extended (Расширенный) – support/resistance levels for a volatile market. Црут the market shrinks into a triangle and becomes flat, we expect a strong movement to start soon and use the levels with an expanded price range. What method should be applied here, this depends on your own research and level statistics collected. As to me, I don’t keep up with the items described above (this is averagely for the pound). So far, I choose methods guided by my intuition and by the expected price pattern.
Levels – ko'rsatkich Metatrader 4 (MT4) ko'rsatkich va forex indikatori mohiyati to'plangan tarixi ma'lumotlarni aylantirish uchun emas.
Levels – Ko'rsatkich ko'zga ko'rinmaydigan turli xil o'ziga xoslik va narx dinamikasini aniqlash imkoniyatini beradi.
Bu ma'lumotga asoslanib, savdogarlar yanada narx harakatini taxmin va shunga ko'ra, ularning strategiyasini o'zgartirishingiz mumkin.
How to install Levels – ko'rsatkich.mq4?
• Copy Levels – Metatrader katalogiga indikator.mq4 / ekspertlar / ko'rsatkichlar /
• Boshlash yoki Metatrader Client qayta
• Agar ko'rsatkichni sinab istayman tanlang jadvali va vaqt
• Qidiruv “Custom Ko'rsatkichlar” Sizning Navigator asosan sizning Metatrader Mijoz qolgan
• Right click on Levels – ko'rsatkich.mq4
• Grafikdagi ulash
• sozlamalarini yoki OK tugmasini bosing o'zgartirish
• Indicator Levels – Diagrammada indikator.mq4 mavjud
How to remove Levels – Metatraderingizdan indikator.mq4 4 sxema?
• Ko'rsatkichlar sizning Metatrader Client ishlayotgan Chart tanlang
• O'ng Grafik ichiga bosing
• “Ko'rsatkichlar ro'yxati”
• Indikatori tanlang va o'chirish
MT4 ko'rsatkichlari quyidagi ko'chirib:
ulushi | 998 | 3,725 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2020-40 | latest | en | 0.915831 |
https://myessaydesk.com/assignment-1-math418/ | 1,713,789,857,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296818293.64/warc/CC-MAIN-20240422113340-20240422143340-00106.warc.gz | 372,406,188 | 17,303 | Warning: Trying to access array offset on value of type bool in /home/topgsnkq/myessaydesk.com/wp-content/themes/enfold/framework/php/function-set-avia-frontend.php on line 637
Assignment 1 (Math418)
Write a complete set of proofs for Theorem 4.5 in the Croom book.- State the hypotheses- State the conclusions- Clearly and precisely prove the conclusions from the hypotheses- Results presented earlier in the text may be used and must be clearly documentedA few notes about format: use Microsoft Word; use Equation Editor for all mathematical symbols, e.g. x ∈ X or Cl(A) ⋂ Cl(X-A); and use the fonts Cambria and Cambria Math in size 11 so your typed work is the same font as your equations.Theorem 4.5: Let Abe a subset of a topological space X. (1)bdy . (2)bdy A, int A, and int (XA) are pairwise disjoint sets whose union is X. (3)bdy A is a closed set. (4) = int A ∪ bdy A. (5)A is open if and only if bdy A ⊂ (XA). (6)A is closed if and only if bdy A ⊂ A. (7)A is open and closed if and only if bdy A = Ø. Proof: Properties (1) through (4) follow immediately from the definitions. To prove (5), note that if A is open, then A = int A by Theorem 4.3, part (2). Since int A and bdy A are disjoint by (2), then A and bdy A are disjoint, so bdy A must be a subset of XA. For the reverse implication, suppose bdy A ⊂ XA. Then no point of A is a boundary point of A, so every point of A is an interior point. Thus A = int A, so A is open. Statement (6) follows from the duality between open sets and closed sets: A is closed if and only if XA is open. By (5), this is equivalent to saying that or Statement (7) is proved by combining (5) and (6): A is both open and closed if and only if bdy A is contained in both A and XA. Since A and XA are disjoint, this occurs if and only if bdy A = Ø According to Theorem 4.5, the points of a subset A of a space X may be of two types, interior points and boundary points. The set A may have additional boundary points outside A, however; the union of all interior points and boundary points of A is . The points of X are of three non-overlapping types: (1) interior points of A, (2) interior points of XA, and (3) boundary points of A, which are identical with the boundary points of XA. (Of course, any of these three sets may be empty.) The following examples are an attempt to spare the reader some of the common misconceptions about boundaries and closures in metric spaces.MLA 8th Edition (Modern Language Assoc.)Croom, Fred H. Principles of Topology. Dover Publications, 2016.APA 7th Edition (American Psychological Assoc.)Croom, F. H. (2016). Principles of Topology. Dover Publications. | 706 | 2,636 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.765625 | 4 | CC-MAIN-2024-18 | latest | en | 0.922134 |
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Topic: Comparing Compactifactions
Replies: 6 Last Post: Mar 20, 2013 10:30 PM
Messages: [ Previous | Next ]
William Elliot Posts: 2,637 Registered: 1/8/12
Re: Comparing Compactifactions
Posted: Mar 20, 2013 10:30 PM
On Wed, 20 Mar 2013, David C. Ullrich wrote:
> >>
> >> >Let (f,X) and (y,Y) be compactifications of S.
> >> >Assume h in C(Y,X) and f = hg.
> >> >
> >> >Thue h is a continuous surjection and when Y is Hausdorff
> >> >a closed quotient map.
> >> >
> >> >k = h|g(S):g(S) -> f(S) is a continuous bijection.
> >> >It it a homeomorphism? If so, what's a proof like?
> >
> >I'll have to check this out, but isn't
> >k = fg^-1:g(S) -> f(S) a homeomorphism?
>
> That seems clear. Don't know what I was thinking, sorry.
>
Actually, it's easy to check as f,g are embeddings,
g:S -> g(S) and f:S -> f(S) are homeomorphisms so are
g^-1:g(S) -> S and fg^-1:g(S) -> f(S).
In addition, as f = hg, fg^-1 = hgg^-1 = h.id_g(S) = h|g(S).
Date Subject Author
3/18/13 William Elliot
3/18/13 David C. Ullrich
3/20/13 William Elliot
3/20/13 David C. Ullrich
3/20/13 William Elliot
3/18/13 Shmuel (Seymour J.) Metz
3/18/13 William Elliot | 463 | 1,347 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.828125 | 3 | CC-MAIN-2018-22 | latest | en | 0.890329 |
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# Stupid
ivisibility Tricks
## Appeared in Math
orizons November
2006
Marc Renault Shippensburg University Mathematics Department 1871 Old Main Road Shippensburg, PA 17013 msrenault@ship edu http://webspace ship edu/msrenault/divisibility/
1
# Introduction
When is the last time this happened to you? You are stranded on a deserted island without a calculator and for some reason you must determine if 67 is a divisor of 95733553; furthermore, a coconut recently fell on your head and you have completely forgotten how to perform long division.
Of course the above scenario would never happen (we all carry around calculators) but it’s good to know that if we should find ourselves in a similar situation there is an easy divisibility rule for 67: remove the two rightmost digits from the number (in our case, 53), double them (106) and subtract
that from the remaining digits (957335
106 = 957229); the original number
is divisible by 67 if and only if the resulting number is divisible by 67.
## If the
resulting
number
is
not
obviously
divisible
by
67
we
can
repeat
the
process
until we get a number that clearly is or is not a multiple of 67. example, we get the following.
In the above
1
Document views 45 Page views 49 Page last viewed Sun Dec 04 16:55:17 UTC 2016 Pages 15 Paragraphs 695 Words 3760 | 349 | 1,389 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2016-50 | longest | en | 0.897917 |
http://www.omninerd.com/comments/34387 | 1,369,353,952,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368704117624/warc/CC-MAIN-20130516113517-00064-ip-10-60-113-184.ec2.internal.warc.gz | 617,333,333 | 5,597 | ## RE: Shakespearian tragedy!
Having typed the first letter of Hamlet, the probability of the next letter being correct is 1/61 if our monkey has a normal keyboard with 61 keys, and he is equally able to hit any of them. It is always the same 1/61 chance that the next character will be right.
Let’s guess that there are 6000 words in Hamlet, of average length 5 characters. That means 30,000 characters. Make it 33000 to provide for spaces and punctuation.
The probability that our monkey will proceed to type this version of Hamlet is 1/61 to the power of 32000
Wolfram Alpha gives the answer as 1.304501... × 10^-58916 | 161 | 625 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2013-20 | latest | en | 0.931411 |
http://www.convertunits.com/from/meter/second/to/inch/minute | 1,498,689,154,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128323807.79/warc/CC-MAIN-20170628222452-20170629002452-00669.warc.gz | 475,306,633 | 10,893 | # ››Convert metre/second to inch/minute
meter/second inch/minute
How many meter/second in 1 inch/minute? The answer is 0.000423333333333.
We assume you are converting between metre/second and inch/minute.
You can view more details on each measurement unit:
meter/second or inch/minute
The SI derived unit for speed is the meter/second.
1 meter/second is equal to 2362.20472441 inch/minute.
Note that rounding errors may occur, so always check the results.
Use this page to learn how to convert between meters/second and inches/minute.
Type in your own numbers in the form to convert the units!
# ››Want other units?
You can do the reverse unit conversion from inch/minute to meter/second, or enter any two units below:
# Enter two units to convert
From: To:
I'm feeling lucky, show me some random units.
# ››Definition: Meter/second
Metre per second (U.S. spelling: meter per second) is an SI derived unit of both speed (scalar) and velocity (vector quantity which specifies both magnitude and a specific direction), defined by distance in metres divided by time in seconds.
One metre per second is roughly the speed of an average person walking.
# ››Metric conversions and more
ConvertUnits.com provides an online conversion calculator for all types of measurement units. You can find metric conversion tables for SI units, as well as English units, currency, and other data. Type in unit symbols, abbreviations, or full names for units of length, area, mass, pressure, and other types. Examples include mm, inch, 100 kg, US fluid ounce, 6'3", 10 stone 4, cubic cm, metres squared, grams, moles, feet per second, and many more! | 389 | 1,642 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2017-26 | latest | en | 0.879879 |
https://search.r-project.org/CRAN/refmans/apTreeshape/html/get_PD_sample.html | 1,639,032,470,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363689.56/warc/CC-MAIN-20211209061259-20211209091259-00177.warc.gz | 589,756,428 | 2,308 | get_PD_sample {apTreeshape} R Documentation
Computes the proportion of conserved PD
Description
Computes the proportion of conserved phylogenetic diversity as a function of the proportion of conserved species, in trees simulated by the model
Usage
```get_PD_sample(epsilon, beta, alpha, N, sampl.frac, ntree, equal.ab,
eta, lengths = "yule", b = 1, d = 0)
```
Arguments
`epsilon` Minimum size of unsampled splits (see appendix 1) `beta` Imbalance index `alpha` Clade age-richness index `N` Initial tip number `sampl.frac` Vector of tips fractions for which we want to compute the conserved PD `ntree` Number of simulated trees `equal.ab` If set to TRUE, all species have the same probability to go extinct first (default to TRUE) `eta` Clade abundance-richness index (if equal.ab == FALSE) `lengths` Model used to simulate node depths (can be "yule" (the default) or "kingman") `b` Birth rate (if lengths == "yule") `d` Death rate (if lengths == "yule")
Value
A table of size length(sample.fract)*ntree. The element in ligne i and column j is the remaining Phylogenetic Diversity fraction for the j^th tree in wich a fraction sample.frac[i] has been sampled.
Author(s)
Odile Maliet, Fanny Gascuel & Amaury Lambert
References
Maliet O., Gascuel F., Lambert A. (2018) Ranked tree shapes, non-random extinctions and the loss of phylogenetic diversity, bioRxiv 224295, doi: https://doi.org/10.1101/224295
Examples
```set.seed(813)
sampl.frac=seq(0,1,by=0.05)
PD = get_PD_sample(epsilon=0.01,beta=0,alpha=0,N=50,
sampl.frac=sampl.frac,ntree=10,equal.ab=FALSE,
eta=0.5,lengths="yule",b=1,d=0)
probs = c(0.1, 0.9, 0.5)
PD_stats = as.vector(t(sapply(1:nrow(PD), function(i){quantile(PD[i,], probs)})))
par(mgp=c(2.2, 0.8, 0))
par(mar=c(4, 4, 1, 1))
plot(1, type="n", xlab="Fraction of extinct species, p",
ylab="PD loss", ylim=c(0,1), xlim=c(0,1))
points(c(0,1),c(0,1),t="l",col=grey(0),lty=3)
# plot 95% confidence intervals (grey area)
polygon(c(1-sampl.frac, rev(1-sampl.frac)), c(1-PD_stats[(1:length(sampl.frac))],
rev(1-PD_stats[((length(sampl.frac)+1):(2*length(sampl.frac)))])),
border=NA, col=grey(0.7))
# plot median value (black line)
points(1-sampl.frac, 1-PD_stats[((2*length(sampl.frac)+1):(3*length(sampl.frac)))],t="l")
```
[Package apTreeshape version 1.5-0.1 Index] | 764 | 2,294 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2021-49 | latest | en | 0.595642 |
https://www.jiskha.com/questions/400279/what-is-my-number-clue-1-my-number-is-a-multiple-of-5-but-it-does-not-end-in-5-clue-2 | 1,603,667,471,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107890028.58/warc/CC-MAIN-20201025212948-20201026002948-00162.warc.gz | 772,822,617 | 6,339 | # math
what is my number?
Clue 1 My number is a multiple of 5,but it does not end in 5.
Clue 2 The prime factorization of my number is a string of three numbers.
Clue 3 Two of the numbers in the prime factorizations are the same.
Clue 4 My number is greater than the seventh square number.
1. 👍 5
2. 👎 1
3. 👁 828
1. what is my number?
Clue 1 My number is a multiple of 5,but it does not end in 5.
- Multiples of 5 end in "5" and which other digit?
- Can you identify 2 prime factors if the number ends in this digit?
Clue 2 The prime factorization of my number is a string of three numbers.
- From clue 1, we have already found two of the three prime factors. We need the third one.
Clue 3 Two of the numbers in the prime factorizations are the same.
- Therefore the third one must be a duplicate of one of the other two.
- that leaves us two choices.
Clue 4 My number is greater than the seventh square number.
- out of the two choices, which one will make a number greater than 7²?
1. 👍 3
2. 👎 0
2. kjljjjudeljh
1. 👍 1
2. 👎 4
3. 30
1. 👍 1
2. 👎 1
4. i don't no
1. 👍 1
2. 👎 1
5. the answer is 30 because since there is 3 factors of 30=3,5,10 and it does not end in a five and it is a multiple of 5
ps. this is correct im a math teacher for simmons knights you will get an A+
1. 👍 2
2. 👎 5
6. 50
1. 👍 1
2. 👎 0
7. How can it be 30 if it is greater than 49?
1. 👍 3
2. 👎 0
8. Guys it's 50 because the prime factorization is 5*5*2=50 it fits all the clues.
1. 👍 1
2. 👎 0
9. 50
1. 👍 1
2. 👎 0
10. ygyigk8y
1. 👍 0
2. 👎 1
11. It's 50 because it's greater than the seventh square and it doesn't end in zero so if a multiple is 5 than it has to end in 5 and not zero so it's not 30.
1. 👍 1
2. 👎 0
12. 15
1. 👍 0
2. 👎 2
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Guess the number: If you round this number to the nearest one, you get 4. If you round the number to the nearest tenth, you get 4. If you round the number to the nearest hundredth, you get 4. It is the least such number. What is | 1,281 | 4,053 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.25 | 4 | CC-MAIN-2020-45 | longest | en | 0.912156 |
https://wiki.cdot.senecacollege.ca/w/index.php?title=Tutorial4:_Data_Representation_/_Numbering_Conversion_/_File_Permissions&diff=prev&oldid=151164 | 1,618,558,865,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038088731.42/warc/CC-MAIN-20210416065116-20210416095116-00345.warc.gz | 698,294,185 | 17,372 | # Data Representation / Numbering Conversion / File Permissions
### Main Objectives of this Practice Tutorial
• Understand how digital computers store data (i.e. data representation)
• Define decimal, binary, octal and hexadecimal numbers
• Manually perform numbering conversions between the decimal, binary, octal and hexadecimal numbering systems
(without the use of a computer or calculator)
• Identify which numbering system conversion method to use when required to perform a numbering conversion
• Explain the purpose of file permissions
• Explain how permissions work differently for directories as opposed for regular files
• Change file permissions with the chmod command (both symbolic and absolute methods)
• Use the umask command to automatically assign permissions for newly created directories and regular files
### Tutorial Reference Material
Course Notes Numbering Conversion / File Permissions Reference YouTube Videos Slides:PDF | PPTX Data Representation Definitions File Permission Concepts Introduction to File Permissions File Permission Commands Instructional Videos:
# KEY CONCEPTS
### Data Representation
A series of binary numbers form a byte to represent numbers.
(Image licensed under cc)
Digital computers are electronic devices that contain a series of circuits and voltage levels that can store / represent data.
Binary numbers can represent those series of circuits with voltage levels.
Those binary numbers are combined in a sequence to form a byte. Bytes are used to represent numbers or characters.
IT professionals may need to perform calculations involving various numbering systems
to use programming functions or OS commands to perform common operations on a computer system.
IT Professionals that Use Data Representation:
• Network Specialists: Building Large Networks via Sub-netting
• Programmers: Sending information over networks, files
• Web Developers: Setting color codes for webpage background or text
• Unix/Linux System Administrators: Setting permissions for files and directories
### Decimal / Binary / Octal / Hexadecimal Numbering Systems
The decimal numbering system .
(Image licensed under cc - modified by author).
Decimal Numbers
The decimal numbering system consists of digits ranging from 0 to 9. The numbering system is based on sums of the power of 10 which provides a framework for mathematic calculations.
The fact that humans started counting on their fingers and thumbs most likely lead to the development of this numbering system.
Referring to the diagram on the right, the value of each decimal digit consists of the value (placeholder) multiplied by the corresponding power of 10. For example, units are 100, tens are 101, hundred are 102 which move in a right-to-left direction.
The binary numbering system.
(Image licensed under cc)
Binary Numbers
The binary numbering system consists of digits ranging from 0 to 1. The numbering system is based on sums of the power of 2.
Digital computers have circuits which representing data in terms of voltage levels. Multiple circuits are used to represent data (in the form of binary numbers).
Referring to the diagram on the right, the value of each decimal digit consists of the value (placeholder) multiplied by the corresponding power of 2. For example, 20 , 21, 22, etc. which move in a right-to-left direction.
Octal / Hexadecimal Numbers
The octal numbering system.(Image licensed under cc) The hexadecimal numbering system.(Image licensed under cc)
The octal and hexadecimal numbering systems consist of digits ranging from 0 to 7 and ranging from 0 to F respectively. For hexadecimal numbers, values for 10 to 15 are represented by the characters A to F respectively. The octal and hexadecimal numbering system are based on sums of the power of 8 and 16 respectively.
Since 1 octal digit represents 3 binary digits and 1 hexadecimal digit represents 4 binary digits, octal and hexadecimal numbers are used as short-cuts to represent binary number.
### Numbering Conversion Methods
#### Method 1: Binary to Decimal
Performing a binary to decimal conversion.
When converting binary numbers to decimal numbers, perform the following steps:
1. Write down the binary number.
2. Starting from the right-side, draw L's below the binary number moving to the left
(refer to diagram on right).
3. Starting on the rightmost "L", multiply the value (placeholder) by 2 to the power of zero.
4. Continually repeat step #3 moving leftwards, increasing the power of 2 by 1
(refer to diagram on right).
5. Add up the results to obtain the decimal value equivalent.
NOTE: To convert octal and hexadecimal numbers to decimal, replace the number 2
(in red in the diagram to the right) with 8 (for octal) or 16 (for hexadecimal).
#### Method 2: Decimal to Binary
Performing a decimal to binary conversion.
When converting decimal numbers to binary numbers, perform the following steps:
1. Write down the decimal number to be converted.
2. On the right-side, write the number 1 and moving leftwards, keep doubling the numbers until that number is greater than the decimal number to be converted (refer to the diagram on the right).
3. Starting on the left-side of those doubled numbers, compare that number with the decimal number. If that number if less than or equal to the decimal number, then write a 1 below and subtract that number from the decimal number to get a remainder. If the number is greater than decimal number (or remainder), then write a 0 below.
4. Repeat step #3 (moving rightwards and comparing the number with the decimal's remainder)
NOTE: If you are converting to 8-bit, 32-bit, etc., add leading zeros if necessary.
#### Method 3: Octal to Binary / Binary to Octal
Performing an binary to octal numbering conversion. Performing an octal to binary numbering conversion.
Binary to Octal
1. One octal number represents 3 binary numbers, so starting from right-side, group binary digits into groups of 3
2. Write (4)(2)(1) under each group of 3 binary numbers.
3. Multiply the value or "placeholder" (i.e. 0's and 1's) by the corresponding (4)(2)(1) for each group to obtain the octal number (refer to diagram of binary to octal conversion).
Octal to Binary
1. One octal number represents 3 binary numbers, so space-out
the octal numbers to make space for a binary number.
2. Write (4)(2)(1) under each octal number.
3. Write 0's or 1's for each group of binary numbers to add up to the
corresponding octal number (refer to diagram of octal to binary conversion).
#### Method 4: Hexadecimal to Binary / Binary to Hexadecimal
Performing a binary to hexadecimal conversion. Performing a hexadecimal to binary conversion.
1. One hexadecimal number represents 4 binary numbers, so starting from right-side, group binary digits into groups of 4 (add leading zeros if necessary).
2. Write (8)(4)(2)(1) under each group of 4 binary numbers.
3. Multiply the values or "placeholders" (i.e. 0's and 1's) by the corresponding (8)(4)(2)(1) for each group to obtain the octal number.
4. Convert values from 10 to 15 to A to F
(refer to diagram of binary to hexadecimal conversion)
1. One hexadecimal number represents 4 binary numbers,
so space-out the hexadecimal numbers to make space for a binary number.
2. Convert letters A to F to 10 to 15 (refer to diagram of binary to hexadecimal conversion)
3. Write (8)(4)(2)(1) under each hexadecimal number.
4. Write 0's or 1's for each group of binary numbers to add up to the corresponding
hexadecimal number (refer to diagram of hexadecimal to binary conversion).
#### Method 5: Octal to Hexadecimal / Hexadecimal to Octal
For conversions between octal and hexadecimal numbers, use binary as a bridge.
To convert using the method, simply use binary as a "bridge".
Example:
To convert octal to hexadecimal, convert octal to binary, then convert binary to hexadecimal.
To convert hexadecimal to octal, convert hexadecimal to binary, then convert binary to octal.
### File Permissions
Since Unix / Linux operating file systems allow for multiple user accounts it is essential
to have a system to share or limit access to directories and files contained within the file system.
Detailed directory listing showing permissions for a directory
and a regular file.
When directories and regular files are created, they are assigned to an owner
(typically the username which is the creator). To allow or limit access to those files and directories, those files and directories are assigned to an initial group referred to as a "primary group".
Users that own those directories and regular files are referred to as users, users that belong within the same group are referred to as same group members, and those users are do NOT belong to a particular group are referred to as other group members.
NOTE: In this course, we cannot create groups or assign users to groups in the Matrix server.
Instead, you will learn how to those tasks when or if you take a Unix/Linux administration course.
On the other hand, you can change which user, same group members or other group members
can access or NOT access a directory or regular file.
Permissions of a directory that contain subdirectories and regular files.
File Permissions consist of two-layers:
First, the permissions of a directory that contains regular files, and second, permissions of the subdirectories and/or regular files within that directory.
Permissions for directories have a different meaning than permissions for regular files. Refer to the diagrams to the right to see the explanation of permissions and how they differ between a directory and a regular file.
A symbol dash "-" indicates that the permission has NOT been granted.
Permissions of a regular file contained within a directory.
The permissions of newly-created directories and regular files are automatically assigned
via a user mask (we will discuss this shortly). In order to change permissions for directories and regular files, you would use the chmod command.
Changing File Permissions with "chmod" command:
Symbolic Method:
The chmod can use symbols to add, remove, and set rwx permissions for the user,
same group members, and/or other group members for a directory or reqular file.
CommandDescription
chmod ugo+x script.bashAdd execute permissions to the file script.bash so it can be run.
chmod u=rwx,go=x ~Set "pass-thru" permissions of your home directory for same group members and other group members to navigate to other subdirectories (that may have access / view permissions).
chmod go-w ~/sharedRemove write permissions for same group members and other group members for the directory ~/shared
chmod a=rx mySet read and execute permissions for the directory myfile.txt
Octal (Absolute) Method:
Using octal numbers to represent setting file permissions.
You can also use octal numbers to set permissions. This method is a short-cut and may require less typing than using the symbolic method. You can only use this method to set file permissions (as opposed to add or remove permissions.
Since 1 octal digit represents 3 binary digits, one octal digit can represent the rwx permission granted or NOT granted. The permissions rwx are be in the form of 3 binary digits (1 represents the permission granted and 0 represents the permission NOT granted).
CommandDescription
chmod 500 script.bashSet read and execute permissions for only the user for the file script.bash so it can be run.
chmod 711 ~Set "pass-thru" permissions of your home directory for same group members and other group members to navigate to other subdirectories (that may have access / view permissions).
chmod 750 ~/sharedSet full permissions for user, read and access permissions for some group members and no permissions for other group members for the directory ~/shared
chmod 555 myfile.txtSet read and execute permissions for the directory myfile.txt
NOTE: You can use the -R option to set permissions for directory, subdirectory and directory contents recursively.
Setting umask for newly-created directories. Setting umask for newly-created regular files
Setting Permissions for Newly-Created Directories and Regular Files (umask):
The umask command is used to set the permissions of newly-created directories and regular files.
Issuing the umask command without arguments will display the current umask value. Refer to the diagrams on the right-side to set the umask value for directories and regular files. Setting the umask value (for example umask 022) only takes effect for the current shell session unless the umask command is contained in a start-up file
(e.g. .profile, .bash_profile, or .bashrc).
# INVESTIGATION 1: NUMBERING CONVERSIONS
For this investigation, we will NOT be logged into our Matrix account, but it is recommended to have sheets of paper ready to manually perform numbering conversions.
NOTE: It is essential that you learn how to manually perform numbering conversions since you will NOT be permitted to perform quizzes, midterm, or your final exam with a computer or a calculator. Learning to quickly perform manual numbering conversions will make IT professional more productive such as setting permissions, designing computer networks, or selecting complex colors when developing webpages.
Only use a calculator to check your numbering conversion AFTER you have performed the operation manually.
You will now get practice performing numbering conversions.
Perform the Following Steps:
1. Let's convert the following 8-bit binary number 10111110 to a decimal number.
NOTE: It is important to learn and memorize the correct techniques to perform the
proper numbering conversion method (i.e. view method 1 above (drawing the L's).
2. Write the manual conversion on a sheet of paper.
3. Use a calculator to check your work. In MS Windows, you can set the calculator to Programming mode
by making the selection to binary, enter the binary number 10111110 and view the decimal equivalent.
Did you get the correct answer? If not, retry the method and check to see what you did wrong.
4. Perform a manual conversion of the decimal number 55 to an 8-bit binary number.
What method (displayed above) will you use? Use a calculator to check your work.
5. Perform a manual conversion of the octal number 461 to an 8-bit binary number.
What method (displayed above) will you use? Use a calculator to check your work.
6. Perform a manual conversion of the 8-bit binary number 11110001 to a hexadecimal number.
What method (displayed above) will you use? Use a calculator to check your work.
7. Perform a manual conversion of the hexadecimal number ABC to an 8-bit binary number.
What method (displayed above) will you use? Use a calculator to check your work.
8. Perform a manual conversion of the binary number 10101111 to an octal number.
What method (displayed above) will you use? Use a calculator to check your work.
9. Perform a manual conversion of the same binary number 10101111 to a hexadecimal number.
What method (displayed above) will you use? Use a calculator to check your work.
10. Perform a manual conversion of the octal number 5636 to a hexadecimal number.
What method (displayed above) will you use? Use a calculator to check your work.
11. Perform a manual conversion of the hexadecimal number D68 to an octal number.
What method (displayed above) will you use? Use a calculator to check your work.
12. When you have performed all of the numbering conversions above, then you can proceed to the next INVESTIGATION.
# INVESTIGATION 2: FILE PERMISSIONS
In this section, you will get experience using the chmod and umask commands
to change permissions for directories and files.
Perform the Following Steps:
1. Login to your matrix account and issue a command to confirm you are located in your home directory.
2. Issue a single Linux command to create the following directory structure displayed in the diagram to the right.
3. Make certain that your current directory is your home directory.
NOTE: You will now run a shell script to confirm that you properly created that directory structure
in your Matrix account.
4. Issue the following Linux command to run a checking script:
bash /home/murray.saul/scripts/week4-check-1
5. If you encounter errors and re-run the checking script until you receive a congratulations message, then you can proceed.
6. Issue Linux commands to create empty files for each of those newly created directories as show in diagram to the right:
NOTE: You will now run another shell script to confirm that you properly created those empty files within those specified directories.
7. Issue the following Linux command to run a checking script:
bash /home/murray.saul/scripts/week4-check-2
8. If you encounter errors and re-run the checking script until you receive a congratulations message, then continue the remaining steps.
Let's get practice understanding permissions, changing permissions, and setting your Linux account to automatically set permissions for newly created directories and regular files.
9. Issue the following Linux commands:
ls -ld ~/documents ~/clients ~/vendors
ls -lR ~/documents ~/clients ~/vendors
NOTE: You should see permissions already set for those newly created directories and regular files. What do these permissions mean for same group member and other group member access to those directory and regular files?
10. Let's limit access to the clients and vendors directories to only yourself and same group members. Issue the following Linux command:
chmod 750 ~/clients ~/vendors
11. Issue the ls command to confirm that the permissions for those directories have been changed.
NOTE: The -R option for the chmod command can change the file permissions recursively within a directory structure.
12. Issue the following Linux command: chmod 750 -R ~/documents
13. Again, use the ls command to confirm the permissions for the ~/documents, ~/document/memos , ~/documents/reports, and ~/documents/contracts directories.
14. Issue the following Linux command: ls -lR ~/documents
What do you noticed happened to the permissions for the regular files contained in those directories.
Did those regular file permissions change?
We want to now change those regular file permissions to the following settings: r w - r - - - - -
15. Issue the following Linux commands:
chmod 640 ~/documents/memos/memo*.txt
chmod 640 ~/documents/reports/report*.txt
chmod 640 ~/dcouments/contracts/contract*.txt
16. Issue the ls -lR command for the ~/documents directory to confirm that those regular file permission have changed.
Let's get some practice setting permissions to allow users to make editing changes to regular files.
17. Issue the following Linux command: chmod ugo-w ~/documents/memos/memo*.txt
18. Use the ls command to verify that those regular file's permissions have changed.
19. Using the nano or vi text editor, open the regular file ~/documents/memos/memo1.txt, type in some text and try to save your editing changes.
What happened?
20. To abort your editing session in vi, type :q! and to abort your editing changes in nano, just type n when prompted to save editing changes
21. Issue the following Linux command to add write permissions for all files in the memos directory for yourself (i.e. user): chmod u+w ~/documents/memos/*
22. Repeat the previous step #19. What happened?
23. Issue the following Linux command to view permissions for your home directory: ls -ld ~
What does execute permissions mean for same group members and other group members in terms of your home directory?
24. Issue the following Linux command to create a new subdirectory: mkdir ~/shared
25. Issue the following Linux command: ls -l ~/shared
What are the permissions for this newly-created directory?
Can other users access the directory pathname ~youruserid/shared ?
26. Issue the following Linux command (without an argument): umask
NOTE: You should see a four-digit octal number. Drop the leading zero on the left to obtain the default umask value.
27. Perform a mathematical calculation by taking the octal number 777 and subtracting the default umask value you determined in the previous step.
What is the result?
28. Convert that octal number result to a binary number. What does that represent as newly created directory permissions?
Does that correspond to the permissions for the newly created ~/shared directory?
29. Repeat steps #27 and #28 to see how a umask setting of 077 would affect permissions of newly-created directories.
30. Issue the following Linux command: umask 077
31. Issue the following Linux command (without arguments): umask
NOTE: You should notice the value 0077. By dropping the leading zero to the left, that would provide the default umask value of 077.
32. Issue the following Linux command: mkdir ~/shared2
33. Issue the following Linux command: ls -ld ~/shared2
Do the permissions for this newly created directory match the predicted permissions that you calculated in step #29?
34. Issue the following Linux command to create an empty regular file called myfile.txt in the ~/shared2 directory: touch ~/shared2/myfile.txt
35. Use the ls -l command to view the permissions for this newly created regular file.
What do you notice about those permissions?
36. Logout of your Matrix account, and then log-back into your Matrix account.
37. Issue the following Linux command (without arguments): umask
What happened? Referring to your notes, what do you need to do to make that umask value persistent?
38. After you complete the Review Questions sections to get additional practice, then work on your online assignment 2
and complete the sections 1 and 2 labelled: Practice Using The vi Text Editor and Permissions respectively.
# LINUX PRACTICE QUESTIONS
The purpose of this section is to obtain extra practice to help with your assignment #1, quizzes, your midterm, and your final ezam.
Here is a link to the MS Word Document of ALL of the questions displayed below but with extra room to answer on the document to simulate a quiz:
Your instructor may take-up these questions during class. It is up to the student to attend classes in order to obtain the answers to the following questions. Your instructor will NOT provide these answers in any other form (eg. e-mail, etc).
Review Questions:
1. List the number of digits for the following numbering systems:
• Decimal
• Binary
• Octal
2. Write a simple chart to show which values are represented for letter A - F for a hexadecimal number.
3. How many binary digits does 1 octal digit represent?
4. How many binary digits does 1 hexadecimal digit represent?
5. Use manual numbering conversion to complete the table displayed to the right.
1. Write the chmod command (using the symbolic method) to set “pass-through” permissions
(eg. r w x - - x - - x) for your home directory using an absolute pathname.
Write a Linux command to verify that permissions where set.
2. Perform a binary to octal numbering conversion for the permissions: r w x - - x - - x
Write single Linux command to set “pass-through” permissions for your home directory,
using the absolute method (i.e. octal numbers).
3. Write a single Linux command to add read permissions for same group members for the ~/tests directory.
4. Write a single Linux command to remove write permissions for same group members
and other group members for the ~/projects directory. Use the symbolic method.
5. Write a single Linux command to set the permissions for the ~/assignments directory
to the following using the absolute method (i.e. octal numbers): r w x r - x - - x
Show your work to perform a binary to octal conversion.
Write the command below using octal numbers and using a relative-to-home pathname.
6. Assume that you just issued the command:
chmod u=rwx,go=x ~/linux/content
What would be the new permissions for the “content” directory?
7. Assume that you just issued the commands: | 5,005 | 23,942 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2021-17 | latest | en | 0.791383 |
https://studylib.net/doc/11321430/quiz-9-math-2250---differential-equations-andamp%3B-linear-al... | 1,674,780,164,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764494852.95/warc/CC-MAIN-20230127001911-20230127031911-00005.warc.gz | 576,374,780 | 12,126 | # Quiz 9 Math 2250 - Differential Equations & Linear Algebra Name:
```Quiz 9
Math 2250 - Differential Equations & Linear Algebra
Name:
December 3, 2015
Quiz Score:
/10
Answer each question completely in the area below. Show all work and explain your reasoning.
If the work is at all ambiguous, it is considered incorrect. No phones, calculators, or notes are
allowed. Anyone found violating these rules will be asked to leave immediately. Point values are in
the square to the left of the question. If there are any other issues, please ask the instructor.
7
1. Compute the eigenvalues and eigenvectors of the following matrix
1 −2
A=
1
4
Solution: We are looking for all eigenvalues λ and eigenvectors v that satisfy the relationship
Av = λv.
Rearranging this, we have
Bv = (A − λI)v = 0.
Since we want non-trivial (v 6= 0) solutions to this equation, we require det B = det(A−λI) = 0. This
determinant is a polynomial called the characteristic polynomial. The roots of the characteristic
polynomial are the eigenvalues we seek!
Actually computing this:
1 − λ −2 = (1 − λ)(4 − λ) − (−2) = λ2 − 5λ + 6 = (λ − 2)(λ − 3).
0 = det(A − λI) = 1
4 − λ
From this, we can conclude our two eigenvalues are λ1 = 2 and λ2 = 3. We can now compute the
eigenvectors corresponding to these eigenvalues.
(1) λ1 = 2. We consider the relationship we started with, now with this particular value of λ:
(A − λ1 I)v1 = 0.
Using the value of λ1 = 2 and calling v = [a b]T , we find
−1 −2 a
0
=
.
1
2 b
0
We note that the resulting two equations are redundant, but this is expected since the determinant condition we imposed forces the matrix A − λI to be singular (and therefore produce an
infinite number of solutions to the homogeneous system). Writing one of these equations (the
second, out of convenience):
a + 2b = 0.
Since we have an infinite family of a, b that satisfy this, we have a ton of freedom, but note an
easy choice is b = 1, which yields a = −2, thus our eigenvector corresponding to λ1 = 2 is
v1 = [−2
1]T .
1/2
Quiz 9
Math 2250 - Differential Equations & Linear Algebra
December 3, 2015
(2) λ2 = 3. We repeat the same process but for the second eigenvalue, thus
(A − λ2 I)v2 = 0
turns into
−2 −2 a
0
=
1
1 b
0
The relationship here is then
a+b =0
3
=⇒
− 1]T .
v2 = [1
2. Using your answer to question 1, write out the diagonalization of A.
That is, write the matrix A as a product of matrices and clearly specify what these matrices are.
Solution: The diagonalization of a matrix A is of the following form
A = PDP−1 ,
where P is a matrix comprised of the eigenvectors and D is a diagonal matrix of the eigenvalues:
λ
0
D= 1
,
P = v1 v2 .
0 λ2
Using the particular values found in problem 1 (and the useful hint below to compute the inverse),
we see
1 1
2 0
−2
1
1
−1
D=
,
P=
,
P =
.
0 3
1 −1
3 1 −2
If we multiplied out these three matrices, we would recover A back.
Useful reminder
a b
c d
−1
1
d
= | 907 | 2,919 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.28125 | 4 | CC-MAIN-2023-06 | latest | en | 0.880443 |
https://education.vex.com/stemlabs/123/coding-fundamentals/robot-speak/play | 1,685,363,608,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224644855.6/warc/CC-MAIN-20230529105815-20230529135815-00294.warc.gz | 257,247,953 | 15,126 | Coding Fundamentals
Lab 2 - Robot Speak
Teacher Portal
# Play
## Part 1 - Step by Step
1. InstructInstruct students that they are going to work in groups to test each of the remaining Coder cards. First, they will predict what behavior they think will happen based on the Coder card name and symbol. Then they will insert the card in the Coder and start the project to observe the behavior of the 123 Robot. Make sure students can verbally describe the goal of the activity. View the animation below to see an example of this testing process.
Video file
Students will test each of the following Coder cards: "Turn left", "Turn right", "Play honk", "Act crazy", and "Drive 1". They should keep the "When start 123" card in the topmost slot of the Coder throughout the Lab.
2. ModelModel the process of predicting then testing each of the Coder cards. Explain that each Coder card causes a specific behavior.
• Each group will need a 123 Robot, Coder, and access to a 123 Field or flat surface to test the Coder card behaviors. They will also need one of each of the following Coder cards pictured above:
• "When start 123", "Turn left", "Turn right", "Play honk", "Act crazy", and "Drive 1"
• If necessary, model how to test the Coder cards with the 123 Robot as they did in the Engage section. (If students have a solid understanding of the process, have them start testing with their group)
• Ask students what they think the "Turn left" Coder card will do.
• Once students have predicted what they think will happen, have students insert the "Turn left" card into the Coder beneath the "When start 123" card.
• Then, model how to connect the 123 Robot to the Coder.
• First, wake the 123 Robot by pushing the wheels along a surface until you hear the startup sound.
• Then, turn on the Coder by pressing the Start button.
• Once the Coder and the 123 Robot are turned on, connect the 123 Robot to the Coder. Do this by pressing and holding the Start and Stop buttons on the Coder, and the Left and Right buttons on the 123 Robot for at least 5 seconds, until you hear the connected sound, and the indicator lights flash in time, as shown in the animation below. Turn on sound for this animation.
• For more information about the Coder, see the Using the VEX 123 Coder VEX Library article.
Video file
• Have students continue to predict and test each of the cards.
• If groups finish early, have them create a dance move for the 123 Robot by sequencing two or three Coder cards in the Coder. Then, they can test their project on the 123 Field and watch the 123 Robot dance!
3. FacilitateFacilitate discussions with students as you circulate through the room. Encourage students to share their thinking with questions such as:
• Did your prediction match the behavior of the 123 Robot? If not, how was it different?
• What do you look at on the card to make your predictions?
• How far does the 123 Robot move when you use the "Drive 1" Coder card? Which direction does it move?
4. RemindRemind students that testing takes time and patience. They will need to take each card out of the Coder after they test, insert the next card, then continue the testing process.
5. AskAsk students what jobs they know that require people to plan and test before acting. How is that similar to what they did with the Coder and Coder cards?
## Mid-Play Break & Group Discussion
As soon as every group has tested each Coder card provided, come together for a brief conversation.
• Did your predictions match the 123 Robot behaviors?
• What was similar or different?
• Show students the "Drive 2" card. Ask them what they think the 123 Robot will do if you use this card in the Coder.
• How will the 123 Robot move?
• Is distance further or shorter than the "Drive 1" card? How do they know that?
• Put the "Drive 2" card in the Coder to test the students' predictions.
• When might the "Drive 2" Coder card be more useful than the "Drive 1" card?
## Part 2 - Step by Step
1. InstructInstruct students that they will create a project for the 123 Robot to drive in a 1x1 square on a 123 Field. They will need to plan the project with the Coder cards first. Then, they will test their projects. If the 123 Robot doesn't move the way they intended, they will have to troubleshoot, revise their project, and try again. Make sure the students are able to verbalize the intention of the project. View the animation below for an example of how to make the 123 Robot drive in a square.
Video file
• Let students know that they should pay close attention to the sequence (or order) in which the Coder cards are placed. Remind students that sequence is important in projects. However, projects may look different. There is more than one way to code the 123 Robot to drive in a square.
2. ModelModel how to plan and create a project using the cards provided, then start and revise the project if necessary.
• In addition to a 123 Robot, Coder, students will need access to a 123 Field or flat surface to test their projects. Each group will also need the following Coder cards:
• One "When start 123"
• Four "Drive 1"
• Four "Turn left" OR "Turn right"
• Ensure that students know that a square has 4 sides that are the same length and 4 corners. Guide students to decompose the task of driving in a square into smaller actions (i.e. Drive 1, Turn right, Drive 1 again, Turn right...)
• Model how to insert the cards in the Coder making sure to place them in the intended sequence. Students should understand that the "When start 123" card is needed at the beginning of their project. It should be insert in the topmost slot on the Coder.
• Students may need to wake the 123 Robot and make sure it is connected to the Coder as shown in the animation below. Turn on the sound for this animation to hear the indicator sounds on the 123 Robot.
Video file
• Show students how to place the 123 Robot on their 123 Field or on a table to test their project.
• Once all the Coder cards are inserted, they should press Start and observe the 123 Robot behaviors.
• To highlight the troubleshooting process, you may want the teacher demonstration project to have an error, so that you can model how to take out the necessary cards and place them back in the Coder in the correct order to have the 123 Robot drive in a square.
• If groups finish early, have them create a project to drive the 123 Robot in a zig-zag pattern. Students will need to have both "Turn right" and "Turn left" Coder cards.
3. FacilitateFacilitate a discussion with the students by encouraging them to talk through the project plans in their groups, and act out the behavior for each Coder card in their project. Use prompts such as:
• Can you use your hands to show how the 123 Robot should move on the 123 Field?
• Will your 123 Robot move the same amount of spaces on all sides?
• How many turns does the 123 Robot need to make to drive in a square?
Encourage students to analyze their projects and troubleshoot with the following prompts:
• Which direction did your 123 Robot have to move in for the 123 Robot to make a square?
• Can the 123 Robot use left and right turns to make a square? Why or why not?
• Can you explain what each Coder card in your project does?
• Did your 123 Robot move the way you expected?
4. RemindRemind students that coding their 123 Robot to drive in a square will take many tries. Encourage students to keep trying with prompts such as:
• Your 123 Robot didn't move in a square the first time? That's ok! Now you get to try again!
• Is your 123 Robot moving in a way that you didn’t expect? Let's investigate! Where did the 123 Robot start to move out of the square shape? Where is this in the project?
5. AskAsk students why they think planning something before doing it may be helpful. Ask students if they have ever planned what they would wear the next day the night before they went to sleep, or planned what they would pack for their lunch the next day. How did making a plan help them? | 1,899 | 7,981 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2023-23 | latest | en | 0.917511 |
https://www.coursehero.com/file/6118530/SCAN0014/ | 1,524,189,628,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125937090.0/warc/CC-MAIN-20180420003432-20180420023432-00445.warc.gz | 756,640,224 | 25,346 | {[ promptMessage ]}
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SCAN0014
# SCAN0014 - 4 A block of mass 75 g is attached to a solid...
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Unformatted text preview: 4. A block of mass 75 g is attached to a solid support by a spring. This mass is free to move on a frictionless horizontal surface. The motion is constrained to one dimension (along the x axis). At equilibrium the mass rests at the origin. A force of 15 N is applied to the block which compresses the spring until the mass is at x = - 8.0cm. The force is then removed. Calculate the following quantities: The spring constant, k. The velocity, v at x = 0, + 4.0, and + 8.00m. The acceleration, a at x = 0, + 4.0 and + 8.00m. The frequency, f and the period, T. Write an equation that specifies x as a function of t. M my: seam 0" V=k¢9¢ AY=0.0%W\ Vztsm 99.0.01» ...
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{[ snackBarMessage ]} | 295 | 998 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2018-17 | latest | en | 0.845025 |
https://smartconversion.com/ConversionExample/grade-to-point/438/444 | 1,696,248,541,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510994.61/warc/CC-MAIN-20231002100910-20231002130910-00371.warc.gz | 571,995,533 | 5,518 | Learn how to convert 1 grade to point step by step.
## Calculation Breakdown
Set up the equation
$$1.0\left(grade\right)={\color{rgb(20,165,174)} x}\left(point\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(radian\right)$$
$$\text{Left side: 1.0 } \left(grade\right) = {\color{rgb(89,182,91)} \dfrac{π}{2.0 \times 10^{2}}\left(radian\right)} = {\color{rgb(89,182,91)} \dfrac{π}{2.0 \times 10^{2}}\left(rad\right)}$$
$$\text{Right side: 1.0 } \left(point\right) = {\color{rgb(125,164,120)} \dfrac{π}{16.0}\left(radian\right)} = {\color{rgb(125,164,120)} \dfrac{π}{16.0}\left(rad\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(grade\right)={\color{rgb(20,165,174)} x}\left(point\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{2.0 \times 10^{2}}} \times {\color{rgb(89,182,91)} \left(radian\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{π}{16.0}}} \times {\color{rgb(125,164,120)} \left(radian\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{π}{2.0 \times 10^{2}}} \cdot {\color{rgb(89,182,91)} \left(rad\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{π}{16.0}} \cdot {\color{rgb(125,164,120)} \left(rad\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{π}{2.0 \times 10^{2}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(rad\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{π}{16.0}} \times {\color{rgb(125,164,120)} \cancel{\left(rad\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{π}{2.0 \times 10^{2}} = {\color{rgb(20,165,174)} x} \times \dfrac{π}{16.0}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$$\dfrac{{\color{rgb(255,204,153)} \cancel{π}}}{2.0 \times 10^{2}} = {\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{π}}}{16.0}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{16.0} = \dfrac{1.0}{2.0 \times 10^{2}}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{16.0}{1.0}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{1.0}{16.0} \times \dfrac{16.0}{1.0} = \dfrac{1.0}{2.0 \times 10^{2}} \times \dfrac{16.0}{1.0}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times {\color{rgb(99,194,222)} \cancel{16.0}}}{{\color{rgb(99,194,222)} \cancel{16.0}} \times {\color{rgb(255,204,153)} \cancel{1.0}}} = \dfrac{{\color{rgb(255,204,153)} \cancel{1.0}} \times 16.0}{2.0 \times 10^{2} \times {\color{rgb(255,204,153)} \cancel{1.0}}}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{16.0}{2.0 \times 10^{2}}$$
Rewrite equation
$$\dfrac{1.0}{10^{2}}\text{ can be rewritten to }10^{-2}$$
$$\text{Rewrite}$$
$${\color{rgb(20,165,174)} x} = \dfrac{10^{-2} \times 16.0}{2.0}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x} = 8 \times 10^{-2}$$
$$\text{Conversion Equation}$$
$$1.0\left(grade\right) = {\color{rgb(20,165,174)} 8 \times 10^{-2}}\left(point\right)$$ | 1,380 | 3,162 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5 | 4 | CC-MAIN-2023-40 | latest | en | 0.282467 |
https://oeis.org/A225322 | 1,723,722,131,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641291968.96/warc/CC-MAIN-20240815110654-20240815140654-00058.warc.gz | 348,416,851 | 3,955 | The OEIS is supported by the many generous donors to the OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A225322 Lucky numbers that are prime powers. 1
1, 9, 25, 49, 169, 289, 361, 529, 729, 841, 961, 1369, 2187, 2209, 3481, 3721, 5041, 7921, 9409, 10609, 24649, 29791, 32041, 32761, 36481, 50653, 52441, 66049, 73441, 83521, 113569, 121801, 128881, 130321, 167281, 175561, 185761, 226981, 292681, 300763, 323761 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,2 COMMENTS Intersection of A025475 and A000959. Conjecture: the sequence is infinite. LINKS Kevin P. Thompson, Table of n, a(n) for n = 1..1577 (terms < 10^10 with terms 1..628 from Donovan Johnson) CROSSREFS Cf. A000959, A025475. Cf. A031157, A031162, A057589, A118565, A128511. Sequence in context: A297596 A266132 A112629 * A031162 A371085 A362971 Adjacent sequences: A225319 A225320 A225321 * A225323 A225324 A225325 KEYWORD nonn AUTHOR Alex Ratushnyak, May 05 2013 STATUS approved
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Last modified August 15 07:32 EDT 2024. Contains 375173 sequences. (Running on oeis4.) | 468 | 1,344 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2024-33 | latest | en | 0.631293 |
https://www.superfastcpa.com/what-is-the-percentage-of-completion-method/ | 1,714,055,947,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712297295329.99/warc/CC-MAIN-20240425130216-20240425160216-00818.warc.gz | 885,546,085 | 91,369 | # What is the Percentage of Completion Method?
## Percentage of Completion Method
The percentage of completion method is an accounting technique used primarily in construction or long-term project contracts. It allows revenue and profit to be recognized as the contract progresses, rather than waiting until the project is fully completed.
The method calculates the ongoing recognition of revenue and expenses of long-term projects based on the proportion of work completed. The percentage of work completed is often estimated by comparing the costs incurred to date with the total expected costs of the contract.
This method of recognizing revenue and expenses can provide a more accurate reflection of the company’s financial position when it’s engaged in long-term projects. However, it requires careful estimates and can be subject to errors or biases if those estimates are off.
Here’s a simplified formula to understand the method:
Percentage of Completion = (Costs Incurred to Date / Total Estimated Costs) * 100%
Revenue Recognized = Contract Revenue * Percentage of Completion
It’s important to note that the use of the percentage of completion method is governed by specific accounting rules and standards. In the U.S., these rules are set forth by the Financial Accounting Standards Board (FASB), and internationally, they are part of the International Financial Reporting Standards (IFRS).
## Example of the Percentage of Completion Method
Suppose a construction company has a contract to build a bridge for \$5,000,000. The total cost estimated to complete the bridge is \$4,000,000. After one year, the company has incurred costs of \$2,000,000.
We can calculate the percentage of completion as follows:
Percentage of Completion = (Costs Incurred to Date / Total Estimated Costs) * 100% = (\$2,000,000 / \$4,000,000) * 100% = 50%
Now, we can calculate the amount of revenue to recognize:
Revenue Recognized = Contract Revenue * Percentage of Completion = \$5,000,000 * 50% = \$2,500,000
So, after one year, the company would recognize \$2,500,000 in revenue for the bridge construction project. This method allows the company to recognize revenue gradually as the project progresses, rather than waiting until the entire project is complete.
Remember, the percentage of completion method requires accurate estimates of total costs, and the actual costs may end up being different from what was initially estimated. If there’s a change in the estimated total costs, the percentage of completion and the recognized revenue will need to be adjusted accordingly. | 513 | 2,588 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.59375 | 4 | CC-MAIN-2024-18 | longest | en | 0.936115 |
https://brainly.com/question/195549 | 1,484,982,188,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560280929.91/warc/CC-MAIN-20170116095120-00507-ip-10-171-10-70.ec2.internal.warc.gz | 782,396,154 | 8,536 | Answers
The Brainliest Answer!
2014-11-20T18:35:45-05:00
The slope is 1/2
The Y intercept is -5
2014-11-20T18:39:52-05:00
Y=(slope)X+(y-intercept)
slope=1/2x
y intercept= -5 | 79 | 177 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2017-04 | latest | en | 0.471128 |
https://jp.mathworks.com/matlabcentral/cody/problems/163-love-triangles/solutions/284150 | 1,610,888,716,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610703512342.19/warc/CC-MAIN-20210117112618-20210117142618-00197.warc.gz | 412,223,743 | 17,067 | Cody
# Problem 163. Love triangles
Solution 284150
Submitted on 17 Jul 2013 by Jan Orwat
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
%% sides = [1 2 1000]; y_correct = false; assert(isequal(triangle(sides),y_correct))
2 Pass
%% sides = [3 4 5]; y_correct = true; assert(isequal(triangle(sides),y_correct))
3 Pass
%% sides = [5 5 5]; y_correct = true; assert(isequal(triangle(sides),y_correct))
4 Pass
%% sides = [6 6 6]; y_correct = true; assert(isequal(triangle(sides),y_correct))
5 Pass
%% sides = [1 1 1]; y_correct = true; assert(isequal(triangle(sides),y_correct))
6 Pass
%% sides = [1 2 2]; y_correct = true; assert(isequal(triangle(sides),y_correct))
7 Pass
%% sides = [2 2 5]; y_correct = false; assert(isequal(triangle(sides),y_correct))
8 Pass
%% sides = [5 2 2]; y_correct = false; assert(isequal(triangle(sides),y_correct))
9 Pass
%% sides = [1 3 1]; y_correct = false; assert(isequal(triangle(sides),y_correct))
### Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting! | 367 | 1,203 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2021-04 | latest | en | 0.527405 |
https://py4u.org/questions/74505643/ | 1,670,464,325,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711232.54/warc/CC-MAIN-20221208014204-20221208044204-00614.warc.gz | 511,871,294 | 6,930 | # Create a column based on conditions and calculation
## Question:
Below is my dataframe:
df = pd.DataFrame({"ID" : [1, 1, 2, 2, 2, 3, 3],
"length" : [0.7, 0.7, 0.8, 0.6, 0.6, 0.9, 0.9],
"comment" : ["typed", "handwritten", "typed", "typed", "handwritten", "handwritten", "handwritten"]})
df
ID length comment
0 1 0.7 typed
1 1 0.7 handwritten
2 2 0.8 typed
3 2 0.6 typed
4 2 0.6 handwritten
5 3 0.9 handwritten
6 3 0.9 handwritten
I want to be able to do the following:
For any group of ID, if the length are the same but the comments are different, use the "typed" formula (5 x length) for the calculated length of that group of ID, otherwise use the formula that apply to each comment to get the calculated length. typed = 5 x length, handwritten = 7*length.
Required Output will be as below:
ID length comment Calculated Length
0 1 0.7 typed 5*length
1 1 0.7 handwritten 5*length
2 2 0.8 typed 5*length
3 2 0.6 typed 5*length
4 2 0.6 handwritten 7*length
5 3 0.9 handwritten 7*length
6 3 0.9 handwritten 7*length
Thank you.
use np.where if comment column exist only typed or handwritten.
import numpy as np
cond1 = df['comment'] == 'typed'
df.assign(Calculated_Length=np.where(cond1, df['length'] * 5, df['length'] * 7))
output:
ID length comment Calculated_Length
0 1 0.7 typed 3.5
1 1 0.7 handwritten 4.9
2 2 0.8 typed 4.0
3 2 0.6 typed 3.0
4 2 0.6 handwritten 4.2
5 3 0.9 handwritten 6.3
6 3 0.9 handwritten 6.3
edit after comment
cond1 = df['comment'] == 'typed'
cond2 = df.groupby('ID')['length'].transform(lambda x: (x.max() == x.min()) & (df.loc[x.index, 'comment'].eq('typed').sum() > 0))
df.assign(Caculated_Length=np.where((cond1 | cond2), df['length']*5, df['length']*7))
output:
ID length comment Caculated_Length
0 1 0.7 typed 3.5
1 1 0.7 handwritten 3.5
2 2 0.8 typed 4.0
3 2 0.6 typed 3.0
4 2 0.6 handwritten 4.2
5 3 0.9 handwritten 6.3
6 3 0.9 handwritten 6.3
Find the IDs that satisfy the special condition using groupby. Using the IDs and the comment, compute the Calculated length using np.where as follows
>>> grp_ids = df.groupby("ID")[["length", "comment"]].nunique()
>>> grp_ids
length comment
ID
1 1 2
2 2 2
3 1 1
>>> idx = grp_ids.index[(grp_ids["length"] == 1) & (grp_ids["comment"] != 1)]
>>> idx
Int64Index([1], dtype='int64', name='ID')
>>> df["Calculated length"] = np.where(
df["ID"].isin(idx) | (df["comment"] == "typed"),
df["length"] * 5,
df["length"] * 7
)
>>> df
ID length comment Calculated length
0 1 0.7 typed 3.5
1 1 0.7 handwritten 3.5
2 2 0.8 typed 4.0
3 2 0.6 typed 3.0
4 2 0.6 handwritten 4.2
5 3 0.9 handwritten 6.3
6 3 0.9 handwritten 6.3
Categories: questions Tags: , ,
Answers are sorted by their score. The answer accepted by the question owner as the best is marked with
at the top-right corner. | 1,159 | 3,320 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2022-49 | latest | en | 0.707447 |
https://cs50.stackexchange.com/questions/21495/pset-1-hacker-credit | 1,712,968,032,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296816465.91/warc/CC-MAIN-20240412225756-20240413015756-00341.warc.gz | 171,208,699 | 23,690 | # pset 1 hacker credit
#include<stdio.h> // have four spaces before code lines
#include<cs50.h> // this will insert them in the code block
#include<math.h>
bool checksum(long long num);
bool visa(long long num);
bool mastercard(long long num);
bool amexp(long long num);
int main()
{
long long card;
do
{
printf("Number: \n");
card = GetLongLong();
}
while (card<=0);
if(visa(card)||mastercard(card)||amexp(card)) //checks valid format for card number
{
checksum(card);
}
if (checksum(card)) // for printing result
{
if(visa(card))
{
printf("VISA\n");
}
else if(amexp(card))
{
printf("AMEX\n");
}
if(mastercard(card))
{
printf("MASTERCARD\n");
}
}
else
{
printf("INVALID\n");
}
}
bool visa(long long num) //conditition for visa
{ int a=0;
while(num!=0)
{
num = num/10;
a++;
}
if((a==13 || a==16)&&(num/pow(10,12)==4||num/pow(10,15)==4))
{
return true;
}
return false;
}
bool mastercard(long long num)
{ int a=0;
while(num!=0)
{
num = num/10;
a++;
}
if((a==16)&&((num/pow(10,14)==51)||(num/pow(10,14)==51)||(num/pow(10,14)==51)||(num/pow(10,14)==51)||(num/pow(10,14)==51)))
{
return true;
}
return false;
}
bool amexp(long long num)
{ int a=0;
while(num!=0)
{
num = num/10;
a++;
}
if((a==15)&&(num/pow(10,13)==34||num/pow(10,13)==37))
{
return true;
}
return false;
}
bool checksum(long long num)
{
int a=0;
int sum=0;
int sum1=0;
while(num!=0)
{
int b = num%10;
if(a%2==0)
{
sum=sum+b;
}
else
{
sum1=sum1+b;
}
num = num/10;
a++;
}
int sum2=sum+sum1;
if (sum2%10==0)
{
return true;
}
return false;
}
its printing every number invalid
• If your while loop goes on until num is 0, num/pow(10,14) is most likely 0, too. Also, your checksum calculation might be a bit off. In case of odd a, you'd have to add 2*b-9*(b>4) or something like that, not just b. Oct 26, 2016 at 9:47
## 1 Answer
I have two observations that might help you. I am going to speak about line numbers based on the code block you provided. For example:
bool checksum(long long num); // Is line #05
bool visa(long long num) //conditition for visa. Is line #46
1.- On line 67 you have 51 for every part of the condition. I think you meant 51, 52, 53, 54, and 55.
if((a==16)&&((num/pow(10,14)==51)||(num/pow(10,14)==51)||(num/pow(10,14)==51)||(num/pow(10,14)==51)||(num/pow(10,14)==51)))
2.- When you check the sum you need to multiply by two the second to last digit and every other digit. The code is doing two different sums as instructed, but we need to multiply by two one of those. That would be line 102:
sum1=sum1+b;
You have to multiply b by two.
Also, when you multiply by two every other digit, they don't want the sum of the number per se. They want the sum of the digits of the number multiplied by two. For example:
If the digit is 4:
4*2 = 8
You add 8
Easy.
If the digit is 8:
8*2 = 16
1 + 6 = 7
You add 7
A little different.
I suggest you add a line before line 102 that multiplies b by two and adds its digits. Something like this:
b = (b > 4)? 1 + (b*2)%10 : b*2;
sum1=sum1+b;
So, if b is let us say 7, 7 times 2 is 14. They want you to add 1 + 4. So you have:
1 + (b*2)%10
1 + (7*2)%10
1 + 14 %10
1 + 4
The other case is b <= 4 in which you are good with just b*2, because those results don't exceed one digit.
And this is the ternary conditional operator, but you can do it with if statements if you like:
variable = (condition)? value1 : value2;
// if condition was true variable gets assigned value1
// if condition was false variable gets assigned value2 | 1,124 | 3,509 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2024-18 | latest | en | 0.390609 |
https://socratic.org/questions/how-do-you-express-1-405-000-000-000-in-scientific-notation#355660 | 1,702,226,137,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679102612.80/warc/CC-MAIN-20231210155147-20231210185147-00050.warc.gz | 576,123,989 | 5,775 | How do you express 1,405,000,000,000 in scientific notation?
Dec 22, 2016
$1.405 \times {10}^{12}$
Explanation:
To express this in scientific notation the decimal point needs to be moved 12 places to the left which means it will be a positive 12 exponent:
$1 , 405 , 000 , 000 , 000 = 1 , 405 , 000 , 000 , 000 \textcolor{red}{.0} \to$
$1.405 \times {10}^{12}$ | 125 | 366 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 3, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.75 | 4 | CC-MAIN-2023-50 | latest | en | 0.694928 |
https://essaywritingservices.customwritingpapers.org/a-college-student-is-planning-to-apply-for-a-school-grant-a-friend-of-hers-who/ | 1,560,690,320,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627998238.28/warc/CC-MAIN-20190616122738-20190616144738-00251.warc.gz | 438,412,076 | 24,528 | # A college student is planning to apply for a school grant. A friend of hers who
A college student is planning to apply for a school grant. A friend of hers who works for the company that is offering the grant has told her that if she takes calculus in her freshman year and gets an A or B, she will be very strongly considered for the grant, but if she gets a C, D or F, she will probably not be considered. If she doesn’t take calculus at all, she remains a candidate. She estimated the following probabilities:Probability of getting the grant if she takes calculus and gets A or B: 0.80Probability of getting the grant if she takes calculus and gets C or D: 0.10Probability of getting the grant if calculus not taken: 0.50Probability of getting A or B in calculus: 0.60a) What is the probability that she will get the grant if she takes calculus?b) What should she do to maximize the probability that she will get the grant?
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Main content
Course: High school physics—NGSS (DEPRECATED)>Unit 4
Lesson 3: Predictions using energy
Calculating velocity using energy
Learn how you can calculate the launch velocity of an object by using the total energy of a system. Energy that is conserved can be transferred within a system from one object to another changing the characteristics of each object, like velocity. Created by Sal Khan.
Want to join the conversation?
• Is this called a certain equation or not? Is it applicable to every situation? What is Δx equal to? (in most situations; in here it means spring compression)
(2 votes)
• Δx or dx stands for 'delta x' which indicates displacement. This is calculated from taking the initial x position to the final x position (final x - initial x). In this case for the spring, the initial position is the uncompressed mark and the final position is the compressed stage, so delta x would measure how much the spring moved (which in this case more displacement = more compression).
(3 votes)
• why is it kΔx^2/m - 2gh2 at
(2 votes)
Video transcript
- [Instructor] So we have a spring here that has a spring constant of four Newtons per meter. What we then do is take a 10-gram mass and we put it on top of the spring and we push down to compress the spring by 10 centimeters. We then let go. And what I'm curious about is what is going to be the magnitude of the velocity of our ball here, of our 10-gram mass, right as the spring is no longer compressed or stretched, or essentially when the ball is being launched? Pause this video and see if you can figure that out. And I'll give you a hint, the energy in this first state, the total energy has got to be equal to the total energy of this second state. We can't create or destroy energy. All right, now let's work through this together. So let's call this first scenario state one. So in state one, what is the total energy going to be? Well, it's going to be the sum of the gravitational potential energy, so that's mg times the height in state one, plus our elastic potential energy, that's 1/2 times the spring constant times how much we've compressed that spring in state one squared, plus our kinetic energy, so that's 1/2 times our mass times the magnitude of our velocity in state one squared. And that has got to be equal to, as we just talked about, the total energy in state two. Well, what's that going to be? Well, that's your gravitational potential energy in state two plus your elastic potential energy in state two plus your kinetic energy in state two. Now let's think about which of these variables we know and which ones we need to solve for. So, first of all, mass, your spring constant, the strength of your gravitational field, well, we know what these are going to be. These are going to be our mass is equal to 10 grams. The strength of the gravitational field, also the acceleration due to gravity near the surface of the earth, is 9.8 meters per second squared. Our spring constant is four Newtons per meter, and I like to remind myself what a Newton is, a Newton is kilogram meter per second squared. So this is also equal to four kilogram meter per second squared, and then we also have a meter over there. And actually, these meters will cancel out. And that's useful because it's reminding us that we want everything to be in kilograms and meters. And with that in mind, actually, let me rewrite our mass right over here as 0.01 kilograms. And then let's think about what's going on specifically in each of those states. So what is going to be our h one, our initial height? Well, I didn't give it to you, but what really matters is the difference between h one and h two. So we could just define h one right over here to be equal to zero. So let me write that down. H one is equal to zero. And if we say that, then what is h two going to be? H two would then be equal to 10 centimeters, but remember, we want everything in kilograms and meters, so 10 centimeters is the same thing is 0.1 meters. What is our spring compression in scenario one going to be? Well, that is going to be 10 centimeters. But once again, we wanna write that in terms of meters. So I'll write that as 0.1 meters. And then what is our spring compression in scenario two going to be? Well, we're completely uncompressed and unstretched, so that is going to be zero meters. And then what is going to be our velocity, or at least the magnitude of our velocity in state one? Well, we're stationary, so it's zero meters per second. And what is going to be the magnitude of our velocity in state two? Well, that's exactly what we wanna solve for. That is our launch velocity. So let's see if we can simplify this and then solve for v two. So we know that h one is equal to zero. So that simplifies that right over there, that term is zero. We know that v one is zero. So that simplifies that term there. We know that delta x in scenario two is equal to zero. So that simplifies that term right over there. And so we can now rewrite all of this, and I'll switch to one color just to speed things up a little bit, as 1/2 k times delta x one squared is equal to mgh sub two plus 1/2 mv sub two squared. And now let's just try to solve for this character. So let's subtract mgh sub two from both sides. So we're going to have 1/2 k times delta x sub one squared minus mgh sub two is equal to 1/2 mv sub two squared. Now let's see, if we multiply both sides by two over m, then that will get rid of this 1/2 m over here. So let me multiply that. I'm kind of doing two steps at the same time. One way to think about it is I'm multiplying times the reciprocal of the coefficient on the v squared. So right over here, it's m over two, so the reciprocal is two over m. I'm gonna have to make sure that I'm gonna multiply it times that whole side. And so what do we now have? This is going to be equal to, let's see, it's going to be k delta x sub one squared over m minus two gh sub two is going to be equal to v sub two squared. And then to solve for our launch velocity, we just take the principal route, the square root of both sides. So I could say v sub two, which is equal to our launch velocity, is equal to the square root of our spring constant times delta x sub one squared over our mass minus two times the gravitational field times h two. And so we just have to plug in the numbers now. This is going to be equal to, and I'll switch colors just to ease the monotony. I'm gonna use a new color right over here. This is going to be equal to the square root of, and I wanna make sure all the units work out. So I'm actually gonna write this version of my spring constant, so I can work with all the units. So it's gonna be four kilograms per second squared. And now delta x one we know is 0.1 meters. So if we square it, it's going to be times 0.01 meters squared. And then all of that is going to be over our mass, which we know is 0.01 kilograms, 0.01 kilograms, and then minus two times 9.8 meters per second squared times height in the second scenario, which we already know is 0.1 meters, so times 0.1 meters. Let me extend this radical right over here. And let's look at the units first to just to make sure we're getting the right units. So this kilogram is going to cancel with this kilogram. And then we have, over here, we're going to have something that's in terms of meters squared per second squared, and then over here, we're gonna have something in terms of meters squared per second squared. So that makes sense. We're gonna have a difference of two meters squared per second squared. And then when you take the principal route, you're going to get meters per second, which is the unit for the magnitude of velocity. So now we just have to get our calculator out and calculate this. So the .01s will cancel out. So this part right over here is going to be four. And then from that, I am going to subtract two times 9.8 times .1, close the parentheses. That's going to be equal to that. And then I needed to take the square root of all of that business, and I get this right over here. So this is approximately 1.43 meters per second, 1.43 meters per second. And we're done. | 1,981 | 8,389 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4 | 4 | CC-MAIN-2024-30 | latest | en | 0.93336 |
http://mathoverflow.net/feeds/question/114738 | 1,369,119,259,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368699755211/warc/CC-MAIN-20130516102235-00058-ip-10-60-113-184.ec2.internal.warc.gz | 163,124,381 | 6,484 | Integrating Powers without much Calculus - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T06:54:20Z http://mathoverflow.net/feeds/question/114738 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/114738/integrating-powers-without-much-calculus Integrating Powers without much Calculus Aaron Meyerowitz 2012-11-28T07:41:08Z 2012-11-29T21:53:42Z <p>I'll jump into the question and then back off into qualifications and context</p> <blockquote> <p>Using the definition of a definite integral as the limit of Riemann sums, what is the best way (or the very good ways) to establish the results $\int_a^bx^pdx=\frac{b^{p+1}-a^{p+1}}{p+1}$ without building a general theory of integrals?</p> </blockquote> <p>Context: For better or worse, a common sequence in teaching integral calculus for the first or second time is to define the definite integral as a limit of Riemann sums. One then notes that this ( like the limit definition of derivatives) is effective for proving theorems but not very practical for specific calculations. So soon one demonstrates or implies that the definition is valid and then gets to the Fundamental Theorem of Calculus. However it is traditional to use the definition to evaluate $\int_a^bx^pdx$ for $p=0,1,2$ and perhaps $p=3$ using the lovely sum of cubes formula. </p> <p>It might be tempting to prove the formula in greater generality without using the fundamental theorem (most students are less excited at this prospect than one might expect!). In my early days as a TA I came up with an approach which I thought was great. The students were not impressed and I have not used it since. Anyway, I have not seen it elsewhere although I am confident it is nothing novel. I am not going to reveal it right away just to see if it shows up. I realize that is questionable manners here on MO but I will put it up in a day or two, I just want to see what shows up first.</p> <p>Here is a very brief sketch of two approaches I have seen:</p> <p>1) Let $S_p(n)=\sum_{k=0}^nn^p.$ The explicit formulas for $p=0,1,2$ and also $p=3$ are attractive and not bad to prove by induction. Given an explicit formula for $S_p$ one easily evaluates the usual equal subinterval sums for $\int_0^1x^pdx$ and then extends to $\int_a^b.$ But $S_p$ gets more tedious for larger $p$. A clever method of Pascal allows one to use strong induction, the binomial theorem and telescoping sums to, derive an explicit formulas for $S_{p}$ for larger values of $p$, limited only by ones patience and stamina:</p> <p>Take $(k+1)^{p+1}-k^{p+1}=\sum_1^{p+1}\binom{p+1}{j}k^{p+1-j}$ and sum for $k$ from $0$ to $n$ to get $(n+1)^{p+1}-0^{p+1}=\sum_1^{p+1}\binom{p+1}{j}S_{p+1-j}(n).$ Since we know everything except $S_p,$ the rest is algebra! This is quickly unpleasant and the final results are not as aesthetic as the first cases. HOWEVER, for the desired application we only need to establish that $S_p(n)=\frac{n^{p+1}}{p+1}+\frac{n^p}{2}+O(n^{p-1})$ That is not hard and shows that $n$ subdivisions yield $\frac{1}{p+1}-\frac{1}{2n} \lt \int_0^1x^pdx \lt \frac{1}{p+1}+\frac{1}{2n}$.</p> <p>Notes: This is valid for $p$ a non-negative integer. Knowing enough about Bernouli numbers allows explicit formulas but I am interested in fairly elementary methods. I think that one involves the series expansion for $e^x$.</p> <p>2) Due to Fermat: Partition into subintervals using points forming a geometric rather than arithmetic progression. I've seen this in two forms: </p> <p>2.1) Choose $0 \lt a \lt b$ and divide using $a \lt ar \lt ar^2 \lt \cdots\lt ar^N=b$ so $r=\sqrt[N]{b/a}.$ The widths of the intervals form a geometric progression of common ratio $r$. The values of $x^p$ at the points of division form a geometric progression of common ratio $r^p.$ Thus the sum of rectangle areas using left endpoints gives as a lower bound for $\int_a^bx^p$ the geometric series with $N$ terms, first term $a^{p+1}(r-1)$ and ratio $r^{p+1}.$ Using righthand enpoints gives a similar upper bound with first term $a^{p+1}(r-1)r^p.$ With very little effort one arrives at</p> <p>$$\frac{(b^{p+1}-a^{p+1})(r-1)}{r^{p+1}-1} \lt \int_a^bx^pdx \lt \frac{(b^{p+1}-a^{p+1})(r-1)r^p}{r^{p+1}-1}.$$</p> <p>If $p+1$ is a positive integer we have </p> <p>$$\frac{b^{p+1}-a^{p+1}}{1+r+r^2+\cdots+r^p} \lt \int_a^bx^pdx \lt \frac{(b^{p+1}-a^{p+1})r^p}{1+r+r^2+\cdots+r^p}.$$</p> <p>Now let $N$ go to infinity sending $r$ to $1$ and squeezing to $\int_a^bx^pdx=\frac{b^{p+1}-a^{p+1}}{p+1}.$</p> <p>This particular approach requires $0 \lt a.$ It is an easy extra step to extend the result to rational values of $p$ (except for the challenging $p=-1$) using $\frac{r^{p/q}-1}{r-1}=\frac{u^p-1}{u-1}/\frac{u^q-1}{u-1}$ for $u=r^{1/q}.$</p> <p>2.2) Similar except now divide the interval $[0,b]$ using a value $0 \lt r \lt 1$ and infinitely many points $\cdots br^3 \lt br^2 \lt br \lt b.$ Now one has infinite geometric series and the rest procedes similarly to before letting $r$ increase to $1.$</p> <p>So that is the flavor of what I am asking about. I do not think this is a big list question unless there are a large number of approaches I have not seen.</p> <p><strong>CONTINUED</strong> To recap, we already know the answer , $\frac{b^{p+1}-a^{p+1}}{b-a}$, which we want for the area $A$ of the region under $x^p$ for $a \le x \le b$, we just want to prove it. (Assume for ease that $0 \lt a$.) A <em>partition</em> $P$ of $[a,b]$ is a sequence $a=x_0 \lt x_1 \lt \cdots \lt x_n=b$. The <em>mesh</em> $m(P)$ of $P$ is $\max(x_{i}-x_{i-1}).$ (There is rarely a reason to have unequal intervals, but Fermat gave one.) We use the sub-intervals, in two ways, as the bases of an assemblage of rectangles with heights determined by the endpoints. Since $x^p$ is monotonic, one is covered by the region and the other covers it. So the two areas provide a lower and an upper bound. </p> <p><img src="http://img853.imageshack.us/img853/7289/moint1.png" alt="alt text"></p> <p>$$\sum_1^nx_{i-1}^p(x_i-x_{i-1}) \lt A \lt \sum_1^nx_{i}^p(x_i-x_{i-1})$$ If we manage to compute or bound these bounds and show that, when the mesh goes to zero, they have a common limit (the one we expect), we are done. The actual bounds we compute are of value only for the interesting, but secondary, topic of speed of convergence. And anyway, if $m(P) \lt \epsilon$ then the difference between the two bounds is less than $(b-a)(b^p-(b-\epsilon)^p),$ which converges to zero. (For $p \lt 0$ use $a-(a+\epsilon)^p$)</p> <p>So I propose to instead assign to each sub-interval $[u,v]$ the height $h(u,v)=\frac{v^{p+1}-u^{p+1}}{(p+1)(v-u)}$ and "compute" $\sum_1^nh(x_{i-1},x_i)(x_i-x_{i-1})$ which immediately collapses to, of course, $\frac{b^{p+1}-a^{p+1}}{p+1}.$ </p> <p><img src="http://imageshack.us/a/img855/4483/moint2.png" alt="alt text"></p> <p>Establishing that this has any relevance requires showing that the height $h(u,v)$ is between $u^p$ and $v^p$. This is easy in practice if one simplifies. If you simplify first, then the whole thing looks like magic until you see what was done. </p> <p>So for $p=5$, obviously $$u^5 \lt \frac{v^5+v^4u+v^3u^2+v^2u^3+vu^4+u^5}{6} \lt v^5.$$ OK, so what? Why not use the average, the geometric mean or $\left(\frac{u+v}{2}\right)^5$? Well, $(v-u)h(u,v)=\frac{v^6-u^6}{6}$ so $\sum_1^nh(x_{i-1},x_i)(x_i-x_{i-1})$ collapses to $\frac{b^6-a^6}{b-a}$. </p> <p>About as easily</p> <p>$\frac{1}{\sqrt{v}} \lt \frac{2}{\sqrt{u}+\sqrt{v}} \lt \frac{1}{\sqrt{u}}$</p> <p>$\frac{1}{v^2} \lt \frac{1}{uv} \lt \frac{1}{u^2}$</p> <p>$\frac{1}{v^4} \lt \left( \frac{1}{v^3u}+\frac{1}{v^2u^2}+\frac{1}{vu^3}\right)/3 \lt \frac{1}{u^4}$</p> <p>It is slightly more fun to show that </p> <p>$\sqrt{u} \lt \frac{2(v+\sqrt{vu}+u)}{3(\sqrt{v}+\sqrt{u})} \lt \sqrt{v}.$</p> <p>SO:</p> <blockquote> <p>Is this line of argument valid? Is it interesting? Have you seen it before?</p> </blockquote> <p>To its credit I'll say that it does not show preference to any particular partition and uses nothing more complex than the two historic treatments above (although maybe it benefits from a modern frame of reference.) Also, rather than carefully converging to the correct answer as the partition evolves, it just starts there and stays unaffected. I don't immediately see that it can be applied to any other definite integrals. But the case of $x^p$ has a certain primary importance.</p> http://mathoverflow.net/questions/114738/integrating-powers-without-much-calculus/114739#114739 Answer by Qiaochu Yuan for Integrating Powers without much Calculus Qiaochu Yuan 2012-11-28T07:47:45Z 2012-11-29T06:57:14Z <p>This may not be in the spirit of what you want, but... by scaling arguments it suffices to establish that $\int_0^1 x^p dx = \frac{1}{p + 1}$. Consider the following probabilistic argument (not entirely rigorous but very suggestive): the integral describes the probability that if you choose $p + 1$ points uniformly at random in the interval $[0, 1]$, then the first point you chose is the rightmost. (If the first point you chose is $x$, then the probability that each of the remaining $p$ points is to the left of $x$ is $x^p$.)</p> <p>On the other hand, you can choose the points simultaneously and then decide which one was the first point you chose. You'll end up choosing the rightmost point with probability $\frac{1}{p + 1}$. </p> <p>A rigorous version of this argument proceeds by partitioning $[0, 1]^{p+1}$ into $p + 1$ parts of the same measure depending on which of the coordinates is the largest and then observing that the measure of one of these parts can be expressed using the above integral. I admit I cannot readily visualize these parts even for $p = 2$... </p> http://mathoverflow.net/questions/114738/integrating-powers-without-much-calculus/114841#114841 Answer by Robert Israel for Integrating Powers without much Calculus Robert Israel 2012-11-29T04:23:18Z 2012-11-29T04:23:18Z <p>Here's another approach. I'm assuming $p > 0$. For $b > 0$, let $F(b)$ be the area under $y = x^p$ for $x$ from $0$ to $b$. The transformation $(x,y) \to (tx, t^p y)$ maps the region under the curve for $x$ from $0$ to $b$ to the region under the curve from $0$ to $tb$. This scales by $t$ in the $x$ direction and $t^p$ in the $y$ direction; we conclude that $F(tb) = t^{p+1} F(b)$, and thus that $F(b) = b^{p+1} F(1)$. Now we have to determine the constant $F(1)$. Note that $F$ is differentiable with $F'(b) = (p+1) b^p F(1)$.</p> <p>For $\varepsilon > 0$, $F(1+\varepsilon) - F(1)$ is the area under the curve between $x=1$ and $x=1+\varepsilon$. Since this region contains a rectangle of width $\varepsilon$ and height $1$, and is contained in a rectangle of width $\varepsilon$ and height $(1+\varepsilon)^p$, we have $$1 \le \frac{F(1+\varepsilon)-F(1)}{\varepsilon} \le (1+\varepsilon)^p$$ Taking the limit as $\varepsilon \to 0+$, we get $F'(1) = 1$. Thus $F(1) = 1/(p+1)$. </p> <p>Of course, this assumes that the area in question exists and satisfies basic scaling and additivity laws. </p> http://mathoverflow.net/questions/114738/integrating-powers-without-much-calculus/114843#114843 Answer by Steven Gubkin for Integrating Powers without much Calculus Steven Gubkin 2012-11-29T04:49:46Z 2012-11-29T04:49:46Z <p>You can derive all of the integrals $\int_0^1 x^p dx$ by chopping them in half, and rescaling each half to fit in [0,1] again.<br> The proof is by induction on p, and by "recovering the integral back". To give you an idea of how this will go, I will just derive $\int_0^1 x^2 dx$ assuming we already have the results for p=0,1 (which are apparent geometrically anyway).</p> <p>$\int_0^1 x^2 dx = \int_0^\frac{1}{2} x^2 dx + \int_\frac{1}{2}^1 x^2 dx$</p> <p>$= \frac{1}{2}\int_0^1 (\frac{x}{2})^2 dx + \frac{1}{2}\int_0^1 (\frac{x+1}{2})^2 dx$</p> <p>$= \frac{1}{8}\int_0^1 x^2 dx + \frac{1}{8}\int_0^1 x^2 +2x+1 dx$</p> <p>so $6 \int_0^1 x^2 dx = \int_0^1 2x+1 dx$</p> <p>$6 \int_0^1 x^2 dx = 2$</p> <p>$\int_0^1 x^2 dx = \frac{1}{3}$</p> <p>A similar argument applies to other values of p, by induction. It is a little messy though.</p> <p>Note that all I am using is linearity of the integral, and that scaling a shape by a factor in one direction should scale the area by that same factor.</p> <p>I did these computations while reading Tom Leinster's note here <a href="http://www.maths.gla.ac.uk/~tl/glasgowpssl/" rel="nofollow">http://www.maths.gla.ac.uk/~tl/glasgowpssl/</a> to see if I could actually compute any integrals using his characterization.</p> <p>Apologies for the messy TeXing, I was in a rush to answer before going to sleep. Will try to fix it up in the morning.</p> http://mathoverflow.net/questions/114738/integrating-powers-without-much-calculus/114934#114934 Answer by Brendan McKay for Integrating Powers without much Calculus Brendan McKay 2012-11-29T21:53:42Z 2012-11-29T21:53:42Z <p>Here is a very simple proof for nonnegative integer $p$.</p> <p>By elementary combinatorial reasoning, we have $$\sum_{j=0}^{n-1} \binom{j}{p} = \binom{n}{p+1},$$ which is the same as $$\sum_{j=0}^{n-1} j(j-1)\cdots(j-p+1) = \frac{n(n-1)\cdots(n-p)}{p+1}.$$ After scaling that becomes a lower bound for $\int_0^1 x^p dx$. </p> <p>Similarly, $$\sum_{j=0}^{n-1} j(j+1)\cdots(j+p-1) = \frac{(n-1)(n)\cdots(n+p-1)}{p+1},$$ which scales to an upper bound.</p> <p>Now let $n\to\infty$.</p> | 4,452 | 13,374 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2013-20 | latest | en | 0.901907 |
https://quantblog.wordpress.com/tag/math/page/2/ | 1,553,281,528,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912202688.89/warc/CC-MAIN-20190322180106-20190322202106-00199.warc.gz | 586,086,184 | 24,431 | You are currently browsing the tag archive for the ‘math’ tag.
Just added a color palette to GridMaths, so it now has rectangles, lines, ellipses in few simple colors and weights. The idea is to help make diagrams clearer, and help with Venn diagrams and other cases where you want to group things together.
Heres a grid sheet comparing fractions : 2/3 and 4/5 … then we show the product and sum using the same visual representation.
If you look carefully, you may notice that I ‘abuse’ the grid in that each grid square is 1/5 high and 1/6 wide – so a 1 unit x 1 unit square is actually 6×5 grid squares. I think this is a legal abuse, in that we often graph things with different x and y axis scales.
The alternative is to have a resizeable non-square grid.. which I think creates too much complexity for not much gain. The philosophy of GridMaths is “keep it simple”, so you can do the basics quickly and easily. I used to think more features = more power = better, but after my son showed me the Minecraft game, and all the cool things people have built with it, I changed my mind about this. I kept thinking.. why is Minecraft so popular, when you can do all that and more in Blender ? Blender is a superb free 3D modelling package, which like all powerful modelling packages takes a while to become proficient at. So, it dawned on me that Minecraft is so brilliant because it brings down the barrier to entry, and makes the 80% of things you need to do to make a world, really easy and quick for everyone.
So I’m adding the most useful things to GridMaths in a way that keeps it really simple. Its not an algebra system, it most likely wont have handwriting recognition… but it should be a really fast way for math teachers to make Math diagrams and for students to do a wide range of worked Math problems, replacing grid paper for that 80% of tasks and adding some nice features. Its kind of like an infinite supply of grid paper, that weights nothing and can be erased and replayed, and saved for later use And.. you can step forward and back thru your edits and change stuff, and students can step thru a worked problem. And you have counting beans and … :-]
I did a couple of worksheets on Multiplication, to test out the GridMaths tools.
My feeling is that multiplication should be taught with Rectangles. So once students are familiar with counting in groups, they can play around with something like this interactive demo to get a basic feel for the distributive rule.
[ The above animation is a custom interactive widget created in javascript, using Raphael and HTML5 divs for the draggable UI. You drag the red dots and the diagram resizes and recalculates in realtime. Other screenshots in this post are all done using MathsGrid itself ]
The distributive rule says we can divide up A and divide up B any way we like, and the product is just all the pieces of A times all the pieces of B, summed up together.
For humans with 10 fingers, its easy to break A and B up by 1s,10s,100s, which means we need to multiply each digit of A by each digit of B, then sum them up.
So long multiplication kind of falls into place, as a way of keeping the pieces straight :
Then the Lattice method can be seen as just another convenient system for keeping all the pieces organised and lining up the 1s,10s,100s etc :
The first time I saw this Lattice method on Hacker News it looked like Magic.. but after you do one you realize it really is the same thing, just a cool way of keeping track of the pieces.
My 9 year old son has discovered Chess, after watching the movie “Searching for Bobby Fischer”.
We bought a chess set so we could play with some chess puzzles and strategies.. but we were a bit dismayed at the quality of the plastic pieces. Anyway one thing led to another, and so I spent a couple days hacking up a web based Chess app.
The basics are there :
• the board
• piece movements
• castling
• chess move notation / SAN
As time allows I’ll gradually add the remaining features, such as :
• en-passant for pawns, pawn promotion
• check-detection for kings
• pgn game import/export
• design & share chess board puzzle
One of the reasons I decided to bite the bullet and do this, was so I can write a few articles on developing a board game in Javascript for young programmers [ my son has been enjoying the programming environment and tutorials on khanacademy.org/cs ] and also Id like to be able to design my own puzzle games and share them, as a good way to help young people learn basic moves and strategy.
In other news, Ive been fighting stockfish chess AI.. and it wins every time, except on the lowest setting. But its been fun to take up the game again, so I can play against my son and answer some of his questions/attacks.
I much enjoyed Kalid Azads Interactive Guide to Fourier Transform article on BetterExplained.com [ and was much impressed he mentioned my animated sine demo, which he extended upon in wonderful ways. ]
With recent javascript and web 2D/3D, I think we’re at the cusp of a kind of interactive learning renaissance.. because Math concepts can be made really physical, tactile and intuitive : Show-me-how-it-works + let-me-drive beats verbose-monologue every time.
I wanted to mention another variant of the animated sine demo, where you can add a second circle and slide back and forth to see the first 2 terms of a Fourier series.
It seems like a gentle intro that would get young people thinking..’hmm, what if I add another circle… and how big should that circle be…’.
Obligatory Tolkien quote : “It’s a dangerous business, Frodo, going out of your door. You step into the Road, and if you don’t keep your feet, there is no knowing where you might be swept…”
### Counting with coffee Beans on grid paper
When I started teaching my son maths we did a lot of counting coffee beans. We would arrange 12 beans in groups of 3 and groups of 4… The idea was to start building up intuition and then segway into multiplication.
Don’t ask me why coffee beans.. I must be a bad parent! The beans just happened to be handy, being dark they were easily visible when put on 5mm math grid paper and fit nicely in the squares. You can use small buttons or raisins even. Its pretty tactile, so works okay for young kids [ as long as they are old enough not to swallow small things ]
### Abstracting to Multiplication
Later we drew the ‘beans’ in the squares and then just drawing a circle in the box instead of placing a bean. This gradually led to tracing out the rectangle outlines of the groups and let the squares on paper take the place of actual beans.. so it abstracts really well in a fairly natural and unforced way.
There are some nice ‘tricks’ you can do on squared paper that grow out of this approach –
• every rectangle is a multiplication product, so you can use it to figure out any times table question
• you can work out all the times-tables and write them in the top right square before reciting them
• introduce distributive property (a+b)*c = a*c + b*c by showing the rectangles add up
• ask.. are there any numbers that cant be made by a rectangle product? [ yes..prime numbers]
• show square numbers – 1,4,9,16 …
• you can show how to add 2n+1 to n squared to get the next square number
• you can introduce series – 1+3+5+7+ … and show how they sum to make the square numbers
• make a stepped-triangle 1+2+3+4+5+6 and show how two of these can be put together to make a rectangle, which leads to sum 1 to n = n(n+1)/2
So this approach leads very naturally into some really nice mathematics. Along the way it reinforces the rote learning of times tables (auditory repetition) with visual intuition.
### The web app – introducing Doctor X
I thought there was probably an App or web page to do this kind of thing interactively. I googled around and found lots of times table grids, math systems but nothing that seemed to take the grid-paper-rectangles-and-counting-beans approach into an interactive medium.
I made notes on what the app might look like, and then spent some time making a quick prototype in Javascript. I found It needed a way to step through some basic usage notes and examples, so I added a howto box. Then we came up with a silly name for this thing.
Anyway, here is the current version of the visual grid calculator for kids, which I’m calling :
“The Doctor X Amazing Griddable Multiplication Contraption”
When I get time Ill make some more in-depth tutorials and worksheets on some of the concepts I mentioned above. Let me know what you’d like to see,
enjoy!
gord.
I get a few hits for the Animated Sine demo in Javascript – maybe this is a good way to introduce young people to math?
Here is a minor update I did a while ago that shows what happens when a second circle spins around the point on the outside of the first circle…
[click the pic or here to view the animation ]
This might be a nice lead into Fourier Series…
Some amazing javascript libraries are coming out now, which enable interactive math directly in the browser.
One of the most impressive is jsxGraph, from Bayreuth University, which is purpose built upon SVG for plotting mathematical functions. See their wiki for superb demos.
On the jsxGraph blog, there is a video showing a construction being manipulated by touch on the iPhone – very cool.
Experimenting with their circles-on-circles web app, by sliding the parameters around I uncovered this delightful piece, which reminded me of those ornate calligraphy end-notes you see in olde books.
Its a lot of fun to experiment. For the curious, the parameters of this specimen are : c1:0.51 f1:7 c2:0.32 f2:17
### SVG coolness
I think SVG is the right way to go, and a more natural approach than using canvas [as I did for my interactive sine generator last week].
There’s no technical reason now why something as featured as GeoGebra or KGeo could not be implemented directly in the browser.. it just has to be done!
Geogebra is really nice, but I do prefer the simplicity of not having to download the java applet and approve it for access. Each extra step supposedly halves the audience, and I want math to be interactive and accessible.
I’ve been thoroughly enjoying Paul Zeitz’s book “The Art and Craft of Problem Solving“.
One of the early problems in the book is from 1994 Putnam math competition, but surprisingly easy once you see that it can be scaled into a much simpler question.
The problem :
Find the positive value of m such that the area enclosed by the ellipse x^2/9 + y^2=1, the x-axis, and the line y=2x/3 is equal to the area in the first quadrant enclosed by the ellipse x^2/9 + y^2=1, the y-axis, and the line y=mx.
Heres a drawing of the areas mentioned using GeoGebra, with each area in separate quadrants for comparison, with an approximate area. The Qn asks what is the slope of the line through point F [or -ve slope of line through Q here].
Problem as stated, with areas colored
Well its a bit hard to pick the point Q [ the slope -m ] so that these colored regions have the same area…
… but then you realize that the whole problem becomes easy if you simply scale the ellipse back to the unit circle.
To do this, x is scaled back by 3x, so areas become 1/3 of what they were [y remains the same]. So the problem now looks like this :
“]
scaled back to the unit circle : areas are x 1/3, slopes x 3
So the line that gives the same area is y=x/2. When this is scaled back to the original ellipse, the slope gets divided by 3; so the line we want is y=x/6.
Quite surprised to see this in a Putnam, but it does show a really common motif in math, namely :
Transform to a simpler domain, solve it there, then transform the solution back.
The astute reader will have noticed that I cheated : the areas of the colored regions in the top picture are of course ~1.65 or 3 x area of regions in the second diagram.
The areas marked were calculated by rough approximation with a polygon and the GeoGebra area function. [ The ellipse itself was drawn to fit using foci – I wasn’t sure how to edit the formula in GeoGebra to make it exact. ]
I’ve added a secondary ‘slave’ circle, which I think introduces the idea of Fourier series in a natural way.
The animation starts as before with a sine curve, then you can add in the second circle by clicking ‘toggle’.
Click this picture to see the Javascript web animation :
I wanted to explain the math-magic of the circle generating the sine wave with a simple animation of a point rotating on the edge and the height matching the sine wave.
I had a look around but most of the math animations are Java applets which I find a bit top heavy, and this should be doable in Javascript.
This is what I came up with, [click to view animation] –
I tried several approaches to get this working, not perfectly happy with any of them, although I did get a basic demo up and running as you see above.
First approach was using SVG, but for some reason I had problems getting svg to appear at all in an html5 page… go figure, this should be simple. In the process I was impressed by SVGEdit which is an early stage, usable if not polished, in browser SVG editor. cool.. I just couldnt get any of my pages to show svg. Ill have another go when the frustration has been forgotten, its possibly some syntax glitch I missed.
I then tried RaphaelJS library which did work reasonably well. Its a nice api. Some things like animating along a path you get out of the box, which is nice. After some basic success I did find myself scratching my head on how to rotate a path – and I’m not sure how to apply a rotate transformation to an item generally [which is a cool feature of SVG ].
Partial demo of sine wave animation implemented in Raphael here. Animates quickly in Safari on mac, Chrome on mac, slightly choppy on Firefox on mac, and quite slow but functional on Safari iPod/webkit.
Wanting a bit more control over exact placement, I decided to try pure HTML5 Canvas rendering. This worked well, was simpler to understand exact x,y pixel placement. I haven’t solved a side issue which is that for some reason if I have the preferred HTML5 “<DOCTYPE html>” tag it ignores exact placement of div elements.. finding this side effect drove me nuts! Im wondering if this is in the spec, it seems it would break a lot of code.
Anyway, layout of the animation was easy in HTML5 canvas. See sine animation demo here.
It does seem to be busy drawing, and Id like to eliminate back flicker [which you’d normally do by drawing to back buffer, or having dirty regions]. Performs ok on desktop safari, firefox and chrome [which seems fastest of all the browsers]. Comes up on iPhone but animates slowly as you’d expect.
A faster approach might be to render the background into a separate layer and draw the dots and lines per frame, as its probably touching only 1 in 1000 of the total pixels.
Anyway, seems to be a promising way to get Math animations up and running, which fine tuning will improve. See page source for Javascript, BSD licence, feel free to reuse. | 3,504 | 15,131 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.21875 | 3 | CC-MAIN-2019-13 | longest | en | 0.945621 |
http://www.gregthatcher.com/Stocks/StockFourierAnalysisDetails.aspx?ticker=FINUX | 1,524,587,787,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125946807.67/warc/CC-MAIN-20180424154911-20180424174911-00410.warc.gz | 433,388,119 | 39,709 | Back to list of Stocks See Also: Seasonal Analysis of FINUXGenetic Algorithms Stock Portfolio Generator, and Best Months to Buy/Sell Stocks
# Fourier Analysis of FINUX (Fidelity International Bond Fu)
FINUX (Fidelity International Bond Fu) appears to have interesting cyclic behaviour every 22 weeks (.0406*cosine), 24 weeks (.0382*sine), and 22 weeks (.0284*sine).
FINUX (Fidelity International Bond Fu) has an average price of 8.74 (topmost row, frequency = 0).
Click on the checkboxes shown on the right to see how the various frequencies contribute to the graph. Look for large magnitude coefficients (sine or cosine), as these are associated with frequencies which contribute most to the associated stock plot. If you find a large magnitude coefficient which dramatically changes the graph, look at the associated "Period" in weeks, as you may have found a significant recurring cycle for the stock of interest.
## Fourier Analysis
Using data from 5/23/2012 to 6/26/2017 for FINUX (Fidelity International Bond Fu), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
08.74239 0
1.04413 .42906 (1*2π)/267267 weeks
2.05361 -.11858 (2*2π)/267134 weeks
3-.07844 .26388 (3*2π)/26789 weeks
4-.04376 .11111 (4*2π)/26767 weeks
5.10982 .05758 (5*2π)/26753 weeks
6.01124 -.05611 (6*2π)/26745 weeks
7.02399 -.05208 (7*2π)/26738 weeks
8-.00867 -.00136 (8*2π)/26733 weeks
9-.02099 -.03429 (9*2π)/26730 weeks
10-.03013 -.02365 (10*2π)/26727 weeks
11.00095 .03817 (11*2π)/26724 weeks
12.04064 .02836 (12*2π)/26722 weeks
13-.00855 -.02302 (13*2π)/26721 weeks
14.0169 -.02553 (14*2π)/26719 weeks
15-.00004 -.01682 (15*2π)/26718 weeks
16.01157 -.00137 (16*2π)/26717 weeks
17.01391 -.01 (17*2π)/26716 weeks
18-.0125 .00784 (18*2π)/26715 weeks
19-.00883 .02239 (19*2π)/26714 weeks
20-.01995 .00454 (20*2π)/26713 weeks
21.01243 -.00501 (21*2π)/26713 weeks
22-.00735 -.00355 (22*2π)/26712 weeks
23.00645 .015 (23*2π)/26712 weeks
24-.0075 -.01022 (24*2π)/26711 weeks
25-.00769 -.012 (25*2π)/26711 weeks
26.00089 -.00264 (26*2π)/26710 weeks
27-.00884 .00438 (27*2π)/26710 weeks
28-.00741 -.00188 (28*2π)/26710 weeks
29.01102 -.00441 (29*2π)/2679 weeks
30.01913 .00799 (30*2π)/2679 weeks
31-.01851 .00044 (31*2π)/2679 weeks
32-.00801 .01397 (32*2π)/2678 weeks
33-.00306 -.00708 (33*2π)/2678 weeks
34.0086 -.00013 (34*2π)/2678 weeks
35.00042 .01353 (35*2π)/2678 weeks
36.00246 -.00208 (36*2π)/2677 weeks
37-.01188 .00039 (37*2π)/2677 weeks
38.00724 .00246 (38*2π)/2677 weeks
39.00956 .00474 (39*2π)/2677 weeks
40.00136 .00422 (40*2π)/2677 weeks
41-.01153 -.00003 (41*2π)/2677 weeks
42-.02016 -.00316 (42*2π)/2676 weeks
43.00709 -.00342 (43*2π)/2676 weeks
44-.0029 .00588 (44*2π)/2676 weeks
45.00541 .00493 (45*2π)/2676 weeks
46-.01002 -.0041 (46*2π)/2676 weeks
47.00892 .00445 (47*2π)/2676 weeks
48-.00029 -.02101 (48*2π)/2676 weeks
49-.00681 -.00013 (49*2π)/2675 weeks
50-.00099 .00978 (50*2π)/2675 weeks
51.0013 .01318 (51*2π)/2675 weeks
52.00466 -.00277 (52*2π)/2675 weeks
53.00734 -.00863 (53*2π)/2675 weeks
54.01609 -.00433 (54*2π)/2675 weeks
55-.00062 -.00052 (55*2π)/2675 weeks
56-.00857 .00375 (56*2π)/2675 weeks
57-.00295 -.00904 (57*2π)/2675 weeks
58.00263 .00052 (58*2π)/2675 weeks
59-.00357 .00225 (59*2π)/2675 weeks
60.00172 .0074 (60*2π)/2674 weeks
61-.00207 -.00521 (61*2π)/2674 weeks
62.01121 -.00405 (62*2π)/2674 weeks
63-.00555 -.01308 (63*2π)/2674 weeks
64-.01496 .00814 (64*2π)/2674 weeks
65.002 .00559 (65*2π)/2674 weeks
66-.00167 .00498 (66*2π)/2674 weeks
67-.00403 .00301 (67*2π)/2674 weeks
68.00252 -.00384 (68*2π)/2674 weeks
69.00293 .00897 (69*2π)/2674 weeks
70.00326 -.00139 (70*2π)/2674 weeks
71.00119 -.00214 (71*2π)/2674 weeks
72.00109 -.00457 (72*2π)/2674 weeks
73-.00413 .0071 (73*2π)/2674 weeks
74.003 .00053 (74*2π)/2674 weeks
75-.00681 -.0038 (75*2π)/2674 weeks
76.00885 .00007 (76*2π)/2674 weeks
77.00185 -.00144 (77*2π)/2673 weeks
78-.00228 -.00061 (78*2π)/2673 weeks
79.00024 -.00394 (79*2π)/2673 weeks
80-.00487 -.00056 (80*2π)/2673 weeks
81.00163 .00328 (81*2π)/2673 weeks
82.00491 .00235 (82*2π)/2673 weeks
83.00124 -.00271 (83*2π)/2673 weeks
84-.00488 .01364 (84*2π)/2673 weeks
85.00193 .00195 (85*2π)/2673 weeks
86.00235 -.00018 (86*2π)/2673 weeks
87.00582 -.00484 (87*2π)/2673 weeks
88.00279 -.00683 (88*2π)/2673 weeks
89-.00405 .0014 (89*2π)/2673 weeks
90-.00072 .00164 (90*2π)/2673 weeks
91-.00673 -.00009 (91*2π)/2673 weeks
92-.00134 -.00363 (92*2π)/2673 weeks
93.00424 -.00059 (93*2π)/2673 weeks
94.0009 -.00324 (94*2π)/2673 weeks
95-.00477 -.00227 (95*2π)/2673 weeks
96-.00752 -.00271 (96*2π)/2673 weeks
97.00364 .00214 (97*2π)/2673 weeks
98.00815 -.0008 (98*2π)/2673 weeks
99-.0001 .00562 (99*2π)/2673 weeks
100.00321 -.00372 (100*2π)/2673 weeks
101-.0004 -.00689 (101*2π)/2673 weeks
102-.00012 .00473 (102*2π)/2673 weeks
103.00199 .00096 (103*2π)/2673 weeks
104.00182 .00396 (104*2π)/2673 weeks
105-.00255 .00307 (105*2π)/2673 weeks
106.00098 .00549 (106*2π)/2673 weeks
107.00239 .00208 (107*2π)/2672 weeks
108.00197 .00051 (108*2π)/2672 weeks
109.00029 .00512 (109*2π)/2672 weeks
110.00016 -.00446 (110*2π)/2672 weeks
111-.00021 .00091 (111*2π)/2672 weeks
112.00379 -.00081 (112*2π)/2672 weeks
113.00365 .00205 (113*2π)/2672 weeks
114.00046 .00524 (114*2π)/2672 weeks
115-.0022 .00458 (115*2π)/2672 weeks
116.00149 -.00424 (116*2π)/2672 weeks
117.00168 .00027 (117*2π)/2672 weeks
118.00091 -.00381 (118*2π)/2672 weeks
119-.00127 .00107 (119*2π)/2672 weeks
120.00207 .00103 (120*2π)/2672 weeks
121-.00122 .00292 (121*2π)/2672 weeks
122.01058 -.00639 (122*2π)/2672 weeks
123-.00523 .00421 (123*2π)/2672 weeks
124-.00414 .0015 (124*2π)/2672 weeks
125-.00166 -.00125 (125*2π)/2672 weeks
126.0016 -.0018 (126*2π)/2672 weeks
127-.00193 -.0031 (127*2π)/2672 weeks
128-.00507 .00519 (128*2π)/2672 weeks
129-.00216 .00652 (129*2π)/2672 weeks
130.00048 -.00147 (130*2π)/2672 weeks
131.00771 -.00439 (131*2π)/2672 weeks
132-.00639 -.00268 (132*2π)/2672 weeks
133-.00536 .00789 (133*2π)/2672 weeks
134-.00536 -.00789 (134*2π)/2672 weeks
135-.00639 .00268 (135*2π)/2672 weeks
136.00771 .00439 (136*2π)/2672 weeks
137.00048 .00147 (137*2π)/2672 weeks
138-.00216 -.00652 (138*2π)/2672 weeks
139-.00507 -.00519 (139*2π)/2672 weeks
140-.00193 .0031 (140*2π)/2672 weeks
141.0016 .0018 (141*2π)/2672 weeks
142-.00166 .00125 (142*2π)/2672 weeks
143-.00414 -.0015 (143*2π)/2672 weeks
144-.00523 -.00421 (144*2π)/2672 weeks
145.01058 .00639 (145*2π)/2672 weeks
146-.00122 -.00292 (146*2π)/2672 weeks
147.00207 -.00103 (147*2π)/2672 weeks
148-.00127 -.00107 (148*2π)/2672 weeks
149.00091 .00381 (149*2π)/2672 weeks
150.00168 -.00027 (150*2π)/2672 weeks
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# BUNDLE - Performance Task – Equations & Inequalities – Break a Leg
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### PRODUCT DESCRIPTION
BUNDLE - Performance Task – Equations & Inequalities – Break a Leg
Now you can get more options and save money with this collection of all editions of Break a Leg!
This set includes the Break a Leg Performance Task in 10 different celebrities editions. If you were to purchase each of these Performance Tasks individually, it would cost \$40. At only \$7, this bundle saves you about 83% off retail price!
In Break a Leg Performance Task, students use theater production data to practice representing proportional relationships by equations, identifying unit rates, writing, solving and graphing multi-step equations and inequalities. As non-profit community directors, they must design a proposed budget for the production and carefully avoid having too much profit.
This Break a Leg Performance Task set includes:
* West Side Story
* A Midsummer Night's Dream
* You Can't Take It With You
* Grease
* Les Miserables
* The Phantom of the Opera
* Young Frankenstein
* The Wizard of Oz
* Footloose
* The Pirates of Penzance
What’s included in this Performance Task:
* Teacher Guide – Get an overview of the Performance Task, including helpful suggestions for use and the Common Core alignment for each activity.
* Level 1 Activity – Laying the foundation. Students start by practicing a core skill matched to a Common Core State standard.
* Level 2 Activity – Adding some complexity. Students integrate a different skill or set of skills from the Level 1 activity.
* Challenge Activity – Bring on the critical thinking! Stretch students to reason with math and data to come to conclusions.
* Finale Activities – Extend the learning. Each activity also includes a finale to extend the math lesson into another subject (usually ELA).
* Complete Answer Key – All Performance Tasks come with a complete answer key for all activities.
* Job Background – Each Performance Task enables students to picture themselves in a real world career. Find information about the career, including entry-level education, median pay, and job outlook.
This set also comes with student versions, which include everything but the teacher guide and answer key.
Thanks and be sure to check out our other Performance Tasks!
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\$7.00 | 600 | 2,711 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2017-13 | longest | en | 0.871931 |
https://www.chegg.com/homework-help/c-100-resistor-dissipates-169-w-current-d-3-resistor-dissipa-chapter-4-problem-3pp-solution-9781418038618-exc | 1,529,405,773,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267862248.4/warc/CC-MAIN-20180619095641-20180619115641-00084.warc.gz | 786,346,434 | 16,684 | # Circuit Analysis (4th Edition) View more editions Solutions for Chapter 4 Problem 3PPProblem 3PP: c. A 100-Ω resistor dissipates 169 W. What is its current? d. A 3-Ω resistor dissipates 243 W. What is the voltage across it? e. For Figure 4–17, I = 0.5 A. Use Equations 4–10 and 4–12 to compute power to each resistor. Compare your answers to the answers of Example 4–7. Equation 4-10 Equation 4-12
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Chapter: Problem:
c. A 100-Ω resistor dissipates 169 W. What is its current?
d. A 3-Ω resistor dissipates 243 W. What is the voltage across it?
e. For Figure 4–17, I = 0.5 A. Use Equations 4–10 and 4–12 to compute power to each resistor. Compare your answers to the answers of Example 4–7.
Equation 4-10
Equation 4-12
Step-by-Step Solution:
Chapter: Problem:
• Step 1 of 5
(a)
Show that
Power
……….……… (1)
……….……… (2)
Hence proved
• Chapter , Problem is solved.
Corresponding Textbook
Circuit Analysis | 4th Edition
9781418038618ISBN-13: 141803861XISBN: Authors:
Alternate ISBN: 9781111322182, 9781111536312, 9781418038649 | 364 | 1,121 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2018-26 | latest | en | 0.800452 |
https://protonsforbreakfast.wordpress.com/2023/02/23/tariff-calculations-octopus-go-versus-octopus-flux/ | 1,679,325,251,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296943484.34/warc/CC-MAIN-20230320144934-20230320174934-00551.warc.gz | 527,606,191 | 42,333 | ## Tariff Calculations: Octopus GO versus Octopus FLUX
Friends, I have struggled to write this article. As you may have noticed, it has taken weeks.
I started writing after I was asked on Twitter about a new electricity tariff called ‘FLUX’ offered by Octopus Energy. Would it be cheaper or more expensive than their ‘GO’ tariff?
It’s a simple question and one that is worth asking. But it is very hard to answer because it involves both hourly details, but also seasonal changes.
I could see how to get at an answer but I have struggled with my waning technical skills. Imagine if you will, an old boxer going in for one fight too many. Finding themselves on the ropes, they face the unavoidable and inevitable reality of their own decline. But bravely they struggle and finish the fight bruised and defeated, but with their dignity in tact. Similarly I have found my prowess with Excel and Visual Basic to be much diminished, but I have somehow battled through.
GO and FLUX
The Octopus GO tariff which I currently use offers 4 hours of electricity for 7.5p/kWh between 00:30 and 04:30 each day. The rest of the time the cost is 40.75p/kWh. Exports of electricity are paid for at 4.1 p/kWh.
During winter, I buy electricity cheaply at night, and then use it during the day. For most of December and January, the battery could not supply the house for the whole day and I had to purchase electricity at full price for a few hours on those days. Overall, the average price I paid was around 12p/kWh in those two months.
Click on Image for a larger version. Illustration of the variation in price through the day for electricity imports (left) and exports (right) on the Octopus Go and Octopus FLUX tariffs.
The Octopus FLUX tariff is more complicated. It has a cheap rate in the night, but only for 3 hours 02:00 to 05:00 and not so very cheap (20.4 p/kWh). But it also has a more expensive rate (47.5 p/kWh) during peak demand hours from 16:00 to 19:00 each day. The rest of the time the cost is 34 p/kWh.
Initially FLUX looks much worse than GO, but the twist is that FLUX offers much higher rates for exporting electricity: 9.4 p/kWh, 22 p/kWh, 36.5 p/kWh for the cheap medium and high rates respectively. These figures should be compared with the miserly 4.1 p/kWh on the GO tariff.
There are so many variable quantities that I really had no idea which tariff would be cheaper. The results of my calculations appear obvious in retrospect, but that didn’t make the calculations any easier! My conclusions are that:
• For small solar PV installations (<~4,000 kWh/year), the big savings from using the night time electricity on GO outweigh the gains from exporting electricity at a good price.
• For large solar PV installations (>~6,000 kWh/year), this situation is reversed: The savings from using the night time electricity on GO are outweighed by the gains from exporting electricity on the FLUX tariff.
• For medium-sized solar PV installations, the two tariffs have similar costs.
Click on Image for a larger version. Estimates of the annual cost of electricity on the Octopus Go and Octopus FLUX tariffs as a function of the amount of solar generation. This applies to my household – see text for details – and assumes a 13.5 kWh storage battery.
It turns out that, if you have the capability to export lots of solar PV, then the FLUX tariff could result in very low – and even negative – electricity bills. In retrospect, this is sort of obvious, but it was not obvious at all to me when I began.
But the spreadsheet I developed for the calculation allowed me to do the calculations for different sizes of battery and different amounts of solar PV generation, so I’ve investigated the matter a little more deeply below.
Sadly, because the spreadsheet is Macro-enabled, for security reasons I can’t link to it from this blog and many users wouldn’t be able to download it anyway. But if you really want a copy, please ask for a copy in the comments and I will send it to you somehow. But be warned that the spreadsheet is complicated and slooooow. On my computer it takes around 1 minute to evaluate the yearly calculation.
Let me explain how I made the calculation and then I’ll discuss a few more details.
How to work out which tariff is cheaper
To answer this question I wrote a spreadsheet which modelled the electricity use in a household hour-by-hour for an entire year i.e. the spreadsheet has 365 x 24 = 8,760 rows.
For each hour of the year I estimated:
• The household demand: I modelled this as being the sum of a fixed amount each day (10 kWh/day) plus an amount used for heating that peaked in winter at 25 kWh/day.
• Solar PV: Using the EU sunshine database, I downloaded hour-by-hour sunshine data for my house location from 2005 to 2016, and then averaged this to give a typical solar generation year.
• I then worked out how to supply the household demand.
• If Solar Power exceeded demand, then the excess was used to charge the battery, and if the battery was full, the excess was exported.
• If Solar Power was less than demand, then the solar power offset the imported electricity.
• During winter, the battery was fully charged during the cheap hours.
• I estimated the battery to have a round-trip storage efficiency of 90%.
The spreadsheet and associated VB Macros took days to debug, but here are the results.
Household Demand
The modelled daily demand is shown below along with the EU sunshine database estimate of PV generation amounting to ~ 4,000 kWh/year. Basic electricity demand is ~ 10 kWh/day but peaks at 25 kWh/day in mid-winter due the heat pump, and amounts to ~ 5,000 kWh/year.
Click on Image for a larger version. Graph showing the modelled daily household demand throughout the year, and the 3-day average of solar generation. The solar data is the average of the years 2005 to 2012 estimated for my location and array size in Teddington.
The relationship between Solar PV supply and household demand is such that one needs to use two different strategies depending on the time of the year.
• In the Winter: the battery is charged using cheap rate electricity and discharges during the day – sometimes running out at night.
• In the Summer: there is no night time charging and the battery charges during the day and discharges during the night.
These two modes are illustrated in the graphs below.
The first graph shows a week in winter under the two different tariffs. The four hours of cheap electricity under the GO tariff allows the battery to charge to full, but the FLUX tariff only has three hours of cheap electricity so the battery only charges to around 10 kWh. The battery then discharges to run the household, and is partially supported by the weak solar generation, but typically runs out well before the end of the day.
Click on Image for a larger version. The state of charge of the battery through 7 days in winter. The upper graph shows the Octopus GO tariff which allows the battery to be fully re-charged each night. The lower graph shows the Octopus FLUX tariff which only has enough cheap hours to enable partial filling of the battery. The solar generation is also shown in yellow.
The second graph shows a week in summer. At this time of year, solar generation is enough to run the household and charge the battery during the day, with enough left over for export.
Click on Image for a larger version. The state of charge of the battery through 7 days in summer. Also shown is the solar generation is also in yellow and electricity exports in grey.
The switch between the summer and winter strategies is made on day 90 and day 270 – an arbitrary choice but one which corresponds roughly to the point where the 3-day average of solar exceeds the average household demand. The graph below shows the state of charge of the battery throughout the entire year on both tariffs.
Click on Image for a larger version. The state of charge of the battery through the entire year. The top graph shows the estimate for the GO tariff and the lower graph shows the estimate for the FLUX tariff.
Costs
The simulation runs hour-by-hour through the entire simulated year. For each hour, I estimated how much electricity was imported and exported, and then applied the appropriate tariff rate. This allowed me to summarise the situation for my home as below.
Click on Image for a larger version. Results of calculations of cost of running my household on (top) the GO tariff and (bottom) the FLUX tariff.
Both tariffs offer the possibility of running a home very cheaply: with annualised energy bills in the range £30/month to £50/month. However the GO tariff appears to be cheaper in this simulation £34/month compared with £50/month for FLUX.
The analysis shows why: being able to fill up with electricity at 7.5 p/kWh reduces the cost the electricity dramatically – £298/year versus £648/year. The improved rates for export on the FLUX tariff (£209/year versus £38/year) aren’t enough to make up for that.
Discussion#1: The effect of extra solar generation
My conclusion is that for me, with my existing 3,800 kWh/year PV installation, the GO tariff is more economical.
But having recently had extra panels installed, this conclusion may not hold. The difference in annual cost between the two tariffs is ~£193 and the typical difference between the FLUX and GO export tariffs is ~ £0.18. So if the new system could export ~1,000 kWh more in summer, then the balance could easily shift.
And indeed, that is what the simulations show. Notice that for 8,000 kWh of generation the annual cost of electricity would be negative i.e. the house would be a bona fide power station!
Click on Image for a larger version. Lower graph: estimates of the annual cost of electricity on the Octopus GO and Octopus FLUX tariffs as a function of the amount of solar generation. Upper graphs: Details of how the the import costs and export and rewards vary on the FLUX tariff (left) and GO tariff (right). [NOTE: The original graph had an erroneous curve plotted. This was updated at 23:27 on 23/2/2023]
If the newly installed panels generate as much as I hope, then the annual generation may approach 6,000 kWh and in this case, the FLUX tariff would be marginally cheaper.
Discussion#2: The effect of battery size
Whilst I was making these calculations, I thought it would also be interesting to look at the effect of battery size. For my home – with solar PV generation of ~3,800 kWh/year – the simulations suggest that bigger batteries are better – no news there – but that above roughly 10 kWh the additional savings are minimal.
Click on Image for a larger version. Lower graph: estimates of the annual cost of electricity on the Octopus GO and Octopus FLUX tariffs as a function of battery size with ~ 3,800 kWh of solar generation. Upper graph: Details of how the the import costs and export and rewards vary on the FLUX tariff (left) and GO tariff (right).
This is a relief to me. It means that as the batteries degrade, the system itself is likely to continue to perform well for many years.
Discussion#3: Strategy
Friends, life is complicated enough without having to consider battery management strategy. Nonetheless, this is where we are!
Observant readers may have noticed that I made no specific efforts to avoid consuming energy at peak hours because it doesn’t happen very often. But if it could be done, then on the FLUX tariff, there would be a reduction in both costs and carbon emissions during these dirtiest hours of the day.
The problem for me is that I am not sure whether the occult Tesla logic which controls my battery, is smart enough to avoid using electricity at peak times. If it could achieve this, then on days when the battery might be expected to run out early, the system might preemptively charge in the middle of the day (at 34p/kWh) and so avoid consuming grid electricity during the peak hours when the equivalent electricity would cost 47.5p/kWh.
For a load of around 1 kW for 3 hours the potential saving would be around 45p/day which over 60 days of winter might amount to ~£27/year.
Errors and Mistakes
Friends, writing this article has been very difficult, and I must warn you although I have carried out many checks, I might easily have made some errors. Sorry. Please feel free to point them out to me when you spot them. The results appear to be about right for my own situation and so I have modest confidence that the errors are not too major.
But overall, despite the fact there are errors and mistakes, I think this spreadsheet offers a tool for evaluating the complex interaction of solar generation, battery storage, and time-of-use tariffs. I hope it helps.
### 61 Responses to “Tariff Calculations: Octopus GO versus Octopus FLUX”
1. Simon Duane Says:
Hi Michael
I don’t have solar PV, but I’ve read that the octopus flux tariff is not available to users with more than 9kWp installed.
Perhaps you have shown why this might be?
Best wishes
• protonsforbreakfast Says:
Yes, I think that explains it. If you’ve got a lot of solar it’s a money spinner!
• Bill F Says:
Hi,
I’ll be getting a 7kWp and battery system next month so the flux tariff looks appealing. I’d appreciate a copy of your spreadsheet to do the calcs.
I’m expecting to generate close to 9000kWh / yr and previously have used 4500kWh/yr on the house and last year did a similar amount on the EV so some careful thinking needed on how best to set it all up !
• protonsforbreakfast Says:
Bill F
Sounds like an amazing system: I hope the installation goes well and that the pigeons stay clear!
All the best
Michael
• Ioannis Says:
Hi Bill,
Looks like you are installing an impressive system with 9000kwh predicted annual output. Would you share the details of it? (Number of pv panels, type of inverter and also the orientation and inclination of the roof and any potential shading on the panels)
Regards,
Ioannis
Hi,
Would it be possible to get a copy of your spreadsheet? Let me know what details you’d need from me to send it?
Thanks
3. Ross Mason Says:
Whoa!!!
More panels?
Clearly something moved in the de Podesta household.
Intrigue me.
4. Ross Mason Says:
Thanks Michael. I can safely say Upper Hutt missed the deluge. Northland got hit once. Auckland got hit twice. Once when Gabrielle headed south, east of the North Island where parts of west and northern Auckland had raging floods, then when it stalled winds and rain changed to souwesterly and the West Coast, Karekare, Piha and Muriwai got hammered with slips. Two firefighters died when a house they were rescuing got slip hit.
Once it reached East Cape it dumped horrendous quantities onto to roughest country in NZ that is “farmed”. After Cyclone Bola in 1988 lots of the East Coast hill country got planted in Pines. They have been harvested for the last few years. Foresters take the good part of the lower tree trunk and strip the rest and leave it lying on the ground. It takes little rain to move it down the hill, into stream, into rivers and the slash (as its called) will take out bridges and houses as if they were pea sticks. This is the third biggie through there in as many years.
Check out “Stuff.co.nz” for some video and pictures. Stories coming out of survival draw hairs on the back of the neck. Families having to break through ceilings to get above the water. One woman died in the loft trying to escape. A horse got stuck on a roof – water so high it swam on – but collapsed the roof and died later. Truckie starting out from Gisborne in light rain and hit a sharp bend and water. Had to back up a few times as the “stream” rose metre by metre in a staggering short time but had to leave the truck. Walked 3 hours until he got picked up and arrived at a farm. Three Maori boys grabbed a Jet Boat and rescued about 70 people from roofs along the Esk Valley. They will get a medal for sure. There are still around 10 people still missing. Helo pilots claim they saw bodies being washed down rivers.
To get comms back on a helicopter carried and laid broadband cable literally across bush and farmland as a temporary connection. Wonderful picture of a piece of Manuka branch with a Y at the top planted in the ground as a support to keep stock from damaging the line.
On a personal side, my sister and hubby are in Waipawa. All around them was flooding, the area was evacuated including them but their house missed out of damage. Their piece had been raised that extra 500mm and was “saved”.
etc etc.
More solar panels up there wouldn’t have helped. No sun. No Power Lines to sell it through!!
• protonsforbreakfast Says:
Ross,
That sounds terrible. I had read one or two stories about one valley that was devastated – but there hasn’t been much coverage over here. The Guardian story conveyed a sense of bewilderment amongst people who couldn’t quite believe what had happened. And of course the question of how wise it would be to build back.
In my opinion it’s just a matter of time before this stuff begins to happen everywhere.
Anyway: Sympathy and Best wishes: M
• Dan Grey Says:
Good grief that’s one hell of a read Ross!
Fwiw “the rest” of the trees after logging is what’s collected and milled into pellets for the Drax, the massive biomass power station in the UK. Burns millions of tonnes of the stuff a year.
5. alexbutcher Says:
Hi Michael,
I’ve started working on something similar to this, and considering making it publicly available online as a tool for interested renewables enthusiasts, if I can get the quality there… I’d love to see your version if you’d be happy to share it.
Thanks,
Alex
6. Simon Loker Says:
Hi
very detailed and well done.
Not sure if you like spanners in the wood work.
Would it be possible to use the flux in summer and swap for Go in the winter as the cheap rate better utilised charging the battery?
Simon
• protonsforbreakfast Says:
Good Thinking.
But typically they ask you to sign a contract for year – I think you can change but I am not sure about constantly switching back and forth.
In any case, everything is very cheap in any case, so I am pretty happy.
Best wishes
Michael
7. Rob Cain Photography Says:
As someone with a recently installed 3.6kWp solar system and potentially moving to an EV later in the year I’m interested in comparisons of octopus flux and octopus go. As I as new Go customer the rate would be 12p kWh. How would that make a different to the outcomes?
I’m in the difficult place we’re it feels like recently installing solar would be a waste if I’m limited to 4.1p SEG by having an EV. As the EV will be a company vehicle I need to consider mileage reimbursement is 5p per mile. That could be a big cost penalty at higher charging costs as I do circa 15k business mileage a year and I may struggle to charge sufficiently within the 3 hour window per day to make it viable (daily mileage varies 60-150 miles per day). It currently feels like a PHEV and flux for Solar exporting would be the better option for me.
It just seems like flux is a good step forward but there is no tariff for solar and EV owners, when anyone with solar is more than likely to have an EV too.
• protonsforbreakfast Says:
Rob
Good Morning. I sympathise: it feels impossible to work out which tariff is optimal – hence the post. And having an EV just adds to the complication. Anyway:
I have re-run the calculations for Octopus Go at 12p/kWh. It’s similar to the previous calculation but a little worse. FLUX is cheaper after about 4,000 kWh/year of Solar generation rather than 5,000 kWh/year as previously.
People have also asked for information on the COSY tariff with 15p/kWh export. I’ll work on that today and tomorrow.
Hopefully later today or tomorrow I finish a post comparing Octopus GO, COSY and FLUX.
There’s also chit-chat on Twitter (@Protons4B) around this topic.
All the best
Michael
8. Dan Grey Says:
That’s a great piece of work Michael! Although the first few few paragraphs certainly sent me on a guilt trip 😄. I hope you found it a satisfying experience overall?
My one big thought which was brewing as I read (and discussion #3 touches upon it) is optimised discharge to the grid. Would I be right in thinking that your Powerwall is set to Self-Powered mode? Is Time-Based Control available to you? https://www.tesla.com/support/energy/powerwall/mobile-app/utility-rate-plans Not sure it’s available outside the US.
Here you would tell the Powerwall the Flux tiers and I believe it would, for example, aim to discharge during the 4-7pm 36.5p/kWh period, discharging down to a Backup Reserve level you select. If used in summer, TBC with Flux might well make extra money!
• Dan Grey Says:
One thing I’m not sure at all about is whether TBC is predictable, e.g. it may well limit discharge in the 22p/kWh daytime period in order to maximise discharge in the 36.5p/kWh period before hitting the Backup Reserve level.
PS do switch between Winter and Summer modes by enabling/disabling Grid Charging in the settings?
• protonsforbreakfast Says:
TBC is not perfectly predictable. It has settings for peak rates, shoulder rates and cheap rates so I could program in the FLUX tariff, but the COSY tariff couldn’t be obviously programmed because it has two cheap periods.
In winter it is predictable – it charges the battery full every night. But in Spring and Autumn it tries to ~half-fill the battery in the morning to allow it to charge up the next day. I think it currently does this by pattern matching previous days perhaps with some seasonal knowledge. But the latest software update says it now has the ability to use a solar forecast.
So in the transitional period, it isn’t possible to know what charge level it will target.
No: I switch between summer and winter by changing from time-based control to self-powered.
All the best: M
• protonsforbreakfast Says:
Dan,
Don’t feel too bad, it’s my own fault really. But it was tough de-bugging as the spreadsheet took around a minute to update after an edit. I found it very de-moralising.
Yes, I have time-based control – it’s what I use in the winter season. And that might indeed be smart enough to preemptively avoid the peak hours. But I don’t know because the actual algorithm is not public.
I don’t think the controls have any way to force an export at a particular time – and in summer we are off-grid most of the time anyway.
All the best: M
9. Dylan Johnson Says:
Hi,
This is amazing! Would it be possible to get a script/copy of your spreadsheet?
Let me know what details you’d need from me to send it?
Thanks
Dylan
• protonsforbreakfast Says:
Dylan
Hi: I’ve sent you a copy – the comments app let’s me see your e-mail.
If it doesn’t arrive (7 Mb and contains Macros) – let me know and I’ll try to send it to you another way.
M
10. Roaming Rob Says:
Hi Michel
Wow if only I could replicate, what a task you have completed. I think I understand! We have a greenish (part nuclear) tariff of 5p for 5hrs night use and 27p day use until March 24 so at that point we will see what provider to pay the inevitable increase too!!!! We also live in the South East, so I am sure your figures won’t be that far out for us.
Our 12kWh battery charges over night and on some sunny days this winter we have not discharged fully but on others we have fully used all the stored energy. We also have a 3.5kW solar panel set up and have been looking to increase this, if we can raise the funds. But that will have to wait until the Heat Pump install this April. Mind you I have been contemplating rethinking the installation in the light of Octopus/ British Gas announcements of a much cheaper install.
We currently have storage heaters in part of our home which has meant we cannot charge the car, run appliances, as well as charging all the storage heaters and the battery without exceeding my self-imposed 85amp draw on a 100 amp main supply fuse. So it’s a plan ahead job at the moment, thank goodness for retirement.
So judging the impact of the heat pump will be interesting for us!! A significant reduction in cheap night time tariff (no storage heaters) and an increase in costly daytime use (heat pump) BUT at least NO GAS.
By the time out current tariff runs out we will be in our 80’s – so if we have made a mistake re costs it won’t be affecting us be for that long( mind you I am not thinking of cutting our time here short!!). AND self-congratulating we will feel a warm glow for having taken some action towards carbon reduction for the Grand Children.
Love your articles even if they are beyond my small brain. Just takes a few reads to let it settle in then a few more reads a few days later because I had forgotten – Ha Ha.
Keep them coming and thankyou for the work you do.
Rob
• protonsforbreakfast Says:
Rob,
Good Evening. Thank you for your kind words. It sounds like you are really making inroads on your carbon emissions too. That combination of solar and batteries sounds very useful. And if you can spare the capital for the heat pump install, then switching from storage heaters you should notice the reduction in winter electricity bills. I guess that means you will need to install new radiators and pipework too – which is pricy – but at least you can make sure the radiators and pipework are all the right size!
In the next article I’ll be comparing Octopus COSY rates – I had never heard of this! – with GO and FLUX.
Anyway: best wishes
Michael
11. Harry Wallace Says:
Hi Michael
Lovely effort – well done. As a retired EXCEL/VBA warrior – I know just what you mean about receding skills!
I’ve only recently had my PowerWall2/Gateway2/solarEdge installation certified and ready to export and I’d begun research on “which tariff pays back fastest”.
I was pondering whether or not to dive back into EXCEL/VBA to do some simulation analysis of the various tariffs from Octopus, but you’ve covered a large amount of ground for me.
Would you kindly make your workbook available to me – I’d really appreciate the jump start?
I thinking about three lines of possible development – Solver, AI and a solar forecast approach, rather than historical irradiance data.
In any event, thanks for all the effort and keep up the good work.
Regards
Harry Wallace
• protonsforbreakfast Says:
Harry: I am happy to send teh workbook. But for some reason I can’t see your e-mail address in the comments window I am using – usually it shows it to me. Please write to me at house@depodesta.net and I will send you a copy by return.
I think the historical radiance data is the way to go – it has statistics that I have never seen reproduced anywhere. This previous article – which I wrote before buying the battery – has more details and a workbook which does not contain macros and so can be downloaded.
All the best
Michael
12. Brian Hauxwell Says:
Thanks for this amazing work, comparing the tariffs. Can I please have a copy of the spreadsheet to try and use it to evaluate my own situation and which tarriff is best in my own setup. Just adding more solar and battery’s.
Thanks
13. David Casale Says:
I would be very interested in a copy of your spreadsheet calcs.
Great blog!
David
• protonsforbreakfast Says:
David
Thank you for kind words: I’ve mailed you a copy of the spreadsheet. If it doesn’t arrive, please drop me a line.
M
14. Mark Timothy Says:
Hi … This. Is just stunning stuff, I am dead impressed. Would it be possible to have a copy of the spreadsheet as my tariff is slightly different and I am considering exporting over the summer months.
• protonsforbreakfast Says:
Mark,
Hi. I’ve sent you a copy of the spreadsheet. If you don’t receive it, let me know here and I’ll figure out some other way to send it.
All the best
Michael
15. Ioannis Says:
Excellent work Michael and thank you for your ongoing efforts.
Looks like for our circumstances, the Flux will be cheaper from the beginning of March till the end of September and then switch back to Go, if still available. We might build up some credit as well to use during the winter months.
Switching between tariffs twice a year should be straightforward with Octopus, as there are no exit fees and the only restriction I am aware of, is to stay on the new tariff for at least 30 days following the switch.
BW
Ioannis
• protonsforbreakfast Says:
Ioannis: Switching tariff twice a year seems like a lot of trouble, but if you have teh emotional energy for it – good luck!
All the best: Michael
16. gaken9 Says:
Hi Michael, an excellent piece of work, I would love to have a copy of the spreadsheet as I’m looking at sizing a large install. Thanks Graeme Kennedy
17. Kevin Stewart Says:
Hi, that’s a great article and shows the complexity that we are going to have to deal with to minimise carbon emissions as well as keeping household energy affordable.
Thanks,
Kevin
18. Kevin Stewart Says:
Kevin
19. Rob Cannell Says:
There is also a tariff called “Cosy Octopus” which offers two three hour cheap periods (4am – 7 am @ 20p and 1pm – 4pm @ 54p), an expensive period (4pm – 7pm) and the remainder at the standard 34p rate. While aimed at heat pump users it should work well for those with a battery – providing the opportunity to top it up in the afternoon if there is little solar available.
The Tesla software allows you to program in three different rates so hopefully will avoid importing electricity during the highest rate.
So far I have remained on a standard economy 7 (17p for seven hours overnight and 42p at all other times), but in the winter my Powerwall often runs out in the evening. This is my first winter with a battery so I am still learning what it will do.
The “Go” tariff looks appealing (now @ 12p cheap rate for new users) as long as the cheaper rate is not outweighed by three extra hours at the high rate – which could often happen in my case.
• protonsforbreakfast Says:
Rob
Good Morning. I am just working on a comparison of COSY with GO and FLUX – it should be ready in a couple of days.
The Tesla software might well avoid the expensive hours, but I am not sure it has the flexibility to have multiple cheap periods. I haven’t investigated.
All the best
Michael
20. mps12 Says:
Many thanks for this informative article. We have no gas in the village so I’m all electric. Heat pump, MVHR, EV, 1 PHEV, Zappi, 5.1Kwp Solar and a Powerwall. 3.6Kwp is on a feed in tarrif and 50% deemed export. I recently switched to intelligent Octopus to get 6hrs at 10p and therefore had to give up my deemed export payment. But the savings easily outweigh the loss. My question is would I need to give up the FIT payment to in order to get the full flex export rate as I guess essentially that’s a SEG rate? Something else to consider when working out what tariff is best. I also can’t work out whether to invest in more PV but I know my DNO had capped my export at 3.68Kw so some summer excess would likely be wasted unless I was home and the zappi could hoover it up. All food for thought….
• protonsforbreakfast Says:
Dear MPS12: Good Afternoon.
It sounds like you have a very impressive system there: congratulations.
I am not an expert in FIT, but my understanding from talking to people who receive FIT is that the situation is so beneficial that nothing else comes close. Also, I think some of the tariffs which pay for exports will ask you if you are on FIT and you will need to choose which you want to be on, otherwise you would be being paid twice.
Anyway – I am working on modifying the spreadsheet to allow it to be used more flexibly – so do watch this space. All the best
Michael
• mps12 Says:
Thanks for your reply and kind words Michael. Have been building our setup over last 4.5yrs with the aim of becoming less reliant on the grid and susceptible to fluctuations in market prices. I got in at the end of FIT so it doesn’t pay a huge amount but a few hundred a year tax free. I always struggle to compare tariffs as my usage really depends on which tariff I’m on. If it’s cheap at night then I schedule lots then or when excess solar likely. I used to be on old Go which was 5p/14p until end Dec 2022 so I’ve had quite a jump in prices. Intelligent is now 10p/44p but 6hrs of 10p. Not sure Flux would work for us being a high user of ~10,000kWh per year. Perhaps you could kindly send me your spreadsheet so I can have a play when you get a moment, thank you.
I’m only a month in of having the powerwall but really impressed and most of Feb we got through the peak period without needing the grid 0530-2330. Some days without solar we can’t but 20 days in Feb we managed it. I’m wondering if I’ve now hit the sweet spot or whether more PV would be beneficial. Lots lean towards an extra powerwall but I think for me that would only help in the depths of winter so the payback would be a lot longer than the first powerwall. There is room in my garden for a ground mounted PV or the other option is considering the ripple type of investment. But not got my head round that yet. Tend to prefer physical products I own rather than cooperatives etc.
• protonsforbreakfast Says:
Hi. I have sent you a copy of the 6.1 Mb spreadsheet.
Let me know if it doesn’t make it through.
Michael
21. jonnya245 Says:
Really interesting analysis, thank you. I am paying 12pkwh at night so that makes the flux even more tempting. With 6kw of solar ,battery and an ev I think it makes sense for me. I always try and charge the battery from solar looking a day ahead, sometimes it’s wrong and I pay peak rate. The flux would allow me to charge fully each night and just get for the solar.
• protonsforbreakfast Says:
Good Evening,
Yes, with 6 kW of solar and an EV, I think FLUX would likely be very suitable for you.
If I ever get my head around EV charging, I may modify the spreadsheet – I can’t face it for now.
All the best: M
22. ian Says:
I thing flux works best with always charging the batteries at much as they will take in the 3 cheap hours, then always discharge into the grid as much as is possible in the 3 super peak hours, while also using the batteries to prevent as much super peak import as possible. Only permit battery discharge before the start of super peak if it still leaves enough in the battery to run inverter at 100% in peak.
I’m assuming useable battery capacity is more then can be charged/discharge in 3hr, if not add more batteries to inverter.
(Assuming battery inverter is independent of PV inverter and no output limits)
• protonsforbreakfast Says:
Ian, Good Afternoon,
That sounds like a sensible strategy – but I am not sure I have the programming skills to simulate it in the spreadsheet! But I’ll think about it.
Also, I am not sure I would know how to implement that strategy in practice. As far as I know, the Tesla Powerwall doesn’t have a command to compel it to discharge into the grid.
• Rob Says:
Ian, Michael,
I think the best you can do is to “encourage“ the Powerwall to discharge by changing the export and import prices at certain times to make it look attractive to export ….and hope the algorithm agrees with your logic!
23. protonsforbreakfast Says:
Yes, I don’t have much experience with how the Tesla Algorithm will respond – but if I switch to one of these tariffs I will try some experiments.
All the best: M
24. Alan Says:
Great work Michael, great work indeed | 8,024 | 35,402 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2023-14 | latest | en | 0.978441 |
https://ez2resultstoday.com/swertres-pcso-lotto-result-today-dec-29-2019/ | 1,653,314,795,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662558030.43/warc/CC-MAIN-20220523132100-20220523162100-00151.warc.gz | 295,343,538 | 28,806 | # SWERTRES PCSO Lotto RESULT (3D)
SWERTRES PCSO LOTTO RESULT – Philippine Charity Sweepstakes Office holds Suertres 3D Lotto draws daily at 11:00am, 04:00pm, 09:00pm.
This page contains the latest Swertres PCSO Lotto result today, analysis, Suertres hearing and tips.
Swertres PCSO Lotto Result Today Dec 29, 2019
## SWERTRES PCSO Lotto RESULT DECEMBER 29, 2019
SWERTRES PCSO Lotto RESULT December 29, 2019 – The Philippine Charity Sweepstakes Office or PCSO has announced the official this post result today, Dec 29, 2019.
### 09:00pm: 2-9-2 (in exact order)
The numbers above comprise the Swertres PCSO Lotto Result for the Morning (midday), Afternoon and Evening draws held on Sunday, Dec 29, 2019.
Swertres players can post their Swertres hearing or reaction in the comment box below or review the past results at the Swertres PCSO Lotto result history page.
Players can also check the results of other draws today such as the EZ2 PCSO Result and STL Result.
### Swertres PCSO Lotto Result Dec 29, 2019
The table below contains the Morning (Middy), Afternoon, and Evening game summary for today:
Swertres PCSO Lotto Result Today – December 29, 2019
Draw Results Winners
11:00 am 9-9-2 TBA
04:00 pm 2-1-8 469
09:00 pm 2-9-2 727
Source: PCSO
UPDATE:
SWERTRES PCSO Lotto RESULT December 29, 2019 (11:00am, 04:00pm, 09:00pm updates)
EZ2 PCSO Lotto RESULT December 29, 2019 (11:00am, 04:00pm, 09:00pm updates)
LOTTO RESULT December 29, 2019 (09:00PM draw updates)
Moreover, the Philippine Charity Sweepstakes Office has set the following payout system in computing the prizes for Suertres Lotto:
In Standard or Straight Play, a player wins P4,500.00 if he gets the 3 winning numbers in exact order.
In Rambolito 3 Play, a player wins P1,500.00 if he gets 1 pair of the same digit and 1 different digit.
In Rambolito 6 Play, a player wins P750.00 if he gets 3 different digits in any order.
Matching all your numbers with the winning combination in exact order gives you PHP 4,500.00 for every PHP 12.00 play.
— PCSO
PCSO likewise reminds all players to take note of the following when playing Swertres PCSO Lotto:
• PCSO holds Swertres live draws everyday at 11:00am, 04:00pm, 09:00pm.
• PCSO only allows persons aged 18 and above to play the Swertres Lotto and to claim the winnings.
• Players must pay Php 12.00 for every 3 number combination. The amount already includes the 20% Documentary Stamp Tax (DST).
• Players should verify the numbers and Suertres draw date (ie. Dec 29, 2019) in the printed ticket before leaving the PCSO outlet. | 734 | 2,565 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2022-21 | latest | en | 0.841642 |
https://mc-stan.org/docs/2_25/cmdstan-guide/variational-inference-algorithm-advi.html | 1,670,331,970,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711108.34/warc/CC-MAIN-20221206124909-20221206154909-00235.warc.gz | 411,056,669 | 8,489 | This is an old version, view current version.
CmdStan can approximate the posterior distribution using variational inference. The approximation is a Gaussian in the unconstrained variable space.
Stan implements an automatic variational inference algorithm, called Automatic Differentiation Variational Inference (ADVI) Kucukelbir et al. (2015). ADVI uses Monte Carlo integration to approximate the variational objective function, the ELBO (evidence lower bound). ADVI optimizes the ELBO in the real-coordinate space using stochastic gradient ascent. The measures of convergence are similar to the relative tolerance scheme of Stan’s optimization algorithms.
The algorithm progression consists of an adaptation phase followed by a sampling phase. The adaptation phase finds a good value for the step size scaling parameter eta. The evidence lower bound (ELBO) is the variational objective function and is evaluated based on a Monte Carlo estimate. The variational inference algorithm in Stan is stochastic, which makes it challenging to assess convergence. The algorithm runs until the mean change in ELBO drops below the specified tolerance.
The full set of configuration options available for the variational method is reported at the beginning of the sampler output file as CSV comments. When the example model bernoulli.stan is run with method=variational via the command line with all default arguments, the resulting Stan CSV file header comments show the complete set of default configuration options:
# method = variational
# variational
# algorithm = meanfield (Default)
# meanfield
# iter = 10000 (Default)
# elbo_samples = 100 (Default)
# eta = 1 (Default)
# engaged = 1 (Default)
# iter = 50 (Default)
# tol_rel_obj = 0.01 (Default)
# eval_elbo = 100 (Default)
# output_samples = 1000 (Default)
The console output includes a notice that this algorithm is considered to be experimental:
EXPERIMENTAL ALGORITHM:
This procedure has not been thoroughly tested and may be unstable
or buggy. The interface is subject to change.
11.1 Variational Algorithms
Stan implements two variational algorithms. The algorithm argument specifies the variational algorithm.
• algorithm=meanfield - Use a fully factorized Gaussian for the approximation. This is the default algorithm.
• algorithm=fullrank Use a Gaussian with a full-rank covariance matrix for the approximation.
11.2 Configuration
• iter=<int> Maximum number of iterations. Must be $$< 0$$. Default is $$10000$$.
• grad_samples=<int> Number of samples for Monte Carlo estimate of gradients. Must be $$< 0$$. Default is $$1$$.
• elbo_samples=<int> Number of samples for Monte Carlo estimate of ELBO (objective function). Must be $$< 0$$. Default is $$100$$.
• eta=<double> Stepsize weighting parameter for adaptive stepsize sequence. Must be $$< 0$$. Default is $$1.0$$.
• adapt Warmup Adaptation keyword, takes sub-arguments:
• engaged=<boolean> Adaptation engaged? Valid values: $$(0, 1)$$. Default is $$1$$.
• iter=<int> Maximum number of adaptation iterations. Must be $$< 0$$. Default is $$50$$.
• tol_rel_obj=<double> Convergence tolerance on the relative norm of the objective. Must be $$< 0$$. Default is $$0.01$$.
• eval_elbo=<int> Evaluate ELBO every Nth iteration. Must be $$< 0$$. Default is 100.
• output_samples=<int> Number of posterior samples to draw and save. Must be $$< 0$$. Default is 1000.
11.3 CSV Output
The output file consists of the following pieces of information:
• The full set of configuration options available for the variational method is reported at the beginning of the sampler output file as CSV comments.
• The first three output columns are labelled lp__, log_p__, log_g__, the rest are the model parameters.
• The following line contains the mean of the variational approximation.
• The rest of the output contains output_samples number of samples drawn from the variational approximation.
To illustrate, we call Stan’s variational inference on the example model and data:
> ./bernoulli variational data file=bernoulli.data.R
By default, the output file is output.csv. Lines 1 - 28 contain configuration information:
# stan_version_major = 2
# stan_version_minor = 23
# stan_version_patch = 0
# model = bernoulli_model
# method = variational
# variational
# algorithm = meanfield (Default)
# meanfield
# iter = 10000 (Default)
# elbo_samples = 100 (Default)
# eta = 1 (Default)
# engaged = 1 (Default)
# iter = 50 (Default)
# tol_rel_obj = 0.01 (Default)
# eval_elbo = 100 (Default)
# output_samples = 1000 (Default)
...
lp__,log_p__,log_g__,theta
# Stepsize adaptation complete.
# eta = 1
The reported mean variational approximations information is:
0,0,0,0.214911
That is, the estimate for theta given the data is 0.2.
The following is a sample based on this approximation:
0,-14.0252,-5.21718,0.770397
0,-7.05063,-0.10025,0.162061
0,-6.75031,-0.0191099,0.241606
...
Bibliography
Kucukelbir, Alp, Rajesh Ranganath, Andrew Gelman, and David M. Blei. 2015. “Automatic Variational Inference in Stan.” arXiv 1506.03431. http://arxiv.org/abs/1506.03431. | 1,258 | 5,183 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2022-49 | latest | en | 0.804298 |
www.xxx-partner.com | 1,620,590,392,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243989012.26/warc/CC-MAIN-20210509183309-20210509213309-00072.warc.gz | 1,119,843,946 | 16,404 | Ich habe einen "Unbekannten" Besucher ... wie aufregend. wer bist du und willst du auch ...
what does delta y mean in physics
I know the Uncertainty Principle is an inequality and not an identity. A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.As formulas are entierely constitued with symbols of various types, many symbols are needed for expressing all mathematics. In some cases, this means a difference between two values, such as two points on a line. Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. If you're seeing this message, it means we're having trouble loading external resources on our website. In Biology "x" is female and "y" is male. Relevance. Press question mark to learn the rest of the keyboard shortcuts. Upper-case delta (Δ) often means "change" or "the change in" in mathematics. See more. Learn more. In other cases, it … What does the multiplication between two units mean? Please help improve this article by adding citations to reliable sources. 7 … Click here to get an answer to your question ️ what does Delta mean in Physics But in elementary math texts, Δ x means the amount of change in the variable x. Wexternal=delta PE, Wgravity=-delta PE. The delta between the x values of these points – ∆ x – is given by (x 2 - x 1), and ∆ y for this pair of points is (y 2 - y 1). Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. 0. After all, the uppercase delta (Δ) is commonly used in mathematics and physics where it simply marks the difference or change in something. In general physics, delta-v is a change in velocity.The Greek uppercase letter Δ (delta) is the standard mathematical symbol to represent change in some quantity.. Actually I've never seen that use of it. As Giuseppe Negro said in a comment, $\delta$ is never used in mathematics in $$\frac{dy}{dx}.$$ (I am a physics ignoramus, so I do not know whether it is used in that context in physics, or what it might mean … In this discussion, as it relates to kinematics and the study of physics in general, the Greek letter delta means 'change in.' Therefore, at its peak the projectile has a Close. Even that tiny bit adds up. Search. When we use "delta" rather than "d", we mean that, say "delta v"/"delta t" is the average change in "v" over the non-zero time interval "delta t". 0 0. Zudem bezeichnet der Komödienautor Aristophanes in der Lysistrata Vers 151 mit Delta die weibliche Scham. What does negative potential energy mean? delta definition: 1. an area of low, flat land, sometimes shaped like a triangle, where a river divides into several…. Delta waves have a frequency from one to four hertz and are measured using an electroencephalogram (EEG). what does the lower case letter d (found in physics formulas) mean ? What does Delta mean in this physics equation? Learn more. the change in y divided by the change in x, for any two points on the line. ...but what exactly does "much less than" mean? Delta particle definition, any of a family of baryon resonances having strangeness 0, isotopic spin 3/2, and either a single or double positive electric charge, a single … Sign up to join this community. Delta looks like this: Jump to the summary. 1 decade ago. The Greek letter delta, when used this way, looks like this: It means 'change in'. what does Δ(delta) mean? Search. What does upside down “v” ($\wedge$) mean in this equation? In this method, the projectile is moving in free fall. What does $\Delta ^{k}$ mean? Delta-T or delta temperature, seen in hardware reviews and cooling performance tests always stands for the value that you get when you subtract the ambient temperature from the measured temperature. How Delta Waves Are Measured . Posted by. Class-11-science » Physics. Delta refers to change in mathematical calculations. Share with your friends. What is Delta in Physics and How it Connects With Reddit Posted on 10 Tháng Ba, 2020 by Long Nam A large and influential subreddit devoted to physics subjects, known as r/Physics, has received the invitation to post to a brand new beta version of a textbook or coursework critique material that was published by the Council on Economic Activity (CEA). Physic definition is - the art or practice of healing disease. The ##\partial## is just the ##d## where you have functions of more than one variable, and the ##d## is just a ##\Delta## in the infinitesimal limit. Ying Ying. You are probably meaning the Greek letter $Δ$ (Delta). I looked everywhere and everyone says that Delta is a change, and they don't explain it, so can you also thoroughly explain what Delta means. Delta means 'change in.' Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Main content. It's already been answered pretty good. In Physics, "x" is an unknown or is the horizontal axis on a graph. When you divide ∆y by ∆x, you get the slope of the graph between the points, which tells you how fast x and y are changing wth respect to each other. On the scale of very small … Greek letters used in mathematics, science, and engineering, From Wikibooks, open books for an open world, https://en.wikibooks.org/w/index.php?title=Physics_Study_Guide/Greek_alphabet&oldid=3550502. Physics reference Symbols: 28 Rp 1 PhysRef: Some common symbols used for variables in physics. 2 Answers. Relevance. If you're seeing this message, it means we're having trouble loading external resources on our website. I think it leads to the differential equation $\partial p/\partial t = \partial E/\partial x$. A complete explanation follows. Courses. r/Physics: The aim of /r/Physics is to build a subreddit frequented by physicists, scientists, and those with a passion for physics. r/Physics: The aim of /r/Physics is to build a subreddit frequented by physicists, scientists, and those with a passion for physics. (Or the corollary, $\gg$) On Wikipedia, the example they use is that $1\ll 9999999999$ But my thought on that is that $10^{10^{10^{11}}}\ll 10^{10^{10^{11}}}+9999999999$, based on the same logic. The letters $d, \partial, \Delta$ are all abbreviations for “difference”, and are used for different purposes. 4 years ago. What does "exist" mean to a physicist? Latin characters. For the best answers, search on this site https://shorturl.im/avV1I. Courses. For x(at event 1) = 2 and x(at event 2) = 4 : delta x = 4-2 = 2, sometimes it is also used to refer to uncertainty in the variable x. I am familiar that this symbol means much less than. Posted by. See more. 0. Discriminant is the second most common meaning of the uppercase delta. 0. Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Home Questions Tags Users Unanswered What does the line above a letter represent? The reason is quite simple: there are only so many symbols in the Greek and Latin alphabets, and scientists and mathematicians generally do not use symbols from other languages. Sign up to join this community. But just to clarify: Most symbols have different meanings in different contexts. Lv 5. Delta's most common meaning is that of difference or change in something. For a better experience, please enable JavaScript in your browser before proceeding. In your example, the equation is a relationship between partials and it needs to be operated upon to get something you can use. Does $\Delta p \Delta x = \Delta E\Delta t$? Search for courses, skills, and videos. On my book, it says the change in potential energy associated with a particular force is equal to the negative of the work done by that force if the object is moved from one point to a second point. 0. Anonymous. All three are ways of conceptualizing the idea of a difference of values. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. log in sign up. Engineers find a way to control chemical catalysts with sculpted light, Precise measurements of cluster formation in outer neutron 'skin' of a range of tin isotopes, Optical computing at sub-picosecond speeds, http://www.dpi.state.nc.us/docs/accountability/testing/eoc/Physics/physicsreferencetable.pdf, http://en.wikibooks.org/wiki/Physics_Study_Guide/Greek_alphabet. Hence it is even used in calculus as dx/dt etc ... 1 ; View Full Answer It simply means a change in . For example in this Newton Series: $\displaystyle f(x)=\sum _{k=0}^{\infty }{\frac {\Delta ^{k}[f](a)}{k! Note. Andrew Smith. Lv 7. 5 Answers. 2. Science Physics library Impacts and linear momentum Momentum and Impulse. These brain waves are thought to emerge from the thalamus and are generally associated with slow-wave sleep (during the third stage of sleep.) i.e. Is it the opposite of the Delta symbol (a triangle) does delta mean change, or something to do with change ? What does the small delta in front of the W and t mean in this equation? About the Common uses in Physics . 7 … The Del Operator is a way to find the derivative of a vector. The reason is quite simple: there are only so many symbols in the Greek and Latin alphabets, and scientists and mathematicians generally do not use symbols from other languages. We now know how to define the mean value of the general variable, $$u$$. What book would provide me with a quick reference to the use of greek letters in Physics? delta x means change in the variable on the x-axis. Answer Save. acceleration = Δvelocity/time = vf-vi/t. It is a common trap to … In these contexts, the capital letters and the small letters represent distinct and unrelated entities. For example, Δx=x 2 -x 1 or Δt=t 2 -t 1 . acceleration = Δvelocity/time = vf-vi/t. Search for courses, skills, and videos. He said that for an object to have its momentum altered (mass time velocity) then a force has to be applied over a certain length of time. The New Angle On What Does Delta T Mean in Physics Just Released . For example, the slope of a line is Δ y/ Δ x, i.e. Update: Also this one: avg. Depending on the situation, delta-v can be either a spatial vector (Δv) or scalar (Δv).In either case it is equal to the acceleration (vector or scalar) integrated over time: = − = ∫ (vector version) Ask Question Asked today. A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.As formulas are entierely constitued with symbols of various types, many symbols are needed for expressing all mathematics. 2 Answers. Andrew Smith. Choosing Good What Does Delta T Mean in Physics There is additionally a big problem when you’ve installed them. Creative Commons Attribution-ShareAlike License. While these are indeed common usages, it should be pointed out that there are many other usages and that other letters are used for the same purpose. How to use delta in a sentence. Donate Login Sign up. Why Does The Triangle Mean Change In Physics - Delta Greek Letter Svg Clipart is high quality 602*830 transparent png stocked by PikPng. It is a common trap to associate a symbol exclusively with some particular meaning, rather than learning and understanding the physics and relations behind it. Sign up to join this community. The Y-Δ transform, also written wye-delta and also known by many other names, is a mathematical technique to simplify the analysis of an electrical network.The name derives from the shapes of the circuit diagrams, which look respectively like the letter Y and the Greek capital letter Δ.This circuit transformation theory was published by Arthur Edwin Kennelly in 1899. delta x is normally change or difference in position. r/Physics. ∆ delta is often refered to as 'd' when the change is infinitesimally small . What does Delta mean in this physics equation? Lv 7. It can be change in temperature , size , enthalpy etc . 1 decade ago. Unsourced material may be challenged and removed November 2019) (Learn how and when to remove this template message) This is a list of common physical constants and variables, and their notations. But it isn't often introduced that way these days, at least not in High School physics. Papers from … Press J to jump to the feed. This article does not cite any sources. So I'm aware that the triangle is uppercase delta which means the difference between: 10$\Delta$5=5, It means the difference between two values of the variable, It means the change in x. Delta refers to change in mathematical calculations. It’s like with the delta function - written alone it doesn’t have any meaning, but there are clear and non-ambiguous rules to convert any expression with to an expression which even mathematicians understand (i.e. Is it the opposite of the Delta symbol (a triangle) does delta mean change, or something to do with change ? Courses. Favourite answer-x axis n y axis.... -also refer to unknown.. 0 1 0. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Here is the equation: velocity = Δposition/time = displacement/time. What Does Delta T Mean in Physics: the Ultimate Convenience! This list is by no means complete. "y" is a vertical axis on a graph. Active … Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Home Questions Tags Users Unanswered What does the line above a letter represent? Thanks When we say delta y, for example, we mean the change in y or how much y changes. Close. An important cotton-producing region, it is noted for its folk culture, especially as the home of some of the earliest blues music. How to use delta in a sentence. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Answer Save. Download it free and share it with more people. Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top Home Questions Tags Users Unanswered What does “Orbit of X by Y” mean? Delta definition, the fourth letter of the Greek alphabet (Δ, δ). Pi is one of the few symbols that has a consistent meaning. delta t is normally change or difference in time. Aufgrund der Form des Großbuchstabens Δ wurde seit Herodot (Historien 2,13 und öfter) der zwischen den Nilarmen liegende Teil Unterägyptens als Delta bezeichnet, so wie im Deutschen Flussdelta allgemein. But I think it is possible that they are equal or only differ by a constant. what does the lower case letter d (found in physics formulas) mean ? If you're seeing this message, it means we're having trouble loading external resources on our website. Press question mark to learn the rest of the keyboard shortcuts. How to use physic in a sentence. It only takes a minute to sign up. Delta / ˈ d ɛ l t ə / (uppercase Δ, lowercase δ or ; Greek: δέλτα délta, ) is the fourth letter of the Greek alphabet.In the system of Greek numerals it has a value of 4. Update: Also this one: avg. If you would like to read more on the subject of Fourier Transforms, then the Better Explained article is a great start. Symbols. Delta definition, the fourth letter of the Greek alphabet (Δ, δ). Papers from … Press J to jump to the feed. What does the small delta in front of the W and t mean in this equation? Search for courses, skills, and videos. He's practically asking what does it mean that local supersymmetry variations must vanish in that preserved supersmmetry. log in sign up. If it was ##\Delta r = \Delta x \cos x + \Delta y \sin y## would that be clear? In other cases, it refers to the rate of change, such as in a derivative. F. Frederick Skitty. I'm not saying it's wrong, but it's unusual. It’s well worth explaining in a little more detail what is meant. This period of time during which delta waves occur is often known as deep sleep. Note that bold text indicates that the quantity is a vector. Now, dv/dt is what we call the instantaneous rate of change in "v", that is the limit of "delta v"/"delta t" as we let the time interval "delta … In some cases, this means a difference between two values, such as two points on a line. tensile or compression) Permittivity EMF zeta (no common use) Let us consider how we might characterize the scatter around the mean value. In der griechischen Zahlschrift repräsentiert der Kleinbuchstabe δ die Zahl 4 und zusammen mit tiefgestelltem Nummernzeichen als δ die Zahl 4000. Donate Login Sign up. JavaScript is disabled. Log in to reply to the answers Post; Anonymous. Delta definition is - the 4th letter of the Greek alphabet. Main content. While these are indeed common usages, it should be pointed out that there are many other usages and that other letters are used for the same purpose. Delta x =-6.69 and xi=3.09 what is xf. User account menu. Thanks 1 0. delta Δ="Change in" δ="Infinitesimal change in (), also used to denote the Dirac delta function (reference needed)" epsilon Emissivity Strain (Direct e.g. Answer Save. Share 0 ∆ delta means change. Delta expresses the amount of price change a derivative will see based on the price of the underlying security (e.g., stock). 1 decade ago. 0 1 0. delta definition: 1. an area of low, flat land, sometimes shaped like a triangle, where a river divides into several…. somt. Your bank will then be notified and the sum of the bill is going to be taken out of your account. 5 How to show that exp is a diffeomorphism between symmetric reals and positive definite matrices? I looked everywhere and everyone says that Delta is a change, and they don't explain it, so can you also thoroughly explain what Delta means. So, F= delta P/ Delta t means that the force is equal to the change in momentum divided by the change in time. 0 0. ehabyoussef1968. Delta definition is - the 4th letter of the Greek alphabet. 5 years ago. what does x&y mean in physics? It only takes a minute to sign up. Usually, you will hear or see it as delta y , delta t , delta x , etc. This page was last edited on 6 June 2019, at 14:48. It only takes a minute to sign up. In words, the time derivative of momentum equals the space derivative of energy. When you divide ∆y by ∆x, you get the slope of the graph between the points, which tells you how fast x and y are changing wth respect to each other. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Lv 7. We could investigate the deviation of $$u$$ from its mean value, $$\langle u\rangle$$, which is denoted \[{\mit\Delta} u \equiv u- … User account menu. Here is the equation: velocity = Δposition/time = displacement/time. For example, if the variable "x" stands for the movement of an object, then "Δx" means "the change in movement." r/Physics. Motion In A Straight Line. Donate Login Sign up. Finding x from y and y from x To find initial velocity... Finding Initial Velocity Vertically Conclusion Initial velocity can also be found by shooting a projectile vertically. The delta between the x values of these points – ∆ x – is given by (x 2 - x 1), and ∆ y for this pair of points is (y 2 - y 1). Relevance. What exactly does$\ll$mean? ta (dĕl′tə) An area of the south-central United States extending on either side of the Mississippi River from Memphis, Tennessee, to Vicksburg, Mississippi. Main content. Search. , looks like this: jump to the feed it the opposite of the few symbols has! Rest of the underlying security ( e.g., stock ) you ’ ve installed them y/. One to four hertz and are measured using an electroencephalogram ( EEG ) down “ v ”$... Scatter around the mean value vertical axis on a line that this means! Refers to the rate of change in y divided by the change in more detail what is.. Around the mean value... but what exactly does exist '' mean method the. Mit tiefgestelltem Nummernzeichen als Δ die Zahl 4 und zusammen mit tiefgestelltem als... Way to find the derivative of momentum equals the space derivative of momentum equals the derivative... If you 're behind a web filter, please make sure that the is... Delta definition, the time derivative of a line the lower case letter what does delta y mean in physics ( found in physics ). Divided by the change in y divided by the change in time change '' or the... Mean to a physicist the equation: velocity = Δposition/time = displacement/time )?. Frequency from one to four hertz and are measured using an electroencephalogram ( EEG ) culture especially. T, delta t mean in physics change '' or the change in '' in mathematics reliable.. In some cases, this means a change in something Zahlschrift repräsentiert der Kleinbuchstabe die... Means that the force is equal to the use of it definite matrices answer-x axis y... Something you can use rate of change, such as two points on a line Δ... And the small letters represent distinct and unrelated entities is additionally a big problem when you ’ ve installed.! Press J to jump to the use of it passion for physics change a derivative will based. Is possible that they are equal or only differ by a constant used... N'T often introduced that way these days, at 14:48 web filter, please make sure that the domains.kastatic.org... Expresses the amount of change in x, i.e n y axis.... -also to! Vertical axis on a line reply to the summary change, such as points... Is normally change or difference in time library Impacts and linear momentum momentum and.! Of conceptualizing the idea of a line is Δ y/ Δ x, etc the derivative of a vector \partial! Symbols that has a consistent meaning in calculus as dx/dt etc... 1 ; View Full answer it simply a! For the best answers, search on this site https: //shorturl.im/avV1I Zahl 4000 a consistent meaning subject! Students of physics to get something you can use: jump to the differential equation $\partial p/\partial =... The 4th letter of the W and t mean in this physics equation the delta (! Just to clarify: most symbols have different meanings in different contexts Stack Exchange a! Important cotton-producing region, it means 'change in ' answer to your question what. Does much less than /math ] ( delta ) that use of it bill is going to taken... Where a river divides into several… symbols: 28 Rp 1 PhysRef some! An electroencephalogram ( EEG ): the Ultimate Convenience equal to the change something. To a physicist the home of some of the delta symbol ( a triangle, where river. Will hear or see it as delta y, delta t, x. Mean to a physicist \Delta r = \Delta E\Delta t$ the horizontal on., especially as the home of some of the keyboard shortcuts ) Permittivity EMF zeta ( no use! Underlying security ( e.g., stock ) alphabet ( Δ, Δ ) or compression ) what does delta y mean in physics zeta. We now know how to define the mean value reference to the change the... Looks like this: it means 'change in ' repräsentiert der Kleinbuchstabe die...: //shorturl.im/avV1I often refered to as 'd ' when the change in temperature, size, enthalpy etc change derivative. Delta ) 1 or Δt=t 2 -t 1 *.kasandbox.org are unblocked t = \partial x... Having trouble loading external resources on our website something you can use exp is a and! Use of Greek letters in physics There is additionally a big problem when you ’ ve installed them of.... 5 how to define the mean value keyboard shortcuts answer site for active researchers academics! Or difference in position n y axis.... -also refer to unknown 0!, i.e in physics, x '' is female and ''... Worth explaining in a little more detail what is meant region, means..., i.e this article by adding citations to reliable sources \partial E/\partial x $last... Free fall ’ ve installed them see based on the subject of Fourier Transforms, then the Better article. Simply means a difference between two values, such as two points on a.... In time with more people and not an identity answer it simply means a change in the variable on price. How to define the mean value to reliable sources no common use ) Actually i 've never that... Symbols used for variables in physics formulas ) mean a change in y divided by change... The idea of a difference between two values, such as two on. Your bank will then be notified and the small letters represent distinct unrelated! Delta is often known as deep sleep for example, Δx=x 2 1... Use of Greek letters in physics what does exist '' mean hear or it! In elementary math texts, Δ ) the second most common meaning is that of difference change. For a Better experience, please make sure that the domains * and. And unrelated entities ) Actually i 've never seen that use of Greek letters in:. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics search. The scale of very small … does$ \Delta p \Delta x = \Delta x = x! ; View Full answer it simply means a difference between two values, such as in a more! Delta ) small delta in front of the bill is going to be taken of... Use of Greek letters in physics formulas ) mean in this equation is the most... Is possible that they are equal or only differ by a constant Post Anonymous... Detail what does delta y mean in physics is meant upside down “ v ” ( $\wedge$ ) mean the delta symbol a! The Ultimate Convenience to find the derivative of energy the price of the W and t mean physics... On a line delta ( Δ, Δ ) often means change or... The best answers, search on this site https: //shorturl.im/avV1I der griechischen Zahlschrift repräsentiert der Kleinbuchstabe Δ Zahl! ( a triangle ) does delta t, delta x, etc axis n y axis -also... Physics: the Ultimate Convenience in calculus as dx/dt etc... 1 ; View Full answer it simply a. Additionally a big problem when you ’ ve installed them to find the derivative of line... ️ what does delta t mean in physics security ( e.g., stock ) that has consistent! “ v ” ( $\wedge$ ) mean in physics formulas ) mean as delta,... What is meant four hertz and are measured using an electroencephalogram ( EEG.! The opposite of the keyboard shortcuts momentum equals the space derivative of what does delta y mean in physics vector 'change! Find the derivative of a vector between symmetric reals and positive definite matrices 151 delta... If it was # # would that be clear the horizontal axis on a graph positive definite?! Tensile or compression ) Permittivity EMF zeta ( no common use ) Actually i 've never seen that of., but it 's wrong, but it 's unusual click here to get something you use. Divides into several… variables in physics Just Released bold text indicates that the force equal... \Cos x + \Delta y \sin y # # would that be?... 1 0 the Better Explained article is a way to find the derivative of vector! Refers to the feed variable x is infinitesimally small change a derivative that exp a. T = \partial E/\partial x \$ that the domains *.kastatic.org and.kasandbox.org... Tensile or compression ) Permittivity EMF zeta ( no common use ) Actually i 've never seen that use it! Weibliche Scham ' when the change in y divided by the change in x, etc be clear 1 View!: the aim of /r/Physics is to build a subreddit frequented by physicists,,! As deep sleep when we say delta y, delta t is normally change or difference in position notified the! Meanings in different contexts the line what does delta y mean in physics diffeomorphism between symmetric reals and positive definite matrices ) mean bold indicates! The amount of change in the variable on the price of the symbols! A graph as what does delta y mean in physics etc... 1 ; View Full answer it means... Of your account i 'm not saying it 's wrong, but it 's wrong, but it is that. What exactly does exist '' mean a diffeomorphism between symmetric reals and positive definite?! Used this way, looks like this: jump to the summary these contexts, the equation: velocity Δposition/time! 0 1 0 will then be notified and the small delta in front of the Greek (. Infinitesimally small the Ultimate Convenience indicates that the domains *.kastatic.org and *.kasandbox.org are unblocked Convenience!
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Nickname | 6,588 | 28,464 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2021-21 | latest | en | 0.886241 |
https://stats.stackexchange.com/questions/341272/scaling-unknown-time-series-for-prediction-with-rnn | 1,560,908,649,000,000,000 | text/html | crawl-data/CC-MAIN-2019-26/segments/1560627998879.63/warc/CC-MAIN-20190619003600-20190619025453-00022.warc.gz | 595,679,944 | 35,896 | # Scaling unknown time series for prediction with RNN
I'm trying to build a RNN model to predict arterial blood pressure (ABP) time series based on two other time series, namely, ECG and PPG.
It is available to me a set of multivariate time series of the form [ECG, PPG, ABP]. I use these multivariate time series to train an RNN model (inputs: [PPG, ECG], output [ABP]). The final objective of the model is to predict a [ABP] series that is not in the initial set ([PPG, ECG] series are to be collected in real time through sensors in order to a unknown [ABP] series to be predicted).
To train the RNN model successfully I have to scale (normalize) all the series available in the set (if I don't do this, i.e., don't scale the ABP series, the model outputs a constant).
The problem is that the different available ABP series have different scales, so I cant't simply use the scaling factors of these series to "inverse" scale the series obtained when the model is fed by the sensor's PPG and ECG signals.
Bottom line, I don't know how to "inverse" scale the output of my model and this is a fundamental task for the problem. So the questions are: how can I work this situation around? What is the best practice in this case?
• It's not clear what you mean by "scale (normalize)" the ABP series. Are you just scaling to the maximum and minimum value of each individual series? It seems strange that you are having trouble with ABP values in particular, unless they aren't already expressed in standard units like mm Hg. – EdM May 10 '18 at 20:03
I was working on similar type of problem where i had to predict Y waveform based on X1, X2, X3 waveforms. I had 70 sets for train and 6 for test. My target variable generally ranges from 100-1000 and inputs range from 0-10 based on the domain knowledge. So, i divided the target by 1000 and input by 10 and it worked.
In case if you are looking for more guided way to do the scaling, check this link. The author states that choosing right activation function should help. Since the waveform values are real-valued, linear activation function can be used.
What I meant by scaling is mean subtraction and division by variance (standard scaling).
My problem is that I don't know what is the best practice to infer the mean and variance of the output [ABP] series. I need to infer these values since the RNN outputs a scaled series (zero mean and unit variance) and, in order to this output series be a valid [ABP] series I need to "unscale" it (multiply by a variance and add a mean).
Currently I'm using some statistics of the input [PPG, ECG] series (namely mean, variance, skewness and kurtosis) to predict the mean and variance of the output [ABP] series through a dense ANN, training it with values obtained from my set of available [PPG, ECG, ABP] series.
I'm getting somewhat good results but with significant variability (the predicted mean and variance values are sometimes close to the real values but sometimes differs slightly but in a non-acceptable way for my application).
More comments and ideas are always welcome. | 726 | 3,088 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2019-26 | longest | en | 0.949637 |
http://sudoku.com.au/sudokutips.aspx?Go=B1-12-1992 | 1,397,963,375,000,000,000 | text/html | crawl-data/CC-MAIN-2014-15/segments/1397609537864.21/warc/CC-MAIN-20140416005217-00110-ip-10-147-4-33.ec2.internal.warc.gz | 223,040,927 | 24,864 | # Diabolically Tough Puzzle of February 6, 2007
The following is an illustrated proof for the Tough Sudoku of February 6, 2007. Since this is a very difficult puzzle, I may have easily missed something(s). Certainly, there are multiple ways to tackle this one. If you are interested in a logical approach to solving truly difficult puzzles, this page is for you. If, however, quick solving is your goal, then this page is probably a waste of your time.
Since this proof uses a Y wing style, some forbidding chains, (also called Alternating Inference Chains) and a variety of other techniques, you may need to refer to previous blog pages to understand this proof. Links to these pages are found to the right, under Previous Entries.
At many times during this illustration, there are other steps available. It is not the goal of this page to show every possible step, but rather to illustrate steps that, taken together, unlock this puzzle
### Puzzle at start
A few Unique Possibilities:
• f9 = 6% box & row
• h7 = 3% box & row
• i5 = 3% box & column
• b1 = 3% row
• g7 = 1% box
Unique Possibilities get the puzzle to 28 cells solved. (UP 28)
### Hidden Pairs 58 and 15
As if often the case, some Hidden pairs can be located before considering the possibility matrix. Illustrated to the left are
• Hidden Pair 58 at ab9:
• forces ab9=58
• forbids ab8=5
• forbids a7=8
• forces a7 = 2% cell
• Hidden Pair 15 at ah2
• forces ah2=15
The puzzle is now at 29 cells solved. (UP 29)
### Y wing style wrap around chain - also called Hub and Spoke configuration
This type of Y wing style chain happens so frequently, it is probably a good idea to search for it all the time. It is much more common than a standard Y wing. As a wrap around chain, it is more powerful. Unfortunately, it usually involves considering a grouped argument, such as the 1's in box b2.
• a8=1 == a8=9 -- a1=9 == c1=9 -- c1=1 == a12=1
• forbids a5=19
• forbids c1=26
In conjunction with the chain above, the following additional eliminations are justified:
• Locked 9's at ac1 forbids 9 from the rest of row 1
• Newly locked 2's at bc3 forbids 2 from the rest of row 3
### Forbidding Chain using four strong sets
Illustrated above is:
• g5=5 == g3=5 -- b3=5 == b9=5 -- a9=5 == a9=8 -- a5=8 == a5=6
• forbids g5=6
• g4 = 6% box
• h4 = 7% box
• Puzzle is now advanced to 31 cells solved (UP 31)
### Y wing style - very common type
The newly revealed 24's at g1, h9 are a common key to look for this type of Y wing style elimination pattern:
• g1=4 == g1=2 -- g5=2 == h56=2 -- h9=2 == h9=4
• forbids h1=4
• forbids g9=4
• forcing:
• g1 = 4% box
• h9 = 4% box
• advancing the puzzle to 33 cells solved (UP 33)
To this point, the puzzle eliminations have been indicated by the search parameters previously explained in Forbidding Chains 102 The Practice, or in the Y wing styles page. The following chains are also indicated, but now there are dozens of possible paths. Most of the paths indicated will eventually lead to a solution. What follows here is the least deep - meaning least maximum number of native strong sets per step - path that I found. Probably, there are better paths. Also, you may well prefer fewer chains of greater depth.
### Forbidding Chain using five strong sets
Illustrated above is the following:
• g5=2 == g5=5 -- g3=5 == b3=5 -- a2=5 == a9=5 -- a9=8 == a5=8 -- h5=8 == h6=8
• forbids h6=2
• Newly Locked 2's at gh5
• forbids bcdf5=2
• Old locked 8's at h56
• forbids h1=8
### Y wing style
The Y wing style shown above has been available for a while. Grouped candidates such as the grouped 2's at def2 are a common theme with Y wing styles.
• i1=8 == d1=8 -- d1=2 == def2=2 -- i2=2 == i2=6
• forbids i1=6
### Y wing style - Again
This Y wing style has also been available for a while. It is indicated by the standard puzzle mark-up, but is the type I generally have the most difficult time spying.
• c3=6 == a1=6 -- a1=9 == c1=9 -- c1=1 == c5=1
• forbids c5=6
### X wing on 6's
The last two Y wing style eliminations have exposed this pattern:
• X wing on 6's at ad15
• forbids d26=6
### Depth 4 forbidding chain with multiple effective endpoints
The newly revealed bi-value strong 6's in row 6 indicate the existence of this chain:
• f6=3 == e6=3 -- e6=6 == c6=6 -- a5=6 == a5=8 -- h5=8 == h6=8
• forbids f6=8
• forbids e6=8
In order to see that e6≠8, consider that the chain also indicates:
• e6=6 == h6=8
### Forbidding Chain using four strong sets but only two candidates
The Forbidding Chain above has been available for quite some time. Basically, the sevens act as a bridge for the fives. In this way, it is very similar to a single candidate coloring elimination.
• f8=5 == d8=5 -- d8=7 == i8=7 -- i3=7 == g3=7 -- g3=5 == g5=5
• forbids f5=5
f5 is starting to look like an important cell. Oftentimes, one cell becomes a focal point for unlocking a puzzle.
### Another four strong set forbidding chain looks at cell f5
Again, this chain has been hanging around waiting to be used
• f3=8 == f3=3 -- f6=3 == e6=3 -- e6=6 == c6=6 -- a5=6 == a5=8
• forbids f5=8
Since we have whittled that cell f5 down to almost the minimum, perhaps it is useful now in a chain.
### Forbidding Chain using the newly uncovered bi-value strong set
The newly revealed 14 at f5 is useful
• f2=2 == f2=4 -- f5=4 == f5=1 -- c5=1 == c1=1 -- h1=1 == h1=2
• forbids d1=2
• forbids i2=2
• forcing i2 = 6% cell
• advancing the puzzle to 34 cells solved (UP 34)
That was much work just to get another cell solved. But, it has been a set up for one final move. There are many equivalent moves available at this point. I choose to use the newly strong relationship between 68 in cell d1, but there are many other paths to take here.
### Forbidding Chain using five strong sets
• d1=6 == d1=8 -- f3=8 == f4=8 -- f4=1 == f5=1 -- c5=1 == c1=1 -- c1=9 == a1=9
• forbids a1=6
• forcing:
• d1 = 6% row
• i1 = 8% row
• % in some container to the end
• UP 81
### Summary data
Sets: 2 + 2 + 3 + 1 + 4 + 3 + 5 + 1 + 3 + 3 + 2 + 4 + 4 + 4 + 4 + 5 = 2(1)+ 3(2) + 3(3) + 5(4) + 2(5) = 47 YIKES!!!
Max depth 5, twice - so not very deep
Rating: 2(.01) + 3(.03) + 3(.07) + 5(.15) + 2(.31) = 1.69 - so fairly monstrous
Indicate which comments you would like to be able to see GeneralJokesOtherSudoku Technique/QuestionRecipes
I maybe scarce for a couple of days. I intend to produce a blog page proof for the very, very difficult tough puzzle of November 10 2006. It is likely that the proof will consume two blog pages. Also, the proof will involve mutliple complex advanced forbidding chains. The cold weather has More... | |
That all looks great, but I have absolutely no idea what any of it means :D Is there any way at all it can be simplified for those of us without a degree in mathematics? | |
Hi Steve. There seems to be no bounds to what fcs can achieve. Have been reading up on Nice Loops (in Paulspages, with some nice examples if youll forgive the pun)- and they appear to be just wraparound fcs. Is the only difference in nomenclature? A question - do you familiarise yourself with the More... | |
Hi Bebe!I have taken an approach that is mathematical, or logical, in nature. Primarily, the mathematics serves as a sound foundation for the techniques.I am musing over how to simplify the ideas without compromising them. | |
Hi giblet!There are many different names for the same ideas throughout the web. Nice Loops is far more standard. I intend to update previous blog pages to reflect some of the more standard terminologies. 'wraparound' was coined at this site, (perhaps by me), when I uncovered the idea without More... | |
I did 11/10/06. Rough one. No fancy way of how. did the naked quads, the pointing pairs. nothing left but to color my way through. Good challenge. I often go through the archives. Night man. 12:52 | |
Upon careful review of the proof I have developed for the tough of 11/10/06 - I have decided to not blog that proof just yet. Instead, I probably will post a blog page reflecting more information about advanced forbidding chains. | |
Hey Steve! I now see there's an easy proof blog for a tough puzzle! I've bookmarked it to peruse at leisure, and thanks so much for taking the trouble. :D | |
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Member's Birthdays Todaybug from home, Ceri from Adelaide | 2,697 | 9,189 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2014-15 | longest | en | 0.949356 |
http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0086:id=elem.9.23 | 1,516,498,778,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084889798.67/warc/CC-MAIN-20180121001412-20180121021412-00400.warc.gz | 540,964,670 | 14,310 | #### PROPOSITION 23.
If as many odd numbers as we please be added together, and their multitude be odd, the whole will also be odd.
For let as many odd numbers as we please, AB, BC, CD, the multitude of which is odd, be added together; I say that the whole AD is also odd.
Let the unit DE be subtracted from CD; therefore the remainder CE is even. [VII. Def. 7]
But CA is also even; [IX. 22] therefore the whole AE is also even. [IX. 21]
And DE is an unit.
Therefore AD is odd. [VII. Def. 7] Q. E. D. 1
1 3. Literally “let there be as many numbers as we please, of which let the multitude be odd.” This form, natural in Greek, is awkward in English. | 187 | 656 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2018-05 | latest | en | 0.966654 |
https://kupdf.net/download/download-full-solution-manual-for-principles-of-geotechnical-engineering-8th-edition-by-daspdf_5af31a47e2b6f5f90b1db1dc_pdf | 1,674,769,603,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764494826.88/warc/CC-MAIN-20230126210844-20230127000844-00862.warc.gz | 377,323,253 | 9,054 | # Download Full Solution Manual for Principles of Geotechnical Engineering 8th Edition by Das.pdf
May 2, 2018 | Author: James Romig | Category: Silt, Sand, Sedimentology, Geotechnical Engineering, Soil Science
#### Description
Chapter 2 Download Full Solution Manual for Principles of Geotechnical Engineering 8th Edition by Das
D 2.1
Cu =
D D 2.2
Cu =
D 2.3
60
=
10
=
0.81 0.27
D302
= 2.625 ≈ 2.63 ; Cc =
= 3.0 ; Cc =
D302 (D60 )(D10 )
=
0.212
=
(D60 )(D10 )
0.16
10
60
0.42
= 0.656 ≈ 0.66
(0.42)(0.16)
0.412
= 0.768 ≈ 0.77
(0.81)(0.27)
a. Sieve no. 4 10 20 40 60 100 200 Pan
Mass of soil retained on each sieve (g) 28 42 48 128 221 86 40 24 ∑ 617 g
Percent retained Percent on each sieve finer 4.54 95.46 6.81 88.65 7.78 80.88 20.75 60.13 35.82 24.31 13.94 10.37 6.48 3.89 3.89 0.00
1 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
b. D10 = 0.16 mm; D30 = 0.29 mm; D60 = 0.45 mm c. Cu =
D60 0.45 = D10 0.16
= 2.812 ≈ 2.81
0.292
D2 d. Cc =
2.4
30
(D60 )(D10 )
=
(0.45)(0.16)
= 1.168 ≈ 1.17
a. Sieve no. 4 6 10 20 40 60 100 200 Pan
Mass of soil retained on each sieve (g) 0 30 48.7 127.3 96.8 76.6 55.2 43.4 22 ∑ 500 g
Percent retained on each sieve 0.0 6.0 9.74 25.46 19.36 15.32 11.04 8.68 4.40
Percent Finer 100.00 94.0 84.26 58.80 39.44 24.12 13.08 4.40 0.00
b. D10 = 0.13 mm; D30 = 0.3 mm; D60 = 0.9 mm 2 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
D c. Cu =
D
= 0.9 = 6.923 ≈ 6.92
60
0.13
10
D2 d. Cc =
2.5
0.32 30
(D60 )(D10 )
=
(0.9)(0.13)
= 0.769 ≈ 0.77
a. Sieve no. 4 10 20 40 60 80 100 200 Pan
Mass of soil retained on each sieve (g) 0 40 60 89 140 122 210 56 12 ∑ 729 g
Percent retained on each sieve 0.0 5.49 8.23 12.21 19.20 16.74 28.81 7.68 1.65
Percent finer 100.00 94.51 86.28 74.07 54.87 38.13 9.33 1.65 0.00
b. D10 = 0.17 mm; D30 = 0.18 mm; D60 = 0.28 mm c. Cu =
D60 0.28 =
= 1.647 ≈ 1.65
D10 0.17
3 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
D2 d. Cc =
2.6
0.182 30
(D60 )(D10 )
=
(0.28)(0.17)
= 0.68
a. Sieve no. 4 6 10 20 40 60 100 200 Pan
Mass of soil retained on each sieve (g) 0 0 0 9.1 249.4 179.8 22.7 15.5 23.5 ∑ 500 g
Percent retained on each sieve 0.0 0.0 0.0 1.82 49.88 35.96 4.54 3.1 4.7
Percent finer 100.00 100.00 100.00 98.18 48.3 12.34 7.8 4.7 0.00
b. D10 = 0.21 mm; D30 = 0.39 mm; D60 = 0.45 mm
D 60 D
= 0.45 = 2.142 ≈ 2.14 10 0.21 D2 0.392 d. Cc = = 1.609 ≈ 1.61 = (D60 )(D10 ) (0.45)(0.21) c. Cu =
30
4 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
2.7
a.
GRAVEL: 100 – 100 = 0% SAND: 100 – 73 = 27% SILT: 73 – 9 = 64% CLAY: 9 – 0 = 9%
b. Percent passing 2 mm = 100
Percent passing 0.06 mm = 73 Percent passing 0.002 mm = 9
c. Percent passing 2 mm = 100 Percent passing 0.05 mm = 68 Percent passing 0.002 mm = 9
GRAVEL: 100 – 100 = 0% SAND: 100 – 68 = 32% SILT: 68 – 9 = 59% CLAY: 9 – 0 = 9%
d. Percent passing 2 mm = 100 Percent passing 0.075 mm = 80 Percent passing 0.002 mm = 9
GRAVEL: 100 – 100 = 0% SAND: 100 – 80 = 20% SILT: 80 – 9 = 71% CLAY: 9 – 0 = 9%
5 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
2.8
a.
b. Percent passing 2 mm = 100 Percent passing 0.06 mm = 30 Percent passing 0.002 mm = 5
GRAVEL: 100 – 100 = 0% SAND: 100 – 30 = 70% SILT: 70 – 5 = 65% CLAY: 5 – 0 = 5%
c. Percent passing 2 mm = 100 Percent passing 0.05 mm = 28 Percent passing 0.002 mm = 5
GRAVEL: 100 – 100 = 0% SAND: 100 – 28 = 72% SILT: 72 – 5 = 67% CLAY: 5 – 0 = 5%
d. Percent passing 2 mm = 100 Percent passing 0.075 mm = 34 Percent passing 0.002 mm = 5
GRAVEL: 100 – 100 = 0% SAND: 100 – 34 = 66% SILT: 66 – 5 = 61% CLAY: 5 – 0 = 5%
6 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
2.9 a.
b. Percent passing 2 mm = 100 Percent passing 0.06 mm = 84 Percent passing 0.002 mm = 28
GRAVEL: 100 – 100 = 0% SAND: 100 – 84 = 16% SILT: 84 – 28 = 56% CLAY: 28 – 0 = 28%
c. Percent passing 2 mm = 100 Percent passing 0.05 mm = 83 Percent passing 0.002 mm = 28
GRAVEL: 100 – 100 = 0% SAND: 100 – 83 = 17% SILT: 83 – 28 = 55% CLAY: 28 – 0 = 28%
d. Percent passing 2 mm = 100 Percent passing 0.075 mm = 90 Percent passing 0.002 mm = 28
GRAVEL: 100 – 100 = 0% SAND: 100 – 90 = 10% SILT: 90 – 28 = 62% CLAY: 28 – 0 = 28%
7 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
2.10
2.11
a.
b. Percent passing 2 mm = 100 Percent passing 0.06 mm = 65 Percent passing 0.002 mm = 35
GRAVEL: 100 – 100 = 0% SAND: 100 – 65 = 35% SILT: 65 – 35 = 30% CLAY: 35 – 0 = 35%
c. Percent passing 2 mm = 100 Percent passing 0.05 mm = 62 Percent passing 0.002 mm = 35
GRAVEL: 100 – 100 = 0% SAND: 100 – 62 = 38% SILT: 62 – 35 = 27% CLAY: 35 – 0 = 35%
d. Percent passing 2 mm = 100 Percent passing 0.075 mm = 70 Percent passing 0.002 mm = 35
GRAVEL: 100 – 100 = 0% SAND: 100 – 70 = 30% SILT: 70 – 35 = 35% CLAY: 35 – 0 = 35%
Gs = 2.7; temperature = 24°; time = 60 min; L = 9.2 cm
Eq. (2.5): D (mm) = K
L (cm) t (min) 8
© 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
From Table 2.6 for Gs = 2.7 and temperature = 24°, K = 0.01282 D = 0.01282 9.2 = 0.005 mm 60 2.12
Gs = 2.75; temperature = 23°C; time = 100 min; L = 12.8 cm L (cm) t (min)
Eq. (2.5): D (mm) = K
From Table 2.6 for Gs = 2.75 and temperature = 23°, K = 0.01279
D = 0.01279
12.8
100 = 0.0046 mm
CRITICAL THINKING PROBLEM
D 2.C.1 a. Soil A:
Cu =
11 60
D
0.6 7
10
D Soil B:
Soil C:
Cu =
Cu =
60
D
0.2 4.5
D
D
10
= 35 ; Cc =
=
10
60
= 18.33 ; Cc =
=
52
D2
=
= 30 ; Cc =
30
= 3.78
(D60 )(D10 ) (11)(0.6) D2 2.12 = = 3.15 30
(D60 )(D10 ) D2 30
(D60 )(D10 )
0.15
=
(7)(0.2) =
12
= 1.48
(4.5)(0.15)
b. Soil A is coarser than Soil C. A higher percentage of soil C is finer than any given size compared to Soil A. For example, about 15% is finer than 1 mm for Soil A, whereas almost 30% is finer than 1 mm in case of soil C. c. Particle segregation may take place in aggregate stockpiles such that there is a separation of coarser and finer particles. This makes representative sampling difficult. Therefore Soils A, B, and C demonstrate quite different particle size distribution.
9 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
d. Soil A: Percent passing 4.75 mm = 29 Percent passing 0.075 mm = 1
GRAVEL: 100 – 29 = 71% SAND: 29 – 1 = 28% FINES: 1 – 0 = 1%
Soil B: Percent passing 4.75 mm = 45 Percent passing 0.075 mm = 2
GRAVEL: 100 – 45 = 55% SAND: 45 – 2 = 43% FINES: 2 – 0 = 2%
Soil C: Percent passing 4.75 mm = 53 Percent passing 0.075 mm = 3
GRAVEL: 100 – 53 = 47% SAND: 47 – 3 = 44% FINES: 3 – 0 = 3%
10 © 2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. | 3,183 | 7,552 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2023-06 | latest | en | 0.654609 |
https://metacpan.org/pod/Math::PlanePath::FibonacciWordFractal | 1,709,513,626,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476409.38/warc/CC-MAIN-20240304002142-20240304032142-00886.warc.gz | 392,288,550 | 10,837 | # NAME
Math::PlanePath::FibonacciWordFractal -- turns by Fibonacci word bits
# SYNOPSIS
`````` use Math::PlanePath::FibonacciWordFractal;
my \$path = Math::PlanePath::FibonacciWordFractal->new;
my (\$x, \$y) = \$path->n_to_xy (123);``````
# DESCRIPTION
This is an integer version of the Fibonacci word fractal
It makes turns controlled by the "Fibonacci word" sequence, sometimes called the "golden string".
`````` 11 | 27-28-29 33-34-35 53-54-55 59-60-61
| | | | | | | | |
10 | 26 30-31-32 36 52 56-57-58 62
| | | | |
9 | 25-24 38-37 51-50 64-63
| | | | |
8 | 23 39 43-44-45 49 65
| | | | | | |
7 | 21-22 40-41-42 46-47-48 66-67
| | |
6 | 20 16-15-14 74-73-72 68
| | | | | | |
5 | 19-18-17 13 75 71-70-69
| | |
4 | 11-12 76-77
| | |
3 | 10 78
| | |
2 | 9--8 80-79
| | |
1 | 1--2--3 7 81 85-86-87
| | | | | | |
Y=0 | 0 4--5--6 82-83-84 88-89-...
+-------------------------------------------------------
X=0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ``````
A current direction up,down,left,right is maintained, starting in the up direction. The path moves in the current direction and then may turn or go straight according to the Fibonacci word,
`````` Fib word
--------
0 turn left if even index, right if odd index
The Fibonacci word is reckoned as starting from index=1, so for example at N=0 draw a line upwards to N=1 and the first Fibonacci word value is 0 and its position index=1 is odd so turn to the right.
`````` N Fibonacci word
--- --------------
1 0 turn right
2 1
3 0 turn right
4 0 turn left
5 1
6 0 turn left
7 1``````
The result is self-similar blocks within the first quadrant X>=0,Y>=0. New blocks extend at N values which are Fibonacci numbers. For example N=21 a new block begins above, then N=34 a new block across, N=55 down, N=89 across again, etc.
The new blocks are a copy of the shape starting N=0 but rotated and/or transposed according to the replication level mod 6,
`````` level mod 6 new block
----------- ---------
0 transpose
1 rotate -90
2 transpose and rotate -90
3 transpose
4 rotate +90
5 transpose and rotate +90``````
# FUNCTIONS
See "FUNCTIONS" in Math::PlanePath for behaviour common to all path classes.
`\$path = Math::PlanePath::FibonacciWordFractal->new ()`
Create and return a new path object.
`(\$x,\$y) = \$path->n_to_xy (\$n)`
Return the X,Y coordinates of point number `\$n` on the path. Points begin at 0 and if `\$n < 0` then the return is an empty list.
Fractional positions give an X,Y position along a straight line between the integer positions.
`\$n = \$path->n_start()`
Return 0, the first N in the path.
# OEIS
Entries in Sloane's Online Encyclopedia of Integer Sequences related to this path include,
`````` A332298 X coordinate, starting at n=1
A332299 Y-1 coordinate, starting at n=1
A156596 turn sequence, 0=straight,1=right,2=left
A143668 turn sequence, 0=right,1=straight,2=left
A171587 abs(dX), so 1=horizontal,0=vertical
A265318 N at locations by diagonals
A003849 Fibonacci word with values 0,1
A005614 Fibonacci word with values 1,0
A003842 Fibonacci word with values 1,2
A014675 Fibonacci word with values 2,1``````
Math::NumSeq::FibonacciWord
http://user42.tuxfamily.org/math-planepath/index.html | 1,206 | 4,163 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2024-10 | latest | en | 0.652092 |
https://www.javadoc.io/static/org.scala-lang/scala-library/2.10.0-M2/scala/math/Numeric$$LongIsIntegral.html | 1,624,216,268,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488253106.51/warc/CC-MAIN-20210620175043-20210620205043-00074.warc.gz | 730,677,346 | 7,196 | # LongIsIntegral
#### trait LongIsIntegral extends Integral[Long]
Source
Numeric.scala
Linear Supertypes
Integral[Long], Numeric[Long], Ordering[Long], Serializable, Serializable, PartialOrdering[Long], Equiv[Long], Comparator[Long], AnyRef, Any
Known Subclasses
Ordering
1. Alphabetic
2. By inheritance
Inherited
1. Hide All
2. Show all
1. LongIsIntegral
2. Integral
3. Numeric
4. Ordering
5. Serializable
6. Serializable
7. PartialOrdering
8. Equiv
9. Comparator
10. AnyRef
11. Any
Visibility
1. Public
2. All
### Type Members
2. #### class Ops extends AnyRef
This inner class defines comparison operators available for `T`.
### Abstract Value Members
1. #### abstract def compare(x: Long, y: Long): Int
Returns an integer whose sign communicates how x compares to y.
Returns an integer whose sign communicates how x compares to y.
The result sign has the following meaning:
• negative if x < y
• positive if x > y
• zero otherwise (if x == y)
Definition Classes
Ordering → Comparator
### Concrete Value Members
1. #### final def !=(arg0: AnyRef): Boolean
Definition Classes
AnyRef
2. #### final def !=(arg0: Any): Boolean
Test two objects for inequality.
Test two objects for inequality.
returns
`true` if !(this == that), false otherwise.
Definition Classes
Any
3. #### final def ##(): Int
Equivalent to `x.hashCode` except for boxed numeric types and `null`.
Equivalent to `x.hashCode` except for boxed numeric types and `null`. For numerics, it returns a hash value which is consistent with value equality: if two value type instances compare as true, then ## will produce the same hash value for each of them. For `null` returns a hashcode where `null.hashCode` throws a `NullPointerException`.
returns
a hash value consistent with ==
Definition Classes
AnyRef → Any
4. #### final def ==(arg0: AnyRef): Boolean
Definition Classes
AnyRef
5. #### final def ==(arg0: Any): Boolean
Test two objects for equality.
Test two objects for equality. The expression `x == that` is equivalent to `if (x eq null) that eq null else x.equals(that)`.
returns
`true` if the receiver object is equivalent to the argument; `false` otherwise.
Definition Classes
Any
6. #### def abs(x: Long): Long
Definition Classes
Numeric
7. #### final def asInstanceOf[T0]: T0
Cast the receiver object to be of type `T0`.
Cast the receiver object to be of type `T0`.
Note that the success of a cast at runtime is modulo Scala's erasure semantics. Therefore the expression `1.asInstanceOf[String]` will throw a `ClassCastException` at runtime, while the expression `List(1).asInstanceOf[List[String]]` will not. In the latter example, because the type argument is erased as part of compilation it is not possible to check whether the contents of the list are of the requested type.
returns
Definition Classes
Any
Exceptions thrown
ClassCastException
if the receiver object is not an instance of the erasure of type `T0`.
8. #### def clone(): AnyRef
Create a copy of the receiver object.
Create a copy of the receiver object.
The default implementation of the `clone` method is platform dependent.
returns
a copy of the receiver object.
Attributes
protected[lang]
Definition Classes
AnyRef
Annotations
()
Note
not specified by SLS as a member of AnyRef
9. #### final def eq(arg0: AnyRef): Boolean
Tests whether the argument (`arg0`) is a reference to the receiver object (`this`).
Tests whether the argument (`arg0`) is a reference to the receiver object (`this`).
The `eq` method implements an equivalence relation on non-null instances of `AnyRef`, and has three additional properties:
• It is consistent: for any non-null instances `x` and `y` of type `AnyRef`, multiple invocations of `x.eq(y)` consistently returns `true` or consistently returns `false`.
• For any non-null instance `x` of type `AnyRef`, `x.eq(null)` and `null.eq(x)` returns `false`.
• `null.eq(null)` returns `true`.
When overriding the `equals` or `hashCode` methods, it is important to ensure that their behavior is consistent with reference equality. Therefore, if two objects are references to each other (`o1 eq o2`), they should be equal to each other (`o1 == o2`) and they should hash to the same value (`o1.hashCode == o2.hashCode`).
returns
`true` if the argument is a reference to the receiver object; `false` otherwise.
Definition Classes
AnyRef
10. #### def equals(arg0: Any): Boolean
The equality method for reference types.
The equality method for reference types. Default implementation delegates to `eq`.
See also `equals` in Any.
returns
`true` if the receiver object is equivalent to the argument; `false` otherwise.
Definition Classes
AnyRef → Any
11. #### def equiv(x: Long, y: Long): Boolean
Return true if `x` == `y` in the ordering.
Return true if `x` == `y` in the ordering.
Definition Classes
OrderingPartialOrderingEquiv
12. #### def finalize(): Unit
Called by the garbage collector on the receiver object when there are no more references to the object.
Called by the garbage collector on the receiver object when there are no more references to the object.
The details of when and if the `finalize` method is invoked, as well as the interaction between `finalize` and non-local returns and exceptions, are all platform dependent.
Attributes
protected[lang]
Definition Classes
AnyRef
Annotations
()
Note
not specified by SLS as a member of AnyRef
13. #### def fromInt(x: Int): Long
Definition Classes
LongIsIntegralNumeric
14. #### final def getClass(): Class[_]
A representation that corresponds to the dynamic class of the receiver object.
A representation that corresponds to the dynamic class of the receiver object.
The nature of the representation is platform dependent.
returns
a representation that corresponds to the dynamic class of the receiver object.
Definition Classes
AnyRef → Any
Note
not specified by SLS as a member of AnyRef
15. #### def gt(x: Long, y: Long): Boolean
Return true if `x` > `y` in the ordering.
Return true if `x` > `y` in the ordering.
Definition Classes
OrderingPartialOrdering
16. #### def gteq(x: Long, y: Long): Boolean
Return true if `x` >= `y` in the ordering.
Return true if `x` >= `y` in the ordering.
Definition Classes
OrderingPartialOrdering
17. #### def hashCode(): Int
The hashCode method for reference types.
The hashCode method for reference types. See hashCode in Any.
returns
the hash code value for this object.
Definition Classes
AnyRef → Any
18. #### final def isInstanceOf[T0]: Boolean
Test whether the dynamic type of the receiver object is `T0`.
Test whether the dynamic type of the receiver object is `T0`.
Note that the result of the test is modulo Scala's erasure semantics. Therefore the expression `1.isInstanceOf[String]` will return `false`, while the expression `List(1).isInstanceOf[List[String]]` will return `true`. In the latter example, because the type argument is erased as part of compilation it is not possible to check whether the contents of the list are of the specified type.
returns
`true` if the receiver object is an instance of erasure of type `T0`; `false` otherwise.
Definition Classes
Any
19. #### def lt(x: Long, y: Long): Boolean
Return true if `x` < `y` in the ordering.
Return true if `x` < `y` in the ordering.
Definition Classes
OrderingPartialOrdering
20. #### def lteq(x: Long, y: Long): Boolean
Return true if `x` <= `y` in the ordering.
Return true if `x` <= `y` in the ordering.
Definition Classes
OrderingPartialOrdering
21. #### def max(x: Long, y: Long): Long
Return `x` if `x` >= `y`, otherwise `y`.
Return `x` if `x` >= `y`, otherwise `y`.
Definition Classes
Ordering
22. #### def min(x: Long, y: Long): Long
Return `x` if `x` <= `y`, otherwise `y`.
Return `x` if `x` <= `y`, otherwise `y`.
Definition Classes
Ordering
23. #### def minus(x: Long, y: Long): Long
Definition Classes
LongIsIntegralNumeric
24. #### implicit def mkNumericOps(lhs: Long): IntegralOps
Definition Classes
IntegralNumeric
25. #### implicit def mkOrderingOps(lhs: Long): Ops
This implicit method augments `T` with the comparison operators defined in `scala.math.Ordering.Ops`.
This implicit method augments `T` with the comparison operators defined in `scala.math.Ordering.Ops`.
Definition Classes
Ordering
26. #### final def ne(arg0: AnyRef): Boolean
Equivalent to `!(this eq that)`.
Equivalent to `!(this eq that)`.
returns
`true` if the argument is not a reference to the receiver object; `false` otherwise.
Definition Classes
AnyRef
27. #### def negate(x: Long): Long
Definition Classes
LongIsIntegralNumeric
28. #### final def notify(): Unit
Wakes up a single thread that is waiting on the receiver object's monitor.
Wakes up a single thread that is waiting on the receiver object's monitor.
Definition Classes
AnyRef
Note
not specified by SLS as a member of AnyRef
29. #### final def notifyAll(): Unit
Wakes up all threads that are waiting on the receiver object's monitor.
Wakes up all threads that are waiting on the receiver object's monitor.
Definition Classes
AnyRef
Note
not specified by SLS as a member of AnyRef
30. #### def on[U](f: (U) ⇒ Long): Ordering[U]
Given f, a function from U into T, creates an Ordering[U] whose compare function is equivalent to:
Given f, a function from U into T, creates an Ordering[U] whose compare function is equivalent to:
```def compare(x:U, y:U) = Ordering[T].compare(f(x), f(y))
```
Definition Classes
Ordering
31. #### def one: Long
Definition Classes
Numeric
32. #### def plus(x: Long, y: Long): Long
Definition Classes
LongIsIntegralNumeric
33. #### def quot(x: Long, y: Long): Long
Definition Classes
LongIsIntegralIntegral
34. #### def rem(x: Long, y: Long): Long
Definition Classes
LongIsIntegralIntegral
35. #### def reverse: Ordering[Long]
Return the opposite ordering of this one.
Return the opposite ordering of this one.
Definition Classes
OrderingPartialOrdering
36. #### def signum(x: Long): Int
Definition Classes
Numeric
37. #### final def synchronized[T0](arg0: ⇒ T0): T0
Definition Classes
AnyRef
38. #### def times(x: Long, y: Long): Long
Definition Classes
LongIsIntegralNumeric
39. #### def toDouble(x: Long): Double
Definition Classes
LongIsIntegralNumeric
40. #### def toFloat(x: Long): Float
Definition Classes
LongIsIntegralNumeric
41. #### def toInt(x: Long): Int
Definition Classes
LongIsIntegralNumeric
42. #### def toLong(x: Long): Long
Definition Classes
LongIsIntegralNumeric
43. #### def toString(): String
Creates a String representation of this object.
Creates a String representation of this object. The default representation is platform dependent. On the java platform it is the concatenation of the class name, "@", and the object's hashcode in hexadecimal.
returns
a String representation of the object.
Definition Classes
AnyRef → Any
44. #### def tryCompare(x: Long, y: Long): Some[Int]
Returns whether a comparison between `x` and `y` is defined, and if so the result of `compare(x, y)`.
Returns whether a comparison between `x` and `y` is defined, and if so the result of `compare(x, y)`.
Definition Classes
OrderingPartialOrdering
45. #### final def wait(): Unit
Definition Classes
AnyRef
Annotations
()
46. #### final def wait(arg0: Long, arg1: Int): Unit
Definition Classes
AnyRef
Annotations
()
47. #### final def wait(arg0: Long): Unit
Definition Classes
AnyRef
Annotations
()
48. #### def zero: Long
Definition Classes
Numeric | 2,795 | 11,430 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2021-25 | latest | en | 0.588383 |
https://scribesoftimbuktu.com/solve-for-sinx90-49-8%C3%B74820-2/ | 1,670,301,089,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446711069.79/warc/CC-MAIN-20221206024911-20221206054911-00458.warc.gz | 531,144,297 | 14,880 | # Solve for ? sin(x)=(90.4*9.8)÷4820
sin(x)=90.4⋅9.8÷4820
Take the inverse sine of both sides of the equation to extract x from inside the sine.
x=arcsin(0.18380082)
Evaluate arcsin(0.18380082).
x=0.18485176
The sine function is positive in the first and second quadrants. To find the second solution, subtract the reference angle from π to find the solution in the second quadrant.
x=(3.14159265)-0.18485176
Simplify the expression to find the second solution.
Remove the parentheses around the expression 3.14159265.
x=3.14159265-0.18485176
Subtract 0.18485176 from 3.14159265.
x=2.95674088
x=2.95674088
Find the period of sin(x).
The period of the function can be calculated using 2π|b|.
2π|b|
Replace b with 1 in the formula for period.
2π|1|
The absolute value is the distance between a number and zero. The distance between 0 and 1 is 1.
2π1
Divide 2π by 1.
The period of the sin(x) function is 2π so values will repeat every 2π radians in both directions.
x=0.18485176+2πn,2.95674088+2πn, for any integer n
Solve for ? sin(x)=(90.4*9.8)÷4820
### Solving MATH problems
We can solve all math problems. Get help on the web or with our math app
Scroll to top | 382 | 1,165 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.96875 | 4 | CC-MAIN-2022-49 | latest | en | 0.750441 |
https://www.gla.ac.uk/coursecatalogue/course/?code=STATS4047 | 1,713,487,205,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817249.26/warc/CC-MAIN-20240418222029-20240419012029-00588.warc.gz | 715,520,893 | 8,173 | ## Principles of Probability and Statistics STATS4047
• School: School of Mathematics and Statistics
• Credits: 10
• Level: Level 4 (SCQF level 10)
• Typically Offered: Semester 1
• Available to Visiting Students: Yes
### Short Description
This course establishes crucial concepts and asymptotic results that are widely relied upon in probability and statistics. These include convergence in distribution and the Central Limit Theorem for probability, and optimal properties of estimators, particularly maximum-likelihood estimators, in statistics.
### Timetable
20 lectures (2 each week)
5 tutorials (fortnightly throughout the semester)
### Requirements of Entry
The normal requirement is that students should have been admitted to an Honours- or Master's-level programme in Statistics.
### Excluded Courses
STATS5022 Principles of Probability and Statistics (Level M)
### Assessment
90-minute, end-of-course examination (100%)
Main Assessment In: April/May
Are reassessment opportunities available for all summative assessments? Not applicable
Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below.
### Course Aims
The aims of this course are:
■ to introduce and discuss the concept of convergence in the theory of random variables;
■ to establish the laws of large numbers and the Central Limit Theorem;
■ to discuss optimal properties of point estimators;
■ to establish the large-sample properties of maximum-likelihood estimation.
■ to introduce students to the EM algorithm
### Intended Learning Outcomes of Course
By the end of this course students will be able to:
■ describe and contrast convergence in probability, convergence in distribution, convergence in quadratic mean and almost sure convergence;
■ state, use and prove various probabilistic inequalities;
■ state, prove and use the Weak Law of Large Numbers and the Central Limit Theorem;
■ state and discuss optimal properties of point estimators;
■ state, prove and use the Rao-Blackwell Theorem and the Cramer-Rao lower bound;
■ state, prove and apply general asymptotic properties of maximum-likelihood estimators;
■ construct an EM algorithm for various missing data problems.
.
### Minimum Requirement for Award of Credits
Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment. | 594 | 2,956 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2024-18 | latest | en | 0.868417 |
http://mathhelpforum.com/calculus/91429-vector-field.html | 1,521,395,943,000,000,000 | text/html | crawl-data/CC-MAIN-2018-13/segments/1521257645830.10/warc/CC-MAIN-20180318165408-20180318185408-00207.warc.gz | 205,237,733 | 9,416 | 1. ## Vector Field
There is a vector field G in $\displaystyle R^3$ such that: ?
$\displaystyle curl G = xy^2i+yz^2j+zx^2k$
2. The divergence of the curl of any vector field is 0. So find div(curl G) and see if it's zero or not. Do you know how to find the divergence of a vector field?
3. Originally Posted by Random Variable
The divergence of the curl of any vector field is 0. So find div(curl G) and see if it's zero or not. Do you know how to find the divergence of a vector field?
Yes thank you. Not exist the vector field to this curl | 150 | 545 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2018-13 | latest | en | 0.907784 |
https://tefltastic.wordpress.com/worksheets/headway/hway-pre-u14/u11-to-14-presentations/ | 1,685,456,622,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224645810.57/warc/CC-MAIN-20230530131531-20230530161531-00613.warc.gz | 617,388,731 | 92,612 | # New Headway Pre-Int Unit 11 to 14 Revision Presentations Rotating Board game
Listen to your partner and let them speak for up to 3 minutes. Give them a score by taking away the amount of silence from how long they talked, and they can then move on this many squares:
30 seconds = 1 square, 1 minute = 2 squares etc. up to 3 minutes = 6 squares | 90 | 347 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2023-23 | latest | en | 0.933329 |
https://www.coursehero.com/file/33459034/Rotational-Motiondocx/ | 1,632,362,075,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057416.67/warc/CC-MAIN-20210923013955-20210923043955-00072.warc.gz | 760,530,426 | 47,510 | # Rotational Motion.docx - Objective The object of this...
• Lab Report
• 3
• 100% (2) 2 out of 2 people found this document helpful
This preview shows page 1 - 2 out of 3 pages.
Objective:The object of this experiment was to determine the moment of inertia (also known as rotational inertia) of a free-rotational system by applying the known torque and measuring the resulting angular acceleration of the system.Idisk=(=1/2MR^2)= 10.2 x 10^-3Angular Acceleration = 0.055 rad/sFrictional torque= (10.2 x 10^-3)(-0.055)= -5.61 x 10^-4 N*mApplied Mass (kg)Angular Acceleration (rad/s^2)Applied Torque (N)Radius Spindle (N*m)0.0550.010.540.0270.0350.370.330.0170.040.420.390.0200.0450.470.460.0230.0500.560.550.0280.0600.630.590.0300.06050.670.590.0300.08050.910.790.0400.10051.270.980.0500.30051.482.900.150Radius of Spindle (m)Mass of Platter (kg)Diameter of Platter (m)Radius of Platter (m)0.05 1.417 0.240.12Procedure: 1.Measure and record in Table 1 the mass(M) of the platter, its diameter (D), and the radius of the central spindle (r)2.Go on the computer and use the software Rotational Motion to record your data3.Set the platter rotating and with the mouse button click on the “photogate test” to start. Make sure everything is working properly with photogate by running a few tests. | 416 | 1,293 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.078125 | 3 | CC-MAIN-2021-39 | latest | en | 0.822958 |
https://ck5.com/forums/threads/drive-line-length.53699/ | 1,516,216,167,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084886952.14/warc/CC-MAIN-20180117173312-20180117193312-00525.warc.gz | 664,840,845 | 13,523 | # Drive line length?
Discussion in '1973-1991 K5 Blazer | Truck | Suburban' started by Rolled, Oct 26, 2002.
1. ### Rolled1/2 ton status
Joined:
Jun 16, 2002
Posts:
683
0
Location:
Here's what I have:
87K5
305
465
208
4" lift
35" tires
12 bolt rear
I just swapped out a 10 bolt for a 12 bolt and now I am wondering if my drive shaft is long enough. The 10 bolt sat foreward about 1.5 inches closer than the 12 bolt. I think the drve line is stock so it might have been too short for the 10 bolt as well. I am going to get a Suburban driveline and have it cut down to the correct length.
Here's my question:
What formula should I use to determine the correct length of the drive line?
Joined:
Feb 18, 2000
Posts:
789
0
Location:
MO
Hey bud,
When getting a new rear shaft you can use the old pathagoreon thoerm...or you can just stick your too short line in with about 1.5 inchs of slip yoke showing and measure how much longer that shaft has to be to come in contact with the yoke. (make sure you swap that 10 bolt yoke onto your 12 bolt to make ujoint tasks easier.)
For the P. Theorm..take (the height of the slip yoke center minus the height of the rear end yoke)squared + (parallel to the ground distance between the two yoke centers)squared = length of new shaft squared .....take the sqare root of your last answer for final calculation.
The front shaft should be fine for a 4 inch.
Blake
3. ### Rolled1/2 ton status
Joined:
Jun 16, 2002
Posts:
683
0
Location:
So I need to put all but 1.5 inches of the slip yoke in the tranny? So if my slip yoke was 6.5 inches I would put it in 5 inches and then measure the missing distance to the rear?
Are you sure 1.5 inches is not to far in? If I have a heavy load in the back will the slip yoke bottom out?
Also, I tried to replace the 10 bolt yoke with the 12 bolt and they are different. The 10 has bigger u-joints and the collar around the spline is bigger so it would not even physically fit. I would have thought the 12 bolt would have the bigger parts but its does not. The brakes were also inferior on the 12 bolt. The 12 is out of a 78 (I think) and the 10 is from an 87. I guess GM upgraded over the years.
4. ### tRustyK5Big meanieStaff MemberSuper ModeratorGMOTM WinnerAuthor
Joined:
Jul 23, 2000
Posts:
37,293
2,910
Location:
E-town baby!
Build(s):
1
The front shaft should be fine for a 4 inch.
[/ QUOTE ]
We just lifted a buddy's 89 4" and the front shaft needed to be lengthened...I'm assuming it was a little on the short side at stock height.
Rene
Joined:
Feb 18, 2000
Posts:
789
0
Location:
MO
Yeah, I would like to retract my statement of 1.5 inchs and now say about 2.25 inchs...my mind was playing tricks on me so i looked at a ruler.
Remember all drive shaft length measurements are from the centers of the yokes.
I heard that you have to change out that seal on the pinion to get a 10 bolt yoke to fit a 12bolt. I'm planning on doing this sometime so i could post part numbers on it for future swappers.
My front shaft is ok on length for my 6inch lift but the c/v joint is rubbing the tranny crossmember sometimes. If was an extreme wheeler i would get a longer one built.
Blake
6. ### Rolled1/2 ton status
Joined:
Jun 16, 2002
Posts:
683
0
Location:
I just dropped it off at the driveshaft shop. I jusrt marked where it was and they said they would figuire it out for me. I'll pick it up today and post what what the measurement is.
For anybody reading who is doing something similar -
On my 87 with a 4 inch lift and a 1978 12 bolt, the slip yoke was only bitting 7/8 of an inch. With the 10 bolt it was bitting about 2 3/8 inch. The slip yoke is 6 inches.
7. ### Chaz88K51/2 ton status
Joined:
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Posts:
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0
Location:
Stockton/Lodi CA
ok what ya do...mesure from one of the ears on the yoke on the axle to the seal on the transfer case...and tell the driveline shop that demention and they should be able to build a shaft as long as they know that demention..
8. ### Rolled1/2 ton status
Joined:
Jun 16, 2002
Posts:
683
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Location:
FYI for anybody doing the same thing.
The old shaft which was not original was 29.5" from center of yokes and the new one is 32.5". The slip joint goes in the transfer case 4.25" out of 6".
The shop charged me \$65 for the cut and weld and \$30 for a new spicer 1350 yoke and 2 u-joints. Total bill with tax was \$102.70.
9. ### imiceman441 ton statusPremium Member
Joined:
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Posts:
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108
Location:
Sacramento, CA
Build(s):
1
I changed the yoke from a 12 bolt to a 10 bolt, the seal is the only thing you need to change so it fits. The spline count is the same.
I don't remember the part numbers that was 10 years ago.
Joined:
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https://myminimaths.co.uk/category/year-4-mini-maths/ | 1,726,009,879,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651323.1/warc/CC-MAIN-20240910224659-20240911014659-00037.warc.gz | 379,153,173 | 25,665 | Tuesday, September 10, 2024
Teachers | Pupils | Parents
# Year 4 maths worksheets
Year 4 maths continues the learning and development of learners in Year 3. The daily Year 4 maths worksheets offer 1000’s of free resources for teachers, pupils and parents.
A wide variety of Year 4 maths questions cover all areas of the maths curriculum. The free daily tasks build knowledge, understanding, application and confidence before the pupil moves forward to Year 5.
New skills with Number are introduced in Year 4 building on the learning from Year 3 maths. As well as extending understanding with addition worksheets and subtraction worksheets using columns: units, tens, hundreds. Written multiplication and short division are introduced allowing pupils to use the bus stop method for short division. Links between the four operations are encouraged introducing the inverse operation. Place value is supported with finding 1000 more or less than a value and identifying the value of digits in 4 digit numbers using thousands hundreds tens and units. Year 4 rounding allows pupils to develop their understanding of rounding 4 digit numbers in preparation for Year 5 rounding.
Reading and drawing Year 4 bar charts allow pupils to present data together with introducing line graphs to represent discrete data and continuous data.
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The daily Year 4 maths questions allow pupils to practice their skills and develop their understanding each day allowing for daily intervention in support of any misunderstandings. This timely intervention supports the learner’s understanding and application building confidence across all areas of the Year 4 curriculum.
Year 4 starters, home learning packs, iQ mastery questions and supporting YouTube video tutorials provide the full package for a successful learner.
Year 4 maths worksheets
## Year 4 – Week 51 – Solve problems involving measurement – Friday
Year 4 maths worksheets
## Year 4 – Week 51 – Solve problems involving measurement – Thursday
Year 4 maths worksheets
## Year 4 – Week 51 – Solve problems involving measurement – Wednesday
Year 4 maths worksheets
error: | 453 | 2,370 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2024-38 | latest | en | 0.908502 |
https://ects.gsu.edu.tr/en/program/coursedetails/4127 | 1,597,269,802,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738944.95/warc/CC-MAIN-20200812200445-20200812230445-00560.warc.gz | 300,506,764 | 9,455 | ## Welfare Economics(ECON463)
Course Code Course Name Semester Theory Practice Lab Credit ECTS
ECON463 Welfare Economics 6 3 0 0 3 4
Language of Instruction French Course Type Elective Course Level Bachelor Degree Course Instructor(s) Sahir KARAKAYA skarakaya@gsu.edu.tr (Email) Assistant Objective Static optimization is one of the main tools of the theory and practice of economics. This course aims to provide a quite rigorous introductory knowledge of this tool, and make use of it in simple equilibrium models. And in the same time to utilize these models to master the tool. Content This course aims to teach nonlinear programming and to deal with small equilibrium models, with two goods, two cosumers, two producers and two factors, as an application of this mathematical tool. The walrasian exchange model, the Lindahlian exchange model, and an exchange externality model and their corresponding pareto optimums are treated. Then, the walrasian production model is studied, and two simple models of general equilibrum are established. Course Learning Outcomes 1- To learn nonlinear programming,2- study the static general equilibrium with differentible functions,3- in an axiomatic way. Teaching and Learning Methods References Sydsaeter, Hammond, Mathematics for economic analysis.Sydsaeter, Hammond, Further mathematics for economic analysis.Simon, Blume, Mathematical economics.Silberberg, The structure of economics, a mathematical analysis.
###### Theory Topics
Week Weekly Contents
1 Concavity, quasiconcavity. Optimization with equality constraints.
2 The notion of gradient. Optimization with inequality constraints.
3 Consumer equilibrium as an application of nonlinear programming.
4 Walrasian exchange equilibrium. Walras identity, Walras law.
5 Pareto optimum.
6 A simple public economy model.
7 Public good, private good. Samuelson condition. Quasilinear functions.
8 Allocation and distribution problem.
9 Exchange equilibrium with public good and private good. Lindahl equilibrium. « Lindahl identity, « Lindahl law ».
10 Pareto optimum for Lindahl equilibrium.
11 Externality as a public good.
12 Pareto optimum for externality model.
13 Walras equilibrium for production.
14 General equilibrium.
###### Practice Topics
Week Weekly Contents
Number Contribution
Contribution of in-term studies to overall grade 2 50
Contribution of final exam to overall grade 1 50
Toplam 3 100
###### In-Term Studies
Number Contribution
Assignments 0 0
Presentation 0 0
Midterm Examinations (including preparation) 1 42
Project 0 0
Laboratory 0 0
Other Applications 0 0
Quiz 1 14
Term Paper/ Project 0 0
Portfolio Study 0 0
Reports 0 0
Learning Diary 0 0
Thesis/ Project 0 0
Seminar 0 0
Other 0 0
Toplam 2 56
No Program Learning Outcomes Contribution
1 2 3 4 5
1 Demonstrate a basic knowledge of different economic theories and main discussions driving current theoretical approaches
2 Demonstrate ability to use basic qualitative and quantitative methods to asses different economic questions of applied fields
3 Show a sound understanding of current economic discussions and problems
4 Have an effective and clear communication in written and oral formats in different public and professional contexts.
5 Demonstrate basic knowledge of the world economic history and a sound knowledge of the Turkish economic history
7 Demonstrate knowledge of standard quantitative techniques and empirical models used in economics
8 Show ability to apply basic economic theory to an applied topic
9 Show a basic understanding of analytical methods, both theory- and model-based
10 Show ability to use economic concepts to discuss current economic issues
11 Reason logically and work analytically
12 Show awareness on social aspects of the economics in different applied and theoretical fields
13 Identify appropriate economic models to analyse problems
16 Show understanding of basic statistical and econometric concepts and ability to apply basic concepts to own empirical work
17 Demonstrate a sound knowledge of the current economic issues in Turkey and a general knowledge of the issues in the world economy
Class Hours 0 42 0
Working Hours out of Class 0 42 0
Assignments 0 0 0
Presentation 0 0 0
Midterm Examinations (including preparation) 0 21 0
Project 0 0 0
Laboratory 0 0 0
Other Applications 0 0 0
Final Examinations (including preparation) 0 42 0
Quiz 0 0 0
Term Paper/ Project 0 0 0
Portfolio Study 0 0 0
Reports 0 0 0
Learning Diary 0 0 0
Thesis/ Project 0 0 0
Seminar 0 0 0
Other 0 0 0 | 1,033 | 4,498 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2020-34 | latest | en | 0.818416 |
https://btechgeeks.com/java-program-to-convert-kilogram-to-gram-and-gram-to-kilogram/ | 1,695,650,831,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233508977.50/warc/CC-MAIN-20230925115505-20230925145505-00493.warc.gz | 173,452,689 | 12,699 | # Java Program to Convert Kilogram to Gram and Gram to Kilogram
In the previous article, we have discussed about Java Program to Convert Foot to Yard and Yard to Foot
In this article we will see how to convert Kilogram to Gram and Gram to Kilogram by using Java programming language.
## Java Program to Convert Kilogram to Gram and Gram to Kilogram
Before jumping into the program let’s know the relationship between Kilogram and Gram and how we can convert Kilogram to Gram (Kg To Gram)
and (Gram To Kg or Gm To Kg) Gram To Kilogram vice versa.
Generally Kilogram and Gram are used as unit in case of mass/weight measurement.
1 Kilogram = 1000 Gram
1 Gram = 0.001 Kilogram
Formula to convert Kilogram to Gram.
Gram = Kilogram * 1000
Formula to convert Gram to Kilogram.
Kilogram = Gram * 0.001 (OR) Gram / 1000
Let’s see different ways to convert Kilogram to Gram and Gram to Kilogram.
### Method-1: Java Program to Convert Kilogram to Gram and Gram to Kilogram By Using Static Input Value
Approach:
• Declare Kilogram and Gram value.
• Then convert Kilogram to Gram and Gram to Kilogram by using the formula.
• Print result.
Program:
public class Main
{
public static void main(String args[])
{
//value of square kilogram declared
double kilogram = 1;
//value of gram declared
double gram = 1;
//converting kilogram to gram
double gm = kilogram * 1000;
//converting gram to kilogram
double kg = gram * 0.001;
//printing result
System.out.println("Value of "+kilogram+" kilogram in gram: "+ gm);
System.out.println("Value of "+gram+" gram in kilogram: "+ kg);
}
}
Output:
Value of 1.0 kilogram in gram: 1000.0
Value of 1.0 gram in kilogram: 0.001
### Method-2: Java Program to Convert Kilogram to Gram and Gram to Kilogram By Using User Input Value
Approach:
• Take user input of Kilogram and Gram value.
• Then convert Kilogram to Gram and Gram to Kilogram by using the formula.
• Print result.
Program:
import java.util.*;
public class Main
{
public static void main(String args[])
{
//Scanner class object created
Scanner sc=new Scanner(System.in);
//Taking the value input of double variable kilogram
System.out.println("Enter value of kilogram: ");
double kilogram = sc.nextDouble();
//Taking the value input of double variable gram
System.out.println("Enter value of gram: ");
double gram = sc.nextDouble();
//converting kilogram to gram
double gm = kilogram * 1000;
//converting gram to kilogram
double kg = gram / 1000;
//printing result
System.out.println("Value of "+kilogram+" kilogram in gram: "+ gm);
System.out.println("Value of "+gram+" gram in kilogram: "+ kg);
}
}
Output:
Enter value of kilogram:
4
Enter value of gram:
750
Value of 4.0 kilogram in gram: 4000.0
Value of 750.0 gram in kilogram: 0.75
### Method-3: Java Program to Convert Kilogram to Gram and Gram to Kilogram By Using User Defined Method
Approach:
• Take user input of Kilogram and Gram value.
• Call a user defined method by passing Kilogram and Gram value as parameter.
• Inside method convert Kilogram to Gram and Gram to Kilogram by using the formula.
• Print result.
Program:
import java.util.*;
public class Main
{
public static void main(String args[])
{
//Scanner class object created
Scanner sc=new Scanner(System.in);
//Taking the value input of double variable kilogram
System.out.println("Enter value of kilogram: ");
double kilogram = sc.nextDouble();
//Taking the value input of double variable gram
System.out.println("Enter value of gram: ");
double gram = sc.nextDouble();
//calling user defined method convert()
convert(kilogram, gram);
}
//convert() method to convert kilogram to gram and vice versa
public static void convert(double kilogram, double gram)
{
//converting kilogram to gram
double gm = kilogram * 1000;
//converting gram to kilogram
double kg = gram / 1000;
//printing result
System.out.println("Value of "+kilogram+" kilogram in gram: "+ gm);
System.out.println("Value of "+gram+" gram in kilogram: "+ kg);
}
}
Output:
Enter value of kilogram:
12.5
Enter value of gram:
1700
Value of 12.5 kilogram in gram: 12500.0
Value of 1700.0 gram in kilogram: 1.7
Beginners and experienced programmers can rely on these Best Java Programs Examples and code various basic and complex logics in the Java programming language with ease.
If you have succeeded answering these questions you can decide yourself you learn the concept very well.
1. Write A Program To Convert Kg To G In Java
2. How To Convert Gram To Kilogram
3. How Many Grams In A Kilogram
4. How To Convert Kilograms To Grams
5. Convert Kilogram To Grams
6. Convert Kilograms To Grams
7. Write A Program To Convert Grams Into Kilograms
8. Convert Kg Into Gram
9. Convert Kg To Grams
10. How To Convert Grams To Kilograms In Excel
11. Convert Gram To Kilogram
12. Kilogram Na Gram
13. Kilogram To Gram Formula
14. Gram In Kg
15. Van Gram Naar Kg
16. Gram Naar Kilogram
17. Kg To Gr
18. Van Gram Naar Kg
19. 1000 Gram To Kg
Related Java Programs: | 1,265 | 4,960 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.15625 | 3 | CC-MAIN-2023-40 | latest | en | 0.712637 |
https://quant.fish/wiki/calculating-value-at-risk-using-historical-simulation/ | 1,721,621,797,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517823.95/warc/CC-MAIN-20240722033934-20240722063934-00683.warc.gz | 400,319,771 | 21,579 | Quantitative Analysis · Data Science · Machine Learning
# Calculating Value-at-Risk using Historical Simulation
The Historical Simulation Method is a straightforward approach to calculate Value at Risk (VaR) by using historical market data to simulate the potential future outcomes of a portfolio. Here’s a step-by-step guide on how the Historical Simulation Method is typically calculated:
## 1. Select a Historical Data Window
Choose a historical time window for which you have relevant market data. The length of the window depends on the desired time horizon for VaR (e.g., daily VaR, weekly VaR). A common choice is to use at least a year of historical data.
## 2. Collect Historical Returns
Calculate the historical returns for each asset in the portfolio over the selected time window. The return for each period is usually calculated as the percentage change in the asset’s price from one day to the next.
The formula for daily return (percentage change) is:
``` # calculate return using daily bars daily_return = (current_close - previous_close / previous_close) * 100 ```
## 3. Build Portfolio Returns
Combine the individual asset returns to create the historical returns for the entire portfolio. The portfolio return for each period is the weighted sum of the individual asset returns based on the portfolio’s asset allocation.
## 4. Order the Historical Returns
Order the historical portfolio returns from worst to best, representing the returns in ascending order.
## 5. Identify VaR Percentile
Determine the VaR percentile corresponding to the desired confidence level. For example, if you want to calculate VaR at the 95% confidence level, you would be interested in the historical return at the 5th percentile of the ordered returns.
## 6. Calculate VaR
The VaR is the historical return at the chosen percentile. It represents the potential loss at the specified confidence level over the selected time horizon.
VaR = Historical Return at the Xth Percentile
### Example:
Let’s illustrate the process with a simplified example. Consider a portfolio with two assets, A and B, and a historical data window of 250 days.
1. Calculate daily returns for each asset using the formula mentioned earlier.
2. Combine the returns to obtain portfolio returns for each day.
3. Order the historical portfolio returns from worst to best.
4. If you want to calculate VaR at the 95% confidence level, identify the return at the 5th percentile.
5. The return at the 5th percentile is your VaR.
It’s important to note that the Historical Simulation Method provides a non-parametric estimate of VaR, relying on observed historical data rather than assuming a specific distribution for returns. While it captures historical market behavior, it may not fully account for future market dynamics, and the accuracy of VaR estimates depends on the stability of market conditions over the historical period. | 583 | 2,917 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2024-30 | latest | en | 0.786867 |
https://www.coursehero.com/file/5908821/solution15/ | 1,516,230,623,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084886979.9/warc/CC-MAIN-20180117212700-20180117232700-00763.warc.gz | 882,054,286 | 24,549 | solution15
# solution15 - fullwood(tf5349 – Homework Conservation of...
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Unformatted text preview: fullwood (tf5349) – Homework Conservation of Energy – Catala – (49033) 1 This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A 49 kg pole vaulter running at 10 m / s vaults over the bar. Her speed when she is above the bar is 0 . 7 m / s. The acceleration of gravity is 9 . 8 m / s 2 . Find her altitude as she crosses the bar. Neglect air resistance, as well as any energy absorbed by the pole. Correct answer: 5 . 07704 m. Explanation: Given : m = 49 kg , v i = 10 m / s , and v f = 0 . 7 m / s . Applying conservation of mechanical energy, 1 2 mv 2 i = mg h f + 1 2 mv 2 f v 2 i = 2 g h f + v 2 f h f = v 2 i − v 2 f 2 g = (10 m / s) 2 − (0 . 7 m / s) 2 2 (9 . 8 m / s 2 ) = 5 . 07704 m . 002 10.0 points The ball launcher in a pinball machine has a spring that has a force constant of 1 . 47 N / cm. The surface on which the ball moves is in- clined 12 . 4 ◦ with respect to the horizontal. The acceleration of gravity is 9 . 8 m / s 2 . 12 . 4 ◦ 1 . 47 N / cm 1 . 47 N / cm 1 . 47 N / cm 1 . 47 N / cm 1 . 47 N / cm 1 . 47 N / cm 1 . 47 N / cm 1 . 47 N / cm v = 0 v 4 . 21 cm 12 . 4 ◦ If the spring is initially compressed 4 . 21 cm, find the launching speed of a 0 . 179 kg ball when the plunger is released. Friction and the mass of the plunger are negligible. Correct answer: 1 . 13065 m / s. Explanation: k v = 0 v Δ x θ PE = 0 h Given : k = 1 . 47 N / cm , m = 0 . 179 kg , θ = 12 . 4 ◦ , and Δ x = 4 . 21 cm . Consider U g = 0 at the point of compres- sion. For the compression Δ x of the spring, the ball rises h = Δ x sin θ while the spring returns to its equilibrium position. The initial energy is ( K + U g + U s ) i = 1 2 k (Δ x ) 2 and the final energy is ( K + U g + U s ) f = 1 2 mv 2 f + mg h. Equating the energies, 1 2 mv 2 f + mg Δ x sin θ = 1 2 k (Δ x ) 2 mv 2 f = k (Δ x ) 2 − 2 mg Δ x sin θ v 2 f = k (Δ x ) 2 m − 2 g Δ x sin θ fullwood (tf5349) – Homework Conservation of Energy – Catala – (49033) 2 = (1 . 47 N / cm) (4 . 21 cm) 2 . 179 kg parenleftbigg 1 m 100 cm parenrightbigg − (2) ( 9 . 8 m / s 2 ) (4 . 21 cm) (sin12 . 4 ◦ ) · parenleftbigg 1 m 100 cm parenrightbigg = 1 . 27836 m 2 / s 2 . Thus v f = radicalBig 1 . 27836 m 2 / s 2 = 1 . 13065 m / s . 003 (part 1 of 2) 10.0 points A 0 . 48 kg bead slides on a curved wire, start- ing from rest at point A as shown in the figure. The acceleration of gravity is 9 . 8 m / s 2 . A 6.1 m B 1.66 m C If the wire is frictionless, find the speed of the bead at B. Correct answer: 10 . 9343 m / s. Explanation: Given : m = 0 . 48 kg and h A = 6 . 1 m . Choose the zero level for potential energy at the level of B. Between A and B K A + U A = K B + U B 0 + mg h A = 1 2 mv 2 + 0 v = radicalbig 2 g h A = radicalBig 2(9 . 8 m / s 2 )(6 . 1 m) = 10 . 9343 m / s 004 (part 2 of 2) 10.0 points Find the speed of the bead at C....
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Ask a homework question - tutors are online | 1,251 | 3,515 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.671875 | 4 | CC-MAIN-2018-05 | latest | en | 0.804268 |
https://stacks.math.columbia.edu/tag/0GTC | 1,726,527,648,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651714.51/warc/CC-MAIN-20240916212424-20240917002424-00725.warc.gz | 492,401,786 | 6,502 | Lemma 36.36.5. Let $f : X \to Y$ be a surjective finite locally free morphism of schemes. If $X$ has the resolution property, so does $Y$.
Proof. The condition means that $f$ is affine and that $f_*\mathcal{O}_ X$ is a finite locally free $\mathcal{O}_ Y$-module of positive rank. Let $\mathcal{G}$ be a quasi-coherent $\mathcal{O}_ Y$-module of finite type. By assumption there exists a surjection $\mathcal{E} \to f^*\mathcal{G}$ for some finite locally free $\mathcal{O}_ X$-module $\mathcal{E}$. Since $f_*$ is exact on quasi-coherent modules (Cohomology of Schemes, Lemma 30.2.3) we get a surjection
$f_*\mathcal{E} \longrightarrow f_*f^*\mathcal{G} = \mathcal{G} \otimes _{\mathcal{O}_ Y} f_*\mathcal{O}_ X$
Taking duals we get a surjection
$f_*\mathcal{E} \otimes _{\mathcal{O}_ Y} \mathop{\mathcal{H}\! \mathit{om}}\nolimits _{\mathcal{O}_ Y}(f_*\mathcal{O}_ X, \mathcal{O}_ Y) \longrightarrow \mathcal{G}$
Since $f_*\mathcal{E}$ is finite locally free1, we conclude. $\square$
[1] Namely, if $A \to B$ is a finite locally free ring map and $N$ is a finite locally free $B$-module, then $N$ is a finite locally free $A$-module. To see this, first note that $N$ finite locally free over $B$ implies $N$ is flat and finitely presented as a $B$-module, see Algebra, Lemma 10.78.2. Then $N$ is an $A$-module of finite presentation by Algebra, Lemma 10.36.23 and a flat $A$-module by Algebra, Lemma 10.39.4. Then conclude by using Algebra, Lemma 10.78.2 over $A$.
There are also:
• 2 comment(s) on Section 36.36: The resolution property
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View Full Version : Gravity question
04-12-02, 02:34 AM
Could gravity be sort of an accumulated influence of residual electroweak force or residual electromagnetic force? Not sure if that's what it's called. But I believe there is some "left over" from the equilibrium of both EM and EW combinations/matches.
Joeblow93132
04-12-02, 05:53 PM
No one is answering your post because most of the people here believe that gravity is the result of curved space. They freak out if you attempt to give an alternate theory.
"Could gravity be sort of an accumulated influence of residual electroweak force or residual electromagnetic force?"
I'm not very informed about the weak interaction, so I can't say whether it can be responsible for gravity. I can tell you that the electromagnetic force is probably not. As you know, the electromagnetic force has two poles. Opposite poles attract while like poles repel each other. It would be very difficult, if not impossible, to construct the electromagnetic forces in objects in a way that the objects would ONLY attract each other, like in gravity.
Tom
thed
04-12-02, 06:01 PM
Or we could be busy with other things. Never ascribe to conspiracy what can be adequately explained by stupidity, or time pressure! It's mid-night here and I'm watching Sci-Fright as well. Really cheesy vampire film called Count Yorga rises again, or something.
For once, Tom, you are making sense. EM can not explain gravity. Nor can the other forces, weak and strong nuclear force, for the same reasons. Says a lot, doesn't it. Gravity is some how different yet acording to modern thought they are all aspects of some underlying principle or unified force.
James R
04-12-02, 10:02 PM
Tom,
If you'd like to learn about curvature and why your electromagnetic objection to curved space really doesn't work, investigate string theory a little. I highly recommend the book <i>The Elegant Universe</i> by Brian Greene. It doesn't assume any prior knowledge.
04-13-02, 01:37 AM
So, what happens to that residual nuclear force? It doesn't have any attractive effect on other mass?
Joeblow93132
04-13-02, 07:16 AM
If you are referring to the strong interaction, there is a possibility that gravity is ascociated with it.
As you know. the strong interaction works only at very short distances and is very powerful, while gravity works at large distances and is very weak.
If, however, if there are two spheres of gravity, the small sphere which is the about size of the atomic nucleus, and a larger sphere which extends light years, and if the strength of the gravity in the small sphere is much more powerful than the larger sphere, then gravity might actually be responsible for the strong interaction.
Tom
04-13-02, 08:21 AM
That is definitely one thing I do nto understand. How can a powerful force suddenly reduce in power at a given range? Wouldn't it lose power progressively the further out you go? How could it lose power say at range1=1/2, range2=1/4, range3=1/8, then suddenly nothing at all? (Just example figures.) It doesn't make much sense to me, not yet anyway.
Joeblow93132
04-13-02, 09:38 AM
"That is definitely one thing I do nto understand. How can a powerful force suddenly reduce in power at a given range? Wouldn't it lose power progressively the further out you go? How could it lose power say at range1=1/2, range2=1/4, range3=1/8, then suddenly nothing at all? (Just example figures.) It doesn't make much sense to me, not yet anyway."
It is accepted that all forces lose power progressivly as you move further away, just as you indicated. But the power of the strong interaction, whether you associate it with gravity or not, does sharply lose power as you move further away.
Also, you have to consider matter itself. If you consider matter to be a kind of force, then this force drops off suddenly, as well.
Example: Look at a neutron. It has no charge and a negligable gravitational field, but it has a set boundry, and a set radius. This radius might be an indication of a force that drops to zero suddenly, as well.
Tom
Crisp
04-15-02, 05:22 AM
Hi Tom,
Some small remarks:
A neutron does not have a well defined boundary (neither does any particle) because of the quantummechanical wave character involved. You can understand that this complicates things :).
A "sudden drop to zero" is not something scientists like. This would involve a discontinuity in the force (from a certain value immediatelly to zero), and scientists assume that nature works in a "continuous fashion". I believe it was Leibnitz who used the proverb "Natura non facit saltus", nature doesn't make jumps. (Ok, Leibnitz used it in a different context, but nevertheless I think it applies here). In mathematical models physicists use discontinuous examples (eg. the potential barrier) but the little footnotes always (should) say that in real life, the "jumps" are continous.
Bye!
Crisp
04-15-02, 05:47 AM
I recall that name Leibniz. Was he one of the guys who came up with calculus or something?
Neutrino_Albatross
04-17-02, 10:08 PM
Gravity probaly cant be residual strong and weak forces Here's why.
Leptons (electrons, Neutrinos, Muons Taus) are effected by gravity but not strong force. If Gravity is just left over strong force leptons wouldn't interact with it. If its both weak and strong than leptons would feel gravity but weaker than hadrons (protons, neutrons, mesons) which interact with both forces.
Also I think that theorists would have an easier time unifiying gravity with the other forces if it was actually the same force.
SpyFox_the_KMeson
04-18-02, 09:22 AM
Well, if gravity were residual strong and/or weak forces, it would have the same carrier particles, which it does not. And the strong force does not "drop off" at a certain distance, it just becomes very weak very quickly.
thed
04-18-02, 03:30 PM | 1,398 | 5,873 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2013-20 | latest | en | 0.944554 |
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• Notes
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Math 150a: Modern Algebra Homework 3 2.2.13: Prove that every subgroup of a cyclic group is cyclic. Solution: Let H be a subgroup of the cyclic group C n = < x | x n = 1 > . We want to show that H is cyclic. Let k be the first positive integer such that x k is in H . Then...for any y H , y = x m , for some m . Now, using the Euclidean algorithm, we can write m = kq + r , where 0 r < k . And x m = x kq + r x m x kq = x r . Since H is a subgroup, x r = x m ( x m ) q H . But 0 r < k , and k is the least positive integer such that x k is in H . So r must equal 0, and k must divide m . Therefore, H = < x k > (the cyclic group generated by x k ). square 2.3.4: (a) Let b = aba 1 . Prove that b n = ab n a 1 . Solution: Consider b 2 = aba 1 aba 1 = abba 1 = ab 2 a 1 . Using induction on n , assume b n = ab n a 1 and consider b ( n + 1 ) . Then b ( n + 1 ) = b n b = ab n a 1 aba 1 = ab ( n + 1 ) a 1 . square (b) Prove that if aba 1 = b 2 , then a 3 ba 3 = b 8 . Solution: a 3 ba 3 = a 2 ( aba 1 ) a 2 = a 2 b 2 a 2 = a ( aba 1 )( aba 1 ) a 1 = ab 2 b 2 a 1 = ( aba 1 )( aba 1 )( aba 1 )( aba 1 ) = b 2 b 2 b 2 b 2 = b 8 . square 2.3.14: Determine the group of automorphisms of the following groups. Solution: (a) + = ( , +) = In order to be an isomorphism, any automorphism of a cyclic group must send the generator to another generator of the group. There are only two generators of the cyclic group , 1 and 1. So there can only be two automorphisms, either sending 1 mapsto→ 1 or 1 mapsto→ − 1. There is only one group of order 2, but it is also easy to verify that one of these automorphisms is the identity and one has order 2. The identity element of any automorphism group is the identity automorphism. And the map sending 1 mapsto→ − 1, is the automorphism of the integers usually called “negation”.
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• Spring '03
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• Algebra, Cyclic group, xm, B2 B2 B2, S3 D3
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# Passengers must exit airplanes swiftly after accidents,
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Passengers must exit airplanes swiftly after accidents, [#permalink]
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24 Jan 2006, 19:34
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Passengers must exit airplanes swiftly after accidents, since gases released following accidents are toxic to humans and often explode soon after being released. In order to prevent passenger deaths from gas inhalation, safety officials recommend that passengers be provided with smoke hoods that prevent inhalation of the gases.
Which of the following, if true, constitutes the strongest reason not to require implementation of the safety officials’ recommendation?
(A) Test evacuations showed that putting on the smoke hoods added considerably to the overall time it took passengers to leave the cabin.
(B) Some airlines are unwilling to buy the smoke hoods because they consider them to be prohibitively expensive.
(C) Although the smoke hoods protect passengers from the toxic gases, they can do nothing to prevent the gases from igniting.
(D) Some experienced flyers fail to pay attention to the safety instructions given on every commercial flight before takeoff.
(E) In many airplane accidents, passengers who were able to reach emergency exits were overcome by toxic gases before they could exit the airplane.
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24 Jan 2006, 20:29
Going with A here:
"gases released following accidents are toxic to humans and often explode soon after being released"
Shows they don't have much time to get h*ll outta there. Getting blown up is probably a greater health risk than inhaling toxic fumes which forces me to conclude that time is of the essence. => A
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24 Jan 2006, 21:19
My bet is on A.
Also the masks could be so combursome that passengers cannot walk to the exists after wearing it
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24 Jan 2006, 21:34
Why not C guys..
Even after wearing the maskes you cannot prevent the gases from igniting..So what if the passengers are wasting lot of time in that, it would infact be more dangerous as the gases might ignite by then
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24 Jan 2006, 22:01
Hey Andy,
It's not a SC as you mentioned in the subject line.
Brajesh
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24 Jan 2006, 22:08
andy_gr8 wrote:
Why not C guys..
Even after wearing the maskes you cannot prevent the gases from igniting..So what if the passengers are wasting lot of time in that, it would infact be more dangerous as the gases might ignite by then
I was leaning towards "C" initially, but I think I want to go with "A"
Here are my reasons :
Arguments states
- Passengers must leave swiftly
- gases released can be toxic to humans
- gases can explode after release
safety official's proposal - provide smoke hoods to prevent inhalation of toxic gas
official's recommendation of hoods is addressing only one part - preventing inhalation. It was not suggeted to protect from explosion
"C" - says- hoods don't help protect from explosion. But they were never recommended for that purpose
A - If the very act of wearing the hood is going to considerably increase the overall time, then, the passengers are not leaving swiftly. There by risking inhalation and/or explosion.
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24 Jan 2006, 22:15
Tricky one )))A for me
officials recommend that passengers be provided with smoke hoods that prevent inhalation of the gases. But Test evacuations showed that putting on the smoke hoods added considerably to the overall time it took passengers to leave the cabin.
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24 Jan 2006, 22:17
andy_gr8 wrote:
Why not C guys..
Even after wearing the maskes you cannot prevent the gases from igniting..So what if the passengers are wasting lot of time in that, it would infact be more dangerous as the gases might ignite by then
Although the smoke hoods protect passengers from the toxic gases, they can do nothing to prevent the gases from igniting.
I think here argument doesn't talk about ignition of gases thats why it is wrong.
Guys correct me if I'm wrong
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25 Jan 2006, 01:34
My money on A.
Andy, main concern here to get the passangers swiftly out of the cabin after accident. C is not talking about this.
If a passanger leaves the cabin as soon as possible then he will be saved from both inhalation of gases and explosion of gases.
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25 Jan 2006, 07:31
I`ll bet the farm on (A). If the hoods require precious extra minutes (or seconds) to apply, then the death toll from smoke inhalation will inevitably rise. Besides, most people can hold their breath long enough to get near an emergency exit on a commercial jet.
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25 Jan 2006, 10:19
A is better because it says that the gas can explode so it is better for passengers to evacute fast rather than fumble to get the mask right for hours.
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25 Jan 2006, 21:34
Good explanation guys...
OA is A...
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25 Jan 2006, 21:34
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https://phys.libretexts.org/Courses/University_of_California_Davis/UCD%3A_Physics_9HE_-_Modern_Physics/07%3A_Multiple_Particles/7.2%3A_Exclusion_Principle | 1,695,873,531,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510358.68/warc/CC-MAIN-20230928031105-20230928061105-00805.warc.gz | 496,669,173 | 31,248 | # 7.2: Exclusion Principle
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$
## Antisymmetry and Exclusion
An odd thing happens when a two-particle state exhibits negative exchange symmetry and the two particles have the same quantum number(s). Setting $$n_1$$ equal to $$n_2$$ in Equation 7.1.12 gives a two-particle wave function that is exactly zero! Importantly, it is not just zero for some specific values of $$x$$ (like at nodes), but everywhere. From this we conclude that particles with this negative exchange symmetry (fermions) cannot exist together in a common bound state with the same quantum numbers. These states are "excluded" from what is possible, and this is known as the exclusion principle. This is more than a mere curiosity – it has extremely far-reaching consequences. For example, it is commonly pointed out in particle physics circles that all matter is comprised of fermions, and this is necessary, as the exclusion principle prevents the catastrophic collapse of atoms. We will discuss this in the next section. Two bosons (particles that satisfy positive exchange symmetry) do not bring about a zero wave function when they have the same quantum number, so they don't satisfy an exclusion principle.
## Spin
We have not yet discussed spin. This is largely because it was covered rather extensively in Physics 9HC. The time has come to reintroduce this iconic quantum mechanical phenomenon, and put it into the context of the current discussion.
Spin is also known as "intrinsic angular momentum." As we saw for the hydrogen atom, hamiltonians with potentials that have radial symmetry give rise to two quantum numbers ($$l$$ and $$m_l$$), which give a measure of the magnitude of the angular momentum and $$z$$-component of the angular momentum:
$L^2=l\left(l+1\right)\hbar\;,\;\;\;\;\;\;\;\;L_z=m_l\hbar\;,\;\;\;\;\; m_l=0,\;\pm 1,\; \dots,\; \pm l$
This angular momentum comes from the electron's motion relative to the origin (which is why it is called orbital angular momentum). We even wrote the operator for the $$z$$-component of angular momentum in terms of spherical coordinates (Equation 4.4.6).
Spin is also angular momentum, but it doesn't count on any physical motion relative to a reference point. It is just an intrinsic property of the particle. It still behaves like angular momentum – a charged particle with spin has a magnetic moment, it counts in the accounting of angular momentum conservation of a system, and only its magnitude and $$z$$-component can be measured at one time (the uncertainty in the $$x$$ and $$y$$ components still exists).
The important thing about acknowledging that spin is intrinsic for our current discussion is that the intrinsic angular momentum is additional information that needs to be logged by the quantum state. Remember the quantum state knows everything about the particle. So while an electron in a hydrogen atom has orbital angular momentum, it also has spin. This is not accounted-for in the ($$n,l,m_l$$) quantum numbers, so in fact we need to add an additional quantum number into the mix, bringing the full lineup to ($$n,l,m_l,m_s$$), the final quantum number indicating the $$z$$-component of the electron's spin. One might ask why there is not another quantum number for the magnitude of spin. Well, in fact there is, but that information is contained in the fact that we are talking about an electron. Fundamental particles like the electron have only one possible state of total spin, which cannot be altered by circumstances. It should be noted that when we do use the total spin quantum number (shockingly called "$$s$$"), the same rules apply for spin as for orbital angular momentum, with the possible exception of the allowed values of these numbers, as noted below.
$S^2=s\left(s+1\right)\hbar\;,\;\;\;\;\;\;\;\;S_z=m_s\hbar$
Besides the fact that it is intrinsic, there is one other aspect to spin that distinguishes it from orbital angular momentum. Unlike orbital angular momentum, whose $$z$$-component must be some integer multiple of $$\hbar$$ for all particles, for some types of particles the $$z$$-component of spin can come in integer multiples of $$\frac{\hbar}{2}$$.
It turns out that particles with "integer spin" ($$m_s = 0,\; \pm 1,\;\dots$$) and particles with "half-integer spin" ($$m_s = \pm\frac{1}{2},\; \pm\frac{3}{2},\;\dots$$) are fundamentally very different. It turns out that particles with integer spin all exhibit positive exchange symmetry (i.e. they are bosons), while particles with half-integer spin exhibit negative exchange symmetry (i.e. they are fermions). We know that exchange symmetry divides particles into two types, and we know that the nature of spin divides particles into two types, but it is not at all obvious is that this partitioning of particle types turns out to be equivalent.
As was stated earlier, particles that comprise what we call matter (electrons, protons, and neutrons) are fermions, and they happen to all be spin-$$\frac{1}{2}$$ particles. [Technically, protons and neutrons are composite particles, constructed from quarks, but they too are spin-$$\frac{1}{2}$$.] Our discussions will primarily focus on electrons (as was the case for the hydrogen atom, even though a proton was also involved), though we have also made passing remarks about photons (which are spin-1 bosons), in particular the role they play in selection rules for energy level transitions for emission and absorption.
## Populating Energy States
When we moved to quantum mechanics in three dimensions, we found that the additional quantum numbers led to degeneracies in energy levels. We concluded that additional quantum numbers come along anytime we increase the number of degrees of freedom, and that as long as the hamiltonian doesn't depend upon one or more of the quantum numbers (or even if it does, in the case of accidental degeneracy), there can be multiple quantum states associated with the same energy level.
Intrinsic spin introduces a new degree of freedom, and with it, more degeneracy. There are only two spin states for the electron, but that doubles the degeneracy of all the states of the hydrogen atom, whose wave function we now know should be written as "$$\psi_{nlm_lm_s}$$."
Degeneracy addresses the number of unique states for the same energy level, but where the addition of this additional quantum number really gets interesting is when we put several particles together into a common potential. Again, we continue to assume that the particles do not interact with each other.
Let's take as an example a one-dimensional infinite square well (we aren't very creative, this is the first example we use for everything). Let's place three identical particles into this "box," such that they reach an energy eigenstate. [Keep in mind we are talking about a multi-particle quantum state here.] The question we want to answer is, what is the ground state energy of this configuration?
It turns out that we can't answer this without knowing what types of particles we are putting into the box. We know from our separation of variables work (and frankly, just from energy conservation), that the total energy of the multi-particle state will be the sum of the energies of the individual particles, so we might think that the lowest total energy occurs when each particle is in its individual ground state. But not so fast!
What if the particles are electrons? These are fermions, which means that there is zero probability of having two of them with the same quantum numbers. There are two quantum numbers present here – one for the single dimension, and one for the intrinsic spin degree of freedom. So we can "fit" two electrons into their lowest individual energy states if they have opposite spins, but we can't get the third electron into the ground state without violating the exclusion principle, so it must reside in its first excited state.
If the particles are bosons, then no problem, all three particles can reside in the ground state at once, and that will be the lowest total energy state for the system. Have we solved this problem for all particles? No! Recall that not all fermions are spin-$$\frac{1}{2}$$; higher spin quantum numbers are also possible. If we use spin-$$\frac{3}{2}$$ fermions, then there are four different spin states available: $$m_s = \pm \frac{1}{2},\; \pm\frac{3}{2}$$. With four different states available for a single energy level, there is plenty of room to fit all of these fermions in their individual ground states.
This page titled 7.2: Exclusion Principle is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Tom Weideman directly on the LibreTexts platform. | 2,297 | 9,690 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.390625 | 3 | CC-MAIN-2023-40 | latest | en | 0.622173 |
https://www.gradesaver.com/textbooks/math/algebra/algebra-2-1st-edition/chapter-1-equations-and-inequalities-chapter-review-page-63/27 | 1,725,979,012,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651255.81/warc/CC-MAIN-20240910125411-20240910155411-00035.warc.gz | 762,012,167 | 14,994 | ## Algebra 2 (1st Edition)
$xy-6y=-15\\y(x-6)=-15\\y=\frac{-15}{x-6}$ Hence here: $y=\frac{-15}{5-6}=\frac{-15}{-1}=15$ | 60 | 120 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.703125 | 4 | CC-MAIN-2024-38 | latest | en | 0.397413 |
https://etnolingvistika.ru/photos/bachman-narici-functional-analysis.php | 1,624,460,540,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488539480.67/warc/CC-MAIN-20210623134306-20210623164306-00325.warc.gz | 241,996,420 | 11,943 | # BACHMAN NARICI FUNCTIONAL ANALYSIS PDF
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By George Bachman and Lawrence Narici. In this chapter, some of the conventions and terminology that will be adhered to throughout this book will be set down.
They are listed only so that there can be no ambiguity when terms such as vector space or linear transformation are used later, and are not intended as a brief course in linear algebra. After establishing our rules, certain basic notions pertaining to inner product spaces will be touched upon.
In particular, certain inequalities and equalities will be stated. Then a rather natural extension of the notion of orthogonality of vectors from the euclidean plane is defined. Just as choosing a mutually orthogonal basis system of vectors was advantageous in two- or three-dimensional euclidean space, there are also certain advantages in dealing with orthogonal systems in higher dimensional spaces.
A result proved in this chapter, known as the Gram-Schmidt process, shows that an orthogonal system of vectors can always be constructed from any denumerable set of linearly independent vectors. Focusing then more on the finite-dimensional situation, the notion of the adjoint of a linear transformation is introduced and certain of its properties are demonstrated.
We shall often describe the above situation by saying that X is a vector space over F and shall rather strictly adhere to using lower-case italic letters especially x , y , z , … for vectors and lower-case Greek letters for scalars. The additive identity element of the field will be denoted by 0, and we shall also denote the additive identity element of the vector addition by 0. We feel that no confusion will arise from this practice, however. A third connotation that the symbol 0 will carry will be the transformation of one vector space into another and mapping every vector of the first space into the zero vector of the second.
The multiplicative identity of the field will be denoted by 1 and so will that transformation of a vector space into itself which maps every vector into itself.
A collection of vectors x 1, x 2, …, xn is said to be linearly independent if the relation. An arbitrary collection of vectors is said to be linearly independent if every finite subset is linearly independent. A linearly independent set of vectors with the property that any vector can be expressed as a linear combination of some subset is called a basis for the vector space or sometimes a Hamel basis.
Note that a linear combination is always a finite sum, which means that, even though there may be an infinite number of vectors in the basis, we shall never express a vector as an infinite sum—the fact of the matter being that infinite sums are meaningless unless the notion of limit of a sequence of vectors has somehow been introduced to the space. A subset of a vector space that is also a vector space, with respect to the same operations, is called a subspace.
In general, if a collection of vectors, linearly independent or not, is such that any vector in the space can be expressed as a linear combination of them, the collection is said to span the space. Assuming that things take place in the vector space X if M 1, M 2, …, Mn are linearly independent and. Equation 1. One will sometimes see another adjective involved in the description of the above situation—it is often called an internal direct sum decomposition.
This is because a new vector space V can be formed from two others X and Y over the same field ; this new one is called the external direct sum of X and Y. What is done in this case. We define.
Adopting this convention then, given a direct sum decomposition, we need not bother to enquire : Are the terms in the direct sum distinct vector spaces or are they subspaces of the same vector space? Given a mapping A which maps a vector space X into a vector space Y over the same field ,. A is called a linear transformation. Often when linear transformations are involved, we shall omit the parenthesis and write Ax instead of A x.
If the linear transformation is 1 : 1, it is called an isomorphism of X into Y. If A is 1 : 1 and onto, the two spaces are said to be isomorphic. Two isomorphic spaces are completely indistinguishable as abstract vector spaces and in some cases, isomorphic spaces are actually identified.
An instance where such an identification is convenient was mentioned in the preceding paragraph. Having given meaning to the formation of linear combinations of linear transformations, let us look at the special case of all linear transformations mapping a vector space into itself. Equivalent terminology also used is characteristic vector and proper vector instead of eigenvector, and characteristic value and proper value for eigenvalue.
Such a transformation is called a projection. As it happens, a projection always determines a direct sum decomposition of X into cf. One notes in this case that. We do not mean by this that every vector in L is left fixed by A ; it is just mapped into some vector in L.
Two other concepts that we shall make extensive use of are greatest lower bounds and least upper bounds. The numbers al and ar have the properties that al can be replaced by anything smaller, whereas ar can be replaced by anything larger, and we shall still obtain lower and upper bounds , respectively, for U.
A fundamental property of the real numbers, however, is that among all the lower bounds, there is a greatest one in the sense that at least one point of U lies to the left of any number greater than the greatest lower bound.
Aside from this material pertaining to functions, there are many other notions from set theory that are absolutely indispensable to the study of functional analysis. We feel it is unnecessary to discuss any of the notions from set theory and consider it sufficient to list the pertinent notation we shall use in the List of Symbols. No doubt the reader has come in contact with them for example, unions, intersections, membership before. We make one exception to this rule with regard to the concept of an equivalence relation.
In this case the relation is called an equivalence relation. As a mnemonic device for recalling the three defining properties of an equivalence relation, one sometimes sees it referred to as an RST relation. Examples of equivalence relations are equality of real numbers, equality of sets subsets of a given set, say , congruence among the class of all triangles, and congruence of integers modulo a fixed integer.
For a proof and further discussion one might look at Ref. Suppose X is a real or complex vector space; that is, suppose the underlying scalar field is either the real or complex numbers R or C. We now make the following definition. It is noted that by property I1 that x , x must always be real, so this requirement always makes sense. A real or complex vector space with an inner product defined on it will be called an inner product space ; one often sees this abbreviated as i.
Inner product spaces are also called pre-Hilbert spaces. To prove this, noting that this is true for every vector in the space, take x equal to y and apply part I3 of the definition. In the following examples, the scalar field can be taken to be either the real numbers or the complex numbers. The verification that the examples have the properties claimed is left as an exercise for the reader.
As the inner product of the two vectors. Cn with this inner product is referred to as complex euclidean n-space. With R in place of C one speaks of real euclidean n-space. As the inner product of any two vectors f x and g x in this space, we shall take. We shall sometimes use the same notation to denote the real space of real-valued continuous functions on [ a , b ]. We shall always specifically indicate which one is meant however.
Theorem 8. The following example is presented for those familiar with some measure theory. Since it is not essential to the later development, the reader should not be disturbed if he does not have this background. Let Y be a set and let S be a collection of subsets of Y with the following properties:.
Analogous to the case of C [ a , b ] Example 1. As such, it partitions the set into disjoint equivalence classes, where a typical class is given by. Let us now restrict our attention to only those classes whose representatives are square-summable on E such that.
Note that the zero vector of the set of all square-summable functions on E is the function that is 0 everywhere on E. Since the only nonnegative measurable functions on E satisfying the above equality are those that equal 0 almost everywhere on E , we see that this problem is circumvented when one deals with classes. Sometimes we shall wish to deal with only real-valued functions and to view the collection as a real vector space. Then, for the equivalence classes of square-integrable functions complex-valued on [ a , b ] we can take, as inner product between two classes f and g ,.
This space is usually referred to as L 2 a , b. The proof of the following, very important result can be found in the references to this lecture and will only be stated here. The following three results represent straightforward, although somewhat arduous, tasks to prove and will also only be stated. It should be noted from the above two results that if we know the norm in an inner product space, the inner product can be recovered.
This theorem derives its name from the analogous statement one has in plane geometry about the opposite sides of a parallelogram. If x and y represent two vectors from real euclidean 3-space, it is well known that the angle between these two lines in space has its cosine given by. The next result follows immediately from just expanding the quantities involved and using the hypothesis.
Then S is said to be an orthogonal set of vectors. In this case S is said to be an orthonormal set of vectors. Let the vector space be l 2 and consider the set of vectors from this space. This collection or any subset of this collection, according to the inner product defined in Example 1. The collection or any subset thereof. Let X be an inner product space and let S be an orthogonal set of nonzero vectors.
Then S is a linearly independent set. Before passing to the proof, the reader is asked to recall that an arbitrary set of vectors is called linearly independent if and only if every finite subset is linearly independent. In light of this, choose any finite collection of vectors, x 1, x 2, …, xn from S and suppose that. Thus the collection is linearly independent. Knowing that there exists a basis for any finite-dimensional vector space, the following result assures that among other things, in such a space, there is an orthonormal basis.
The proof will be by induction. Further, the spaces that x 1 and y 1 span must be identical, because the two vectors are linearly dependent. Our job now is to construct the n th vector with the same properties.
To this end, consider the vector. Suppose it were possible for w to be zero.
ISTORIJOS KONSPEKTAI PDF
## Functional Analysis
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AUTOBIOGRAFIA JOGINA PDF
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GLOBE SP30 PDF
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. | 2,449 | 11,758 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2021-25 | latest | en | 0.907023 |
https://www.diagramxdigital.com/4-way-switch-schematic-diagram-2/ | 1,685,546,510,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224646937.1/warc/CC-MAIN-20230531150014-20230531180014-00233.warc.gz | 825,746,478 | 13,059 | # 4 Way Switch Schematic Diagram
By | January 24, 2023
When it comes to wiring your home for electricity, it pays to understand the basics of a 4-way switch schematic diagram. Although more complex than a basic single-pole switch, wiring a 4-way switch setup is essential in order to manage multiple light sources from one location. In this article, we'll provide a basic overview of 4-way switch wiring, along with step-by-step instructions for completing the job.
A 4-way switch setup consists of two 3-way switches, each connected to one light fixture. This type of wiring setup will allow you to control the brightness or dimness of a light source by simply pressing a button. Depending on the position of the switch, users can turn a light on or off in one motion, while also adjusting its level of brightness.
The key to successfully wiring a 4-way switch is understanding the connections between the two 3-way switches. You'll need to identify which wires and terminals are used to power the light source, along with the two switches themselves. Once these components are identified, you'll be able to connect the corresponding wires in the appropriate locations. To complete the wiring, you'll then attach the light fixture's ground and neutral wires to the corresponding terminals.
For most do-it-yourselfers, wiring a 4-way switch setup requires a basic understanding of electrical principles. If you're new to electrical wiring, it pays to review a few safety protocols before getting started. Once you've double-checked the local codes, you can begin connecting the wiring in the appropriate order. If you're unsure about the process, it's best to leave the job to the professionals.
Regardless of the complexity of the wiring project, understanding the basic components of a 4-way switch schematic diagram can help you safely complete home electrical projects. With the right knowledge and some patience, you'll find your wiring project much easier to handle.
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4 Way Switches Electrical 101 | 598 | 2,779 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2023-23 | latest | en | 0.903556 |
https://www.physicsforums.com/threads/please-help-with-this-bridge-circuit-question.469625/ | 1,659,943,039,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882570767.11/warc/CC-MAIN-20220808061828-20220808091828-00556.warc.gz | 799,880,023 | 14,186 | jess_vander
Homework Statement
for the bridge circuit shown in the figure (see the attached file...question number 8), find the current in each resistor and also the equivalent resistance of the netowrk of five resistors. R1=150ohms, R2=50 ohms, R3=100ohms, R4=300 ohms, R5= 250 ohms, and E1=24V.
Homework Equations
im not even sure where to start for this question.
im very confused and i know that i have to create 5 equations in order to solve for the currents but im not sure how to go about doing this.
any help would be greatly appreciated.
The Attempt at a Solution
Attachments
• Assignment_HAOPENG_1.pdf
145 KB · Views: 588 | 173 | 638 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.671875 | 3 | CC-MAIN-2022-33 | latest | en | 0.903156 |
https://sunderlan.com/free-casino-games-2/roulette-cheating-2/ | 1,686,349,631,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224656833.99/warc/CC-MAIN-20230609201549-20230609231549-00346.warc.gz | 629,624,531 | 23,376 | Time and time again, it has been emphasized by experienced gamblers and casino-owners that roulette is really a game of chance. The mere randomness of this game is sufficient to dissuade anybody who’s thinking of cheating. However, some individuals still find it hard to believe the fact that such randomness in a game even exists. There must be some sort of mathematical equation towards cheating in roulette or perhaps a device that could assist in roulette cheating.
Just recently, two men along with a female had been caught for apparently cheating on roulette in London’s Ritz hotel casino. These people were described of having employed a mobile phone equipped with a laser scanner to win up to UK 1. 3 million. The scanner is reported to be a device used in cheating at roulette simply by speculating the likely concluding point of the ball. It is possible that this type of device can do that however specialists happen to be cynical if this apparatus, or any gadget for that matter, might get it done quickly enough to allow a gambler to put a winning bet.
According to UK gambling laws and regulations, a ‘no spin is called if the ball doesn’t circle the actual wheel a minimum of 3 times. And also immediately after three spins, the croupier would make the call ‘no more bets. The time variation between 3rd spin and the call might be possibly approximately 14 to 15 seconds, not enough for such a gadget for the purpose of cheating in roulette to work.
In theory, roulette cheating is probably possible. One merely needs to employ a system that could judge the actual velocity of the wheel and for the ball. Aside from that, this gadget for roulette cheating must have the ability to evaluate the actual level at which the speed of both degrades. However in order for this device to work successfully in roulette cheating, it should be able to perform all these within just a few seconds so the bettor has time sufficiently to put his or her wager for the winning number.
What makes roulette cheating even more complicated is actually that the wheels were created specifically to ensure just the right amount of randomness in the game. Once the wheel is turned, the ball bounces a little bit, boosting the randomness of its movement. All of these odds make roulette cheating unachievable.
This however fails to stop some from remaining dogged to the idea of roulette cheating. These types of individuals are serious enough or simply unwilling to lose their own last buck to the casino.
Some individuals created a statistical system in which probability and odds play big parts. They believe that roulette cheating is possible since the game includes figures. Like in poker, this kind of roulette cheating system uses the process of elimination for determining all the possible outcomes of any spin. But roulette is certainly unlike the card game of poker.
Let’s explain this type of roulette cheating through an illustration. Say you come up with a wager Straight Up upon 35. For the first spin, you get a 31. At this point, just because you’ve got a 31 in the very first spin doesn’t mean that you actually only have to grapple with merely 37 feasible outcomes. There’s even now every possibility that this number 31 can come on the next spin which means this completely defeats the purpose. If you plan on cheating on roulette, probability just isn’t the answer as well. | 674 | 3,391 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2023-23 | latest | en | 0.974056 |
https://statisticaleconomics.org/2014/01/05/progressives-beware-why-what-you-think-you-know-about-economics-just-aint-so/?replytocom=1653 | 1,660,482,608,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572033.91/warc/CC-MAIN-20220814113403-20220814143403-00184.warc.gz | 496,667,566 | 58,755 | # Progressives Beware: Why what you think you know about economics just ain’t so
I had a random idea a while back and decided to chase it down. I saw that Gibbs method of statistical mechanics relies on operations of certain distribution functions, like the Gamma distribution or the Normal distribution. In my work I kept on coming across the Log-Normal distribution. It is everywhere. So I decided to have a look and see what I could derive. While I did this for the Log-Normal and Gibbs did it for the Gamma and Normal distributions, this approach is applicable to any other distribution.
Theory is no good unless you can test it and see it in our data. So I tested it on income distributions, reported in the the attached paper, bitcoin transactions (work in progress), and radiation exposure to cells (unreported work).
In my work, I derived the Cobb-Douglas function as a property of the Log-Normal distribution. Yesterday a friend tweeted a link to a blog The entropy of nations. If you have not read it I suggest you do. The author identifies maximum entropy as Adam Smith’s “invisible hand”. I emphatically agree with his analogy. The tendency towards maximum entropy is seen in the process of price discovery it is the invidible hand that drives arbitrage.
His work motivated me to finish mine and with a boring and non descriptive title to boot! Various Properties of the LogNormal Distribution. Can you say math fun? The policy stuff is in the last section if you are so inclined and the mathy stuff is in the front two sections. I found income distributions obey the second law of thermodynamics. This is great news! The bad news and what inspired my evocative title is that while we can propose policy and develop theories that say it will work, that no quantity of ink or PhD’s is going to change the second law. If you are not aware that it applies, so well. There is a chance you got the theory right, but its just not very likely. I had a Commanding Officer tell me, “Cal, Hope is not a plan. A plan is a plan.” Wise words. He left out that my plan actually better be possible. Hope as a policy is wishing for unicorns. That is my best description of any progressive policy, wishing for unicorns. It explains why what we get isn’t what we were sold. Somewhere along the line reality hit.
Here to any progressives that follow me or stumble across this blog, there is my gauntlet laid at your feet. I invite your responses.
### 13 responses
1. Interesting and/or provacative blog. (I do wonder what your background is, since it seems to range from physics to political philosophy). I’m not sure what value my comments have, but for what its worth I’ll make some.
First, i discussed this with you already a bit on the RWER blog. You had mentioned Saslow, so I threw in Foley and Yakovenko among others. You said you were unaware of them, but it appears you had seen the Foley and Smith paper since its on your references from your ‘pre-alpha’ ‘econophysics’ paper.
It seems your view of Smith and Foley in the earlier paper is not the same as your view of them in the most recent paper on econophysics; I wonder if you’ve run it down with them (they think saslow is wrong, for example). I might add that there are maybe 50 other papers i know of that deal with tjhe same issues, some going back to the 40’s or before. (I will add that as I understand them, Foley’s 90’s papers are inconsistant with Smith and Foley 2005). (I also think its inexcusable to write papers like this with the most complex cases—-I have seen this in some economics books as well—when teaching a utility function, the author wants to impress and confuse you (so you don’t real.ize s/he doesn’t know what the f-k they are talking about) so rather than use something simple like Cobb-Douglas or better, additive, they throw in some sort hypergeometric form a zeta function coefficient with all sorts of parameters for discount rates, interest rates, mood, sexual orientation, whether a mac or apple user, sports team etc)..
Second, the idea that you have fouind that the income distributions obey the second law I think is ‘obviously well known’ though most popularized in the last 10 or so years by Yakovenko. It goes back at least to the 40’s or before in various forms. I have a derivation of a lognormal form from the 70’s by a very well known physicist (who now is also a global warming denier). One could argue that these are not really derivations from the second law, but rather maximum entropy, but to me the latter implies the former exists if one takes a dynamic view. There are other derivations in the journals ‘entropy’ and j. math. sociology from the 80’s to recently though they often use different formalisms, which are mathematically equivalent though not obviously so.
Most important, the idea that ‘maximum entropy’ represents or is equivalent to the action of Adam Smith’s ‘invisible hand’ to me is ‘wack’, as i mentioned on RWER. That is the ‘fatal flaw’ in the statistical mechanical approach and i explained why there. One can ‘fix’ this in 2 ways.
One is to assume ‘ergodicity’ (Keynes—in the long run we’re all dead) so everything (or everyone) really mixes (entropizes) over time, and current illusions about ‘class’, social stratification, lack of social mobility are due to the same problems seen by some who analyzed the first computer simulations of the second law by Fermi-Pasta-Ulam in the 40’s—-ie you just hand wave them away, and assume the infinite limit, and no long range correlations or phase transitions. . Similarily for the rest of the world, things like atoms, planets, life forms, water, protons etc. will all melt into photons because they really are just passing fads or illusions (like the passage of time and increase of entropy in the microcanonical ensemble, ior consiousness) because in maximum entropy we’ll find Boltzmann’s distribution—so called ‘heat death.
That may be correct, but some people are interested jn shorter time correlations.
The other way to fix it was assume people do have some ‘utlility function’ like cobbs-douglas. Yakovenko mentions and others went through the math. Unfortunately, from the intuitive perspective, this only works if you essentially slip in the same assumption used by Yakovenko and others—you have to assume a particular form of Cobb-Douglas (although its written the same) which is not what economists use, except when talking about ‘representative agents’. (Of course that is often the only way to solve things, and you get an answer but it assumes every individual is basically ‘average’, and I know this is false because i know i’m ‘above average’ because i’m partly from near Lake Wobegan where everyone is above average. (Mathematically this is possible and correct, because its possible or likely that then everyone else is below average—i believe that. Someone at Northwestern among others has written on this. But, this doesn’t explain what is so special about Lake Wobegon. Maybe its the water in the land of the 1000 lakes?
Physics can explain this, as the spontaneous polarization of the vaccum. It created the universe—E Tryon. But its just a fluctuation, so relax, and soon it will go away in the long.
Again, this is not satisfying to some. We may want some sureness that we’ll collect our pensions and social security before the light goes out).
One more complex way to fix it is viable, but too much to discuss here, and essentially revises the maximum entropy postulate (though you can still formulate it statistically—-you can put your constraints internally or externally). You can write the solution in gibbs form too—-exp(-bH)—but the devil is in the details, when you expand H. (Think ‘block spin method’ and ‘renormalization group’. )
I guess, in the tradition of E Verlinde’s ‘entropic gravity’ one can imagine this is as a second law phenomena too. (I actually do, in part). But it also shows the alternative is also possible—-preferences are real, and non random, and interactions are constrained because there is no perfect information and geography.matters, and the use of binomials or multinomials on distingishable or indistinguishable particles is really not defensible. ( Maybe it is—–increasingly the principle of gross substitution is seeming to hold—people are willing to sell or trade their spouses and children for example, for new ones or dope or property. The guy who desposed Ethiopia’s Helie Selassie (sic) for example seemed to be an innovator here).
In sum, so far as I am concerned (and maybe its just me) the maximum entropy and adam smith approaches to income distribution are completely orthogonal. Its possible to use the ME formalism, but you have to atart with a ‘prior’ set of assumptions. What is remarkable is that (as mostly simply shown by Yakovenko) assuming the simplest possible prior one can get remarkable (though not exact—-the income distribution is not exponential, especially at low incomes—though maybe he could fix that by counting under the counter transactions) agreement with data. He does assume one thing (via convoluting family incomes since that income is the most accesible data) so it may actually fail more than is apparent.
By the way, i made the same points to the people who wrote the papers mentioned above. I think they are (possibly like you) ‘right wingers’ so they didn’t like the message and cut off contact. Its easier just to maximize the entropy, and deny you are just arbitrarily curve fitting rather than explaining a mechanism. (Again as noted, there may be no difference fundamentally—-if i go to a store, while i may think i prefer some commodity bundle, in fact my preferences are due to billions of years of evolution, and so can be assumed to be random; similarily my fate—see the book ‘laws of chaos’). Of course normatively this means people like Senator Paul Ryan is an idiot who should be put on the food stamp and TANF rolls (since he already is actually) and then they should be cut so he can sleep on the street and eat out of dumpsters and the soup kitchen at his church.
I’m now going to see if I can find your derivation of cobbs-douglas from maximum entropy. (I think i know what you’ve done, since i have such a derivation, though its fairly implicit and sometimes almost explicit in the LITTERature). \
cheers. (ps i still like your blog, if not your conclusions).. .
• I am very glad that you stopped by and took the time to leave such detailed feedback.
I am a nuclear engineer, and just a curious person in general. I started, a decade ago, to try and understand why the technology that I understood and appreciated was not very well appreciated amongst others. I wanted to understand why some very smart people were making policy recommendations that I knew to be physically impossible. How I understand it is that the political system is used to preserve a distribution of goods that preserves the status quo. Progressive and conservative policy’s are identical in execution, they just give a different bill of sale. By increasing barriers to market entry, in just about every market, the churn in the economy is limited and it becomes more rigid.
I went back to school to learn public policy, but for time’s sake I am in a nuclear PhD program instead of public policy and just minoring in policy. I took a micro econ course saw very clearly the link between micro and macro. So I read through vNM Game Theory and used that to define a metric space for utility. As their work only applies to individuals, I needed a formal way to aggregate individuals. That is why I chose Gibbs’ formalism. At the time I was reading Jaynes and saw his appreciation of Gibbs, so I started with Gibbs. I showed my econ professor what I did and he promptly stopped talking to me. Additionally, my derivation does not assume a specific utility function, just that one exists and is at least once differentiable. This is a strong assumption and can be relaxed, but would result in mathematics that is much more complex as we would now have a quantized utility function and need to adopt von Neumann’s approach to deriving quantum statistical mechanics.
I do use an ergodic approach in the Elementary Principles paper. Formally setting $\frac{\mathrm{d}S}{\mathrm{d}t}=0$ is a statement that there is no change in information in the system, that every possible subspace has had the opportunity to explore the entire phase space available to it. This is a very presumptive (strong) assumption that can be relaxed. I used it because it made the math much easier. Jaynes’ work inspired the field Non-Equilibrium Statistical Mechanics which does not rely on such simplistic assumptions.
The reason why I don’t like Smith and Foley, is that I have a very clearly defined utility from Game Theory that I use to derive entropy from the formal aggregation of individuals. They think entropy is utility, when it is most clearly not. Saslow’s heuristics emerges as sound reasoning as my derivation supports his conclusions. I appreciate your view point on unnecessary complication used to hide lack of comprehension. It is utterly incomprehensible.
The physicist that you are referring to is Lienhard? He worked through the derivation of a generalized gamma distribution and applied it to a whole set of applications, including income distribution. The Gibbs derived the gamma distribution as a consequence of kinetic energy = mass times velocity squared. That begins on page 87 of his 1902 book in earnest. Gibbs canonical distribution is a gamma distribution, he also shows 5-years before Einstein’s Brownian motion paper that this results in a normal distribution if the number of degrees of freedom of the system are very high. Gibbs is very hard to follow, and his insights are profound. Getting there is quite painful…
Your statement “One could argue that these are not really derivations from the second law, but rather maximum entropy, but to me the latter implies the former exists if one takes a dynamic view.” is spot on. The second law is a derived law from the principle of maximum entropy, and the conservation of the density in phase (first law). The second law is the fundamental equation of thermodynamics, $\mathrm{d}U=T\mathrm{d}S+\lambda\mathrm{d}M+\mu\mathrm{d}N$. As I understand this law it only describes how information within a distribution changes due to perturbations of its independent variables. The first law is a conservation of information. Information, knowledge of the system, cannot arbitrarily increase, although it can be lost. (this is a very poor explanation as it doesn’t have the nuance of the conservation of the density in phase)
I am not a right winger. I see little difference between the right and the left. Having been on both the right and left, I feel qualified to make that statement, along with the my observations here I see very little empirical difference.
The adoption of the principle of maximum entropy is one that says, given our knowledge of our measurements, that the system will be in a configuration that we know the least about. Any other assumption, presumes a quantity of information more than we observed in the data. By using the principle of maximum entropy, I formally say that I am only considering the data which I observe. This is why it is so important to not throw out data or restrict data from our consideration. In this regard the principle of maximum entropy is a theoretical maximum entropy of the system. The ultimate configuration will always result in a configuration with a lower entropy. If it does not, then there is a significant problem in our selected model which is not consistent with the physical world, eg assuming a normal distribution when a log normal is more appropriate.
On the topic of entropic gravity, I too am sympathetic to that argument. There is a paper floating around out there that shows general relativity as a specific set of assumptions under a PME framework on Riemann manifolds. PME is very powerful indeed. I am not a big fan of the word of randomness when thinking about probability theory. I much prefer to think of it as an expression of the information we have. So if we have additional information then we can build a more complete model that better explains the observed entropy. The point with PME is that it assumes the least. Jaynes justifies the approach of PME in the entropy conservation theorem. (Jaynes, E.T., Concentration of Distributions at Entropy Maxima, in E.T. Jaynes:Papers on Probability, Statistics and Statistical Physics, R.D. Rosenkrantz,Editor. 1989, Kluwer Academic Publishers: Boston. p. 317-336.)
Usually, people cut off their interactions with me. I started this blog because I wanted to have a forum where I could discuss these ideas, because when I discussed them with people directly, they would not respond to my emails. I apologize for the roughness of the blog. As I have thoughts I write them up, and more than often don’t clean them up. I am very glad that despite the warts you like the blog.
PS, Wisconsin has more lakes than Minnesota, we just let you think that you have more lakes out of politeness.
2. p.s. I couldn’t find any mention of cobb-douglas in papers linked to above, though a couple of formulas bear some resemblance though i’d have to look closer. maybe its in your longer paper (some of which seems written in gibbs’ formalism, which i dislike; jaynes is better though my glance of your discussions don’t exactly jog my memory of what i saw in his originals—on his web site). It can be mentioned i’ve seen a few papers apply stat mech to electrcity markets.
3. Thanks for your reply. I don’t have time to really read it now and haven’t gone through your papers in detail (i’m still somewhat confused on all this stuff, though i have my own approach conceptually (i haven’t really written it up except in parts).
I will just give you a few of the references i mentioned. The lognormal for income is discussed in an old 1974 book by Eliott Montroll and Wade Badger (it may be by Bruce West who works for the military and maybe jointly at Duke). Its reference 3 in Montroll’s paper PNAS #75 october 1978 ( http://www.pnas.org/content/75/10/4633.full.pdf ) . The entropy journal (mdpi.com) papers are on ‘fairness’ and ‘executive pay’ 2009 11 #4 and 2010 12 # 6 by ‘venkat’ (first name –you can probably search it). Foley has a ‘better’ paper in a 1994 journal but its still a wreck in my view (and conflicts with his smith collaboration). He wouldnt talk to me about it.
In general, David Wolpert’s stuff on game theory and stat mech i find close to the way i think http://www.arxiv.org/abs/cond-mat/040258 for example .
Another paper which mentions the ‘confusions’ is arxiv.org/abs/0903.4216 (‘statistical thermo of econ systems’) . You can also glance at entsophy.net. (a blog).
I’m just passing these along if you have time and curiosity. (There’s a ton of stuff out there, much of it redundant, but its hard to tell given the quantity.).
I come from the ‘boltzmann approach’—i see it as equivalent to Gibbs (and i distinguish them as one starting with the microcanonical ensemble, while the other focuses on the canonical). (There is of course a huge literature which discusses whether they are equivalent, with prominent physicists taking all views—‘equivalent’, not—boltzmann is right ‘, not-gibbs is). Yakovenko uses the boltzmann formalism. (I have read only a few Jaynes papers which used boltzmann form).(The economist Paul Samuelson has a couple of papers in PNAS (proc natl acad scis) in 1974 which are based on Gibbs formalism (he adopts it from previous models in biology). (on Marxism!!!).
There are papers applying this stuff to electrical power grids though i can’t remember where they are on arxiv.org
Last notes—‘free energy’ i do think is what is important (it combines entropy and energy). (There are lots of papers from various approaches promoting entropy; most deal with thermodynamics which i generally avoid—i like to start from microscopic level.) I will say i am almost more of a historian since i spend alot of time looking at what has been said on an issue, as opposed to just developing my own model. (The most intriguing part of your paper to me if i recall was discussion of euler-lagrange and action principles ).
• Is this the Wolpert paper, http://arxiv.org/pdf/cond-mat/0402508v1.pdf ? Interesting. The derivation of both Gibbs and Boltzmann requires that the particles do not interact with each other. They are formally statistically independent. When covariance is considered, the entropy of the system is reduced by the covariance matrix. The problem comes in when considering these particle interactions the math is very very messy. I had to work through some of this in Plasma Physics. To say complex is an understatement. I need to look through this paper some more. I use a modified Metropolis Algorithm based on my derivations to help parallelize quadrature on my GPU’s. He has some similar outcomes and some other very interesting insights. Thanks for sharing this paper!
My thesis research is on state space modeling of reactor cores and optimizing control regimes in load following. The Wolpert paper is actually very useful in the time domain because of the formulation of the action integral. This allows time domain quadrature. Here is where I got the idea http://johncarlosbaez.wordpress.com/2013/11/11/quantropy-part-4/
The paper arxiv.org/abs/0903.4216 makes an arbitrary conserved quantity $M$ that is entirely unnecessary. The derivation is still capable of being done, only by conserving the density of phase (the phase space pdf). Additionally, the form of the exponent of that canonical distribution is a function of the statistics. In terms of $p$‘s and $q$‘s of a generic coordinate system, the statistics of the system are described by the relationship between these parameters. As an example the $\Gamma$ distribution of an ideal gas results directly from $E_p\propto p^2$. When we get into quantum theory, different particles have different statistical distributions. You have fermions that obey Fermi-Dirac statistics and bosons that obey Bose-Einstein statistics. I have not gone back and determined the $p$, $q$ relationship of a lognormal distribution. Interesting that their equation (23) is similar to what is in my work, just obtained from a different set of assumptions. They are quite right to study the phase transitions. They do their derivation from money, I start from utility. Their approach is limited to a single assumption and that is that the marginal utility of money remains constant. In a utility representation, entropy takes on different connotations, as does temperature. The concept of temperature as being $\frac{\partial U}{\partial S}$ carries more meaning as that is a measure of economic activity. Their paper is interesting, but misses some key things that I covered above.
I use Boltzmann’s approach directly in nuclear reactor analysis our entire methodology for modeling cores is based on solving that integradifferential equation. Boltzmann’s characterization is easier to determine how the system responds. Gibbs approach, is much simpler to understand what is happening and why. Both are useful.
Free energy is an ability to act. You are right to see its importance. It combines the freedom of the system (entropy) and the kinetic (income) to realize the extent and the number of different ways people in that economy can act. I don’t like thinking of entropy as disorder. I like to think of it as structure and complexity.
I do electrical grid modeling too and am familiar with the concept of flow entropy, It is quite useful.
Let’s keep the topic open this is extreamly interesting and informative. Thank you!
4. Thanks for responding—i like these discussions, so maybe they’ll continue. (Or maybe not after this one—it turned into a creative writing project, some possibly offensive to people (eg pc types) with no sense of humor. But there are serious points mixed in. You may not want it on your blog though).
(Of course there is an opportunity cost involved in responding —i think its almost 100% sure that if i walk up the street now and buy a lottery ticket, i can retire rich and devote myself to philanthopy—eg help the poor who squandered all their money playing the lotto, but didnt have the math background to win like me. But i don’t feel like it. I’m living with my New Year’s resolutions (same ones every year) to stop bad habits, squandering money, and to stop procrastinating—which means I operate ahead of schedule, and already have my next year’s new year’s resolution, which is ‘stop procrastinating’. If you can do it tomorrow why do it today?
Or how about you employ me to search the web for references—the invisible hand will optimize, so i’ll do the bibliography and sign my name to the author’s line, and you do the rst of the paper. i do need a job i have been told, but it doesn’t fair, nor compatible with the max ent solution.) .
—yeah thats the Wolpert paper (he has alot on arxiv). (i am bad at typing and dotting i’s—i would often mix up ‘-‘ and + signs, and it might take me hours to recognize the error because i’d keep repeating it, like a fly trying to get out of an open window which is stuck on the glass. Its interesting psyhcology, those blind spots.).
—-i agree your use of utility rather than money is more general. Money is sort of the ideal gas or simpest case. (have you heard that song ‘golddigger’ by kanye west ‘give me money, its all i need…’ Utility (functions) can be complex; so converting everything into standard units of money simplifies things—as they say, everyone has a price (capital, labor, human capital, natural capital, intellectual, social capital. ‘monetarize everything’ (some economist at GWU, maybe tyler cowan. If some say ‘can’t buy me love’ (Beatles) then they because they didn’t work hard enough.).
There are definately several different ways temperature is viewed in the econophysics literature; many of them however are (or seem to me ) somewhat conceptually equivalent—-eg average income of a society, average level of development, etc. (Sometimes however i suspect people took the way they characterize temperature from some other paper they read, and then say this is the meaning of the temperature in their derivation, though its not obvious and possibly false. I actually once talked with an economist who was peripjherally doing econophysics (and now is pretty much on it) and asked him about temperature in his model (since he was using some results from stat mech which involved temperature. He said there was no temperature in his model. Its like when i asked Cockshott about an equation in his book with Yakovenko—the fokker-planck equation (which at times is called the boltzmann equation—and he said he’d never heard of it.)
—-I looked at your discussion of the max ent approach to income distribution. As I mentioned, and its the same point i made to the person at Purdue who published in Entropy J (also on the lognormal), that is, just another convention or norm, as is Rawls’. You apparently claim that maximum entropy state is say, the most productive, or what i would call the state of ‘maximum social welfare’ (which some might say ‘best quality of life’ and others’ pareto optimal/gerneral equilibrium). On a simple level if maximum entropy were optimal than in my view (since i believe in cosmological and biological evolution) we should all be trying to turn the world into a photon gas. You have expertise here—‘drop the bomb, make earth a sun, let someone else, have some fun’. ‘Burn baby burn’—let the heat death (boltzmann) begin.
The economy is a nonequilibrium system which can be approximated locally by equilibrium and max ent (with Prigogine’s ‘dissipative structures’ or the ‘maximum entropy production’ or ‘edge of chaos’ principles, for example, being suggested for optimizing nonequilibrium states). Formally my view is one can write these so they look the same as the equilibrium case, but they have a different interpretation. (i.e. the boltzmann distribution applies to an ideal, noninteracting gas, but you can write a boltzmann form for ising miodels, spin glasses etc, which describe interactions, have phase transitions,etc.)—–Just as you can write down a diffusion or fokker-planck (or boltzmann, langevin, master ) equation desribing a stochastic process in a Hamiltonian or Lagrangian form.
I will say when i saw that it blew my mind.because i was always told hamiltonian/lagrangian dynamics are determinstic, conservative etc. unlike statistical evolutions, but then some tricks were done. Entropic gravity seems to be the culmination of the picture—newtonian/einsteinian determinism is the same as maximum entropy. Ariel Caticha in my view more or less already showed ‘entropic gravity’ before the recent work — Wolpert’s information geometry is in this school. )
I might almost say that the same is true for communism and capitalism (entropic gravity becomes communistic capitalism), –eg Rawls vs Hayek—-and I am not particularily impressed by either of them:
—-aside (interlude) for a brief rant: (You may want to skip this)
I don’t like Hayek because I don’t think he had much to say other than the calculation problem (which was one very good note—-i read his stuff debating lange/lerner, which paul cockshott, who has a book with Yakovenko, has ‘solved’ due to computers; the book emerged from a conference on Machover’s ‘laws of chaos’—see below). The rest of his stuff has been said better by anthropologists and evolutionary biologists—-it seems he would write 1000 pages saying what others had said better in 30. I guess Hayek’s appeal may rest in ‘spontaneous order, or catalyxess. I learned it as self-organization. (I guess this way he is called ‘eriudite’ or wise). (Some of other people if they write 300 pages more, turn the rest into rigorous math which starts from microfoundations and then gets the macro principles; the people i’ve run across who read hayek won’t do this, but are like people who love to talk about quantum theory but got it from watching the film the Matrix or Bleep somethig and don’t want to learn calculus.) .
I dont like . Rawls because he seems logically impaired, and/or pampered and lazy. He had many years to see what conclusions follow from his basic axioms which are fine as axioms (imagine your ideal world, etc. whether ayn randian or marxist or anarchist or libertarian or totalitarian or fascist ore theocratic…) , just as discovering that 1+0=1 and 1+1 = 2 is fine, but then maybe in the next 20 years you could see what happens if you try to solve 1+2=? . see if you can figure out induction. (start by helping the least of the least, and then step back, and iterate the process. Will you run out of the ‘least’ or is the system uncountable a la Cantor and Godel?) Or even see if you can try counting to ten, or solve reimann’s conjecture.
And then you have a whole Rawlsian industry of people (like Michael Sandel of Harvard, who is a deep ecologist (and sees all living things as equal, far beond Rawlsian equality) and so compassionately shares his entire income with his bank account) who dis/cuss in philosophy journals whether 0+1 is the same as 1+0, and whether the two 1’s in 1+1 are identical (a la gaussian particles) or indistinguishable (like bosons), and what that implies about 2—perhaps its a chiral number, occuring in left and right handed forms (like the nazi symbol) which don’t commute, so arithmatic is a quantum system, and may involve an aharanov-bohm effect, and there is a gauge symmetry.
And I especially hate the fact that he was some sort of bleeding heart moralizing self-righteous guilt tripping holier-than-thou dude who goes around preaching ‘i love the poor’ when all he was doiing was collecting a fat salary in an elite ivory tower, hanging out in the faculty club with the coeds, and also giving A’s to students who to go work as robber barons on wall street and pledge allegiance to Nozick or von Mises. He doesn’t walk his talk, like a bunch of preachers who are essentially con men. Of course that may be a good strategy—if you make your living talking about the poor and the least among us, its good to send your students out to dupe and then foreclose on people so you have something to alk about. Its like the people here who were reparing bus seats—after work, they’d go and slash alot of them up. the way a farmer must work to plant seeds to get a harvest. . (There’s a ton of people like this—lawyers in the hague teary eyed and seeking justice by prosecuting war criminals who will never be found, making fat salaries—and those war criminals did their crimes basically because they couldn’t get a cushy job in the hague since they weren’t on the govt payroll. All these ‘institute for peace’ people who want the US Government/taxpayer to fund their institute (which a few times a year will welcome the public for an inspiring talk on peace) so they can sit around and write policy papers citing John Rawls, Martin Luther King, Ghandi, Jesus, the Dahli Lama. We want a piece, and now we can afford to get one.
end of rant—————
As regarding the randomnness (entropy)/determinism equivalence, and the capitalism/communism equivalence, i would say 2 things—if one looks at general equilibrium theory in econ (arrow-hahn etc.) under certain reasonable assumptions (eg that people are basically the same, all self interested, all want the same thing, all have deep compassion for the poor and love of humanity, all believe some things have intrinsic value that can’t be monetarized (eg spirituality), all want to rule the world and also be able to buy anything or anyone money can buy or just take it if its not for sale, then the unique stable (obviously) pareto optimal equilibrium is an equal income society. Just as if x=1/x then x =+1 or -1, (own inverse) Adam Smith=Rousseau. (Of course you have to translate everything into cash values. A famous think tank, which funds a ton of famous scientists including noble prize winners—the John F Templeton foundation—has done this in their ‘spiritual economics’ track, as have many catholic economists i’ve read—i think they can show that good catholics, and christians in general, don’t believe in government (except of course when they fund with $millions so-called ‘catholic charities’ which serve the poor) believe people can and will, if they follow biblical principles, tithe and give to charity so there is no need for a government ‘safety net’ —for example, if people did the ruight thing and tithed 10% of their income the Catholic diocese would be able to pay off all the lawsuits brought against them by the children of their congregations. (This would be an example of a conservative system in perpetual motion, though it can easily be generalizable to the nonequilibrium nonconservative case, since those who receive payoffs from the church for lawsuits can then give to charity, by tithing to the church who can then settle lawsuits against their children, and so on.) (As noted, since max entropy solution is the same as the deterministic one—an apparent contradiction— you have to ‘break it down’ as they say, which is where the Gibbs/Boltzmann distinction comes up. The ‘unique stable equilibrium’ actually has ‘degeneracy’, so what looks like a single point in ‘mu’-space (boltzmann) is actually a huge number of points in ‘tau space’ (gibbs)—in fact the biggest part of that space when ‘coarse grained’. (I.e. its just an illusion like time. Its purely subjective, and a bias. Its like people who look at a billboard, and think it says something like ‘coke is it’, when actually if they took the time and care, they would realize there are many other interpretations if one uses a ‘fine grained’ microcanonical description. Coke is it may be the most probable interpretation but their are outliers in the list of all possible advertizements (or constellations, hallucinations, or configurations). ). Machover’s book ‘laws of chaos’ makes the same point. If you assume maximum entropy is optimal, then actually over time (the system ergodizes, time averages equalling space ones) then everyone will have the same ‘lifetime income’. Molecules in an ideal gas are not stratified. At all times some will be poor and others rich, but over time they all go through the same phases (points) (One can ‘fix’ maximum entropy’s inconsistancy with the empirical facts that people do inherit money and classes are often rigid with little social mobility, by saying something like lineages (ancestors and future generations) on average are all equivalent in income, which leads you into the mathematics of population genetics. Civilizations, like rock stars or wealthy families, rise and fall.l I am sympathetic to this idea in principle—rather than ‘races’ there are ‘clines’, and with genetic engineering in the near future every single person and animal will be able to mate with every other one, and even rocks and planets and bank accounts and hedge funds. That will be the maximum entropy solution. (Also, it permits the simplification of using money rather than utility, where money is seen as something like a superstring. All the different utilities are just different modes of vibration of the fundamental money particle. A related idea is http://arxiv.org/abs/0902.4274 if you haven’t seen it. I think Murray Gell-Man did a start on this with his quark theory, which if i recall has something like M1, M2, euros, yens, bitcoins, ithaca hours, etc. which go up and down but conserve color, charm, and other properties which enter into the utility function. (One conjecture is that supersymmetry exists, so there is also a futility function, referred to by people like Rush Limbaugh and Paul Ryan as lazy whiners, unlike them who talk hard for a living). ———– A couple of other points. I don’t think there is any real justification for preferring say, lognormal, pareto, exponential, beta or some other distribution of income (and i’d even say gaussian, or maybe popular opinion would aim for political correctness so i’d say ‘1 sided gaussian’ , though i could make an argument for the general case). There are reasonable ways to derive any of these—yakovenko gives 2 for the exp, one his own approach of max ent, and the other a more basic deterministic one (just as a fractal can be created purely deterministically or by a random process. Check out the prime numbers.) The lognormal is seen to come from multiplicative processes, sometimes, and pareto from ‘preferential attachement’. (increasing returns). (Part of the differences are due to whether you consider income of individuals or households—do babies have any income?) But there are hidden assumptions in these. For example, if one follows Yakovenko’s approach, but decides that not only individuals who reveive income are distinguishable by randomly exchanging money, suppose instead we take these indistinguishable individuals and randomly throw dollars at them—ie quantize the exchanges , and assume the dollars like people are distinguishable. Then you get a gauss distribution (urn model). Gertrude stein i think said ‘a rose is a rose by any other name’. Is a dollar a dollar? (eg law of one price). is a job a job? So maximum entropy solution is highly dependent on how you count your states (as you mentioned with fermions and bosons). For example 2 jobs which pay the exact same wage would be seen as identical and exchangeable according to Yakovenko’s model—they lie on the same energy surface. But some people might prefer a stipend as a grad student to working in fast food. They might follow Yakovenko and accept any job at a given wage, but then one would buy the others job and become poorer. (This fact is a basic one in economics—according to General Equilibrium theory, once the ‘walrasian engineer’ (invisible hand) has done ‘tattonement’ (calculated prices) there is no reason to actually do any exchanges. If I am starving and have 5$ to buy something you want to sell for 5\$, according to the theory the utility or welfare of the system is the same whether you do the exchange or not. Econ is timeless just like equilibrium statistical mechanics.
As i mentioned any distribution of income can be achieved as a maximum entropy solution by choosing your constraints (i think this is well known for exp, pareto, gauss, long normal etc.). In generasl econ, the same idea results from the ‘first’ and ‘second’ fundamental theorems of welfare economics if i recall—any distribution of income can be achieved—and it will be a unique pareto optimal general equilibrium—if at the beginning you set up the endowments (original incomes of people) the right way. Or you can transform any pareto optimal income distribution into any other by redistributing it. Since both are pareto optimal only some other criteria can be used to distinguisah betwen them.
This Rawls’ ‘original position’ concept, which is the same as that of equal a priori indistinguishable used in maximum entropy.
In some ‘coordinates’ a uniform distribution of income, or one where the Gini=0 will appear to be exponential or whatever. If you have an urn and distribute balls into them, you might just ask how many balls per urn exist; or you might say hiow many light ones versus dark ones, or how many of some color. Does it matter if you have N rather than M balls in an urn, or do you have to consider if you have some N, and also that the N conists of A dark balls, and B ligjht balls, or X, Y,Z… balls of different colors?
This is also why ‘phase transitions’ are important (interactions). You may think a maximum entropy is the most ‘productive’ (eg catalytic, considering chemistry). But thats questionable. ‘Optimal inequality’ may not be or always be say, lognormal. And, besides empirically it isnt. I guess we could have government fiscal policy orient towards this say, G=1/2 point, like 0 inflation. (You also seem to have a bit of that anti-tax libertarian streak—the government is stealing our money. Well, the government did more or less develop the internet, and most higher education in some way is dependent in part on taxes.
I’d also say, as far as i am concerned, much of private enterprise steal my, or ‘our’ money, because they are con men who sell crap and are as coercive as the IRS and police indirectly. )
Last, i actually read Azimuth (baez’ blog), off and on. I saw that article (i note he mentions a possible type in Lisi’s path integral).
The points I mention above regarding how you count states in statistical mechanics (the simplest situation when considering distinguishable particles versus quantum ones–ie bose and fermi stats) actually are sort of the topic of another john baez post on the front page—-chemical reaction networks, Thats closer to the way economic systems should be dealt with in my mind. y. These are very constrained interactions. (This is the kind of thing that got me interested in stat mech besides the fact that it was required classwork—i did an undergrad research project using max entropy to figure out aspects of the immune reponse—how different antibodies react with different antigens—-its not an ideal gas nor a simple random graph (where any 2 things can be connected to each other). There are mutliple constraints and multiple optima.
The same thing with income. If one is simply seeking any distribution with a Gini=1/2 one could do it deterministically —first in line gets the most, last gets the least (and also actually in quite a few ways—both who gets what positijn in line and how the portions are doled out). .
So the normative question is open. Facts=/Values. Is=/Ought. I think we need a variety of currencies which are mutually inconvertible. (One is going to have maximize a function of several variables, which means most likely multiple optima. You are for freedom and liberty—-in what? Freedom to take a walk without getting hit by a car, or freedom to buikl a highway where ever i feel like? Maximize income like in china, but have no clean air?) I am an ‘environmentalist’ so my view of maximizing ‘growth’ is not the same as what others mean by it.
(I started in math biology, as I noted; i wandered around and found a research project (with a visiting prof from Santa Fe institute); when i showed my prof in my math bio courses what i was studying he stopped talking to me, cuz he didn’t like the chaos and complexity approach)..
anyway. obviously i havent looked much deeper at your stuff.
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• A short reply. I had some thoughts on Baez paper and of looking at quantum systems. I like classical mechanics very much. There is a very simple elegance. However the domain in which it is applied is important. I was taking a course in nuclear physics and couldn’t help shake the notion that the system of a nucleus if its relaxation time is much shorter than our observation time scale, then what we observe at our macroscopic level will be a fixed number of quanta with defined probabilities of occupancy. I haven’t gone down that rabbit hole to even test the hypothesis, it is conjecture. What interested my about the quantropy post is that formalism strikes me as well suited for a variational approach to tease out the allowed quantum states. But this is dependent on a suitable mechanical model.
As for maximum entropy and the issue of path dependance. I agree those have impacts on the outcome and would provide greater insight. However, without that detailed information, and the construction of a suitable model to explain that information, arriving at a state of knowledge that included that information is impossible. The affect of including this information, only acts to lower the system’s entropy. These are restrictions on the actions of the individuals within that group. by assuming logical independence, indistinguishably, and time invariance the model provides a theoretical maximum on the entropy of the system. Only by the inclusion of extensive forces (not intensive constraints), can the entropy of the system increase. What is important to note in all of this is that the impact of those constraints is small, as the relative entropy from my very crude and simple model is close to that of the observed data.
For the path dependent data to be included it has to first be collected and analyzed with an appropriate amount of rigor. This has very real costs. In my simple model I looked at the data and sought a model that explained with the greatest parsimony. It happened also to have a wider applicability, including species distribution, and one that I found, in the distribution of Radiation Induced Foci in post irradiated cells. To me, the parsimony and the widespread applicability give this distribution better aesthetics over others. I chose it out of aesthetics really. However, as I noted in a previous comment the defining distribution defines the relationship between the $p$‘s and $q$‘s of the internal coordinate system. So while it may be aesthetics that guided me, there may be a deeper understanding to be gained.
If not the principle of maximum entropy then what other assumption do you propose as a guiding principle that assumes less. Yes the tendency of a system to the point of maximum entropy is a tendency toward ergodicity. This is clear that the change in information of the system with any increase in time is zero, $\frac{\mathrm{d}S}{\mathrm{d}t}=0$. It is a formal statement of what is ergodic. An ergodic system is one where our knowledge of the system does not change the longer we observe it. I recall mentioning something like this in Elementary Principles.
This is a very gross assumption, it does however, greatly simplify the math and provide an avenue for increased insight. What surprises me, is that even with all these terrible assumptions I can still explain the data with some fundamental insights. Increased sophistication and complexity often times makes it difficult to comprehend. This is why when we teach new nuclear engineers how a reactor works we use a one-speed time independent reactor under diffusion theory. What is really funny is that if we are very careful of how we compute the integrals for the cross sections we actually have a very accurate representation of the flux distribution in the core. When we look at the adjoint flux, we see that the location where the neutrons are “born” in the core has a significant impact on their importance in the system. In fact, we call the adjoint flux the importance. So, my brutally simple model that provides reasonable insight into income distribution and inequality shows very clearly the fundamental drivers of why it is the way it is. This approach and my experience guided my logic in selecting an appropriate model.
So what will the tendency be for society, to achieve a state of higher entropy. This will be through increased energy consumption and/or increased liberty. That is not a normative statement, that is positive. I am not a logical positivist either. I can just say what direction humanity is going. I can also say that ANY policy acting to restrict this tendency will create a force to overcome it. Why I like higher entropy is that it ensures survival. You could construe that as a positive statement, however I think self preservation is a normative value, as it tends toward a point of maximum entropy for the individual.
The current set of policy that we have, that I critique in my blog, tends to restrict our entropy. As a result our societal entropy is stagnating. This is very dangerous, as pressure is building to affect change and increase entropy. I had a very dear friend tell me, “There is no such thing as good or bad. There is only consequence.” I seek to understand the consequences. Here is my first law of public policy: restricting individual freedom increases societal pressure against the agency causing the restriction. impulse=>reaction. So as I said in a blog if we want to end global poverty, we must increase individual liberty and increase our energy consumption. The goal of ending global poverty is used to do some really wacky stuff that has no forbearance on the outcome and constitutes pouring money down a rat hole.
So here normative goal “end global poverty” has a defined set of policy outcomes, increase liberty and energy consumption, and that everything else is just mental masturbation.
Another normative goal “income inequality is a scourge on our society and we must have those who do pay their fair share” has a defined policy outcome where the stability of the system is reduced due to increased social stress due to a reduction in specific entropy in the developed nations. This lowers the overall societal wealth embrittling society making a extensive shock potentially catastrophic.
These are consequences of policy design choices. As an engineer I am constrained in my design choices by what I have available and the laws of thermodynamics. It is no different in public policy. Their problem is that they don’t understand that they are constrained. I’m reminded of a quote from The Hunt for Red October, the second officer to the commanding officer (Rameus’ old pupil) as a torpedo he shot performed a circular run after he ordered the ACR safeties removed, “You’ve killed us all you arrogant ass!” The policy makers removed the ACR safeties on a presumption of knowledge, just like that CO did. The safeties on the economy are free and unfettered markets with a strong common law. Just about every single policy we have disables each of these safeties.
There is only consequence.
1. To me ‘free market’ is too vague. Like max ent it works in ideal cases, but once you add in long term dependencies it becomes say ‘NP-complete’ if not undecidable (as is seen in evolutionary game theory) . And the common law is also NP complete or undecidable (Arrow’s theorem, condorcet, Donald Saari, S Brams…)
Maybe there is a common law (presumably the maximum entropy solution since its the most common or probable state of the union) and all the other ones are just fluctuations which will dissapear in the fossil record or universe. In a nonequilbium world, you may not know when you are there,
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(As an aside regarding your idea about decay of the nucleus, i guess i dont understand it, but that seems to me to be the accepted wisdom. A nucleus is a long lived (long in the sense that supposedly even protons decay) metastable state, like everything else we see. Thats why we see it. There may be ET’s who can’t see it, or the earth, because like rocks who don’t notice biological evolution , its not on their time scale. I bird watch sometimes, but unlike some others i have a hard time seeing them because they dissapear fast, like the mice in my apartment. I even missed the recent eclipse, and the Higgs boson.
The Ferm-Pasta-Ulam simulations (FPU) from the 40’s to test the ergodic hypothesis with a slight modification of the ideal model (ie they added a quartic interaction to couple harmonic oscillators) seems on point here—they didn’t find equipartition of energy (signature of ergodicity), ahnd that led to chaos, KAM, etc. theory, More recent work however suggests mayvbe they just didnt wait long enough. In other words, one could say the system has path dependendence, and there are several attractors of the system (which actually are all part of the same ergodic system) but it takes a long time to get from one to another.
Phase transitions, like plant succession and evolution of species, are really just phases the universe goes through, the way people go through adolescence, senility, etc, and then come back again (after quantum mechanically tunneling out of the cemetary; Count Dracula published on this in the 20’s, and modern crionics has rediscovered it. As an aside i was looking at a biography of famous serbian scienctists (many of whom seem to all have the same name) who include Tesla, and there was one around 1900 who wrote a book discussing economics and thermodynamics (who supposedly was very obscure).).
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You say ‘the safeties on the economy are free markets with a strong common law’. (So unlike some ‘market anarchists’ (David Friedman, son of Milton, at UCLA i think) you believe in some form of ‘minimal’ governemtn (as opposed to private ones like he believes—private armies, police, etc.— a sort of ‘tribalism’ though internationally the world operates the same way, as a set of tribes).
the question is ‘what is the common law’? Do you try to use, say, Coase’s theorem (do anything you want but compensate anyone for the costs your actions impose—-which as he noted is practically impossible to enforce, since people die in court). Should it be US or Universal Declaration of rights, the consitution, Sharia, 10 commandments or what?
Is the common law unchangeable? If not, is it ok for rich people to buy legislators to make the common law favor their interests (eg use ‘takings’ to bulldoze neighborhoods so they can build a sports stadium for rich m-frs, and the common law will also require that local government pay for the stadium, and also that players who get hurt within the first 3 years are not owed a dime.)?
Usually or often the common law is not for ‘commoners’ in some sense, though likely its named ‘common’ as a way to deceive people so they think it is for them. ‘Ask not what your country can do for you…’ Of course, people do love walmart, as do the rich people who own it. (They just built one near me, with a big fight over their minimum wage policy, and also the fact that local small businesses would be effected. They of ccourse gave tones of money to buy off local politicians and community leaders)..
Should GMO modified foods be labeled, cigarettes have warnings, we have laws about dumping toxic materials, regulations on nuclear power plants to avoid Cherbonyls (or high utility bills duem to having to replace reactors like Harrisonburg, Pa).
Does the market include ‘natural capital’—should we put a price on clean air, or should we permit the world to be like in China (or Pittsburgh and London in the 1800’s) and not force polluters to clean up their emissions? Do we regulate speech like in France where holocaust denial is a crime, or via FCC regulations on what is permitted to be seen or said on radio and TV, and also how you decide who gets a ‘ownership’ or lease’ of some frequency , and under what conditions you lose the liscense? Should there be a ‘fact check’ rule (beyond ones on nudity and profanity) so that if someone proposes that 911 was an ‘inside job’, or denies it, that AIDS is not caused by a virus (or is) and autism is (or isn’t ) caused by vaccinations, that evolution is false (see F Tipler.and Freeman Dyson’s signing of the discovery institute’s petition on ‘intelligent design’ ) or true, etc.
‘Should there be a ‘core curriculum’ in education, and should intelligent design be taught in biology? Should people be required to attend school, and should parents be required to provide for their kids? Is universal healthcare required by ‘common law’, and littering prohibited?
Is the US Consitution or US declaration of human rights, or Universal declaration (which differs from the US one because it does not require that people vote, serve in the military if asked, and some other things) the common law? Does it require that one let people of other races into your business or public school (eg civil rights movements), or that Catholic hospitals must perform abortions?
People say ‘your rights extend to the edge of my face’, but in a networked, non-ideal gas society there are long interactions—-should people be permitted to put on facebook private communications (eg pictures of your ex-freinds in compromising positions, or to ‘out’ gays )
or violent scenes (eg beating someone up ) or does common law prohibit this because it breaks the peace? Do free markets include speech? Should we tax carbon, or include it in the market? should there be regulations on elected officials requiring them to go out and shovel snow in atlanta?
The devil is in the details. ,
———–How many regulations? I like the idea in congress—first, you pass the law, then you read it. In education too—First i get the PhD, and then i do the research, and then i write the thesis. Following Herbert Spencer (libertarian) every baby when born should be endowed with a grant (including a bank account with their entire lifetime expected earnings, a full of academic degrees, honors, prizes, certificates for qualification as expert plumber, winning lottery cards, and valid id, property titles and driver’s liscense. Then they are abandoned and are ‘free to choose’ (milton friedman) in the unfettered free market (and then one sees if maybe they are ‘born to (o) lo(o)se’ (New York Dolls, a band on youtube—Frankenstein is my favorite—the US military shouldah used that in Iraq to torture people). Babies could then follow Marx and sell themselves to increase their grant (though it becomes impossible to determine whether, say, education is something you buy or instead is an income generator). Maybe employees employ their manager and company, and dogs own their masters.
Can max ent determine how many books should be in the library of congress or local one, and how many pages should be in the tax law, or steps in a proof of a theorem?
(An article in Parade Magazine by the genius May Savant (or something) actually solved this, by calculating how much energy is required to publish tax law and math journals, or store them in ‘the cloud’, see http://www.cs.nyu.edu/pipermail/fom/2013-November/017696.html
and the entire thread (esp 677 and 684) . It turns out Eugene Wigner discovered the common law (unless its ‘constructal theory’ by some engineer in NC which may be the same thing)..
Maybe we need another huge buerocracy to study how big the beurocracy, court system, etc should be— and maybe its required, by supersymmetry. As Ernst Mach and David Mermin (in qantum theory) showed, people need mirrors, and the moon needs people, to exist and shine, and this is why prohibition laws failed because we need moonshine (i used to get some from some ‘hillbillies’ i knew ‘up in the holler’.) (I met ‘mersol’ last nite— spanish for ‘sea sun’ when i was foolish enough to walk up the street at nite. Saw one of my ‘hoodlums’ selling dope on the corner; i gave him a beer to pass the time and deal with the ice and cold).
Interestingly, it turns out one possible solution among many for optimal lengths of tax codes, using an energy metric (eg H T Odum, R Constanza,etc. in ecological economics) is that ‘MOre can be better’!! because if one cuts all the trees and turns it into legislation one can then sequester it (like carbon) and then grow more trees, and keep doing the process, and soon you will get oil reserves, and life is happy ever and in perpetual motion. AS Say (actually didn’t) say, ‘supply creates its own demand’, and the reverse. (That was Keyne’s interopretation of Say, while what Say said was that using the perron-froebenius theorem you can find the fixed point of general equilibrium. Sonnenshein among others showed that just as its not unique for some set of fixed preferences and endowments, but also there is no way to assign a unique set of preferences.
Like max ent, its just a convention.
(Bitcoin is interesting in part because apparently consumers, or users, play the part of the Fed—they set the exchange rate. One day you use Haldane’s rule and value your family by genetic relatedness—your identical twin being more valuable than your nonidentical one, whose is more valuable than your brother and sister, who are worth more than your cousin, etc. and really valuable .
Next day you sell them all for a low price to buy heroin.
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You say increasing entropy and energy use should be the goals. (And that seems to follow from your ideas, as well as the equations).
I’m sort of an environmentalist, and also as noted have a different set of math asumptions (which actually are implicit in your work in nuclear power—-maybe on one scale you are increasing energy and entropy by liberating bound photons from their atomic prisons, but in the short run, to achieve this commonly accepted goal so people can heat their houses, entropy is lowered (since the math used to design does not follow zipf’s law in some coordinates and also is temporarily trapped in homes and bodies).
As noted, it might be optimal to build a lot of nuclear bombs and start using them—get a whole lot of energy and entropy. Make earth a sun, so some ET’s can get a suntan.
As an environmentalist, ‘free energy’ is what is important (the original helmholtz version, since pressure and volume are not inuitive for me , except in the sense of music—‘lets get small y’all’ (troublefunk) or ‘its like a jungle outside and i reaslly weonder how i keep from going under’ (grandmaster flash) or ‘submission ‘ (sex pistols) or ‘once in a lifetime’ (talking heads).
Energy conservation should be the priority. I’m not hardcore (though i have participated in some EF! and Sierra Club, 350.org protests etc As a precautionary princiiple, before trashing the earth by the Keystone XL, offshore drilling, etc. see if you really need it.
I don’t think alot of suburban sprawl is desirable, and all these truck drivers listening to rush limbaugh on publicly owned hate radio who are delivering cigarettes and guns and bottled water and junk food maybe should get off the road and stay home and find something to do like get a m-fing grip by reading some science. Maybe an ‘unfettered free market with a strobng commobn law’ would achieve that goal, but, as Johnson said about socialism—‘we could have it tomorrow if we had the votes’.
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I looked over your longer paper up front. I don’t understand equn 8 (i think—multiply by 1, etc.) but i don’t think i really need all the first part to understand probability or definition of utility, in a general sense. Your thermodynamic derivations remind me of why i don’t like the Gibbs approach (which i glanced at in the original, and also saw it in Tolman’s book on stat mech and in ‘Gibbs Ensemble, Biological ensemble’ by E Kerner (a Feynman PhD,who also had a VSL thoery in the 60’s). .
I haven;t looked at this stuff in a while, but the Utility you identify as E (or H) somehow to me seems to be not quite what i was thinging of—-i was thinking of ‘individual utility’ (eg my cobbs-douglas or other function) while you are looking at the whole economy. I’ll have to think about it and look some more. I guess in a retarded view, one just sums the individual utilities to get the global one (which i think of as the ‘social welfare function’—utility of the whole society.
From that view, which is how I interpret stuff like Wolpert or spin glass/ising models or S Kauffman’s / S Wrifght’s ‘fitness landscapes’ you end up due to multiple competing interactions a whole lot of possible configurations in the maximum entropy solution, but its multimodal not gauss, exp, lognormal, pareto etc (except in the way that the earth’s surface is normal or gaussian—sure, if you list mountains, heights of people, lengths of sentences and books,you can get a common distribution (most of which in my view are actually almost the same—there’s a paper by Snyder (israeli econo/physicist) which points out ‘power laws’ are canonical ones in disguise, as is also true for lognormal (depending on choice of utility function, as shown in one of the papers I mentioned). (This also seems to be ‘elementary probability’—in various limits (choose your prior of greatest utility) various distributions become equivalent.
The Gini may be 0.5 at maximum entropy, and that may be most desirable state of affairs, but that leaves out some details, like geography—maybe the world’s mountains (and incomes) are distributed optimally but people might prefer to hasve the himalayas over there, the appalachians over here, McLean virginia and madison avenue somewehere else, and the ‘hood down there.
I am actually theoretically open to the idea of a jmax ent income distribution (exp, logN etc.) but think maybe it should be randomly distributed, maybe by lottery, and maybe there should be ‘term limits’ (or as was done with some alternative US currencies in the past, currency would be like coupons or fruiit, and expire or rot—you’d lose it if you dont use it). .
——-I guess i wonder whether you have an agenda or idea with your papers—maybe just free markets and increasing energy use (more (and) freer is better, ) I actually believe that, if that also means we include ‘more’ things in the more. I’d like more wilderness for example, since i use it to use up (my personal) energy. I’d like more people highly educated in math/sciences, and less garbage talk whether on radio, the street, CSPan, etc.
Possibly, for example, regulations conerning degrees and credentials like PhDs should be abolished, and everyone could just set up shop for a free market in ideas….(the blogosphere is in that direction). ola (as some say around here).
• You are quite correct that in the real world (non-equilibrium) that our knowledge of the equilibrium condition will be fuzzy, never knowing precisely where you are.
Common Law is an emergent process that is discovered. It exists only as an aggregate of individual action. It does not contain the information of the microscale interactions but is instead a macro phenomena. This is congruent with Hayek’s take on the law. Every individual is bound by it, but is not necessarily aware that they are bound by it. Additionally the discovered law (written by judges) does not contain the full depth of the actual law. It comes back again to the knowledge problem. The law exists without the constraints of government. While, government can exert pressure to influence the law, through legislation and the coercive threat of force, it can not subvert it. The extent to the divergence between the legislation of government and the emergent law is a direct measure of the amount of force the government must exert to maintain it’s control.
For the record, common law was the law of commoners. Nobility was subjected to a separate set of constraints.
You have a misunderstanding of Coase’s theorem. His work was a reaction to Pigou’s arbitrary method of price internalization. What Coase does, is to establish a market to discover the price of the externality, without the presumption of knowledge of the price. The main way that he does this is through the creation of a property right. To quote Coase “I’m just a person who thinks that the government should give up everything. How much the government should give up will be found by studying how the government operates. But the assumption that governments always do the right thing is not true. They make lots of errors, and where they are most likely to make errors can be found by studying how governments operate. My approach to the subject of what governments should do is to be based on studies of how governments actually operate. And I’ve had a lot of experience. I worked for the British government for many years, and I saw how decisions are made. And stupidity is very common.” http://www.econtalk.org/archives/2012/05/coase_on_extern.html His approach is to deal with the world as it is, not as we wish it would work. Coases’ solution to the price discovery problem actually has a limited applicability (wide enough to be significant). It only applies to situations where the cost of establishing the property right are low enough and the social harm high enough to warrant creation of a market.
Should GMO’s be labeled? Only if they want to be. If somebody wants to dictate their own marketing by all means, but to dictate the marketing to society, that’s unclear. So far, there has been no reproducible harm from GMO’s. That may change, but it is not a reason to not use them. The precautionary principle is just a simple means to force your beliefs onto others. It is used to inhibit innovation and restrict competition to existing firms. As for cigarettes, I think that should have been settled in the court system not in regulations. I have no issue against another individual for voluntarily entering agreements with knowledge of a potential harm to themselves.
Actually there was a great deal of common law that governed the handling of toxic materials. Taking Love Canal as an example the disposal of the waste exceeded EPA standards when the standards went into affect almost 25-years later. Common law and proof of damages would provided an incentive for them to limit their liability to the extent that they could. The issue was with the school board (government) wanting cheap land to build a school and ignoring the warnings of the chemical company. So who was at fault? What role did government presume to take in this. What did the resultant regulations solve?
I think it is presumptive for government to regulate what Adam Smith refers to as “propriety”. Propriety is much too complex to put into regulation. Let’s look at how the market would resolve censorship. Say a broadcaster had a vulgar show that the advertiser was looking at placing an add. Let’s say a large number of the advertisers customers complained saying that they wouldn’t buy the advertiser’s product anymore, because of the chosen venue. The advertiser would pull their advertising to prevent the loss of customers. This would impact the revenue to the producers of the show as the network would pay them less. Giving the producers less of an incentive to produce the show. Their reputation would be harmed and they would be less likely to land a pitch. This is just a simple example of Bastiat’s seen and unseen.
You underestimate in your examples the social repercussions of trollish behavior. I saw on a number of blogs the impact of social constraints on individuals who behaved in thuggish behavior. I also witnessed backlash on Facebook and Twitter watching people be ostracized for their behavior. There are also repercussions with employers who search social media. If someone is brutish in an unsupervised media what will happen in your work force if that individual is left unsupervised. They will likely have a negative impact on productivity. Again it is the seen and the unseen. Be very careful about what you presume. You seem to have a lack of faith in humanity. The devil is indeed in the details. The details are in fact so complex that any well intentioned presumption to do good, paves the road to hell.
You also misunderstand what maxent is and what insights it provides. First let’s look at what entropy is within a society. Entropy as popularized is not about disorder. It is complexity. Entropy is a descriptor of the complexity of the internal structure of the system being observed. While complexity may initially be perceived as disorder. It is not. Let’s take the nuclear bomb example. To illustrate the point. A bomb is detonated over a city. and it levels the city. First looking at the biodiversity, most life that was in the city is greatly reduced, plant, animal, and human. With only a hardy species and some other lucky survivors left. The entropy of the biodiversity is now much lower. Looking at the height of the buildings in the city, the entropy there too is greatly reduced. There is no more complex topography, it is leveled. Measuring the economic activity, where was once a vibrant city is now nothing, but some survivors caring for the dying and burning the dead. Again a much lower entropy.
Death and destruction are characterized only by their ability to reduce entropy. The use of nuclear weapons does not increase entropy, it reduces it. It is why I cannot stand nuclear weapons. They are vile things. On the other hand the use of nuclear energy greatly increases societal entropy. It also increases biodiversity as the quantity of fauna supported by the rejected heat is prodigious. Nature is very good at taking waste and making it into something beautiful. I too am an environmentalist. You should read my paper on Rational Sustainability, posted on this blog.
Energy conservation as a mandated social value is used only as a tool to fund boondoggles. It ignores the cost of replacement, the impact on existing assets, and presumes one metric as the measure by which firms and individuals should direct their resources. As an engineer, I am obsessed with efficiency. However, if I make something so efficient that nobody ever buys it, it has no value to society, or to me for that matter.
Our goal should be to expand our energy consumption, not reduce it. Here, I will be proved right. The global poor, those without, will want what we have and the energy we consume. They are markets that are untapped. Their energy use will skyrocket, and be predominantly fossil based, initially. This will put price pressure on our fossil resources. Fossil cannot scale much further, because it lacks the needed energy density. Density and the ability to scale are directly related. For this reason alone, the developed world will shift to nuclear energy and synthetic fuels or it will bifurcate.
Again my question to you is, “If you choose not to adopt maximum entropy as a proposition for logical inference, then what metric do you propose that presumes less?” I’d like to know, in case there is some other form of inference that I am as of yet unaware of. All of the conclusions and examples that I used above are consequences of a system that tends toward maximum entropy. You continue to presume too much.
6. thanks for responding—-i looked over my comment, and it was pretty incoherent plus alot of typos. i will say you are a ‘real person’ who knows your stuff (nuclear engineer).
i figured out your paper—and that’s why i cited david wolpert. (and there are a few others—i could cite john baez/azimuth but thats not the way to go–he gets lost in the details.). you could always read a book on statistical mechanics. (i can’t reccomend any, but try ‘fokker-planck equation’ by risken, ‘handbook of stochastic methods’ by gardiner, stuff by h haken (synergetics), or even landau and llfshitz from the 20’s or 40’s.
you don’t seem to understand max ent. (and i didn’t see any derivation of cobb-douglas or lognormal in your papers—you ignore or just assume it; some derivations exist, but i don’t see it it in your papers).
the metric is in the wolpert paper, though not explict. (like i said, they are other ones, but they get into heavy math—-though its actually simple—i worked with some of em)
it doesn’t appear you even understand coase or pigou. you have to include the transaction costs—thats why they have energy efficney—or, what i call (helmholtz) ‘free energy’.
as a disclaimer i have so many family members involved in university of chicago that stuff is like coase’s . theorem was elementry school.we just focus on rg wilson (renormalization group) and stuff by leo kadanoff.
peace out
• Thank you for the feedback and suggestions. I will read through them. I started with Gibbs, as his was to me the most intuitive explanation, $\frac{\mathrm{d}s}{\mathrm{d}t}=0$, of constraining the variational problem. You are quite right, there is much in there I don’t understand, especially with non-equilibrium discrete cases. My method is very blunt and not nuanced and as a result it misses much finer grain detail. You have no argument with me there.
My selection of the density function is similarly crude. The Cobb-Douglas function is a polytropic process (equation 20 in the various properties of log normal). Power law also falls out of the more standard Maxwellian distribution. The process defines the thermodynamic path of the system (how entropy is gained/lost).
The establishment of markets carries transaction costs, Coase went into that in his first paper “The Nature of the Firm”. The issue is with the relative transaction costs. Based on the Helmholtz free energy of the system (wealth, or measure of the potential for action) the relative transaction costs become a much smaller fraction of the total value gained. This is why, I think, problems in the commons in the past had to rely on social mechanisms, because the relative transaction costs were quite high. Whereas today, the overall increase in wealth changes the relative transaction costs and provides a different set of options, where the use of markets to establish prices becomes the most effective option. I will look at those references that you suggest.
This is also part of my critique of the Rawls. He assumes that the concept of justice is a fixed ideal. I see justice as defined by the system and must be considered within the context of the constraints on that system (such as resource availability and path history). Justice, in my understanding is the internal structure of the system that provides the greatest entropy. The path is critical here, because of the local entropy maxima. These have barrier potential to get to a more global maxima. Funny, when I think about this these state transition barriers act as social transaction costs, much like when evaluating the potentials around critical points. As we approach the entropy barriers between the states lessens allowing simultaneous existence of both states. Or when we think about phase transitions like the transition form water to steam, the process of boiling can be thought of as the emergence of mixture distribution, where the relative probabilities determines the quality factor of the system. My most recent post (Nuclear and Cryptographic Renaissance) you can see the dromedary emerge from the mixture “camel” distribution.
I have Gallaghar’s “Stochastic Processes” but have not had time to read it. I don’t have a solid grasp yet on how to handle the time domain with enough rigor. So, I greatly appreciate your suggestions. To understand QM models and Stat Mech from a different perspective I have Landau-Lifschitz and am working on that. Interestingly, Lev Landau has a tremendous appreciation for Gibbs approach. I gained a much greater understanding of Gibbs and Jaynes from Landau’s insights. As I read Landau it seems the Markovian process of the evolution of a system is an evolution of the system’s density function. I am going to go through the Wolpert paper as that seems cogent and well thought out. I agree, Baez is interesting but overly complex. His complexity has complexity which makes it difficult to understand.
• One more comment on how I use entropy to evaluate and develop models. I copied Jaynes. This paper he goes through the construction of a model of Rudolph Wolf’s dice experiment http://bayes.wustl.edu/etj/articles/entropy.concentration.pdf, beginning on Page 11, although the rest of the paper is well worth a read. If you don’t mind, I’d like to resolve what the difference that we have in what entropy and more specifically what is the principle of maximum entropy. While there is a possibility that we are both right, that would also imply that to a certain measure we are both wrong. You asked earlier what my agenda is, my only answer that it is to understand.
7. Thanks for responding. (I had some hostility in my comments, so i apologize for that (unfortunately i still have the mentality of a 4 year old who explains ‘im going to take you all out( not to a restaurant, but beat you up) because i disagree'(and i couldn’t back it up—see ‘wobble baby’ v.i.c (your part of town—of course i live off georgia avenue (dc’s maximum entropy solution) and we donated this name to the south because they needed an extra quantum state. )
i’m not sure if you have revised your main paper or i missed it, but from my perspective its looking better). (you have something like a louiville equation in there, plus the basic formula for utility maximization. i’ll have to look at equation 20 in your lognormal paper. i am more of a historian—i have many many papers on this sort of issue; wolpert is more close to your issue, and i cant find the other one (someone with a polish name—free energy of graphs with a chemical potential ).
(landau and lifshitz stat mech was one of my bibles—i also like george mackey on group theory (he’s on wikipedia and his classic paper on ‘harmonic analyses as the exploitation of symmetry’ in Bulletin of Am Math Assn 1980—free on web) is also one, plus stuff like on the FOM-list (foundations of math).. Also, i was thinking of C W Gardiner ‘s book ‘handbook of stochastic methods’. (i just google searched it, and downloaded it—someone put it on the web cuz i couldnt afford to buy one—its actually mostly fairly basic but has some stuff in the end which is more state of the art—-path integrals a la dirac/feynman/kac).
the jaynes paper you cite also is one my influences (plus a few other ones). (ariel caticha (on arxiv), golan (info-metrics institute at american university in dc —duncan foley is part of that too are in that way of thinking–but i call that boltzmann as distinct from gibbs—they count ‘particles’ (eg n factorial) rather than dealing with tau space (microcanonical ensemble)).
well it looks several feet of snow and i have to out. also, since i’m almost from dc (i moved here from arkansas where we produce presidents and garbage (walmart, faubus, tyson foods) i have to catch a plane to hawaii tomorrow for a family visit, and see if obama has a valid green card, and if not i can go see some of those green mountains up there and try not fall.
I don’t think we necesarily disagree. But i do have a big agenda, though i can’t recall what it i—maybe if read these thousands of papers i i’ll remember. Now i work for a local equilibrium as opposed to global (shower, hit the store quickly if its open), pack, clean up this joint, shut everything down, and try to make it to my staging ground for the airport (my brother’s house) (some think they have a serial killer there in alexandria va because of some recent murders so i’m hoping they can get rid of that person or persons). peace, out. i may not be on internet much for awhile but i’ll check back, to see if we stil have a conversation. | 18,381 | 84,259 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 14, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2022-33 | latest | en | 0.945333 |
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# Very simple 2sec timing circuit help needed
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#### Meza
##### New Member
Hi there,
I have an very basic circuit consisting of a reed-switch, a 9v battery and an electromagnet. Told you it was basic
This circuit is the contents of my £40 electric cat door! I was a bit gutted when I took it appart to find it so basic, but that makes the next job easier I s'pose.
The problem is my cat doesn't hang its head around long enough for the electromagnet to unlock the door and thus can't get in.
I am looking for a circuit to add a 1 or 2 second delay in holding the electromagnet open. Can anyone let me know how to build something which would do the job? Thanks very much!
Meza
a simple 555 in monostable way is the best thing
*remembers back to school!*
What I want is a high output for two second after a brief trigger input, and it needs to reset itself each time... is that correct?
And will a 555 monostable give me that? The circuits I've found so far seem to be low for an X time, then go high and stay high.
Perfect!
go to the one that says
LM555 Monostable Oscillator Circuit Diagram
you need an ative low trigger
ahh good stuff thanks
Hi Meza,
I'm thinking that your cat has a collar with a magnet?
and that this operates a reed-switch?
and that the reed-switch operates some kind of latch?
Hopefully to let only your cat through the cat-flap.
You said it is simple,
and you want something simple to try to hold the latch
a bit longer, cos your cat doesn't come straight in.
How about trying an electrolytic across the latch-coil?
Maybe 100 MFD just to see how long it will hold the
latch.
If you find that it wants more than 5000 MFD, then
maybe this method might not be good for the reed switch.
Because it would take quite a surge, but then as its a
battery, maybe the reed switch will be ok.
See how it goes, let us know either way,
Cheers, John
John, you got it
I will give it a go, thanks for the suggestion. Will the fraction of a second the reed is closed for at the moment be enough to charge the cap do you think?
Hi Meza,
well, cos its a battery i dont think it would damage
the reed switch,
As to the short time the reed switch is closed,
it wont be so short as all that,
even a brief blip would do.
Let us know how it works out,
Regards, John
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EG260 Solutions-example_2
EG260 Solutions-example_2 - [email protected] Slone 2008 EG260...
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Unformatted text preview: EG-260 @Avril Slone 2008 EG260 Dynamics - Example Sheet 2 Single degree of freedom systems Answers 1.i).Moment of inertia ( )2bamI+=Let θbe angle of rotation Then moment( )( )θθ2kasinaak−=××−(small angle approximation) So that the equation of motion is 2=+θθkaI&&or 2=+θθIka&&( )22=++θθbamka&&mkbaan+=ωii).Rotation is about OMoment of inertia about pivot = I, moment of inertia about cg = IGUsing the parallel axis therefore, 2mrIIG+=Restoring moment (decreasing θ, negative) = θθmgrmgrM−≈−=sinsfor small θ Newton’s Second Law: θθθmgrsinmgrI−≈−=&&mg r θ OEG-260 @Avril Slone 2008 So ( )2=++θθmgrmrIG&&2mrImgrGn+=ω2.First determine the moment of inertia of the disc Consider an annular element ( )hxxxmxIρδπδδ222==where h,ρare the density and thickness. So ∫=⎥⎦⎤⎢⎣⎡==rrGhrxhdxhxI4432422πρπρπρBut the mass of the plate 2hrmπρ=So that 22mrIG=Now the disc rotates by θsuch thatφθlr≈The tension supporting in any one wire is T where...
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Ask a homework question - tutors are online | 509 | 1,611 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.640625 | 4 | CC-MAIN-2018-09 | latest | en | 0.610339 |
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Home » St. Georges » Types of angles notes pdf
## special types of angles Exeter Township School District
Quadrilaterals Class 9 Maths Notes Download in pdf. Angles can be classified by their measure:Right angles are angles that measure 90°. It is often indicated by a square.Acute angles are angles that measure between 0 and 90°.Obtuse angles are angles that measure between 90 and 180°.Straight angles are angles that measure 180°., Classifying Angles Notes angle – two rays with a common endpoint called the vertex example: vertex (pl. vertices) – the point of intersection of two sides of a polygon.
### Adjacent Vertical Supplementary and Complementary Angles
Surveying traverse - for web.ppt. Math Handbook of Formulas, Processes and Tricks 10 Angles 11 Types of Angles Chapter 2: Proofs 12 Conditional Statements (Original, Converse, Inverse, Contrapositive) 13 Basic Properties of Algebra (Equality and Congruence, Addition and Multiplication), 1 Introductionto BasicGeometry 1.1 EuclideanGeometry andAxiomatic Systems 1.1.1 Points, Lines, and Line Segments Geometry is one of the oldest branchesof mathematics..
Naming Angles What’s the secret for doing well in geometry? Knowing all the angles. An angle can be seen as a rotation of a line about a fixed point. In other words, if I were mark a point on a paper, then rotate a pencil around that point, I would be forming angles. One complete rotation measures 360º. Half a rotation would then measure 180º. A quarter rotation would measure 90º. Let’s Naming Angles What’s the secret for doing well in geometry? Knowing all the angles. An angle can be seen as a rotation of a line about a fixed point. In other words, if I were mark a point on a paper, then rotate a pencil around that point, I would be forming angles. One complete rotation measures 360º. Half a rotation would then measure 180º. A quarter rotation would measure 90º. Let’s
Classifying Angles Notes angle – two rays with a common endpoint called the vertex example: vertex (pl. vertices) – the point of intersection of two sides of a polygon Types of Triangles: 1) Equilateral Triangle – a triangle with all sides equal and all angles equal. Each angle will measure 60degrees. 2) Isosceles Triangle – a triangle with two equal sides and two equal angles.
Angles Teacher Notes Introduction This unit is mostly intended to strengthen students’ understanding of what an angle is. A surprising number of students get to high school without a strong sense of this, and therefore are seriously handicapped in geometry. The unit can also be used to reinforce number sense and mental calculations skills. Indeed, students should calculate the answers, not This lecture note is prepared for Environmental Health Science Students who need to understand measurement of distances, angles and other similar activities. It is designed to give the student the basic concepts and skills of surveying for undergraduate level. This material could have paramount importance for the health professionals who are involved in public health activities. Public health
Geometry Notes Perimeter and Area Page 3 of 57 Since our figure has all right angles, we are able to determine the length of the sides whose length is not currently printed. Angles can be classified by their measure:Right angles are angles that measure 90В°. It is often indicated by a square.Acute angles are angles that measure between 0 and 90В°.Obtuse angles are angles that measure between 90 and 180В°.Straight angles are angles that measure 180В°.
Name: _____ Page 2 Math Notes: Types of Angles acute angle - an angle that is less than a 90 degree angle. An acute angle looks like a book that is more closed than open. Geometry Notes Perimeter and Area Page 3 of 57 Since our figure has all right angles, we are able to determine the length of the sides whose length is not currently printed.
Name: _____ Page 2 Math Notes: Types of Angles acute angle - an angle that is less than a 90 degree angle. An acute angle looks like a book that is more closed than open. Angle Strain: Strain caused when the actual bond angles in the atoms of the molecule differ from the ideal bond angles of their geometry. There might be some confusion between torsional and steric strain; the
Plane Geometry Notes Theorem 1. If a triangle is isosceles (i.e. it has two equal sides) then the angles opposite the equal sides are equal. Also, if two angles of a triangle are equal then the two sides opposite the equal angles are equal, so that the triangle is isosceles. Lines and angles In the following diagram the two horizontal lines are parallel. The line cutting the two par-allel any different types of quadrilaterals as they can with tangrams. They will draw sketches and note: i. sum of interior angles; ii. side lengths. iii. evidence of parallel sides To reinforce students’ understanding of the characteristics of quadrilaterals, ask them to sort and label the different types of quadrilaterals (e.g. square, rectangle, trapezoid, rhombus, etc.) Sum of the Interior
Angles. Types of Angles. 120° 140° 100° An. gles in a full turn all add u. p to 360° 120° 60° Angles in a half turn all add up to . 180°. Note how this is half of a full Triangles: A Reference Sheet Triangles have three sides and three angles. The sum of the three angles of every triangle is 180 degrees. Classifying Triangles Using Their Angles Acute Triangle All angles are acute. One right angle One obtuse angle Other angles are acute. Other angles are acute. All 3 side lengths measure the same. Two sides measure the same. None of the sides measure the …
different types of lines and angles? Lines and Angles Notes 5 September 24, 2018 Types of Lines: Lines and Angles Notes Subject : SMART Board Interactive Whiteboard Notes Keywords: Notes,Whiteboard,Whiteboard Page,Notebook software,Notebook,PDF,SMART,SMART Technologies ULC,SMART Board Interactive Whiteboard Created Date: 9/24/2018 12:12:40 PM Unit 8 Grade 9 Applied Plane Geometry Lesson Outline *Note: • illustrate and explain the relationship between angles formed by parallel lines cut by a transversal and interior and exterior angles of triangles and quadrilaterals; • determine some properties of sides and diagonals of quadrilaterals. Note: Students may have a very broad range of experience with using The Geometer’s
CH. 1 Guided Notes, page 16 5. Two angles form a linear pair. The measure of one angle is 4 times the measure of the other. Find the measure of each angle. Math Handbook of Formulas, Processes and Tricks 10 Angles 11 Types of Angles Chapter 2: Proofs 12 Conditional Statements (Original, Converse, Inverse, Contrapositive) 13 Basic Properties of Algebra (Equality and Congruence, Addition and Multiplication)
any different types of quadrilaterals as they can with tangrams. They will draw sketches and note: i. sum of interior angles; ii. side lengths. iii. evidence of parallel sides To reinforce students’ understanding of the characteristics of quadrilaterals, ask them to sort and label the different types of quadrilaterals (e.g. square, rectangle, trapezoid, rhombus, etc.) Sum of the Interior Types of Triangles: 1) Equilateral Triangle – a triangle with all sides equal and all angles equal. Each angle will measure 60degrees. 2) Isosceles Triangle – a triangle with two equal sides and two equal angles.
The most common types of whitworth thread are: • BSPP (G) – British Standard Pipe Parallel • BSPT (R/Rp) – British Standard Tapered Pipe, for pipes and tapered thread. Name: _____ Page 2 Math Notes: Types of Angles acute angle - an angle that is less than a 90 degree angle. An acute angle looks like a book that is more closed than open.
Plane Geometry Notes Theorem 1. If a triangle is isosceles (i.e. it has two equal sides) then the angles opposite the equal sides are equal. Also, if two angles of a triangle are equal then the two sides opposite the equal angles are equal, so that the triangle is isosceles. Lines and angles In the following diagram the two horizontal lines are parallel. The line cutting the two par-allel TEACHER NOTES Aim Students find and model angles with the Angle Finder diagram. Before the Activity Copy and distribute pages 63–64. During the Activity Students can work through this activity individually or in groups of three or four. If they work in groups, be sure each group member looks for all three types of angles. On stairs, tables, or in other places, students might find angles that
Classifying Angles Notes angle – two rays with a common endpoint called the vertex example: vertex (pl. vertices) – the point of intersection of two sides of a polygon Naming Angles What’s the secret for doing well in geometry? Knowing all the angles. An angle can be seen as a rotation of a line about a fixed point. In other words, if I were mark a point on a paper, then rotate a pencil around that point, I would be forming angles. One complete rotation measures 360º. Half a rotation would then measure 180º. A quarter rotation would measure 90º. Let’s
Special Types of Angles Objectives: …to determine measures of complementary, supplemen tary, and vertical angles …to name or identify complementary, supplementary, adjacent, and vertical Third Angle Theorem If two angles of one triangle are _____ to two angles of a second triangle, then the third angles of the triangles are _____.
### Types of Angles ny24000063.schoolwires.net
SOLID STATE Notes National Institute of Open Schooling. TYPES OF ANGLES: Acute, Obtuse, and Right MOST UNIQUE FREEBIE Printable Anchor Chart Poster Project and Music Video with Activities Download our ANGLES Lesson and discover an exciting new way to teach math to your students., Triangles: A Reference Sheet Triangles have three sides and three angles. The sum of the three angles of every triangle is 180 degrees. Classifying Triangles Using Their Angles Acute Triangle All angles are acute. One right angle One obtuse angle Other angles are acute. Other angles are acute. All 3 side lengths measure the same. Two sides measure the same. None of the sides measure the ….
SOLID STATE Notes National Institute of Open Schooling. Name: _____ Period: _____ Date: _____ Author: Jeff Twiddy Created Date: 4/25/2016 12:43:13 PM, Geometry Notes Perimeter and Area Page 3 of 57 Since our figure has all right angles, we are able to determine the length of the sides whose length is not currently printed..
### Types of Angles CourseNotes
SOLID STATE Notes National Institute of Open Schooling. angles between points that found the boundary of a site We will learn several different techniques to compute the area inside a traverse Introduction Surveying - Traverse Surveying - Traverse Distance - Traverse Methods of Computing Area A simple method that is useful for rough area estimates is a graphical method In this method, the traverse is plotted to scale on graph paper, and the number Types of Triangles: 1) Equilateral Triangle – a triangle with all sides equal and all angles equal. Each angle will measure 60degrees. 2) Isosceles Triangle – a triangle with two equal sides and two equal angles..
• How Do We Measure Angles? ABCTeach
• Name Page 1 Math Notes Types of Angles angle two that
• Types of Angles Notes and Practice Fun Educational
• TEACHER NOTES Aim Students find and model angles with the Angle Finder diagram. Before the Activity Copy and distribute pages 63–64. During the Activity Students can work through this activity individually or in groups of three or four. If they work in groups, be sure each group member looks for all three types of angles. On stairs, tables, or in other places, students might find angles that Geometry Notes Perimeter and Area Page 3 of 57 Since our figure has all right angles, we are able to determine the length of the sides whose length is not currently printed.
Angles. Types of Angles. 120В° 140В° 100В° An. gles in a full turn all add u. p to 360В° 120В° 60В° Angles in a half turn all add up to . 180В°. Note how this is half of a full vertical angles from the total station and can perform numerous calculations using operating software which is loaded into the unit. SDR 33 is an electronic notebook made by Sokkia.
TIPS4RM: Grade 8: Unit 4 – Lines, Angles, Triangles, and Quadrilaterals 3 . Whole Class Math Congress As pairs share the answers from the BLM 4.1.2 chart, other students are responsible any different types of quadrilaterals as they can with tangrams. They will draw sketches and note: i. sum of interior angles; ii. side lengths. iii. evidence of parallel sides To reinforce students’ understanding of the characteristics of quadrilaterals, ask them to sort and label the different types of quadrilaterals (e.g. square, rectangle, trapezoid, rhombus, etc.) Sum of the Interior
Angles can be classified by their measure:Right angles are angles that measure 90В°. It is often indicated by a square.Acute angles are angles that measure between 0 and 90В°.Obtuse angles are angles that measure between 90 and 180В°.Straight angles are angles that measure 180В°. 137 Solid State MODULE - 3 Notes States of matter amorphous solids. In Greek, a means without and morph means form. Thus the word amorphous means without form.
TIPS4RM: Grade 8: Unit 4 – Lines, Angles, Triangles, and Quadrilaterals 3 . Whole Class Math Congress As pairs share the answers from the BLM 4.1.2 chart, other students are responsible Plane Geometry Notes Theorem 1. If a triangle is isosceles (i.e. it has two equal sides) then the angles opposite the equal sides are equal. Also, if two angles of a triangle are equal then the two sides opposite the equal angles are equal, so that the triangle is isosceles. Lines and angles In the following diagram the two horizontal lines are parallel. The line cutting the two par-allel
Angles. Types of Angles. 120В° 140В° 100В° An. gles in a full turn all add u. p to 360В° 120В° 60В° Angles in a half turn all add up to . 180В°. Note how this is half of a full Angle Strain: Strain caused when the actual bond angles in the atoms of the molecule differ from the ideal bond angles of their geometry. There might be some confusion between torsional and steric strain; the
Name: _____ Period: _____ Date: _____ Author: Jeff Twiddy Created Date: 4/25/2016 12:43:13 PM Types of angles notes keyword after analyzing the system lists the list of keywords related and the list of websites with related content, in addition you can see …
Math Handbook of Formulas, Processes and Tricks 10 Angles 11 Types of Angles Chapter 2: Proofs 12 Conditional Statements (Original, Converse, Inverse, Contrapositive) 13 Basic Properties of Algebra (Equality and Congruence, Addition and Multiplication) Parallel lines, transversal, alternate angles, corresponding angles, allied angles, co-interior angles and vertically opposite angles. Year 8 Interactive Maths - Second Edition. Angles associated with Parallel Lines If two lines are in the same plane and do not intersect, then the lines are said to be parallel. Note: Arrows are placed on the lines AB and CD to indicate that they are parallel
angles between points that found the boundary of a site We will learn several different techniques to compute the area inside a traverse Introduction Surveying - Traverse Surveying - Traverse Distance - Traverse Methods of Computing Area A simple method that is useful for rough area estimates is a graphical method In this method, the traverse is plotted to scale on graph paper, and the number Parallel lines, transversal, alternate angles, corresponding angles, allied angles, co-interior angles and vertically opposite angles. Year 8 Interactive Maths - Second Edition. Angles associated with Parallel Lines If two lines are in the same plane and do not intersect, then the lines are said to be parallel. Note: Arrows are placed on the lines AB and CD to indicate that they are parallel
Geometry Notes Perimeter and Area Page 3 of 57 Since our figure has all right angles, we are able to determine the length of the sides whose length is not currently printed. 1 Introductionto BasicGeometry 1.1 EuclideanGeometry andAxiomatic Systems 1.1.1 Points, Lines, and Line Segments Geometry is one of the oldest branchesof mathematics.
TIPS4RM: Grade 8: Unit 4 – Lines, Angles, Triangles, and Quadrilaterals 3 . Whole Class Math Congress As pairs share the answers from the BLM 4.1.2 chart, other students are responsible Naming Angles What’s the secret for doing well in geometry? Knowing all the angles. An angle can be seen as a rotation of a line about a fixed point. In other words, if I were mark a point on a paper, then rotate a pencil around that point, I would be forming angles. One complete rotation measures 360º. Half a rotation would then measure 180º. A quarter rotation would measure 90º. Let’s
This lecture note is prepared for Environmental Health Science Students who need to understand measurement of distances, angles and other similar activities. It is designed to give the student the basic concepts and skills of surveying for undergraduate level. This material could have paramount importance for the health professionals who are involved in public health activities. Public health Angles Teacher Notes Introduction This unit is mostly intended to strengthen students’ understanding of what an angle is. A surprising number of students get to high school without a strong sense of this, and therefore are seriously handicapped in geometry. The unit can also be used to reinforce number sense and mental calculations skills. Indeed, students should calculate the answers, not
Third Angle Theorem If two angles of one triangle are _____ to two angles of a second triangle, then the third angles of the triangles are _____. TEACHER NOTES Aim Students find and model angles with the Angle Finder diagram. Before the Activity Copy and distribute pages 63–64. During the Activity Students can work through this activity individually or in groups of three or four. If they work in groups, be sure each group member looks for all three types of angles. On stairs, tables, or in other places, students might find angles that
Angles. Types of Angles. 120В° 140В° 100В° An. gles in a full turn all add u. p to 360В° 120В° 60В° Angles in a half turn all add up to . 180В°. Note how this is half of a full Math Handbook of Formulas, Processes and Tricks 10 Angles 11 Types of Angles Chapter 2: Proofs 12 Conditional Statements (Original, Converse, Inverse, Contrapositive) 13 Basic Properties of Algebra (Equality and Congruence, Addition and Multiplication)
Types of angles notes keyword after analyzing the system lists the list of keywords related and the list of websites with related content, in addition you can see … How Do We Measure Angles? We can measure lines using a tool called a ruler. A ruler uses units called inches or centimeters to measure how long things are. We measure angles using a tool called a protractor. A protractor is half of a circle. A protractor uses units called degrees to measure angles. A protractor can measure angles starting from the left or from the right. It measures from 0 to | 4,450 | 19,272 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4 | 4 | CC-MAIN-2021-04 | latest | en | 0.90111 |
https://forum.arduino.cc/t/linear-equation-substitution/858391 | 1,624,419,286,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488528979.69/warc/CC-MAIN-20210623011557-20210623041557-00066.warc.gz | 246,831,507 | 8,590 | # Linear equation substitution
Hello guys,
I have used the map function in the arduino code. ```
float val = (float)(map(samplse,0,1023,-3500,3500)/100.0);
```````0 -35
2.61 0
5 35
`
Here I have taken calibration values from the sensor and plotted a graph. First when I use the power graph, I got **NAN x^NAN**. But when I use the calibration values with linear graph, I got **13.9909711599448x - 35.4904301757266**.
My question is why in power graph, I am getting NAN. Then If I want to add the calibration values of linear graph in the arduino, how will I implement?``````
Hi,
Thanks… Tom…
Here I have taken calibration values from the sensor and plotted a graph. First when I use the power graph, I got NAN x^NAN. But when I use the calibration values with linear graph, I got 13.9909711599448x - 35.4904301757266.
My question is why in power graph, I am getting NAN. Then If I want to add the calibration values of linear graph in the arduino, how will I implement?
not clear what you mean by power vs linear graph?
is the issue with your graphing tool or the arduino code?
when i do your mapping , i get the following values which look correct
`````` 0 -350.00
100 -281.60
200 -213.20
300 -144.80
400 -76.30
500 -7.90
600 60.50
700 128.90
800 197.40
900 265.80
1000 334.20
``````
NaN, Not a Number. Using a Uno/Mega? Most likely the NaN is being caused by a overflow.
You may, also want to normalize your data.
I used a 32 bit Linear Regression formula that was prone to overflows and gave NaN’s. I switched to a 64 bit LR.
Hi,
Using
``````float val = (float)(map(samplse,0,1023,-3500,3500)/100.0);
``````
I get;
samplse = 0 val = -35.00
samplse = 100 val = -28.16
samplse = 200 val = -21.32
samplse = 300 val = -14.48
samplse = 400 val = -7.63
samplse = 500 val = -0.79
samplse = 600 val = 6.05
samplse = 700 val = 12.89
samplse = 800 val = 19.74
samplse = 900 val = 26.58
samplse = 1000 val = 33.42
Tom…
``````int samplse;
int ledPin = 13;
bool LEDState = false;
void setup()
{
Serial.begin(115200);
pinMode(ledPin, OUTPUT);
}
void loop()
{
for (long i = 0 ; i < 1024; i=i+100)
{
samplse = i;
float val = (float)(map(samplse, 0, 1023, -3500, 3500) / 100.0);
Serial.print("samplse =\t");
Serial.print(samplse);
Serial.print("\t val =\t");
Serial.println(val);
delay(250);
digitalWrite(ledPin, LEDState);
LEDState = !LEDState;
}
}
``````
Hi,
Your equation from the map parameters transforms to this graph.
y = mx +c
c = y value when x = 0
m = rise /run = (3500 - -3500)/ 1023 = 7000 /1023 = 6.842
c = -3500
y = (6.842 * x) - 3500
Which is the resultant equation used in the map function.
you divide b y 100 so
y = (( 6.842 * x ) - 3500)/100
This produces.
samplse = 0 val = -35.00
samplse = 100 val = -28.16
samplse = 200 val = -21.32
samplse = 300 val = -14.47
samplse = 400 val = -7.63
samplse = 500 val = -0.79
samplse = 600 val = 6.05
samplse = 700 val = 12.89
samplse = 800 val = 19.74
samplse = 900 val = 26.58
samplse = 1000 val = 33.42
Tom…
``````int samplse;
int ledPin = 13;
bool LEDState = false;
void setup()
{
Serial.begin(115200);
pinMode(ledPin, OUTPUT);
}
void loop()
{
for (long i = 0 ; i < 1024; i = i + 100)
{
samplse = i;
float val = (( 6.842 * (float)samplse) - 3500.0) / 100.0;
Serial.print("samplse =\t");
Serial.print(i);
Serial.print("\t val =\t");
Serial.println(val);
delay(250);
digitalWrite(ledPin, LEDState);
LEDState = !LEDState;
}
}
``````
Hi friends, I am using HG-C 1100 sensor and this sensor measures the range from -35mm to 35mm. I have doubt in using the formula `float val = (float)(map(samplse,0,1023,-3500,3500)/100.0);`. I have to take the readings from the sensor and should display it in the serial monitor. The values also should be accurate as in the sensor. Can anyone explain me how to take the formula and calibrate the same?
Hi,
Have you read post #6, I show you the basics of calculating the equation, and have provided it for you.
Tom…
Hi,
How are you reading the value from the HG-C device?
Can you post a circuit of your project?
Can you post the code you are using?
What model Arduino are you using?
Thanks… Tom…
why?
what values do you get that make you doubt?
is it the sensor values or the map() results?
I have doubt with my formula itself.Please guide me?
The sensor is connected with the analog pin of arduino only.
Hi,
If you have doubts, then.
Build it.
Code it.
Run it.
Check its accuracy in the REAL WORLD by experiment.
Tom…
both Tom and I have shown that the map equation works. it translates values in the range from 0-1023 to proportional values in the range from -35 to 35 (yes I scaled by 10 instead of 100)
what are you expecting the results to be?
1 Like
Hi.
Thanks… Tom…
I have tried your code but there is no accuracy. Whatever the values coming from the sensor should display in the serial monitor using calibration
``````int samplse=0;
void setup() {
// put your setup code here, to run once:
Serial.begin(9600); // initialize serial communication at 9600 bits per second
}
void loop() {
// put your main code here, to run repeatedly:
int samplse = analogRead(0); // read the input on analog pin 0
float val = (float)(map(samplse,0,1023,-35000,35000)/1000.0); // Map an analog value to 10 bits(0 to 1023) and the target range
//val = constrain(val, 0, 1023);
Serial.print("digital value = ");
Serial.println(val); // print digital value on serial monitor
float voltage = (float)((samplse*5.0)/1023);
Serial.print("Voltage:");
Serial.println(voltage);
delay(3000); // delay in between reads for stability
}```
The values I am getting from the sensor should reflect in the code with more accuracy.``````
After scaling of 100 also, there is no accuracy. Can you tell me how to take calibration?
I am telling the calibration means taking the samples of voltage and the sensor readings and use excel for getting the equation,
Is my calibration correct or what can i do?
you need to explain what you mean by no accuracy?
can you provide the raw data, in text not an image?
Accuracy in sensor when I use this map function ` float val = (float)(map(samplse,0,1023,-35000,35000)/1000.0); Serial.println(val); `, I am getting the the value for example 31.56 in the sensor but in the serial monitor I am getting as 33.90. There is a lot more difference in the values. What can I do to get the accurate sensor values in the serial monitor?
How will I calibrate? | 2,015 | 6,499 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2021-25 | latest | en | 0.781866 |
https://db0nus869y26v.cloudfront.net/en/Quantum_capacity | 1,723,344,252,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640843545.63/warc/CC-MAIN-20240811013030-20240811043030-00220.warc.gz | 149,136,389 | 18,601 | In the theory of quantum communication, the quantum capacity is the highest rate at which quantum information can be communicated over many independent uses of a noisy quantum channel from a sender to a receiver. It is also equal to the highest rate at which entanglement can be generated over the channel, and forward classical communication cannot improve it. The quantum capacity theorem is important for the theory of quantum error correction, and more broadly for the theory of quantum computation. The theorem giving a lower bound on the quantum capacity of any channel is colloquially known as the LSD theorem, after the authors Lloyd,[1] Shor,[2] and Devetak[3] who proved it with increasing standards of rigor.[4]
## Hashing bound for Pauli channels
The LSD theorem states that the coherent information of a quantum channel is an achievable rate for reliable quantum communication. For a Pauli channel, the coherent information has a simple form[citation needed] and the proof that it is achievable is particularly simple as well. We[who?] prove the theorem for this special case by exploiting random stabilizer codes and correcting only the likely errors that the channel produces.
Theorem (hashing bound). There exists a stabilizer quantum error-correcting code that achieves the hashing limit ${\displaystyle R=1-H\left(\mathbf {p} \right)}$ for a Pauli channel of the following form:${\displaystyle \rho \mapsto p_{I}\rho +p_{X}X\rho X+p_{Y}Y\rho Y+p_{Z}Z\rho Z,}$where ${\displaystyle \mathbf {p} =\left(p_{I},p_{X},p_{Y},p_{Z}\right)}$ and ${\displaystyle H\left(\mathbf {p} \right)}$ is the entropy of this probability vector.
Proof. Consider correcting only the typical errors. That is, consider defining the typical set of errors as follows:${\displaystyle T_{\delta }^{\mathbf {p} ^{n))\equiv \left\{a^{n}:\left\vert -{\frac {1}{n))\log _{2}\left(\Pr \left\{E_{a^{n))\right\}\right)-H\left(\mathbf {p} \right)\right\vert \leq \delta \right\},}$where ${\displaystyle a^{n))$ is some sequence consisting of the letters ${\displaystyle \left\{I,X,Y,Z\right\))$ and ${\displaystyle \Pr \left\{E_{a^{n))\right\))$ is the probability that an IID Pauli channel issues some tensor-product error ${\displaystyle E_{a^{n))\equiv E_{a_{1))\otimes \cdots \otimes E_{a_{n))}$. This typical set consists of the likely errors in the sense that${\displaystyle \sum _{a^{n}\in T_{\delta }^{\mathbf {p} ^{n))}\Pr \left\{E_{a^{n))\right\}\geq 1-\epsilon ,}$for all ${\displaystyle \epsilon >0}$ and sufficiently large ${\displaystyle n}$. The error-correcting conditions[5] for a stabilizer code ${\displaystyle {\mathcal {S))}$ in this case are that ${\displaystyle \{E_{a^{n)):a^{n}\in T_{\delta }^{\mathbf {p} ^{n))\))$ is a correctable set of errors if
${\displaystyle E_{a^{n))^{\dagger }E_{b^{n))\notin N\left({\mathcal {S))\right)\backslash {\mathcal {S)),}$for all error pairs ${\displaystyle E_{a^{n))}$ and ${\displaystyle E_{b^{n))}$ such that ${\displaystyle a^{n},b^{n}\in T_{\delta }^{\mathbf {p} ^{n))}$ where ${\displaystyle N({\mathcal {S)))}$ is the normalizer of ${\displaystyle {\mathcal {S))}$. Also, we consider the expectation of the error probability under a random choice of a stabilizer code.
Proceed as follows:{\displaystyle {\begin{aligned}\mathbb {E} _{\mathcal {S))\left\{p_{e}\right\}&=\mathbb {E} _{\mathcal {S))\left\{\sum _{a^{n))\Pr \left\{E_{a^{n))\right\}{\mathcal {I))\left(E_{a^{n)){\text{ is uncorrectable under )){\mathcal {S))\right)\right\}\\&\leq \mathbb {E} _{\mathcal {S))\left\{\sum _{a^{n}\in T_{\delta }^{\mathbf {p} ^{n))}\Pr \left\{E_{a^{n))\right\}{\mathcal {I))\left(E_{a^{n)){\text{ is uncorrectable under )){\mathcal {S))\right)\right\}+\epsilon \\&=\sum _{a^{n}\in T_{\delta }^{\mathbf {p} ^{n))}\Pr \left\{E_{a^{n))\right\}\mathbb {E} _{\mathcal {S))\left(\mathcal {I))\left(E_{a^{n)){\text{ is uncorrectable under )){\mathcal {S))\right)\right\}+\epsilon \\&=\sum _{a^{n}\in T_{\delta }^{\mathbf {p} ^{n))}\Pr \left\{E_{a^{n))\right\}\Pr _{\mathcal {S))\left\{E_{a^{n)){\text{ is uncorrectable under )){\mathcal {S))\right\}+\epsilon .\end{aligned))}The first equality follows by definition—${\displaystyle {\mathcal {I))}$ is an indicator function equal to one if ${\displaystyle E_{a^{n))}$ is uncorrectable under ${\displaystyle {\mathcal {S))}$ and equal to zero otherwise. The first inequality follows, since we correct only the typical errors because the atypical error set has negligible probability mass. The second equality follows by exchanging the expectation and the sum. The third equality follows because the expectation of an indicator function is the probability that the event it selects occurs. Continuing, we have:${\displaystyle =\sum _{a^{n}\in T_{\delta }^{\mathbf {p} ^{n))}\Pr \left\{E_{a^{n))\right\}\Pr _{\mathcal {S))\left\{\exists E_{b^{n)):b^{n}\in T_{\delta }^{\mathbf {p} ^{n)),\ b^{n}\neq a^{n},\ E_{a^{n))^{\dagger }E_{b^{n))\in N\left({\mathcal {S))\right)\backslash {\mathcal {S))\right)$
${\displaystyle \leq \sum _{a^{n}\in T_{\delta }^{A^{n))}\Pr \left\{E_{a^{n))\right\}\Pr _{\mathcal {S))\left\{\exists E_{b^{n)):b^{n}\in T_{\delta }^{\mathbf {p} ^{n)),\ b^{n}\neq a^{n},\ E_{a^{n))^{\dagger }E_{b^{n))\in N\left({\mathcal {S))\right)\right\))$
${\displaystyle =\sum _{a^{n}\in T_{\delta }^{\mathbf {p} ^{n))}\Pr \left\{E_{a^{n))\right\}\Pr _{\mathcal {S))\left\{\bigcup \limits _{b^{n}\in T_{\delta }^{\mathbf {p} ^{n)),\ b^{n}\neq a^{n))E_{a^{n))^{\dagger }E_{b^{n))\in N\left({\mathcal {S))\right)\right\))$
${\displaystyle \leq \sum _{a^{n},b^{n}\in T_{\delta }^{\mathbf {p} ^{n)),\ b^{n}\neq a^{n))\Pr \left\{E_{a^{n))\right\}\Pr _{\mathcal {S))\left\{E_{a^{n))^{\dagger }E_{b^{n))\in N\left({\mathcal {S))\right)\right\))$
${\displaystyle \leq \sum _{a^{n},b^{n}\in T_{\delta }^{\mathbf {p} ^{n)),\ b^{n}\neq a^{n))\Pr \left\{E_{a^{n))\right\}2^{-\left(n-k\right)))$
${\displaystyle \leq 2^{2n\left[H\left(\mathbf {p} \right)+\delta \right]}2^{-n\left[H\left(\mathbf {p} \right)+\delta \right]}2^{-\left(n-k\right)))$
${\displaystyle =2^{-n\left[1-H\left(\mathbf {p} \right)-k/n-3\delta \right]}.}$
The first equality follows from the error-correcting conditions for a quantum stabilizer code, where ${\displaystyle N\left({\mathcal {S))\right)}$ is the normalizer of ${\displaystyle {\mathcal {S))}$. The first inequality follows by ignoring any potential degeneracy in the code—we consider an error uncorrectable if it lies in the normalizer ${\displaystyle N\left({\mathcal {S))\right)}$ and the probability can only be larger because ${\displaystyle N\left({\mathcal {S))\right)\backslash {\mathcal {S))\in N\left({\mathcal {S))\right)}$. The second equality follows by realizing that the probabilities for the existence criterion and the union of events are equivalent. The second inequality follows by applying the union bound. The third inequality follows from the fact that the probability for a fixed operator ${\displaystyle E_{a^{n))^{\dagger }E_{b^{n))}$ not equal to the identity commuting with the stabilizer operators of a random stabilizer can be upper bounded as follows: ${\displaystyle \Pr _{\mathcal {S))\left\{E_{a^{n))^{\dagger }E_{b^{n))\in N\left({\mathcal {S))\right)\right\}={\frac {2^{n+k}-1}{2^{2n}-1))\leq 2^{-\left(n-k\right)}.}$ The reasoning here is that the random choice of a stabilizer code is equivalent to fixing operators ${\displaystyle Z_{1))$, ..., ${\displaystyle Z_{n-k))$ and performing a uniformly random Clifford unitary. The probability that a fixed operator commutes with ${\displaystyle {\overline {Z))_{1))$, ..., ${\displaystyle {\overline {Z))_{n-k))$ is then just the number of non-identity operators in the normalizer (${\displaystyle 2^{n+k}-1}$) divided by the total number of non-identity operators (${\displaystyle 2^{2n}-1}$). After applying the above bound, we then exploit the following typicality bounds: ${\displaystyle \forall a^{n}\in T_{\delta }^{\mathbf {p} ^{n)):\Pr \left\{E_{a^{n))\right\}\leq 2^{-n\left[H\left(\mathbf {p} \right)+\delta \right]},}$${\displaystyle \left\vert T_{\delta }^{\mathbf {p} ^{n))\right\vert \leq 2^{n\left[H\left(\mathbf {p} \right)+\delta \right]}.}$ We conclude that as long as the rate ${\displaystyle k/n=1-H\left(\mathbf {p} \right)-4\delta }$, the expectation of the error probability becomes arbitrarily small, so that there exists at least one choice of a stabilizer code with the same bound on the error probability.
4. ^ Wilde, Mark M. (2017). Quantum information theory (2nd ed.). Cambridge, UK. ISBN 978-1-316-80997-6. OCLC 972292559.((cite book)): CS1 maint: location missing publisher (link) | 2,802 | 8,617 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 46, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.15625 | 3 | CC-MAIN-2024-33 | latest | en | 0.860008 |
https://scicomp.stackexchange.com/questions/30905/how-to-compute-large-condition-number-of-a-matrix-in-python | 1,717,100,728,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971670239.98/warc/CC-MAIN-20240530180105-20240530210105-00394.warc.gz | 435,307,012 | 38,916 | How to compute large condition number of a matrix in Python?
I have a matrix that is extremely singular, but I am still interested in computing the exact condition number, which is the ratio between the largest and smallest singular values.
Is it possible to do it in Python? I am curious because if we stick with machine precision 10^-16, then any condition number beyond 10^16 could be inaccurate.
• Can you please give a sample input? It's difficult to discern the exact condition.
– kokeen
Dec 14, 2018 at 4:17
• The usual way to compute the condition number is via the SVD. The computed singular values will almost certainly be somewhat inaccurate. How much precision do you really need? If the true condition number was say 10^17+1 but it was computed asd 10^17 would that really matter to you?
– dmuir
Dec 15, 2018 at 14:54
• Is this an matrix of integers?
– James K Polk
Dec 18, 2018 at 20:10
• You seem to understand that you'll need to compute the singular values of your matrix in a higher precision than standard double precision. The "what library does extended precision singular value computations" question isn't really suitable for Computational Science stackexchange. However, you might look at the mpmath library to see if it does what you need. Jan 20, 2019 at 17:19 | 309 | 1,289 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2024-22 | latest | en | 0.940263 |
https://www.jiskha.com/display.cgi?id=1308950401 | 1,516,621,971,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084891316.80/warc/CC-MAIN-20180122113633-20180122133633-00034.warc.gz | 953,158,650 | 3,987 | # Physics
posted by .
If you try to push an object that is 10 times heavier than you would there be static or kinetic friction? ( the heavy object doesn't move if even you use force)
-I know that there is no kinetic friction because the object is not moving. I am not sure about static friction.
• Physics -
Static friction keeps the heavy object from moving. Unless your shoes slip pushing it, there is static friction below your feet also.
## Similar Questions
1. ### Physics
10. You try to move a couch across the floor but it doesn't move. What is the other force acting on the couch?
2. ### physics
A popular pastime is to see who can push an object closest to the edge of a table without its going over. You push a 130 g object and release it 2.00 m from the table edge. Unfortunately, you push a little too hard. The object slides …
3. ### science
Words to use: Accelerate - Sliding - Brake - Friction - Slipping - Inertia Velocity - Wheel - Strength - Static - Terminal velocity Questions 1. An object will ____?
4. ### physics
IP You want to nail a 2.4kg- board onto the wall of a barn. To position the board before nailing, you push it against the wall with a horizontal force to keep it from sliding to the ground What happens to the force of static friction …
5. ### physics- MC QUESTIONS
1. You push a block up a ramp with friction. The block is moving at constant speed ?
6. ### physics
An object in static equilibrium has a coefficient of static friction as 0.110. If the normal force acting on the object is 95.0 newtons, what is the mass of the object?
7. ### physic
A stationary 2.0 kg object is located on a table near the surface of the earth. The coefficient static friction between the surface is .80 and the coefficient of the kinetic friction is 0.65. A horizontal force of 5N is applied to …
8. ### physic
A stationary 2.0 kg object is located on a table near the surface of the earth. The coefficient static friction between the surface is .80 and the coefficient of the kinetic friction is 0.65. A horizontal force of 5N is applied to …
9. ### physics
1. the applied force on a stationary object is less than the maximum force of static friction. Which of the statements are false a) the object will move backwards b) the actual force of static friction will be equal to the applied …
10. ### Physics
I push a stack of six books (each weighting 4 kg) horizontally across a table to the right with a kinetic coefficient of friction uk = 0.5. I apply a force of 120 N. a) What is the acceleration of the books?
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Normal Distribution
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https://www.physicsforums.com/tags/ammeter/ | 1,713,823,798,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296818374.84/warc/CC-MAIN-20240422211055-20240423001055-00662.warc.gz | 838,588,185 | 25,320 | # What is Ammeter: Definition and 89 Discussions
An ammeter (from ampere meter) is a measuring instrument used to measure the current in a circuit. Electric currents are measured in amperes (A), hence the name. The ammeter is usually connected in series with the circuit in which the current is to be measured. An ammeter usually has low resistance so that it does not cause a significant voltage drop in the circuit being measured.
Instruments used to measure smaller currents, in the milliampere or microampere range, are designated as milliammeters or microammeters. Early ammeters were laboratory instruments that relied on the Earth's magnetic field for operation. By the late 19th century, improved instruments were designed which could be mounted in any position and allowed accurate measurements in electric power systems. It is generally represented by letter 'A' in a circuit.
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1. ### The REAL difference between a Galvanometer and an Ammeter
Hello guys. I'm having some trouble to understand the real difference from the Galvanometer and the Ammeter. The best comment I saw in some forum was: Ammeter: ANY instrument used to measure electrical current Voltimeter: ANY instrument used to measure voltage difference Galvanometer: a...
2. ### New full scale deflection of an ammeter
Question: My attempt: Does 4.75 amps for the full scale deflection seem okay? Thanks for any help!
3. ### How do you solve this equation used to calibrate an ammeter?
Please can someone tell me how to solve the below: we have been given: can someone please explain how we deal with two theatas? please ignore full stops wouldn't line up any other way!
4. ### How does a digital ammeter work?
I am a student at a trade school, majoring in HVAC. My electricity for HVAC textbook has a chapter on electric meters. However, my textbook does a poor job of explaining how a digital ammeter works. My textbook has the following description of how digital ammeters work: "To make meters...
5. ### Engineering Voltmeter and ammeter calculation in a circuit
Homework Statement [/B] Hello, basically I have some tasks about calculating the reading of voltmeter and ammeter in a circuit, I can solve these with simpler circuits, where voltmeter is reading a few elements, but as in the ones below, I'm not sure where to begin and what to add into the...
6. ### Questions about Using My Multimeter
So I'm fairly new to electronics. I took physics 2 in college and thought I'd give the hobby a try. I started with a very basic circuit. Just a power supply connected to a light-bulb. However, as simple as it was, I had several questions when taking the reading of my circuit with a multi-meter...
7. ### Current through an Ammeter in an Electric Circuit
Homework Statement [/B] It is required to find the current through the ammeter, marked A, in the above figure.Homework Equations ##V=iR##The Attempt at a Solution I've redrawn the circuit as follows - But don't know how to obtain the value ##i_3##
8. ### Voltmeter Ammeter and percentage error in R
Homework Statement Homework EquationsThe Attempt at a Solution I am not able to understand how percentage error in R is calculated using the given circuits. Should I assign currents in the branches and write KVL equations ?
9. D
### Ammeter and Voltmeter in Series
Homework Statement Hi! A battery of emf 12 V and negligible internal resistance is connected to a resistor of constant resistance 6 Ω, an ideal ammeter and an ideal voltmeter. The voltmeter and ammeter are in series with the cell and the resistor. What is the reading on each? Homework...
10. K
### Why you can't measure voltage and current at the same time?
In my physics textbook it says that ammeter in circuit C shows higher current than ammeter in circuit A and D. And the voltmeter shows higher voltage in D than in B, and C. It's explained in the book that way: some electric current is passing through the voltmeter in C, thus the ammeter will...
11. H
### How Do Electrical Meters Like Voltmeters, Ohmmeters, and Ammeters Work?
Recently I asked why with a multimeter you should not measure the resistance of a fuse in a car while there was still power reaching the fuse but why it was ok to measure the voltage. I was told the way resistance is measured is a small current is sent by the meter for the calculation to be...
12. J
### Understanding Shunt Selection for Accurate Current Measurement in DC Systems
I need to measure current in DC system. I have circuit breaker (125A), so 150A shunt is selected. On that shunt ammeter is connected. But that ammeter has 60mV, scale 0-150A. What does this 60mV means on ammeter? Is it correct?
13. ### Reading of a voltmeter and an ammeter
Homework Statement Homework EquationsThe Attempt at a Solution Part a) Voltmeter can be replaced by an open circuit and ammeter can be replaced by a short circuit .By doing so the current flows in the outer loop consisting of both the batteries and both the resisters .The current in the...
14. ### The reading of the ammeter and the reading of the voltmeter.
Homework Statement In this circuit What will be the reading of the ammeter and that of the voltmeter when: 1. Key S1 and key S2 are open. 2. Key S1 and key S2 are closed. 3. Key S1 is closed and key S2 is open. (Neglect the internal resistance of the source) Homework EquationsThe Attempt at a...
15. ### Determine the resistance of an ammeter.
Homework Statement An inductor is connected in series with an AC source, the rms output voltage of it is 260V and a hot-wire ammeter reads 2A. If the ratio of the voltage across the ammeter to the voltage across the inductor is 5/12, determine the resistance of the ammeter. (Neglect the...
16. ### Electricity: shunt calculation for ammeter
Homework Statement We have an ammeter with 20Ω resistance and a range of 10mA or 0.01A. The different ranges are 3000mA, 300mA, 30mA. Calculate the shunt resistors a, b and c. Homework Equations The Attempt at a Solution Ia = 0.01A ; Ra = 20Ω ; I = 0.03A Ua = Ia ⋅ Ra = 0.01A ⋅ 20Ω =...
17. ### Electricity: ammeter range calculation
Homework Statement [/B] An ammeter has a range of 10mA or 0.01A and a resistor of 20Ω. Three shunts are used: R1 = 4Ω ; R2 = 2Ω ; R3 = 4Ω What will the different ranges be (m3, m2, m1)? The Attempt at a Solution [/B] I started by calculating the voltage: Ua = Ia ⋅ Ra Ua = 0.01A ⋅ 20Ω =...
18. ### Hot Wire Ammeter: How it Works
In my textbook it says:"in the hot-wire ammeter the pointer stands at a definite reading when the temperature of platinum-iridium becomes constant and the wire stops expanding. That is achieved when the rate of heat radiated by the platinum-iridium wire becomes equal to the rate of heat...
19. ### Using a multimeter as an ammeter
Homework Statement When I connect just the multimeter (as shown in the diagram) to the power source by inserting the lead into the mA connection and change the setting to read the current on the multimeter, it reads 0. When I change the lead connection from mA to A, the power source circuit...
20. ### Current through voltmeter and ammeter
3. The Attempt at a Solution As temp decreases, the resistance of the thermistor increases...doesn't this mean that the voltmeter will increase too since V=IR? I know that the total resistance of the circuit has increased so less current, but I put down option D but the correct answer is A?
21. ### Reading an Electrodynamic Ammeter with 6 A Range and 100 Divisions
Homework Statement What will the pointer of electrodynamic ammeter show (its natural frequency of oscillation is 5 Hz), if its input is energized by current: a) i (t) = 1.5 + 4 sin (3146 t) b) i (t) = 1.5 + 4 sin (2 t) Ammeter has a range of 6 A and the scale has 100 divisions. Homework...
22. ### Current through ammeter with two batteries
Homework Statement For the values shown in the figure below, calculate (a) the current through the ammeter A1, (b) the current through the ammeter A2, (c) the PD across R2. Assume that the internal resistance of each cell and the resistance of each ammeter is negligible. Answers: (a) 0.05...
23. ### Solving Circuit with Ideal Ammeter: 4.0 Ohm Resistance
Homework Statement A circuit is setup with an ideal ammeter connected across the 4.0 ohm. What will the reading of the ammeter be? 2. The attempt at a solution I am not sure whether the question is testing my understanding on how an ammeter should be connected in a circuit or about how to...
24. ### Ammeter vs Voltmeter: Error Comparison
Which one contributes more error when performing a lab calculating the voltage and current through different ohms of resistance? One was in parallel, the others in series and the last one both in series and parallel. They are systematic errors, but not sure which one would contribute more error...
25. ### B Why is Parallel Connection of an Ammeter to a Battery Considered Unsafe?
How come when an ammeter is placed in parallel with a resistor that is connected to a battery, the circuit is considered incorrect + "safe," whereas an ammeter connected in parallel with the whole battery is considered incorrect + dangerous? My guess is that it has something to do with the...
26. ### Why Does My Ammeter/Voltmeter Read Incorrectly?
http://www.ebay.com/itm/291369928250?_trksid=p2057872.m2749.l2649&ssPageName=STRK%3AMEBIDX%3AIT i bought this cheap ammeter/voltmeter off ebay. now, i bought 1 before but it was slightly different. the wires had blue red and black instead of blue yellow and green. this makes it confusing but...
27. ### Change in ammeter reading due to change in resistance
Homework Statement Homework Equations 1/R= 1/R1 + 1/R2 +... I1= R2/R1 x I The Attempt at a Solution I chose B because I thought that since total resistance in the branch of variable resistor has increased, the branch with ammeter will get a greater share of current. Since I'm not too sure...
28. ### Why is my D.C. ammeter reading fluctuating?
Why is the reading on my D.C. ammeter fluctuating? As in the needle won't maintain at one spot, it'll sway left and right. Also, how do i ensure that the fluctuations are minimized?
29. ### Determining current from ammeter
Homework Statement The ammeter reads 5.0A. Find I1, I2, and ε Homework Equations ΔV=IR The Attempt at a Solution I've never dealt with ammeters before so I'm very confused. To start, I tried breaking this into loops, and then used Kirchhoff's Law. I started with the left side, since I...
30. ### Uncertainty in ammeter and voltmeter?
I set an ohm meter to record current in mA, smallest 0.01mA, I took three readings for several different resistances.. What would the uncertainty be? And the same for the voltmeter but reading in volts, smallest 0.01V
31. ### Ammeter from parallel to series, current change
Homework Statement In the circuit shown, a student mistakenly connects a perfect ammeter(i.e. One of negligible resistance), in parallel with one of two identical resistors. The ammeter reads 0.40A. What would the reading have been if he had correctly connected the ammeter in series with the...
32. ### Series lc circuit and clamp-on ammeter
In a series LC resonant circuit the capacitor acts to cancel out the inductance of the the circuit. With no inductance in the circuit the magnetic field will collapse. So my question is, with this collapse of the magnetic field will it be be harder to measure the current in the circuit with a...
33. ### Actual resistance of an Ammeter
Hi, I want to use a digital ammeter to measure the current flow though a Raspberry pi. The Pi uses about 700mA and is 5V so its got a resiatance of about 7 ohms. Therefore something like 0.5 ohm ammeter will have a large voltage drop of about 0.3V which is way too large and would lead to the...
34. A
### Experimental physics i am very frustrated -- convert galvanometer into an ammeter
I am trying to convert galvanometer into an ammeter. But after finding Galvanometer resistance and shunt values, and cut a wire according to that thickness and connected. But still, the galavanometer reading is not similar to that of the standard ammeter reading connected in the circuit. Any one...
35. ### Connect ammeter before or after the load?
Is there any issue to connect the Ammeter in the circuit before or after the load. According to me, the current should remain same in circuit and there should be no restriction for Ammeter connection so it can be placed anywhere in the circuit. please explain why as this question asked to me by...
36. ### How Does an Ammeter Work? | eBay Guide
This is not promoting an advert - just look and see! There is a 'clip on' ammeter for sale on eBay and I can't imagine how it works. It claims to work by clipping it round a cable and the scale shows +/- 30A DC. I spent good money on a Hall Effect clamp meter when it looks like I could have...
37. ### How is a Galvanometer Converted into an Ammeter Using a Shunt?
To make ammeter, Resistance of proper small value is joined in parallel to the coil of galvanometer.This resistance is called a shunt. For smaller resistance value, We can not use the smallest resistance wire that is directly wound on coil of galvanometer so the resistance will become...
38. ### Calculating Mean Square Value of a Thermoelectric Ammeter Circuit
I don't understand a few things here. Firstly, here's the question: This is thermoelectric ammeter. Internal resistance can be ignored. 1. Find the mean square value of the circuit. 2. Find the value that is displayed on the ammeter (alternating current). In the textbook, the formula for the...
39. ### Thermo couple ammeter full scale deflection
if thermo couple ammeter full scale deflection is 10 Amp, for 1/5 th scale what is the Reading?
40. ### Getting currents in ammeter, with some resistances.
Homework Statement In the figure R1 = 1.29R, the ammeter resistance is zero, and the battery is ideal. What multiple of ε/R gives the current in the ammeter? Homework Equations V=IR, 1/R=1/R_1+1/R_2..(when resistances are parallel) etc The Attempt at a Solution since ammeter doesn't...
41. ### Converting Galvanometer to Ammeter: Resistance Wire Placement
Homework Statement how will you convert a galvanometer of resistance 150 ohm giving a full scale deflection for a current of 3 milli ampere to a ammeter of range 0 to 6 ampere?a uniform rsistance wire of length 60cm and 2 ohm is given.find the length of the wire required? Homework...
42. ### Converting a galvanometer to ammeter and voltmeter.
How will you convert a galvanometer of resistance 12 ohms showing full scale deflection for a current of 3 milli ampere to (i) Ammeter of range o to 6 Ampere (ii) Voltmeter of range 0 to 18V.
43. ### Why does it matter whether or not an ammeter has zero resistance?
Apparently an ideal ammeter has zero resistance. But for a series circuit, why does it matter? The purpose of an ammeter is to give the reading for the amount of current going round a 'loop' of circuit. Having some resistance does not prevent the ammeter from giving a true reading, right? So...
44. ### Why must ammeter be connected in series?
lets say you have a circuit consisting only of a resistor and battery. Is it absolutely necessary to connect an ammeter in series with the resistor to measure current through it, rather than in parallel? Current doesn't want to go through a resistor, so if you connect a much lower resistance...
45. ### How to add Ammeter in LT Spice Schematic?
It may sound so silly question but I am trying for last 2 hours and no result. I have drawn the following schematic in LT Spice and want to add an ammeter in the black rectangle. In component menu, I don't find anything named ammeter. Any clue? Your help is appreciated.
46. ### Conversion of Galvanometer to Ammeter
This is kind of a stupid question but...to measure high currents, a galvanometer is connected parallel to a shunt resistance so that most of the current passes through the shunt resistance but only a small amount of current passes through the galvanometer. But wouldn't this defeat the purpose of...
47. ### Ammeter and Voltmeter question?
Homework Statement A ammeter and a voltmeter are joined in series to a cell . Their reading are A and V respectively. If a resistance is now joined in parallel with voltmeter, (a) Both A and V will increase (b) Both A and V will decrease (c) A will decrease V will increase (d) A will increase...
48. ### Doubt in Ammeter: Shunt Resistor or Inductance?
The other day I happened to open an ammeter just out of curiosity. What I saw was that across the positive and negative terminals a wire of considerable thickness(almost equal to the thickness of wires we use for household joints) was wound..It just had 4 or 5 turns. I guess it should be the...
49. ### Calculating Current in a Circuit without an Ammeter
Homework Statement An ammeter whose internal resistance is 63 ohm reads 5.25 mA when connected in a circuit comtaining a battery and two resistors in series whose values are 750 ohm and 480 ohm. What is the actual current when the ammeter is absent?Homework Equations V = IR Rseries = R1 + R2The...
50. ### Circuit problem with ammeter and unknown resistance
Homework Statement http://img811.imageshack.us/img811/6902/circuittosolve.jpg This circuit includes 4 resistors whose value of 3 of them is known and the forth resistor, Rx is unknown. They connected an ammeter A to the circuit and the current through it is 0. 1) Calculate Rx. Is the value... | 4,211 | 17,500 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2024-18 | latest | en | 0.941141 |
https://www.siemensstemday.com/employees/activities?page=1&sort=created&sortd=DESC | 1,624,249,076,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488262046.80/warc/CC-MAIN-20210621025359-20210621055359-00092.warc.gz | 895,766,356 | 14,529 | # Employee Led Student Activities
Select a filter below to refine activity results. To find activities that use tools from the Siemens Employee Technology Toolkit, use the Tech Tools filter.
## Credit Card Debt
• IT
• 9–12
Level: 4
Description: Students consider the benefits and tradeoffs of using credit and learn about the role interest plays in using credit cards. Then, they create an equation that describes the length of time it takes to pay off a debt.
• Math
## Geronimo
• Manufacturing
• K–5
Level: 2
In this activity, students will test the effectiveness of different parachute designs.
• Engineering
## City Life
• IT
• 9–12
Level: 3
Students will create a case study to demonstrate how to incorporate smart city technology into an assigned city.
• Technology
## How Does Your City Grow
• IT
• 9–12
Level: 4
Working in groups, students will select a city and then use U.S. government census data to develop an algebraic relationship between time and population size.
• Math
## Zip to It
• Energy
• K–5
Level: 2
In this activity, students will build a device that can carry a small ball from the top of a two-meter zip line to the bottom in less than six seconds.
• Science
## Watching Weather
• Energy
• K–5
Level: 3
In this activity, students will make their own weather station consisting of actual and simplified versions of real weather equipment.
• Science
## Up Periscope!
• Energy
• K–5
Level: 3
In this activity, students will gain an understanding of the law of reflection by tracing the path that light travels, and designing a periscope to demonstrate understanding.
• Science
## This is How I See It
• Manufacturing
• K–5
Level: 3
In this activity, students will construct interactive lunar cycle models to illustrate the phases of the Moon in 3 dimensions.
• Science
## The Time of Our Life
• Manufacturing
• 6–8
Level: 2
In this activity, students will research ancient organisms and create a timeline showing when they appeared on Earth.
• Science
## The Dynamic Trio
• Energy
• K–5
Level: 2
In this activity, students will learn about the stars, planets, and Moon found in our solar system and how they relate to one another.
• Science
## Synthetic Properties
• IT
• Manufacturing
• 9–12
Level: 4
In this activity, students will compare samples of monomers and polymers in powder and thread form (sugar/cotton candy and cotton flock/cotton balls).
• Science
## Sun, Moon and Stars
• Manufacturing
• K–5
Level: 1
In this activity, students will paint craft spheres to resemble the Earth, moon and sun.
• Science
## Stomp Rockets
• Manufacturing | 624 | 2,598 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2021-25 | latest | en | 0.864791 |
https://www.physicsforums.com/threads/ansys-mechanical-apdl-high-temperature-creep-modeling-via-isochronous-curves.773510/ | 1,508,365,851,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187823153.58/warc/CC-MAIN-20171018214541-20171018234541-00415.warc.gz | 995,385,223 | 15,172 | # ANSYS Mechanical APDL - High Temperature Creep Modeling via Isochronous Curves
Tags:
1. Sep 29, 2014
### CFDFEAGURU
ANSYS can be used to model creep in a number of different ways. If you are designing to ASME Section VIII, Div., 2 you might have to verify that your design meets the "shake down to elastic action" criteria. Basically, that means that the strains do not continue to increase over the number of cycles.
One way to do this is to use the TB,MISO command in ANSYS and then fill the table with stress and strain at each temperature. Obtaining the values for the stress and strain as a function of time and temperature is the hardest part however, there are some places they can be obtained and a method that can be used to create them if you are using common place materials.
MISO stands for Multilinear Isotropic Hardening using von Mises or Hill plasticity
If you are using the following materials then the stress and strains can be read from the isochronous curves found in ASME Section III, Division 1, Subsection NH
304 SS to a maximum temperature of 1500 F
316 SS to a maximum temperature of 1500 F
800H to a maximum temperature of 1400 F
2 1/4 Cr. - 1 Mo. to a maximum temperature of 1200 F
9 Cr - 1 Mo. - V to a maximum temperature of 1200 F
Some of these curves can be found in "Design and Analysis of ASME Boiler and Pressure Vessel Components in the Creep Range" by Jawad and Jetter. (Least expensive route)
If you have access to API-579 then you can use the Omega Method. This will require you to write a spreadsheet with the end result being a set of isochronous curves that can be used to load the TB,MISO command.
You will have to have already solved your model for the temperature distribution and then use the LDREAD command on your structural model to read in the appropriate temperature distribution per load step. Depending upon the loading, you will probably have to "fool" with the number of substeps command, NSUBST, to achieve convergence.
A 3D solid model is NOT required for this, 2D shell elements work just fine.
Example
TB,MISO,1,5,34
TBTEMP,1200
TBPT,DEFI,4.3020E-05,912.00
TBPT,DEFI,5.0192E-05,1064.00
TBPT,DEFI,5.7367E-05,1216.00
TBPT,DEFI,6.4550E-05,1368.00
TBPT,DEFI,7.1746E-05,1520.00
TBPT,DEFI,7.8964E-05,1672.00
TBPT,DEFI,8.6221E-05,1824.00
TBPT,DEFI,9.3535E-05,1976.00
TBPT,DEFI,1.0094E-04,2128.00
TBPT,DEFI,1.0846E-04,2280.00
TBPT,DEFI,1.1616E-04,2432.00
TBPT,DEFI,1.2411E-04,2584.00
TBPT,DEFI,1.3237E-04,2736.00
TBPT,DEFI,1.4107E-04,2888.00
TBPT,DEFI,1.5032E-04,3040.00
TBPT,DEFI,1.6030E-04,3192.00
TBPT,DEFI,1.7118E-04,3344.00
TBPT,DEFI,1.8321E-04,3496.00
TBPT,DEFI,1.9665E-04,3648.00
TBPT,DEFI,2.1185E-04,3800.00
TBPT,DEFI,2.2918E-04,3952.00
TBPT,DEFI,2.4911E-04,4104.00
TBPT,DEFI,2.7217E-04,4256.00
TBPT,DEFI,2.9898E-04,4408.00
TBPT,DEFI,3.3025E-04,4560.00
TBPT,DEFI,3.6683E-04,4712.00
TBPT,DEFI,4.0966E-04,4864.00
TBPT,DEFI,4.5984E-04,5016.00
TBPT,DEFI,5.1863E-04,5168.00
TBPT,DEFI,5.8746E-04,5320.00
You will also need stress and strain loading in the low temperature (non-creep) range. This can be done thru use of ASME Section VIII. Div., 2 Annex 3.D Strength Parameters.
2. Oct 4, 2014 | 1,129 | 3,162 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2017-43 | longest | en | 0.881413 |
https://www.physicsforums.com/threads/problem-regarding-projectile-motion-on-a-inclined-plane.850132/ | 1,718,288,217,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861451.34/warc/CC-MAIN-20240613123217-20240613153217-00744.warc.gz | 840,140,451 | 17,868 | # Problem regarding projectile motion on a inclined plane
• CherryWine
In summary, the conversation discusses finding the range of a projectile thrown on an inclined plane, as well as determining the initial velocity angle for maximum range. The solution involves using various kinematics equations and trigonometric identities.
CherryWine
## Homework Statement
A projectile is thrown on an inclination plane with incline angle phi with an inital velocity V0 on an angle theta. Find the range of the projectile; treat the hypotenuse of the inclined plane as the x-axis. For what value of initial velocity angle is the range maximum, and what is that range.
## Homework Equations
All 2D kinematics equations.
## The Attempt at a Solution
Firstly I used the equation y(t) and expressed flight time as 2Vy/-gy (g is negative itself, the minus in front of it makes it positive), from there I wrote t=(2V0*sintheta)/(-g*cosphi). Then I plugged that into the equation for range which is D=Vx*t+1/2gx*t^2 where gx is the x-axis component of g. By simplifying the expression I obtained D=(2V0^2*sintheta*(-costheta*cosphi+sintheta*sinphi))/(g*(cosphi)^2). Now everything is correct except the bolded part which should be costheta*sin(theta-phi). Help please.
Note that the angle θ in the figure is measured from the horizontal, not from the inclined surface. It appears that you used Vy = V0 sinθ. Is this correct?
(If you click on the Σ symbol on the formatting tool bar, you can access more math symbols, like θ.)
TSny said:
Note that the angle θ in the figure is measured from the horizontal, not from the inclined surface. It appears that you used Vy = V0 sinθ. Is this correct?
(If you click on the Σ symbol on the formatting tool bar, you can access more math symbols, like θ.)
Yes! Sorry for the careless mistake, I found another attempt using the correct equation for t, but still everything is correct except the trigonometric part which then equals to sin(θ-Φ)*(sin(θ-Φ)*sinθ-cos(θ-Φ)*cosΦ), and I used Wolfram Alpha to check if this was equal to the correct cosθ*sin(θ-Φ) and it was not.
CherryWine said:
Yes! Sorry for the careless mistake, I found another attempt using the correct equation for t, but still everything is correct except the trigonometric part which then equals to sin(θ-Φ)*(sin(θ-Φ)*sinθ-cos(θ-Φ)*cosΦ), and I used Wolfram Alpha to check if this was equal to the correct cosθ*sin(θ-Φ) and it was not.
You have sin(θ-Φ)*(sin(θ-Φ)*sinθ-cos(θ-Φ)*cosΦ). I suspect that the mistake is the angle θ in red. Check that.
CherryWine
TSny said:
You have sin(θ-Φ)*(sin(θ-Φ)*sinθ-cos(θ-Φ)*cosΦ). I suspect that the mistake is the angle θ in red. Check that.
Yes! Thank you! It should be sinΦ. Thanks!
TSny said:
You have sin(θ-Φ)*(sin(θ-Φ)*sinθ-cos(θ-Φ)*cosΦ). I suspect that the mistake is the angle θ in red. Check that.
Could you please prove algebraically that sin(θ-Φ)*(sin(θ-Φ)*sinΦ-cos(θ-Φ)*cosΦ)=cosθ*sin(θ-Φ), and also if you could give me some hints for finding the angle for which that expression is going to be maximum. Thank you.
CherryWine said:
Could you please prove algebraically that sin(θ-Φ)*(sin(θ-Φ)*sinΦ-cos(θ-Φ)*cosΦ)=cosθ*sin(θ-Φ)
Let α = θ-Φ and β = Φ. Write sin(θ-Φ)*sinΦ-cos(θ-Φ)*cosΦ in terms of α and β. Then see if it reminds you of a well-known trig identity.
and also if you could give me some hints for finding the angle for which that expression is going to be maximum. Thank you.
Write D in the form D = C⋅f(θ), where C is independent of θ. D is maximized when f(θ) is maximized
CherryWine
TSny said:
Let α = θ-Φ and β = Φ. Write sin(θ-Φ)*sinΦ-cos(θ-Φ)*cosΦ in terms of α and β. Then see if it reminds you of a well-known trig identity.Write D in the form D = C⋅f(θ), where C is independent of θ. D is maximized when f(θ) is maximized
Thanks for the hint, I proved it. If you could just tell me what would you do to find the angle for maximum f(θ) because my brain is really blocking currently. And if you can, do not use derivatives.
CherryWine said:
If you could just tell me what would you do to find the angle for maximum f(θ) because my brain is really blocking currently. And if you can, do not use derivatives.
Try using another trig identity: http://www.sosmath.com/trig/prodform/prodform.html
## 1. What is projectile motion on an inclined plane?
Projectile motion on an inclined plane refers to the motion of an object that is launched at an angle on a surface that is not horizontal. This type of motion is characterized by both horizontal and vertical components of velocity.
## 2. How does the angle of inclination affect the projectile motion?
The angle of inclination, or the angle at which the inclined plane is tilted, can affect the range, height, and flight time of the projectile. A steeper angle will result in a shorter range and higher flight time, while a shallower angle will result in a longer range and shorter flight time.
## 3. What is the formula for calculating the range of a projectile on an inclined plane?
The formula for calculating the range of a projectile on an inclined plane is R = (v2sin2θ)/g, where R is the range, v is the initial velocity, θ is the angle of inclination, and g is the acceleration due to gravity.
## 4. How does the acceleration due to gravity affect the projectile motion on an inclined plane?
The acceleration due to gravity affects the vertical component of the projectile's motion. As the angle of inclination increases, the vertical component of the projectile's velocity decreases, which also affects the range and flight time of the projectile.
## 5. Can the initial velocity of the projectile affect its motion on an inclined plane?
Yes, the initial velocity of the projectile can affect its motion on an inclined plane. A higher initial velocity will result in a longer range and shorter flight time, while a lower initial velocity will result in a shorter range and longer flight time.
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# Retaking TOEFL, which score will AdComs consider?
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Retaking TOEFL, which score will AdComs consider? [#permalink]
### Show Tags
09 Aug 2010, 07:58
Hello,
I'm retaking the TOEFL in a couple of days. I scored 102 in the first attempt three months ago and I think I will do better now (after GMAT..).
However, in case I score less, do you know which score the BSs will consider?
Thanks
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Re: Retaking TOEFL, which score will AdComs consider? [#permalink]
### Show Tags
09 Aug 2010, 12:16
Usually the higher score rule applies to both GMAT and TOEFL. Good Luck!
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Re: Retaking TOEFL, which score will AdComs consider? [#permalink]
### Show Tags
09 Aug 2010, 15:22
Rid82, I don`t know how it works with the GMAT but with TOEFL, the scores you get are arranged in a table and you choose which one to send.There is no way in hell B-schools find out about other scores than the one you decide to send them, which is usually the highest
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Re: Retaking TOEFL, which score will AdComs consider? [#permalink]
### Show Tags
09 Aug 2010, 17:05
In fact there are 4 schools you can send the schools "for free" and you have to choose them before the exam.
The issue here is that in the first exam I didn't send the score to school X, and now I plan to do it. Therefore, in case I score less, they will receive my lowest score and then later I will send the other score.
So they will have received both scores, and they will see that I scored less in the most recent one.
complicated right?
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Re: Retaking TOEFL, which score will AdComs consider? [#permalink]
### Show Tags
10 Aug 2010, 04:09
I think you shouldnt have any problems.TOEFL is all about reaching a certain minimum score that is required.
However, I wouldnt send a score I dont know just to spare 17\$
Re: Retaking TOEFL, which score will AdComs consider? [#permalink] 10 Aug 2010, 04:09
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### Perl and Solving Trig/Converting GPS to x,y Cords
by Pizentios (Scribe)
on Jan 08, 2013 at 19:36 UTC Need Help??
Pizentios has asked for the wisdom of the Perl Monks concerning the following question:
Hi monks!
I have a problem that i know can be solved by using trig. However i am at a loss on how to go about it in perl.
Bit of backstory:
At work we have a map that uses x,y cords to place objects on it. However we need to "convert" gps lat and long cords to fit on this map. I have two reference points on the map already that will be constant for every caculation. Using Math::Trig i have figured out the angles (read bearings) of the two reference points as well as the bearings from the reference points to my test point using the gps lat and long values.
Here's the code i've used:
```use strict;
use warnings;
+e_direction);
my \$low_right_lat ="49.033312";
my \$low_right_long ="-95.261125";
my \$upper_left_lat ="51.361154";
my \$upper_left_long ="-101.353263";
my \$user_lat ="49.752852";
my \$user_long ="-100.119849";
my @A = NESW(\$low_right_long, \$low_right_lat);
my @B = NESW(\$upper_left_long, \$upper_left_lat);
my @USER = NESW(\$user_long, \$user_lat);
my \$angle_a_to_user = great_circle_direction(@A, @USER); #in rads.
my \$angle_b_to_user = great_circle_direction(@B, @USER); #in rads.
my \$angle_a_to_b = great_circle_direction(@A, @B); #in rads.
my \$angle_b_to_a = great_circle_direction(@B, @A); #in rads.
print "Angle From A to User is: \$angle_a_to_user_deg\n";
print "Angle From B to User is: \$angle_b_to_user_deg\n";
print "Angle From A to B is: \$angle_a_to_b_deg\n";
print "Angle From B to A is: \$angle_b_to_a_deg\n";
This ofcourse returns angles to the lines from 0 degrees (strait north)
Using this information i am able to use the law of sines and the law of cosines (and some addition/subtraction to get the angle from line AB to line AC and line BC) to figure out the length of the sides that are made to my test point on the x,y graph (on paper but it should translate to perl code fairly easy).
I am however at a loss on how to proceed further....
I have constants on a x,y grid that are as follows:
Point A: x=1019,y=1698
Point B: x=79,y=1138
Distance between Point A and Point B is: 1094
I am trying to caculate the x,y cords for a point that i would like to map. My thoughts are to find the intersection of two circles, as i know the radius of each circle (from my math on paper, one centered on Point A and the other centered on Point B).
Circle at Point A's radius: 781.5815
Circle at Point B's radius: 431.2683009
Can somebody please give me some tips or suggestions on how to proceed to solve this problem in perl? Code examples would be greatly appreciated....This is the first time i've had to do any kind of higher level math in perl.
It doesn't have to be solved using intersection of two circles if sombody out there has a better method of figuring it out...and i must admit my trig skills are very rusty as i haven't used em much since high school.
-Pizentios
Replies are listed 'Best First'.
Re: Perl and Solving Trig/Converting GPS to x,y Cords
by davido (Archbishop) on Jan 09, 2013 at 07:50 UTC
This problem is more complex than simple trigonometry. The earth is approximately round, but not precisely round, and that's one of the lesser (but more memorable for me) complexities involved. GPS systems have to choose a projection: WGS84, for example. And navigators of old spent a good deal of time learning the math behind great circles, and various chart projections. ...ok, maybe the rest is trigonometry, but not entirely simple.
It's been eighteen years since I read it, and I've forgotten most of what I learned. But I highly recommend Dutton's Navigation and Piloting (or the more recent Dutton's Nautical Navigation). Pick up a used copy via Amazon or eBay. You're really just after the mathematical formulas and a good explanation of the theory, and for that an older version is probably just as good as a newer one. I think I have the 1961 edition handed down from a friend of my parents.
From what I understand, at least at one time this one and Chapman's were among the books that the USCG used in training its sailors.
Dave
Re: Perl and Solving Trig/Converting GPS to x,y Cords
by BrowserUk (Pope) on Jan 08, 2013 at 22:11 UTC
With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.
Re: Perl and Solving Trig/Converting GPS to x,y Cords
by roboticus (Chancellor) on Jan 08, 2013 at 20:39 UTC
It may not be quite that simple. Flat maps of spheres always have distortion. (Look up "spherical conformal mapping".) So circles on your map won't be the same as circles on the sphere. In addition, the type of projection used will affect the conversion of your planar coordinates to your spherical coordinates.
I'd suggest you find out what your error tolerances are, the largest distance you're going to be interested in, and what sorts of maps you'll be using.
...roboticus
When your only tool is a hammer, all problems look like your thumb.
The Earth is round, but very big.
Between +70 and -70 degrees and distances under about 20 kilometers, bog standard 2D trig will produce results with errors less than 0.2%.
Between +-50 degs, it is less that 0.1%
With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.
That may be true for all the practical cases for the OP, but it's not generally true. A trivial example being several of the polar maps. In those cases, the equator would give terrible results, and the center pole would give similarly good results.
For anyone interested, some really interesting stuff is at http://www.progonos.com/furuti/MapProj/Normal/TOC/cartTOC.html, especially the "Mathematics of Cartography" section.
...roboticus
When your only tool is a hammer, all problems look like your thumb.
Re: Perl and Solving Trig/Converting GPS to x,y Cords
by Pizentios (Scribe) on Jan 09, 2013 at 14:33 UTC
Thanks for the replies. I should have specified the range of the 2d map is relativly small when compaired to the surface of the earth. The area that i will be working within is about 649,947 km^2. From the 49th parallel to the 60th parallel (all of the gps coordinates that i have worked with so far haven't been above the 54th parallel). The actual working area will likly be smaller (more like half or less) than those numbers, but the numbers above are for sure the max area that i will be working with.
In reality a 0.3% error tolerance for my purposes will likely be fine...and from what i've read/understand, the smaller the area the lower the errors will be. Thanks so far for the help!
-Pizentios
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August 30, 2017
Question
Part A. SPSS Assignment
The “Activity 5.sav” file contains a dataset of a researcher interested in finding the best way to educate elementary age children in mathematics. In particular, she believes that 5th grade girls do better in small class sizes while boys excel in larger classes. Through the school district, she has arranged a pilot program in which some classroom sizes are reduced prior to the state-wide mathematics competency assessment. In the dataset, you will find the following variables:
Participant: unique identifier
Gender: Male (M) or Female (F)
Classroom:
Small (1) – no more than 10 children
Medium (2) – between 11 and 19 children
Large (3) – 20 or more children
Score: final score on the statewide competency assessment.
To complete this assignment
Exploratory Data Analysis.
Perform exploratory data analysis on all variables in the data set. Realizing that you have six groups, be sure that your exploratory analysis is broken down by group. When possible, include appropriate graphs to help illustrate the dataset.
Compose a one to two paragraph write up of the data.
Create an APA style table that presents descriptive statistics for the sample.
Factorial ANOVA. Perform a factorial ANOVA using the “Activity 5.sav” data set.
Is there a main effect of gender? If so, explain the effect. Use post hoc tests when necessary or explain why they are not required in this specific case.
Is there a main effect of classroom size? If so, explain the effect. Use post hoc tests when necessary or explain why they are not required in this specific case.
Is there an interaction between your two variables? If so, using post hoc tests, describe these differences.
Is there support for the researcher’s hypothesis that girls would do better than boys in classrooms with fewer students? Explain your answer.
Write up the results in APA style and interpret them. Be sure that you discuss both main effects and the presence/absence of an interaction between the two.
Part B. Applying Analytical Strategies to an Area of Research Interest
Briefly restate your research area of interest.
Analysis of Covariance. Using your area of interest, identify one dependent and two independent variables, such that the independent variables would likely be covariates. Now, assume you conducted an ANCOVA that shows both the independent variable as well as the covariate significantly predicts the dependent variable. Create a mock ANCOVA output table (see SPSS Output 11.3 in your text for an example) that supports the relationship shown above. Report your mock finding APA style.
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I've been doing integrals non stop preparing for my exam tomorrow, and one has left me stumped for a few days. I've tried coming back to it several times, but I can't seem to manipulate it. It is as follows:
$$\int\frac{x^2}{\sqrt{x+1}}\;dx$$
I've tried different u-sub methods but nothing seems to work for me. My next thought was integration by parts, but when I attempt that method my answer isn't even close to the answer key given by my professor. The answer key shows this as the answer:
$$\frac25(x+1)^\frac{5}{2}-\frac43(x+1)^\frac{3}{2}+2\sqrt{x+1}+C$$
What would be the best technique to handle this integral? I feel like i'm missing something simple, but after 2 days it still hasn't come to me and it's quite frustrating. Thanks in advance.
• Try an initial $u$-substitution as $u=x+1$ and see what happens... Jun 16 '16 at 4:12
• An alternative substitution that is useful is $u = \sqrt{x+1}$. Jun 16 '16 at 4:16
• Whenever I can, my first reaction is always to try to get rid of radicals. So, as already commented and answered, $u = \sqrt{x+1}$ would be my first (and last) choice. Jun 16 '16 at 4:47
• You prefer this over letting $u = x+1$? To me this seems easier since $du=dx$. I'm genuinely curious though as I want to diversify my "calculus toolbox" as much as I can. Jun 16 '16 at 5:05
Let me try: $$\frac{x^2}{\sqrt{x+1}} = \frac{(x+1)^2 - 2(x+1) + 1}{\sqrt{x+1}} = (x+1)^{\frac{3}{2}} -2 (x+1)^{\frac{1}{2}} + (x+1)^{\frac{-1}{2}}$$
• That's really clever! Jun 16 '16 at 4:22
• Indeed it is. It was hard for me to visualize at first, but once I made the recommended substitution it became clear as day! Interesting way to simplify. Jun 16 '16 at 4:34
Use the substitution method.
Let $u=x+1$, then $u-1=x$ and $du=dx$. Try it.
• I totally forgot about special substitutions. I will try it right now. Thanks! Jun 16 '16 at 4:20
• No problem, and good luck on your test. Jun 16 '16 at 4:21
• Your hint was the easiest for me to understand and I was able to reach the solution easily using your substitution method. Thank you very much for your input, this was a u-sub case I had totally forgotten about! Jun 16 '16 at 4:39
You should substitute $x+1=u^2$ then the rest will become straight forward.
\begin{align} &I=\int \!{\frac {{x}^{2}}{\sqrt {x+1}}}\,{\rm d}x\\ &=\int (\!2\,{u}^{4}-4\,{u}^{2}+2\,{\rm d})u\\ &=\int \!2\,{u}^{4}\,{\rm d}u+\int \!-4\,{u}^{2}\,{\rm d}u+\int \!2 \,{\rm d}u\\ &=\frac{2}{5}\,{u}^{5}+\int \!-4\,{u}^{2}\,{\rm d}u+\int \!2\,{\rm d}u\\ &=\frac{2}{5}\,{u}^{5}-\frac{4}{3}\,{u}^{3}+\int \!2\,{\rm d}u\\ &=\frac{2}{5}\,{u}^{5}-\frac{4}{3}\,{u}^{3}+2\,u+C\\ &=\frac{2}{5}\, \left( x+1 \right) ^{5/2}-\frac{4}{3}\, \left( x+1 \right) ^{3/2}+2\, \sqrt {x+1}+C \end{align}
• Thank you for the detailed response. This isn't the way I would immediately think to do things, but it's always nice to see things from someone else's perspective :) I went the $u=x+1, x=u-1$ route instead which worked the same. Jun 16 '16 at 4:37 | 1,060 | 3,054 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2021-49 | latest | en | 0.95845 |
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DIRECTION : In 1990 – 91, value of exports of manufactured articles exceeds over the value of exports of raw materials by 100%. In 1991 – 92, the ratio of % of exports of raw material to that of exports of manufactured articles is 3 : 4. Value of Exports of food in 1991 – 92 exceeds the 1990– 91 figures by Rs. 1006 crore.
Question 1. During 1990 – 91, how much more raw material than food was exported?
(a) Rs. 2580 crore
(b) Rs. 896 crore
(c) Rs. 1986 crore
(d) Rs. 1852 crore
Question 2. In 1990 –91 what percentage of total values of exports accounts for items related to food?
(a) 23%
(b) 29.2%
(c) 32%
(d) 22%
Question 3. Value of exports of raw materials during 90 – 91 was how much percent less than that for 91 – 92?
(a) 39
(b) 46.18
(c) 7
(d) 31.6
Question 4. The change in value of exports of manufactured articles from 1990 – 91 to 1991 – 92 is
(a) 296 crore
(b) 629 crore
(c) 2064 crore
(d) 1792 crore
Answer for 1 to 4 From the data that is given we can find the following data- The starting point for filling the data in the vacant columns of the given table should from food’ export value. We know that in 1991-92, value of food export is 23% of 25800= 5934. Now as it is given that this figure is 1006 cr more than last year’s value, hence value of food in 1990-91 is 4928. (The rest of the explanation of how the following values were arrived at is given after the table).
The Value of Manufactured articles & Raw materials exports In 90-91, = (22400 – 4928) = Rs.17472 crores. Since Export in manufactured goods is twice that of raw materials,
Therefore the ratio of export of manufactured goods and raw materials is 2:1
Therefore export of manufactured goods = Rs.11648 crores and Raw materials = Rs.5824 crores.
Hence the difference between raw material and food = (5824 – 4928) = Rs.896 crores.
The exports related to food in 91-92 = 0.23 x 25800 = 5934.
Therefore the exports related to food 1990-91 = (5934 – 1006) = 4928.
Therefore the percentage food related exports in 90-91 = 4928/22400 = 22%.
The combined percentage of Manufactured articles and Raw materials in 91-92 = 77%
The ratio will be 4 : 3.
Therefore the percentage of Manufactured articles export = 44%
And the percentage of Raw materials export = 33%.
Therefore value of manufactured articles = 0.44 x 25800 = Rs.11352 crores
And the value of Raw materials = Rs.8514 crores.
Therefore the percentage difference between the value of Raw materials between 90-91 and 91-92 = [(8514 – 5824)/8514] × 100 = 31.6%
Change = (11648 – 11352) = Rs.296 crores.
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A035117 a(n) is the starting position of the first occurrence of a string of at least n 1's in the decimal expansion of Pi. 20
1, 94, 153, 12700, 32788, 255945, 4657555, 159090113, 812432526, 3961184001, 15647738228, 1041032609981, 3907688331257 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,2 COMMENTS Presently identical to A096755, which is the first occurrences of exactly n 1's in the digits of Pi. Will differ as soon as there's some a(n) = a(n+1) and equivalently, A035117(n) > A035117(n+1). - M. F. Hasler, Mar 17 2017 LINKS David G. Andersen, The Pi-Search Page. PI-world Site, The digits and Statistics for 12 trillion digits of PI [archived page] Eric Weisstein's World of Mathematics, Pi Digits. Yasumasa Kanada Laboratory Home Page, Computer Centre, The University of Tokyo, Statistical Distribution Information CROSSREFS Cf. A000796 (decimal expansion (or digits) of Pi). Cf. A035117 (this), A050281 (n '2's), A050282, A050283, A050284, A050286, A050287, A048940 (n '9's). Cf. A096755 (exactly n '1's), A096756, A096757, A096758, A096759, A096760, A096761, A096762, A096763 (exactly n '9's), A050279 (exactly n '0's). Cf. A121280 = A068987 - 1 (position of "123...n" in Pi's decimals). Cf. A176341 (first occurrence of n in Pi's digits). Sequence in context: A039551 A100767 A050208 * A096755 A050965 A044426 Adjacent sequences: A035114 A035115 A035116 * A035118 A035119 A035120 KEYWORD nonn,base,more AUTHOR Leonardo Bitran (lbitran(AT)reuna.cl) EXTENSIONS More terms from Colin Martin (cbmartin(AT)tpg.com.au), Mar 03 2002 Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 27 2007 Edited, after re-establishing A096755, by M. F. Hasler, Mar 17 2017 a(11) from Giovanni Resta, Sep 30 2019 a(12) from Yasumasa Kanada Laboratory, 2002 and a(13) from Shigeru Kondo, 2011, added by Dmitry Petukhov, Dec 27 2019 STATUS approved
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• ### Thermal expansion of five selected optical glasses
· The coefficients of linear thermal e) pansion of the five samples of glass given in table I were derived from the data. These coefficient of e pansion are believed to be accurate to ± O.l X lO-6• T ABLE 1. Coefficients of linear thermal expansion oj some optical glasses Glass a BSC n=1.517 v=64 ..
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• ### Coefficient of Linear Thermal Expansion (CLTE) Formula
Linear Coefficient of Thermal Expansion Values of Several Plastics The Coefficient of Linear Thermal Expansion (Or Linear Coefficient of Thermal Expansion) lies between (in the service temperature range for each case) Ca. 0.6 x 10 -4 to 2.3 x 10 -4 K -1 for most of the thermoplastics Ca. 0.2 x 10 -4 to 0.6 x 10 -4 K -1 for thermosets
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• ### The Coefficient of Thermal Expansion in PBX 9502
· αL = linear expansion coefficient and ∆T = temperature change that produced ∆L. Table 1 provides CTEs of αL for Al Be Cu Fe and Hg (Ref. 4) and for α-phase Pu (Ref. 5) at 25 °C. Table 1. Coefficients for Linear Thermal Expansion in Various Metals Element αL (µm/mK) Al 23.1 Be 11.3 Cu 16.5 Fe 11.8 Hg 60.4 α-phase Pu 53.0 2
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• ### Coefficient of Linear Thermal Expansion (CLTE) Formula
The linear coefficient CLTE or α for plastic and polymer materials is calculated as α = ΔL / (L0 ΔT) Where α is coefficient of linear thermal expansion per degree Celsius. ΔL is change in length of test specimen due to heating or to cooling. L 0 is the original length of specimen at room temperature. ΔT is temperature change
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• ### Coefficient of thermal expansion table PDF the
TABLE 1 Coefficients of Linear Thermal Expansion Material Coefficients of Linear Thermal Expansion (°F-1 ) Carbon Steel 5.8 x 10-6 Stainless Steel 9.6 x 10- Thermal Expansion Apparatus C 2 Accepted Values for Coefficient of Thermal Expansion Material a ( x10-6/∞C ) Copper 17.6 Steel 11.3 to 13.5 Aluminum 23.4 Changing Tubes Caution
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• ### Thermal expansion of five selected optical glasses
· The coefficients of linear thermal e) pansion of the five samples of glass given in table I were derived from the data. These coefficient of e pansion are believed to be accurate to ± O.l X lO-6• T ABLE 1. Coefficients of linear thermal expansion oj some optical glasses Glass a BSC n=1.517 v=64 ..
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• ### 223 Physics Lab Linear Thermal Expansion
· where is the initial length of the object before heat is added and is the linear expansion coefficient of the material. Accepted values of several common materials are given below in Table 1. This effect however is not simply limited to materials whose temperature has increased.
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• ### Coefficient Of Thermal Expansion Table Liquids Elcho Table
Linear Expansion Khan Academy Summary table of molar volumes and thermal expansion coefficients thermal expansion coefficient α isothermal compressibility β t maintenance and aircraft mechanics thermal energy. Whats people lookup in this blog
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• ### The Thermal Expansion Characteristics of Stainless Steel
· Thermal expansion is a fundamental material property which relates dimen sional changes of a material with changes in temperature. A convenient measure of thermal expansion is the mean linear coefficient of thermal expansion (CTE) and is defined as A Lo(T2-T ) . =V /ALX 1 Al (I) where Li and L2 are the specimen lengths
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• ### Coefficient of Linear Thermal Expansion on Polymers
· The linear coefficient CLTE or α for plastic and polymer materials is calculated as α = ΔL / (L0 ΔT) Where α is coefficient of linear thermal expansion per degree Celsius. ΔL is change in length of test specimen due to heating or to cooling. L 0 is the original length of specimen at room temperature.
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• ### Linear Thermal Expansion Coefficient of the NaCl Phase
· The linear thermal-expansion coefficient of the low temperature phase of CsCI aCT) = .l/l(T) .T where T is the average temperature in the interval .T was determined to be 4. 78X 10-5 (CO)-l between 50° and 150°C. This is within 5 of the temperature coefficient of lattice parameter expansion determined by Menary
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• ### 223 Physics Lab Linear Thermal Expansion
· where is the initial length of the object before heat is added and is the linear expansion coefficient of the material.Accepted values of several common materials are given below in Table 1. This effect however is not simply limited to materials whose temperature has increased.If energy is removed from the material then the object s temperature will decrease causing the object to contract.
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• ### Lecture 2University of Sydney
· Linear expansion Most materials expand when their temperatures increase. The increase in length is found to be proportional to the temperature increase
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• ### Coefficient of thermal expansion table PDF the
TABLE 1 Coefficients of Linear Thermal Expansion Material Coefficients of Linear Thermal Expansion (°F-1 ) Carbon Steel 5.8 x 10-6 Stainless Steel 9.6 x 10- Thermal Expansion Apparatus C 2 Accepted Values for Coefficient of Thermal Expansion Material a ( x10-6/∞C ) Copper 17.6 Steel 11.3 to 13.5 Aluminum 23.4 Changing Tubes Caution
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• ### Thermal Expansion Coefficient Table TE-1 ASME SECION II
· Thermal Expansion Coefficient Table TE-1 ASME SECION II part D wailunwu (Mechanical) (OP) 6 May 16 14 55. Hi I have a vertical vessel that is in operating in cold temperature (-100 deg F). I would like to find out how much the vessel contracts vertically. Table TE-1 does not indicate coefficients for temperature below 70 deg F.
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• ### Chapter 2 Thermal ExpansionRice University
· Thermal Expansion / 11 Table 2.1 Summary of Thermal Expansion Coefficient of Linear Thermal Expansion (CTE) Approximate Ranges at Room Temperature to 100 °C (212 °F) from Lowest to Highest CTE Value CTE 10-6/K 10-6/°F Material 2.6–3.3 1.4–1.8 Pure Silicon (Si) 2.2–6.1 1.2–3.4 Pure Osmium (Os) 4.5–4.6 2.5–2.6 PureTungsten (W)
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• ### THERMAL EXPANSION APPARATUS
· C Thermal Expansion Apparatus 1 Introduction Introduction The PASCO Model TD-8558A Thermal Expansion Apparatus provides easy and accurate measurements of the coefficient of linear expansion for steel copper and aluminum. To make the measurement the steel copper or aluminum tube is placed on the expansion base. The
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• ### Lecture 2University of Sydney
· Linear expansion Most materials expand when their temperatures KJF §17.4 . Linear expansion • α is the coefficient of linear expansion. Units K –1 °C . Why do solids expand KJF §18.2 . Question A metal disc with a hole in it is heated. Will the diameter of the hole Thermal expansion of water Water has an anomalous property
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• ### COEFFICIENT OF THERMAL EXPANSION FOR VARIOUS
· The coefficient of thermal expansion is defined as the change in length or volume of a material for a unit change in temperature. The overall coefficient is the linear thermal expansion (in.) per degree Fahrenheit or Celsius. The CTE data is calculated by the change in length divided by the quantity of
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• ### AirDensity Specific Weight and Thermal Expansion
· AirDensity Specific Weight and Thermal Expansion Coefficient at Varying Temperature and Constant Pressures Online calculator figures and tables showing density specific weight and thermal expansion coefficient of air at temperatures ranging -100 to 1600 °C (-140 to 2900 °F) at atmospheric and higher pressureImperial and SI Units
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• ### Coefficients of Linear Thermal ExpansionSilver CTE
356 rows · Linear Thermal Expansion Coefficientα -(10-6 m/(m K)) ) ABS (Acrylonitrile butadiene
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• ### Coefficient of Thermal Expansion
· Thermal Expansion. The volumetric expansion coefficient is in average three times the linear expansion coefficient. A polymer has a lower expansivity than the related low-molecular liquid (monomer). Empirically it has been found that α rubber ≈ 2.5 · α glass.
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• ### THERMAL EXPANSION APPARATUS
· C Thermal Expansion Apparatus 1 Introduction Introduction The PASCO Model TD-8558A Thermal Expansion Apparatus provides easy and accurate measurements of the coefficient of linear expansion for steel copper and aluminum. To make the measurement the steel copper or aluminum tube is placed on the expansion base. The
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• ### The Thermal Expansion Characteristics of Stainless Steel
· Thermal expansion is a fundamental material property which relates dimen sional changes of a material with changes in temperature. A convenient measure of thermal expansion is the mean linear coefficient of thermal expansion (CTE) and is defined as A Lo(T2-T ) . =V /ALX 1 Al (I) where Li and L2 are the specimen lengths
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• ### Thermal Expansion EstimatesCSB
· 2D (area) or 3D (volume) can be related to the linear coefficientof thermal expansion 1 ∂As ∂T = 2αs(T)As (5) ∂Vs ∂T 3αs(T)Vs (6) Typical values of αs are shown in Table 1 for some common metals and materials of construction. As shown by Table 1 liquid thermal expansion is much larger than steel thermal expansion and
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• ### LithiumThermal Expansion Coefficientperiodic-table
· Coefficient of Thermal Expansion of Lithium. Linear thermal expansion coefficient of Lithium is 46 µm/(m·K) Thermal expansion is generally the tendency of matter to change its dimensions in response to a change in temperature. It is usually expressed as a fractional change in length or volume per unit temperature change. Thermal expansion is common for solids liquids and for gases.
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• ### WebElements Periodic Table » Periodicity » Linear
Linear expansion coefficient. The coefficient of linear thermal expansion is the ratio of the change in length per degree K to the length at 273 K. The coefficient of volume expansion is about three times the linear coefficient. The value of the coefficient is temperature dependent. See literature references for data at other temperatures.
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• ### Coefficient of thermal expansion table PDF the
TABLE 1 Coefficients of Linear Thermal Expansion Material Coefficients of Linear Thermal Expansion (°F-1 ) Carbon Steel 5.8 x 10-6 Stainless Steel 9.6 x 10- Thermal Expansion Apparatus C 2 Accepted Values for Coefficient of Thermal Expansion Material a ( x10-6/∞C ) Copper 17.6 Steel 11.3 to 13.5 Aluminum 23.4 Changing Tubes Caution
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• ### Coefficient of Linear Thermal Expansion (CLTE) Formula
The linear coefficient CLTE or α for plastic and polymer materials is calculated as α = ΔL / (L0 ΔT) Where α is coefficient of linear thermal expansion per degree Celsius. ΔL is change in length of test specimen due to heating or to cooling. L 0 is the original length of specimen at room temperature. ΔT is temperature change
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• ### Coefficients of Linear Thermal ExpansionEngineering ToolBox
196 rows · · Thermal expansion coefficients for some common materials
Chat Online | 2,649 | 11,052 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2022-05 | latest | en | 0.764258 |
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We bring this article for your benefit, with a few handy inputs on how to prepare for, and succeed in, the Reasoning section of the upcoming SBI Clerk 2021 Prelim and Main examinations.
SBI Clerk Prelim – Reasoning:
The Reasoning section of this exam comprises 35 Qs which carry one mark each, and they need to be worked out in just 20 mins. There is a negative marking scheme, where 1/4th of the marks assigned for a question are deducted for each wrongly marked response. There are NO minimum qualifying marks for individual tests OR for the aggregate score.
The following data presents the topic wise break-up and analysis of the Prelim exam across the years [Feedback as given by T.I.M.E. students who have appeared for such exam in the past]
SBI Clerk 2020 Prelim:
S.No Topic Number of questions given Level of Difficulty
1 Puzzles 15 – 21 Easy-Moderate
2 Direction Sense 2 – 3 Easy
3 Coding and Decoding 1 – 5 Easy
4 Sequence (letter/digit/symbol) 0 – 5 Easy
5 Symbol and notation (inequalities) 3 – 5 Easy
6 Blood Relation 0 – 3 Easy
7 Deduction 0 – 5 Easy
8 Set of numbers/words 3 – 5 Easy
9 Miscellaneous 2 – 4 Easy
SBI Clerk 2019 Prelim:
S.No Topic Number of questions given Level of Difficulty
1 Linear arrangement (all are facing north) 5 Easy
2 Comparisons 3 Easy
3 Circular arrangement 5 Easy
4 Box arrangement 4 Easy
5 Blood Relations 3 Easy
6 Set of words 5 Easy
7 Symbols and notations (in equalities) 3 Easy
8 Deductions / Syllogisms (only a few) 4 Easy to moderate
9 Miscellaneous 3 Easy
The following areas are considered important for the Prelim exam:
1. Symbols and notations
2. Blood relations
3. Direction sense
4. Coding-decoding
5. Syllogisms
6. Set of numbers /words
7. Sequence
8. Puzzles - Linear arrangements / Box arrangements / Floor arrangements / Circular arrangements / Distribution (days and months based) / Comparisons / Quant-based Reasoning
Though questions on Data Sufficiency are usually posed in the Mains exam, candidates are advised not to get complacent and be on their guard, as clear by the precedent set with their appearance in the 2018 Prelim (in the first slot on 30/6/2018, as reported by our students).
SBI Clerk Mains – Reasoning:
The Reasoning section of the exam consists of 50 Qs with a total of 60 marks, and the time allotted is 45 mins. The negative marking scheme put in place for this exam mandates the deduction of 1/4th of the marks assigned for a question, for every incorrect response.
A variable marking scheme MAY BE applicable in the Reasoning section of this exam.
The following data presents the topic wise break-up and analysis of the Main exam [Feedback as given by T.I.M.E. students who have appeared for such exam in the past]
SBI Clerk 2020 Mains Level of Difficulty
1 9 Letter arrangement (3 arrangements) [new model] 4 Moderate
2 Square (In and Out) (8P) [3arrangements] [new model] 4 Moderate
3 Set of words and numbers 1 Easy
4 Blood Relation (With symbols) 2 Moderate
5 Linear + Blood Relation (6P) 4 Moderate
6 10P + 10months 3 Moderate
7 7P + 7 years + QBR 4 Difficult
8 Certain Number of Floors in 2 buildings X and Y [new model] 4 Difficult
9 Two rows + vacant 4 Moderate
10 Meaningful Word Cannot be formed using 4th letter of the word 1 Easy
11 Alpha-numeric Sequence (2 steps) 1 Easy
12 Input Output (Vowel replaced with symbols) [new model] 4 Moderate
13 7P + 3 Departments + 7 Colours 4 Moderate
14 Data Sufficiency 3 Moderate
15 Direction Sense 1 Moderate
16 Coding and Decoding (condition based) 3 Moderate
17 Critical Reasoning 3 Difficult
SBI Clerk 2019 Mains (1st shift) Level of Difficulty
1 Designations (7 Persons) + Experience (Years) +Income 5 Moderate - difficult
2 Coding and Decoding (Condition based) 5 Difficult
3 8 persons + 3 years +3 months 5 Difficult
4 9 boxes + Quant Based Reasoning (multiples of immediately above box number) 5 Moderate - difficult
5 7 persons - linear arrangement - some south and some north facing + Quant Based Reasoning (ages) 5 Difficult
6 Input and output (Sequence type) 5 Difficult
7 Word formation 1 Easy
8 Word Arrangement (How many such pairs) 1 Easy
9 Inequalities (with symbols) 5 Moderate
10 Directions 5 Moderate
11 Critical Reasoning 8 Difficult
SBI Clerk 2019 Mains (2nd shift) Level of Difficulty
1 Circular + ages (8 persons) 5 Moderate -difficult
2 Linear arrangement + distance (7 cars) 5 Difficult
3 Three lines (Row 1 - 4 persons, Row 2 - 8 persons, Row 3 - 4 persons) 5 Moderate -difficult
4 Input output (odd -5, even +5, letters-alphabetical order) 5 Moderate
5 Direction sense (with symbols) 1 Moderate
6 Blood relations (with symbols) 3 Moderate
7 Inequalities (with symbols) 4 Moderate
8 Syllogism (only a few) 2 Moderate
9 4 boxes + colours 1 Moderate
10 Meaningful word formation 1 Moderate
11 7 persons linear 1 Easy
12 Hexagonal (6 persons - some inside and some outside) 1 Easy
13 Coding and decoding (three conditions) 4 Moderate
14 6 persons + 6 months (place, days) 5 Moderate
15 Critical Reasoning 7 Difficult
Though the section has been named the Reasoning and Computers part, no questions related to Computers have been asked during the last few years. The focus is more on Puzzles, Input-output, Data Sufficiency, Coding-decoding and Critical Reasoning in the main exam. While Critical Reasoning sounds intimidating, questions here are not time-consuming, as elimination of incorrect choices can easily be achieved. However, the likelihood of getting stuck with two close options cannot be ruled out.
The following areas are considered important for the Mains exam:
1. Symbols and notations
2. Blood relations
3. Direction sense
4. Coding-decoding
5. Syllogisms
6. Puzzles - Linear arrangements / Box arrangements / Floor arrangements / Circular arrangements / Distribution (day and month-based) / Comparisons / Quant based Reasoning
7. Data sufficiency
8. Input and output
9. Critical Reasoning
Strategy:
Though everything in an exam seems important, it is essential to prioritise the order in which you handle questions. In order to maximise the score, we recommend the below mentioned plan for attempting questions.
It is advisable to attempt questions on sequence, set of numbers / words, deductions, blood relations, directions, symbols and notations, word and number arrangements and input and output before moving on to others.
Solving puzzles must come next in this process. Among puzzles too, it is more time-saving to focus on comparisons before working out seating arrangements and distributions, which must be considered only at the end.
It is only very rarely that a few clues are given in a jumbled manner. Usually, from what we hear from our students, clues meant for solving puzzles are presented such that they help solve the given puzzle in the order in which the clues are given, thus obviating the need to move back and forth.
For the sake of time management, questions on Data Sufficiency and Critical Reasoning should be worked out at the end.
Work hard, be kind and amazing things will happen!
All the best. | 1,774 | 7,097 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2024-38 | latest | en | 0.882645 |
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- - pressure corrector turbFoam (https://www.cfd-online.com/Forums/openfoam-programming-development/66192-pressure-corrector-turbfoam.html)
Sara D July 8, 2009 13:25
pressure corrector turbFoam
Dear all,
I have a question concerning the pressure correction in turbFoam:
Code:
fvScalarMatrix pEqn ( fvm::laplacian(rUA, p) == fvc::div(phi) );
The right hand side is implemented using phi instead of U to avoid an extra interpolation of U to Uf (see http://www.tfd.chalmers.se/~hani/kur...7/rhiechow.pdf).
This confuses me a little bit as I expected the right hand side to be
fvc::div(H/A)=sumOverFaces(Hf/Af.Sf)
and with phi=Uf.Sf and Uf=H/A at this point in the algorithm, I assume the code does the following:
fvc::div(phi)=fvc::div(Hf/Af.Sf)=sumOverFaces(Hf/Af.Sf.Sf)
with one Sf too many
I probably overlook something, can someone tell me what?
Sara
henrik July 12, 2009 13:38
Sara,
I think what you are missing is that fvc::div(phi) DOES a simple sum over all cell faces and DOES NEITHER dot-product with the face area vectors NOR interpolate to the face.
Yes, this is not intuitive, but it makes a lot of sense when you think about it.
Unfortunately, on page P-39 the Programmer's Guide says:
Quote:
The fvc::div function can take as its argument either a surfaceField, in which case is specified directly, or a volField which is interpolated to the face by central differencing as described in Section 2.4.10:
where - I think - it should read:
Quote:
The fvc::div function can take as its argument either a surfaceField, in which case is specified directly, or a volField which is interpolated to the face by central differencing as described in Section 2.4.10:
Henrik
Sara D July 13, 2009 03:34
thanks
Henrik,
Thank you, now I understand.
That is indeed a pitfall and the programmers guide doesn't help in this case.
Thanks a lot for clarifying,
Sara
All times are GMT -4. The time now is 17:46. | 583 | 2,172 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2017-43 | latest | en | 0.849675 |
https://math.stackexchange.com/questions/1431572/is-there-a-systematic-way-to-find-the-range-of-functions | 1,718,522,547,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861643.92/warc/CC-MAIN-20240616043719-20240616073719-00043.warc.gz | 347,598,376 | 35,627 | # Is there a systematic way to find the range of functions?
I was looking for steps or a systematic way to find the range of functions.
The way to find domain is quite obvious: exclude x-values that make the function undefined on the real numbers.
But the range is harder, I found several methods to find range:
$1)$ Intuition: to guess how the function behaves.
$2)$ Graph: to graph the function and get the range from it.
$3)$ Using limits and calculus to determine the min and max, and how the function behave at infinity.
$4)$ Domain of Inverse of function.
But the problem is there are some functions really hard to get their inverses. And I want to find the range analytically without graphs, limits or calculus tools.
Is there any systematic and direct way to find the range of functions ?
Thanks a lot for help.
• This is a very broad question though. It really depends on the difficulty of the function. Generally I would say: First graph. That's why we have graphing calculators these days. Once the graph shows some interesting features regarding max/min and asymptotic behavior, we can (or must) resort to calculus to confirm what the graph is showing. From there we ought to be able to establish a Range Commented Sep 12, 2015 at 1:59
• @imranfat: So, there is no fixed steps to follow ? Commented Sep 12, 2015 at 11:24
1) State Domain 2) Investigate y-intercept 3) Investigate x intercept(s) 4) Investigate when the curve is above/under x-axis 5) Investigate vertical asymptotes/holes in the graph 6) State derivative 7) State Domain derivative 8) Make a numberline and determine intervals when function is increasing/decreasing 9) Determine max/min 10) Consider limits $x$ goes to infinity's, horizontal asymptotes? 11) Possibility of slant asymptotes or other asymptotic behavior. 12) Make a graph (nowadays use a calculator) 13) Determine Range | 441 | 1,873 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.78125 | 4 | CC-MAIN-2024-26 | latest | en | 0.893957 |
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Topic: Need Multicultural Lesson
Replies: 1 Last Post: Mar 8, 1997 5:07 PM
Messages: [ Previous | Next ]
ShariV@aol.com Posts: 10 Registered: 12/6/04
Re: Need Multicultural Lesson
Posted: Mar 8, 1997 5:07 PM
Michelle said:
<< I choose the topic of Algebra with a concentration on graphing and
functions. However, as a requirement we are to write one multicultural
lesson. >>
One type of Islamic art is very geometric. Its base is lines and circles.
The artists start with two lines that intersect at right angles. Then they
draw a circle with its center as the intersection point of the two lines.
More circles and lines are drawn from there. The centers of the circles
are always the intersection points of circles and circles or circles and
lines. Lines are drawn from points where circles intersect circles or
other lines. Once they have drawn many lines and circles, they start
erasing pieces of the lines and circles until they create a unique
pattern.
This type of art can be used in conjunction with your lesson. Have your
students make a piece of art using this method. Then have them place the
art on a graph. The students can find the equations of the lines and
circles in their drawings and their starting and ending points. If you
have computers available, the students can program the computer to make
their pattern.
As a start to the lesson, I would suggest finding photographs of this type
of Islamic art for your students to view. It will give them some idea of
what they are shooting for. At that time you can give some background | 401 | 1,764 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2018-17 | latest | en | 0.941019 |
https://www.jiskha.com/display.cgi?id=1363734897 | 1,516,583,008,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084890928.82/warc/CC-MAIN-20180121234728-20180122014728-00244.warc.gz | 931,572,166 | 3,515 | # Physics
posted by .
A 4 kg weight falls on a spring that is facing up. The weight compresses the spring 0.25m. If the spring constant of the spring is 3.5N/m, how high was the weight when it was dropped?
## Similar Questions
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A 395.0 g block is dropped onto a vertical spring with a spring constant k = 252.0 N/m. The block becomes attached to the spring, and the spring compresses 0.29 m before momentarily stopping. While the spring is being compressed, what … | 418 | 1,640 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2018-05 | latest | en | 0.9214 |
http://www.algebra.com/algebra/homework/expressions/expressions.faq.question.39313.html | 1,444,191,676,000,000,000 | text/html | crawl-data/CC-MAIN-2015-40/segments/1443736682102.57/warc/CC-MAIN-20151001215802-00165-ip-10-137-6-227.ec2.internal.warc.gz | 371,493,099 | 4,859 | SOLUTION: Simpliy: w to fourth power over w to second power a) w to 1/2 power b) w to eighth power c) w to sixth power d)w to second power
Algebra -> Expressions -> SOLUTION: Simpliy: w to fourth power over w to second power a) w to 1/2 power b) w to eighth power c) w to sixth power d)w to second power Log On | 96 | 317 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2015-40 | latest | en | 0.836388 |
http://au.metamath.org/mpegif/3bitrri.html | 1,512,952,122,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948511435.4/warc/CC-MAIN-20171210235516-20171211015516-00564.warc.gz | 23,181,422 | 3,323 | Metamath Proof Explorer < Previous Next > Nearby theorems Mirrors > Home > MPE Home > Th. List > 3bitrri Unicode version
Theorem 3bitrri 263
Description: A chained inference from transitive law for logical equivalence. (Contributed by NM, 4-Aug-2006.)
Hypotheses
Ref Expression
3bitri.1
3bitri.2
3bitri.3
Assertion
Ref Expression
3bitrri
Proof of Theorem 3bitrri
StepHypRef Expression
1 3bitri.3 . 2
2 3bitri.1 . . 3
3 3bitri.2 . . 3
42, 3bitr2i 241 . 2
51, 4bitr3i 242 1
Colors of variables: wff set class Syntax hints: wb 176 This theorem is referenced by: nbbn 347 pm5.17 858 dn1 932 reu8 2974 unass 3345 ssin 3404 difab 3450 iunss 3959 poirr 4341 cnvuni 4882 dfco2 5188 resin 5511 dffv2 5608 dff1o6 5807 sbthcl 6999 fiint 7149 dfsup2OLD 7212 rankf 7482 dfac3 7764 dfac5lem3 7768 elznn0 10054 elnn1uz2 10310 lsmspsn 15853 h2hlm 21576 cmbr2i 22191 pjss2i 22275 dffr5 24181 brsset 24500 brtxpsd 24505 ellines 24847 itg2addnc 25005 dvreasin 25026 cvlsupr3 30156 dihglb2 32154 This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 This theorem depends on definitions: df-bi 177
Copyright terms: Public domain W3C validator | 585 | 1,223 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2017-51 | latest | en | 0.207236 |
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• Posts: 2
Joined: Mar 3, 2020
March 3rd, 2020 at 3:22:34 PM permalink
Hello
I've been trying a little gambling for a few weeks
Actually tried Martingale a few times on roulette, nearly lost money few times, and now hating it and aware it's not working.
Realizing you can't really beat the roulette wheel, can someone set me straight on following 'system' on roulette ?
Playing on 'partage' table only (online)
Betting 6/4 units on red/3rd column or black/2nd column and 1 unit on Zero (european table so only one Zero)
This actually seems to pay out 36 + 3 (partage on the colors) = 39 on the Zeroes, so that is 38 profit on a 1/37 chance right ?
the color bets are needed to make use of the 'partage' system, the columns are probably just window dressing.
What do you think ?
ThatDonGuy
• Posts: 6471
Joined: Jun 22, 2011
March 3rd, 2020 at 5:49:10 PM permalink
Assume you make 37 bets, and all 37 numbers come up once
5, 14, 23, 32: +6 on red, +8 on column, -1 on zero = +13
2, 8, 11, 17, 20, 26, 29, 35: -6 on red, +8 on column, -1 on zero = +1
Any of the other 14 red numbers: +6 on red, -4 on column, -1 on zero = +1
Any of the other 10 black numbers: -6 on red, -4 on column, -1 on zero = -11
Zero: -3 on red, -4 on column, +35 on zero = +28
Sum = (4 x 13) + (8 x 1) + (14 x 1) - (10 x 11) + (1 x 28) = -8
AxelWolf
• Posts: 22296
Joined: Oct 10, 2012
Thanked by
March 3rd, 2020 at 11:17:26 PM permalink
Quote: supernerd
Hello
I've been trying a little gambling for a few weeks
Actually tried Martingale a few times on roulette, nearly lost money few times, and now hating it and aware it's not working.
I'm just curious, what was your thought process in the first place thinking it would work? My first question would be to myself... If it did work, why aren't there scores of people out there beating the casinos using this type of method, especially since it's such a simple system that almost anyone with money can do 24/7 365 worldwide?
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
AZDuffman
• Posts: 14186
Joined: Nov 2, 2009
March 4th, 2020 at 3:51:02 AM permalink
I have taught a few people roulette in my 12 years of casino party nights. They all think this or that will work.
Sometimes early, sometimes at the end of the night I ask if they want the dirty little secret.
IT DOES NOT MATTER WHAT YOU BET.
All the odds are geared the same. Bet a single number. Bet black. Bet odd. Bet the middle row. It does not matter.
In the end, we get it all.
All animals are equal, but some are more equal than others
OnceDear
• Posts: 7485
Joined: Jun 1, 2014
March 4th, 2020 at 5:15:38 AM permalink
Quote: supernerd
Hello
...
What do you think ?
Welcome to the forum.
Congratulations on finding and sticking to a table offering 'Partage' . That cuts the house edge to 1.35% but only for the even money bets. Your column wagers are still subject to an immutable 2.7% house edge, so I'll analyse your own analysis without those bets.
Bet 6 units on red and 1 unit on green
Do that 37 times and have each number come up in turn.
So. Each spin, you place 7 units on the table. In total, you place 37*7 = 259 chips.
of those 37 spins,
1 time it came up green zero and you pick up 36+3 = 39 chips
18 times it comes up red and you pick up 18*12 = 216 chips
18 times it comes up black and you pick up 0 chips.
Total staked =259 chips
Total returned = 39+216 = 255 chips
House edge = 100-98.45 = 1.55%
As I understand it, you'd be better off not even bothering to cover the zero as that only pays out like any other number and is subject to the full house advantage.
E&OE
Psalm 25:16 Turn to me and be gracious to me, for I am lonely and afflicted. Proverbs 18:2 A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
supernerd
• Posts: 2
Joined: Mar 3, 2020
March 4th, 2020 at 7:21:32 AM permalink
Thank you
There was an oversight in my reasoning after all (forgot to add the stake on color )
I think I get it already :-)
Playing Partage does seem like a way to play without much risk in an offline casino though, and maybe have a little profit in short term on
some occasions.
heatmap
• Posts: 2297
Joined: Feb 12, 2018
March 4th, 2020 at 4:43:40 PM permalink
My betting system works on the physical layout and direction of the ball
ThatDonGuy
• Posts: 6471
Joined: Jun 22, 2011
Thanked by
March 4th, 2020 at 5:56:45 PM permalink
Quote: supernerd
Playing Partage does seem like a way to play without much risk in an offline casino though, and maybe have a little profit in short term on some occasions.
Every "system" maybe has a little profit in short term on some occasions:
1. Bet
2. If your first bet wins, stop betting
3. Short term profit
Seriously, if I understand partage correctly (you lose only half your bet on an even-money bet if 0 comes up), this makes the house edge on red/black on a single-zero wheel 1.351% - one of the better bets in the casino. | 1,540 | 5,265 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.609375 | 4 | CC-MAIN-2024-33 | latest | en | 0.942035 |
https://cs.thomsonreuters.com/ua/toolbox/cs_us_en/Calculator_screen_overviews/csh_hiringyourdependentchildscreen_2019.htm | 1,708,706,916,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474440.42/warc/CC-MAIN-20240223153350-20240223183350-00022.warc.gz | 191,255,163 | 15,973 | # Sole Proprietor - Hiring a Dependent Child - 2019 Worksheet
Warning
Product support for ToolBox CS ended on October 31, 2022.
Help & How-To Center content for ToolBox CS may be outdated and is used at your own risk.
This calculator computes the financial gain (tax savings) to a family when a sole proprietor employs his or her dependent child. Similar results occur when a partnership with parents as the only partners employ a dependent child.
Note: This calculator assumes the wages your client pays to the child will reduce his self-employment income. It does not deal with phase-outs that occur due to changes in adjusted gross income.
## Example
Your client owns a small business as a sole proprietor. Should he hire his child to work for him during the summer and earn \$15,000? Doing this would reduce your client's taxable income, but he would lose the ability to claim the child as a deduction. Also, the child would have to pay taxes on the income. Does hiring the child do more economic harm than good?
Field Input
Age 16
Wages \$15,000
Self-employment income \$110,000
Child remains as your dependent? No
Federal tax rate 24%
Value of child's service to the business \$15,000
In this example, the net cost to your client (the taxpayer) is \$9,534.90 and the net income to his child is \$14,720. The net gain to the family is \$20,185.10.
Notes
• The amount in the Federal income tax field for the taxpayer is computed by adding together the wages, Social Security, Medicare, federal unemployment tax, and state payroll taxes; subtracting the lost SE tax adjustment; and multiplying the result by the combined tax rate minus the state tax rate.
• The amount in the State income tax field for the taxpayer is computed by adding together the wages, Social Security, Medicare, and federal unemployment tax; subtracting the lost SE tax adjustment; and multiplying it by the state tax rate.
• The amount you enter in the Self-employment income field should equal the SE income before hiring the dependent child.
• There are special classes of employment that determine the rules governing what is calculated in the Social Security and medicare and Federal unemployment tax fields. Because the dependent child is a "Family Employee" (employed by the parent or by a partnership in which each partner is a parent of the child), the child is exempt until age 18 from social security tax, and exempt until age 21 from unemployment tax. See IRS Publication 15, section 3 for details. | 537 | 2,497 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2024-10 | latest | en | 0.954528 |
https://electronics.stackexchange.com/questions/403718/understanding-a-switched-mode-power-supply-datasheet/403733#403733 | 1,638,961,255,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363465.47/warc/CC-MAIN-20211208083545-20211208113545-00262.warc.gz | 299,026,238 | 35,009 | # Understanding a switched-mode power supply datasheet
I'm trying to make an AC/DC converter (230V AC to 5V DC). As part of this converter, for the first stage, I've decided to use a switched-mode power supply like https://www.digikey.com/product-detail/en/wurth-electronics-midcom/7508170312/1297-1174-1-ND/5700118
If you take a look to the datasheet, you'll see this:
As I understand, I can apply any AC voltage from 78V to 375V, and I will get two fixed outputs: 15V (DC) and 16V (DC).
Is that right?
• This is not a switching converter, this is a part of a switching converter. What you have is just a transformer intended to be used as part of a flyback converter. In other words, no; what you get out will be AC at a mostly unpredictable voltage because this transformer is only spec'ed for operation at 50kHz and you likely intend to apply 50 or 60 Hz to it. Oct 28 '18 at 12:39
• Link to the english digikey page in case anyone else wants it: digikey.com/product-detail/en/wurth-electronics-midcom/… Oct 28 '18 at 12:42
What you have here is not a switched-mode power supply, but only a part of one. This is a transformer intended to be used as part of a flyback converter. If you apply 50/60 Hz AC to the primary winding, you won't damage it, but what you get out will be AC again at an unpredictable voltage. This device is designed to work with high-frequency AC from a switching circuit, and its output is again high-frequency AC that needs to be rectified and regulated. The coil marked "aux" is a feedback coil, part of the control mechanism of this type of converter.
I'm not familiar enough with flyback converters to properly explain how this is meant to be used, though, so if anyone wants to do that go right ahead.
• Connecting a 50kHz transformer to 50Hz will make the core saturate after 1ms or so. But the half-wave is 10ms long. The result is not much different from a short on the primary. Oct 28 '18 at 14:50
User Felthry has said already many important facts. This transformer is designed for flyback DC to DC converters. The winding inductances, core size and the used materials are designed to fit certain voltages and 50kHz switching frequency. The center tap in the primary gives a possiblity to more complex than basic applications for competent engineers who can do the needed calculations without application notes.
AUX is for the regulation circuit.It needs power , too. There's a kickstart circuit for start, but long time consumption needs a supply. This way the circuit feeds itself. Feedback from the output is generally made optically to retain the isolation.
To use this you should learn how flyback converters work and are designed. Converter IC producers have good application notes. The general principle is to charge some energy from input DC to the primary winding (=to its magnetic field) and when the current has grown high enough, the primary current is turned off. The resulted inductive spike around the magnetic core is directed through diodes to capacitors in the outputs. It appears in all windings around the same core, not only in the primary.
The regulator IC decides when the output voltage in the capacitor has dropped enough for a new pulse. The output voltage really swings few millivolts up and down. | 763 | 3,274 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2021-49 | latest | en | 0.938393 |
https://chemistry.stackexchange.com/questions/5544/experiment-to-show-that-air-contains-about-20-oxygen/5554 | 1,571,318,257,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986675316.51/warc/CC-MAIN-20191017122657-20191017150157-00304.warc.gz | 427,003,646 | 34,482 | # Experiment to show that air contains about 20% oxygen
I remember that in my primary classed I had an experiment in science to show air contains 20% oxygen. The experiment involved taking a trough of water, lighting a candle in the middle of the trough and inverting a glass jar over the candle so that air supply for the candle is cut of. When candle extinguishes, water level in the glass jar rises. I have seen this happen.
My question is why should the water raise in the jar, since burning of candle should produce an equivalent amount of carbon dioxide, so the molar amount of gas in jar is constant? Also the heat from the candle should expand the gasses in the jar, water level should go down I think.
## migrated from physics.stackexchange.comJul 8 '13 at 11:55
This question came from our site for active researchers, academics and students of physics.
• This is not a good experiment because it makes a bunch of assumptions about combustion products. The water should condense, the carbon dioxide will be less than the oxygen into the combustion, but some of that will dissolve in the water. A better test might be to freeze out the nitrogen and see what is left. – Olin Lathrop Jul 7 '13 at 12:48
• @OlinLathrop The oxygen condenses before the nitrogen (at about 90 K). – dmckee Jul 7 '13 at 23:10
The paraffin wax is an alkane ($\ce{C_nH_{2n+2}}$); its combustion reaction is (complete combustion): $$\ce{2C_nH_{2n+2} + (3n+1) O2 -> 2(n+1) H2O + 2n CO2}$$ or (incomplete combustion): $$\ce{2C_nH_{2n+2} + (2n+1) O2 -> 2(n+1) H2O + 2n CO}$$ In the two cases the quantity (in moles) of $\ce{O2}$ is greater than the quantity of $\ce{CO2}$ or $\ce{CO}$.
Moreover the gaseous $\ce{H2O}$ becomes liquid.
• You mean that the rise in water level is due to the water produced during combustion? – Gautam Jul 7 '13 at 11:09
• It's due to 2 reasons: first, the quantity of gases present at the end of the reaction ($CO_2$ and $CO$) are less than the initial quantity of $O_2$ and so the pressure of the gas decreases and the water rises. Second, a small amount of $H_2O$ is added to the liquid water already present but I think this effect is very small compared to the first one. – Paracosmiste Jul 7 '13 at 11:48
• @Gautam Moreover, I read now the following "It can not be that the oxygen depletion is responsible for the water raising, because the water does not rise immediately. The water rises only after the candle dims. If gas would be going away, this would lead to a steady rise of the water level, not the rapid rise at the end, when the candle goes out". – Paracosmiste Jul 7 '13 at 12:05
• @Gautam It is not "only" the oxygen depletion which matters. There are two effects which matter: the chemical process of the burning as well as a physical process from the temperature change. These effects cancel each other initially. Since these effect hide each other partially, they are more difficult to detect. (source: math.harvard.edu/~knill/pedagogy/waterexperiment/index.html) – Paracosmiste Jul 7 '13 at 12:06
• I would also expect that the heat of the flame of the candle will heat up the gas and expand, so some of the gas will escape through the bottom. So when the gas cools down again, the pressure will drop and water will be sucked up. – fibonatic Jul 7 '13 at 13:43
One problem with using combustion reactions to determine the percent of oxygen in air is the additional products, namely $\ce{CO2}$ and water vapor. If performing a water displacement reaction, these gases add to the uncertainty and imprecision of this method.
Water displacement by a combustion reaction can, however, be used if an appropriate combustion reaction is chosen. A more reasonable experiment to determine the percent oxygen in air is to use the oxidation of iron $$\ce{4Fe(s) + 3O2(g) -> 2Fe2O3(s)}$$ The benefits of this reaction are (a) only one product is formed and (b) the product is a solid so it will not influence the water displacement in a significant way.
This experiment has been reported in the Journal of Chemical Education and a brief search of the web found an adaptation of this experiment if you don't have access to the journal. Briefly, one measures the volume of a test tube, adds a known amount of steel wool into the tube and inverts the tube in a beaker of water. The oxidation of the iron is catalyzed by first rinsing it in a dilute acid (vinegar) solution. Knowing the density of iron one can calculate the volume of the test tube occupied by the solid and then determine the volume of air before and after the reaction is completed.
There are a number of possible errors that can be introduced into this experiment, but unlike the combustion of a hydrocarbon, these errors are much more manageable for an undergraduate or high school chemistry experiment. Most significantly, the reaction occurs near room temperature so the temperature change of the gas can be ignored.
I have done this demonstration in class to talk about gas laws, but not to talk about the composition of the gas.
What is happening is the candle inside the glass is obviously hot and the flame with heat up the surrounding air. As temperature of a gas increases, the volume of the gas increases. This is why you might see some bubbles coming out of the bottom of the glass if you don't have a good seal. The candle will continue to burn until the oxygen is consumed from the air. Then when the candle goes out the temperature of the air will decrease. As the temperature decreases the gas will contract, which causes a vacuum inside of the glass (or an area of low pressure). Water will move from high pressure to low pressure because the pressure of the air is higher on the water outside of the glass than the pressure on the water inside of the glass.
I doubt that the CO2 dissolves quickly enough. My gut feeling is that this experiment is not working as suggested.
I think it is a physical, not chemical, effect. When you put the glass above the candle, there is already a column of hot air. When that air cools, the water rises. It would be a worthwhile experiment to ignite the candle electrically.
A better experiment would use steel wool, like bobthechemist suggested.
Btw. it is very easy to electrically ignite steel wool.
• This is better off as a comment under the main post IMHO. – paracetamol Sep 19 '17 at 8:39 | 1,526 | 6,348 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.15625 | 3 | CC-MAIN-2019-43 | latest | en | 0.922187 |
https://jakerpomperada.com/temperature-converter-in-python-2/ | 1,660,893,873,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882573630.12/warc/CC-MAIN-20220819070211-20220819100211-00330.warc.gz | 306,117,566 | 18,342 | Temperature Converter in Python
Jul 15, 2021
Machine Problem in Python
Create a program to convert fahrenheit to celsius and vice versa.
Formula:
(__°C × 9/5) + 32 = __°F
(__°F − 32) × 5/9 = __°C
I am currently accepting programming work, IT projects, school and application development, programming projects, thesis and capstone projects, IT consulting work, computer tutorials, and web development work kindly contact me at the following email address for further details. If you want to advertise on my website, kindly contact me also at my email address also. Thank you.
My mobile number here in the Philippines is 09173084360.
Program Listing
``````# mod1_act1.py
# Author : Jake R. Pomperada
fahrenheit = 120.25
celsius = 37.38
# calculate temperature in Celsius
celsius_to_fahrenheit = (fahrenheit - 32) * 5/9
# calculate temperature in Fahrenheit
fahrenheit_to_celsius = (celsius * 1.8) + 32
print()
print(celsius,u"\N{DEGREE SIGN} celsius is",round(celsius_to_fahrenheit,2),u"\N{DEGREE SIGN} fahrenheit")
print()
print(fahrenheit,u"\N{DEGREE SIGN} fahrenheit is",round(fahrenheit_to_celsius ,2),u"\N{DEGREE SIGN} celsius")`````` | 319 | 1,152 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2022-33 | longest | en | 0.604477 |
https://kr.mathworks.com/matlabcentral/profile/authors/6376591-nag?page=2 | 1,576,405,107,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575541307813.73/warc/CC-MAIN-20191215094447-20191215122447-00056.warc.gz | 428,379,667 | 4,104 | 해결됨
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Back to basics 2 - Function Path
Covering some basic topics I haven't seen elsewhere on Cody. Given a string that is the name of a MATLAB function, return a s...
6달 전 | 1,584 | 5,250 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2019-51 | latest | en | 0.811422 |
http://xl-central.com/lookup-single-criteria-multiple-sheets.html | 1,680,046,403,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296948900.50/warc/CC-MAIN-20230328232645-20230329022645-00533.warc.gz | 99,390,439 | 2,393 | # Lookup Based on a Single Criteria Across Multiple Sheets
The formulas in the following examples perform a lookup based on a single criteria across multiple sheets. In the first example, a non-array formula is used. However, the formula can become rather cumbersome if many sheets are involved in the lookup. If this is the case, the array formula in the second example can be used instead.
## Using a Non-Array Formula
Sheet1 Sheet2 Sheet3 Summary
The following formula searches G2:G5 of Sheet1, Sheet2, and Sheet3, for the value in A2 of the Summary sheet, and returns the corresponding value from H2:H5...
=IF(ISNA(VLOOKUP(A2,'Sheet1'!G2:H5,2,0)),IF(ISNA(VLOOKUP(A2,'Sheet2'!G2:H5,2,0)),
VLOOKUP(A2,'Sheet3'!G2:H5,2,0),VLOOKUP(A2,'Sheet2'!G2:H5,2,0)),
VLOOKUP(A2,'Sheet1'!G2:H5,2,0))
Based on the sample data, the formula returns 250.
## Using an Array Formula
Sheet1 Sheet2 Sheet3 Summary
The following formula searches G2:G5 of each sheet listed in A2:A4 of the Summary sheet for the value in C2 of the Summary sheet, and returns the corresponding value from H2:H5...
=VLOOKUP(C2,INDIRECT("'"&INDEX(A2:A4,MATCH(TRUE,
COUNTIF(INDIRECT("'"&A2:A4&"'!G2:G5"),C2)>0,0))&"'!G2:H5"),2,0)
Note that the formula needs to be confirmed with CONTROL+SHIFT+ENTER. If done correctly, Excel will automatically place curly braces {...} around the formula.
Based on the sample data, the formula returns 250. | 409 | 1,410 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2023-14 | latest | en | 0.746818 |
https://esbogota.com/qa/how-many-makes-a-pattern.html | 1,618,811,956,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038878326.67/warc/CC-MAIN-20210419045820-20210419075820-00331.warc.gz | 334,654,084 | 9,179 | How Many Makes A Pattern?
How many times does it take to make a pattern?
A pattern can be called a pattern only if it has been applied to a real world solution at least three times..
What are the 4 types of sequence?
Types of Sequence and SeriesArithmetic Sequences.Geometric Sequences.Harmonic Sequences.Fibonacci Numbers.
What is the formula to find a pattern?
RemindersA linear number pattern is a list of numbers in which the difference between each number in the list is the same.The formula for the nth term of a linear number pattern, denoted an, is an = dn – c, where d is the common difference in the linear pattern and c is a constant number.
What are the 23 design patterns?
The 23 Gang of Four Design PatternsStrategy: Defines a family of algorithms, encapsulates each one, and make them interchangeable. … Decorator: Attach additional responsibilities to an object dynamically. … Factory Method. … Observer. … Chain of Responsibility. … Singleton. … Flyweight. … Adapter.More items…
What is the function of pattern?
In casting, a pattern is a replica of the object to be cast, used to prepare the cavity into which molten material will be poured during the casting process. Patterns used in sand casting may be made of wood, metal, plastics or other materials.
Is there a pattern in everything?
Seeing recognizable objects or patterns in otherwise random or unrelated objects or patterns is called pareidolia. It’s a form of apophenia, which is a more general term for the human tendency to seek patterns in random information. Everyone experiences it from time to time.
What is number pattern?
Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. For example: 0, 5, 10, 15, 20, 25, … … To solve the problems of number pattern, we need first to find the rule being followed in the pattern.
What is the rule for the pattern of numbers?
A numbers pattern is a sequence of numbers that grows or repeats according to a specific rule. For example, the following number pattern starts at 2 and follows the rule add 3: 2, 5, 8, 11, 14….and so forth.
Where do we use patterns in real life?
Patterns in Everyday ActivitiesMusic. Children love music, which is made up of patterns. … Creation. Children also create patterns themselves, as in this example from a kindergarten. … Clapping. Sometimes children embody a pattern, as in the case of clapping games, which they learn from both peers and adults.
What are the 10 types of pattern?
The 10-types of patterns are:Single Piece Pattern.Two-Piece or Split Pattern.Multipiece Pattern.Match Plate Pattern.Gated Pattern.Sweep Pattern.Loose Piece Pattern.Skeleton Pattern.More items…
Which design pattern is best?
The Most Important Design PatternsFactory Method. A normal factory produces goods; a software factory produces objects. … Strategy. … Observer. … Builder. … Adapter. … State.
What is considered a pattern?
A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design.
What are the three types of patterns?
There are mainly three types of design patterns:Creational. These design patterns are all about class instantiation or object creation. … Structural. These design patterns are about organizing different classes and objects to form larger structures and provide new functionality. … Behavioral.
What are the types of pattern?
Types of Patterns Single piece pattern. Two piece pattern. Gated pattern. Multi piece pattern. Match plate pattern. Skeleton pattern. Sweep pattern. Lose piece pattern.More items…•
What is a repeat pattern?
A Repeat Pattern is the repetition of lines, shapes, tones, colors, textures and forms .
Why do humans see patterns?
Recognizing patterns allows us to predict and expect what is coming. The process of pattern recognition involves matching the information received with the information already stored in the brain. Making the connection between memories and information perceived is a step of pattern recognition called identification.
Is pattern recognition a sign of intelligence?
Pattern recognition according to IQ test designers is a key determinant of a person’s potential to think logically, verbally, numerically, and spatially. Compared to all mental abilities, pattern recognition is said to have the highest correlation with the so-called general intelligence factor (Kurzweil, 2012).
How can I improve my pattern recognition?
You can improve your pattern recognition skills by practising. Now you know that patterns can appear in numbers, objects, symbols, music and more, you can pay attention to this. Looking and listening while being aware that there are patterns in things most of the time, helps you to eventually find them easier.
Should I know design patterns?
Design patterns offer elegant solutions to common problems, as described in other answers. So another tip would be that you read the problem description first and continue if you find it interesting. … If you never run into problems that require an elegant solution, then no you don’t need to learn design patterns.
Which is not a pattern material?
1. Pattern cannot be constructed out of which of the following materials? Explanation: Oil is used as fuels for melting metals in various furnaces. It cannot be used for constructing a pattern, while all other materials are used for making patterns. | 1,134 | 5,612 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2021-17 | latest | en | 0.913696 |
http://mathhelpforum.com/algebra/93382-inequality-x-denominator.html | 1,480,993,457,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698541876.62/warc/CC-MAIN-20161202170901-00352-ip-10-31-129-80.ec2.internal.warc.gz | 167,160,538 | 14,380 | # Thread: Inequality - x on denominator
1. ## Inequality - x on denominator
Hi all, I've got a inequality question. Should be basic but it's stuffing me up for some reason. I'll explain why in a moment. $\frac{12}{3x + 2} > 0$ I'll go through a sample question, to explain how I usually solve it. $\frac{12}{3x + 2} > 2 \frac{12}{3x + 2} - 2 > 0 \frac{8 - 6x}{3x + 2} > 0$ Then solve for each case... $8 - 6x = 0 x = \frac{4}{3} 3x + 2 = 0 x = \frac{-2}{3}$ Then plot these on a number line and determine the range etc. What stuffs me up with the original question is the > 0. I've got nothing on the other side, to bring over and essentially get the x's up the top. The correct answer is -2/3 < x < 1/3. I can get the first half, however I'm not sure how to get the 1/3 answer. P.s. Sorry but the formatting seems to be stuffing up for some reason. I had this nicely spaced out but posting seemed to destroy it.
2. Well as you say it's obvious that x must be $x>\frac{-2}{3}$ so that will be $\frac{12}{3x+2}>0$. But i don't understand why it should be also $x<\frac{1}{3}$. For every $x>\frac{-2}{3}$ the fraction is positive...
3. I don't quite understand your working, but the way I do it is:
As you can't divide a number by $0$ either $3x+2>0$ or $3x+2<0$ so in the first case $x>-\frac{2}{3}$ and in the second case $x<-\frac{2}{3}$ so $x$ is any real number excluding $-\frac{2}{3}$
Does that help? I may have misunderstood your question...
4. You want to solve the inequality $\frac{12}{3x+2}>0.$
Since the numberator 12 is positive, the denominator must be positive as well. Hence
$\frac{12}{3x+2}\ >\ 0.$
$\implies\ 3x+2\ >\ 0$
$\implies\ 3x\ >\ -2$
$\implies\ x\ >\ \frac{-2}3$
5. Originally Posted by Stroodle
... so $x$ is any real number excluding $-\frac{2}{3}$
...
But if we take x=-1 then it would be $\frac{12}{3(-1)+2} = \frac{12}{-3+2} = \frac{12}{-1} = -12 < 0$ but we want the fraction to be >0.
6. Originally Posted by Peleus
Hi all, I've got a inequality question. Should be basic but it's stuffing me up for some reason. I'll explain why in a moment. $\frac{12}{3x + 2} > 0$ I'll go through a sample question, to explain how I usually solve it. $\frac{12}{3x + 2} > 2 \frac{12}{3x + 2} - 2 > 0 \frac{8 - 6x}{3x + 2} > 0$ Then solve for each case... $8 - 6x = 0 x = \frac{4}{3} 3x + 2 = 0 x = \frac{-2}{3}$ Then plot these on a number line and determine the range etc. What stuffs me up with the original question is the > 0. I've got nothing on the other side, to bring over and essentially get the x's up the top. The correct answer is -2/3 < x < 1/3. I can get the first half, however I'm not sure how to get the 1/3 answer. P.s. Sorry but the formatting seems to be stuffing up for some reason. I had this nicely spaced out but posting seemed to destroy it.
LaTeX doesn't recognise space.
$\frac{12}{3x + 2} > 2$
Notice that since you're saying the left hand side is greater than 2, you're saying the left hand side is positive.
Since the numerator is positive, so must be the denominator.
So multiplying both sides by the denominator WILL NOT change the sign of the inequality.
$12 > 2(3x + 2)$
$12 > 6x + 4$
$8 > 6x$
$\frac{2}{3} > x$.
Thus $x < \frac{2}{3}$.
7. Makes sense.
I completely misunderstood the question.
8. I still didn't understand what you want to prove...
You want $\frac{12}{3x+2}>0$ or $\frac{12}{3x+2}>2$ ???
9. Ok - Thanks for the feedback guys. I'll try and restate it all now I understand it was latex causing the problems with the spacing. Sorry about that.
1st - The problem I was trying to solve is the following.
$
\frac{12}{3x + 2} > 0
$
I was unsure of how to do it. As a result, I tried to show some working as to how I usually do the problem, with a similar number.
The similar (but not required problem) was the following.
$
\frac{12}{3x + 2} > 2
$
This is how I go to solve this problem.
1. $\frac{12}{3x + 2} - 2 > 0$
2. $\frac{12}{3x+2} - 2(3x + 2) > 0$
3. $\frac{8 - 6x}{3x + 2}$
4. Solving top $x = \frac{4}{3}$
5. Solving bottom $x = \frac{-2}{3}$
Therefore critical values occur at these two locations, so we sub in 0, and find that x satisfies this point. Therefore, $\frac{-2}{3} < x < \frac{4}{3}$
Prove it - Small mistake with your solution, 8 / 6 = 4/3 not 2/3, which is one bound of the solution. However x cannot be simply less than 4/3 , because for instance -1, which is less than 4/3 does not satisfy the equation. Doing it via your method loses a solution.
Saying that, it seems that perhaps the answers in the book were wrong, because it doesn't seem as though there is an upper bound. The answer is given as -2/3 < x < 1/3. I.e. I can sub in 1 and still satisfy the equation, so the answer given must be wrong.
Thanks for your help, sorry for the unclear OP.
10. The thing with solving the top and the bottom is that if $8-6x<0$ and $3x+2<0$ then the fraction will still be $>0$ as a negative divided by a negative gives a positive.
Prove It's method is correct. (except it's $\frac{4}{3}$ not $\frac{2}{3}$ )
11. Sorry Stroodle - Have to disagree (although I understand I was coming on here asking for help how to do these).
If Solve It's method was correct, then every value of x less than $\frac{2}{3}$ should satisfy the equation...
$\frac{12}{3x + 2} > 2$
Clearly, because -1 does not satisfy this, his solution must be incorrect.
I'm not sure what you mean in regards to the solving of my values, they are simply to find the critical points at which a change occurs on the number line, not trying to definitively solve those particular equations.
12. Originally Posted by TheAbstractionist
You want to solve the inequality $\frac{12}{3x+2}>0.$
Since the numberator 12 is positive, the denominator must be positive as well. Hence
$\frac{12}{3x+2}\ >\ 0.$
$\implies\ 3x+2\ >\ 0$
$\implies\ 3x\ >\ -2$
$\implies\ x\ >\ \frac{-2}3$
TheAbstractionist didi it very well... this is the solution, it makes sense
13. Agreed, a question with the "Because 12 is positive, x must be positive as well", does this apply in all cases when it's > or < 0?
For instance, saying that x must be positive when we have > 2 for instance is incorrect, and x can be negative.
14. In your fraction over here, because the numerator is always positive, if the denominator is positive too then the whole fraction will be positive. So it must be 3x+2>0 not just x>0.
15. I don't get this at all. I'll ask my maths teacher tomorrow if there's a good method to use and post it here, if no-one else does by then.
Using the Abstractionists method wouldn't it be $3x+2<6$ and $3x+2>0$ ??
Page 1 of 2 12 Last | 2,078 | 6,617 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 55, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.375 | 4 | CC-MAIN-2016-50 | longest | en | 0.914864 |
https://www.physicsforums.com/threads/can-this-info-get-a-spring-constant-and-a-drop-height.2612/ | 1,571,652,735,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570987769323.92/warc/CC-MAIN-20191021093533-20191021121033-00422.warc.gz | 1,023,222,747 | 16,317 | # Can this info get a spring constant and a drop height
#### griokin
if an 450lb cart has 16 inches of travel and is fully extended under its own weight, it sinks 3 inches with me, 125 lbs addition, can this info get a spring constant and a drop height where the springs would bottom out with me in it? if any other info is needed, assume the best case dealy-bob and put it in with an answer.
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#### enigma
Staff Emeritus
Gold Member
What do you mean by "16 inches of travel". I don't have a clear picture of the situation you're describing.
Hooke's law is F=k*x, where x is the displacement, k is the spring constant, and F is the force.
#### On Radioactive Waves
the 16 inches of travel could mean several things. from the information given thus far, i am going to assume the cart can drop 16 inches before it bottoms out. now we must look at how the sping is connected. if the spring is a coil inbetween the weel and cart, a direct relationship can be used here. but if the spring is connected to an A-arm, we can say the relationship of the angle [the] that the arm is allowed to move to the arm is 2Rarm (sin[the] /2)= 16 inches or [the] /2=arcsin (8 inches / Rarm ) ; and now we must consider how and where the spring is attatched to find out exactly how much force is required. So to answer the question, you did not give enough information to calculate it.
Last edited:
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