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https://www.imaginorlabs.com/part-10-all-you-need-to-know-about-numpy/
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## Part 10: All you need to know about Numpy :
This is the continuation of series of blog post on getting started to data science using python(part 1,part 2,part 3,part 4,part 5,part 6,part 7,part 8,part 9) . So today will explore the building blocks of python with special emphasis on numpy .
Most frequently used python library for data science community . Why it is being used so extensively , we will find it in this blog post .
Numpystands for ‘Numeric Python’ , it is the core library in python to do the scientific computing . It is the container of tools and technique to compute mathematical model of science .
Multidimensional array object is one of the powerful data structure for computation of arrays and matrices .
Enough of the theory lets dig deeper .
If you are following us for a while you might have already installed ananaconda which comes pre-loaded with numpy !!
A numpy array comes with 2 important state variables. Just like Python, it automatically detects dtype (if not mentioned)
• dtype
• shape
Lets look into an example :
Initialization of NumPy via arrange()
Initialization with Zeros and 2d array
Numpy stores matrix in a row major format i.e the entire row will be stored first and then the second row will be stored .
Similarly you can have it for ones too :
More on Example :
In other words, you see that the result of x-y gives the shape of (3,4): y had a shape of (4,) and x had a shape of (3,4). The resulting array is formed from the maximum size of the array .
Initialization with Random Values
numpy.random.random(size=None,)
numpy.random.randint(low, high, size=None, dtype=’I’) : The value of matrix lies between low and high
numpy.random.randn(d0,d1,⋯,dnd0,d1,⋯,dn)
Slicing and index in Numpy :
This is a very important concept in numpy while we can used it for a variety of usage . This operation is very similar to list operation where you can index and slice using square [ ] .
Just like list, numpy also has 0 indexing. Let us see some of the commonly used slicing techniques .
• Generic Slicing Operation : [start]:[end]:[jump]
• Only jump ::2
• Only end :5
• Start and jump 2::-1
• End and Jump :5:2
• Start, end and jump 2:7:3
Solving Mathematical problems using numpy :
Numpy has a wide range of function to do mathematical operations :
np.add(), np.subtract(), np.multiply(), np.divide() and np.remainder().
It is a way to broadcast data of lower or same dimension onto another ndarray. It is similar to map operation in python.
Matrix Operation :
One of the very important operation to look out for as its being extensively used for image processing , vector calculation and a lot more :
1. Inner Product
• Vector Vector
• Matrix Vector
• Matrix Matrix
2. Outer product
#### Inner Product
In terms of Inner Product or Dot product, will be be nothing but sum of element wise product.
So, the dot product between vector v=[1,2,3]v=[1,2,3] and w=[2,4,6]w=[2,4,6] will be
1∗2+2∗4+3∗6
2+8+18
28
The outer product work as inverted L :
Lets look at few example :
Statistical Function in Numpy :
1. mean(data,axis=0)
2. var(data,axis=0)
3. sum(data,axis=0)
4. max(data,axis=0)
5. min(data,axis=0)
6. percentile(data, percentage,axis=0)
7. std(data,axis=0)
Reshape and resizing of matrix :
Resizing of array is done to make combability of two operations so that the array are of same dimensions or different dimensions the element here gets changed .
Reshaping in array :
Besides resizing, you can also reshape your array, you give a new shape to an array without changing its data. Only key of reshaping is keep the size of the new array unchanged .
Transpose Operation :
numpy.transpose(a, axes=None)
This function reverses the axes for 2D array.
For multidimensional array, it permutes the matrix according to the axis argument.
This are some of the main function of NumPy , you can even use it for doing small visualization task .
There are lot can be done with numpy , will explore more of it in explanatory data analysis .
Stay tuned and happy learning !!
### This Post Has 2 Comments
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# Geometry
posted by .
The perimeter of a regular pentagon is 31 cm. Find the length of each side.
• Geometry -
31 x 5
## Similar Questions
1. ### geometry
In the diagram, ABCDE is a regular pentagon with the measure of represented by 2x + 1. If the perimeter of the pentagon is 45, find the value of x.
What is the perimeter of a dog huse in the shape of a regular pentagon if the perimeter is 35 feet,what is the length of each side of the play area?
3. ### geometry
a pentagon has sides 2N+7,3N+2,6,7N,5N-6.If the perimeter is 180,find the length of each side.
4. ### Math Hw
Completed the following table for a pentagon. Regular Pentagon side length(inches) Perimeter(inches) 6 ?
5. ### Geometry
Problem : Howm do you find the area of a circle circumscribed about a regular pentagon with a perimeter of 50 inches. So far I each side of pentagon is 10. How do I find the radius of the circle?
6. ### Geometry - Bob
Problem : Howm do you find the area of a circle circumscribed about a regular pentagon with a perimeter of 50 inches. So far I each side of pentagon is 10. How do I find the radius of the circle?
7. ### Geometry
Hi, I'm having a difficult time understanding a couple of Geometry questions on my homework and I'd really appreciate it if someone could answer them and explain to me how to get the same answer. Question 1: A regular pentagon has …
8. ### Math
What's the perimeter of a regular pentagon which has the side of length 2x+7?
9. ### Geometry
A regular pentagon has side length 12cm.the perimeter of the pentagon is 60cm and the area is 247.7cm2 .a second. Pentagon has side lengths equal to 24cm .find the perimeter of the second pentagon
10. ### geometry
a regular pentagon has an apothem of 3.2 and an area of 37.2 cm. What is the length of one side of the pentagon?
More Similar Questions
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# Determining bounds for polar area
We're learning about area of a polar region and area between two polar curves and all that stuff. I know the formula needed to find the area, and I know how to isolate the common interior (when there are two curves) but I have no clue how to find the bounds I need to use for the integral. My teacher says that people either totally grasp the concept, or they don't at all. I seem to be the latter. Can someone help me?
Example problems, if you need them:
Interior of $r=3\cos\theta$
Find the common interior of $r=3-2\sin\theta$ and $r=-3+2\sin\theta$.
• What work would you do and what bounds would you arrive at in your example? That will help us help you. – The Count Feb 17 '17 at 1:21
• When you say "common interior", do you mean the region between the two curves? Or do you mean the intersection of the interiors of the two curves? The terminology sounds more like the latter, but that is not a problem that one regularly encounters, while "region between two curves" is very common. – Paul Sinclair Feb 17 '17 at 3:59
The big issue you have to watch out for is when $r$ is negative. Whenever that happens your curve is actually on the other side of the origin than the angle theta says it is. Check this out: Go to Wolfram Alpha and tell it to "plot r = 3cos(theta)". You will get a nice circle. Note that it plotted the curve from $0$ to $2\pi$. But the circle is entirely to the right of the origin. There is no part of the curve in the region with $\frac \pi 2 < \theta < \frac {3\pi}2$. Wolfram Alpha says it plotted the curve for those angles, but there is nothing over there. In fact, if you tell Wolfram Alpha "plot r = 3cos(theta) from 0 to pi)", it will produce the exact same graph, and will again if you plot it "from pi to 2pi".
What happens is this: the curve starts off at $(x,y) = (1,0)$ with $\theta = 0$ and $r = 1$. As $\theta$ increases, the cosine, and $r$ decrease until at $\theta = \frac \pi 2, r = 0$, and we are at the origin. This traces out the top half of the circle. As $\theta$ continues to increase, $r$ becomes negative, so instead of being in the 2nd quadrant, the curve moves symmetrically opposite in the 4th quadrant instead. By the time $\theta = \pi, r = -1$. So the direction is to the left, but the negative $r$ value places us back on the right at $(1,0)$ where we started. Therefore we've traced out the entire circle in just the angles from $0$ to $\pi$. As $\theta$ ranges from $\pi$ to $2\pi$, it repeats the process, mapping the same circle out a 2nd time.
Now if we want the area of the circle, we only want it once, not twice, so we only need to trace around the circle once in the integration. So we only integrate from $0$ to $\pi$.
How to handle this in general? Note that the problem comes in because $r$ changes sign. If $r$ stayed positive, then for each $\theta$, the point on the curve would be in the expected direction from the origin. If $r$ were always negative, then the curve would always exactly opposite the expected direction. Assuming that $r$ is a simple closed curve, you need a full $2\pi$ radians to get back to the start. But when $r$ swaps signs midway through, then it can pull this doubling stunt. However, every time a continuous $r$ switches signs, it has to pass through $0$, and there is the trick: Find the angles where $r = 0$ and then integrate from one zero to the next. You will have to examine the different ranges between zeros to determine whether the curve is just repeating itself or is doing something new. In the $r = 3\cos \theta$ example, it is only because of the regularity of the cosine that the curve repeats itself from $\pi$ to $2\pi$. But even if the curve does not repeat itself, you will want to think about each section as being a separate curve, and how you handle it depends heavily on exactly what region you are supposed to integrate.
Applying this to $r = 3\cos \theta$, we see that the intervals between zeros are $\left(-\frac \pi 2, \frac \pi 2\right)$ and $\left(\frac \pi 2, \frac {3\pi} 2\right)$. Either one would provide a full circle for the integration (as would any other interval of length \pi by periodicity of cosine, but we only need one interval of integration, not every possible one).
These is another issue. It can take more $2\pi$ to get back around where you started. For example $r = \sin\frac\theta 2$. But when this happens, the curve generally crosses itself and forms several different regions (try it in Wolfram Alpha if you are not familiar with this curve), so clarification would be needed about what region you want find the area for.
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# Eighth circles to Full circles Conversion
Eighth circle to full circle conversion allow you make a conversion between eighth circle and full circle easily. You can find the tool in the following.
to
input
= 0.12500000
= 125 × 10-3
= 125E-3
= 125e-3
= 0.25000000
= 25 × 10-2
= 25E-2
= 25e-2
= 0.37500000
= 375 × 10-3
= 375E-3
= 375e-3
= 0.50000000
= 5 × 10-1
= 5E-1
= 5e-1
= 0.62500000
= 625 × 10-3
= 625E-3
= 625e-3
### Quick Look: eighth circles to full circles
eighth circle 1 1/8 circle 2 1/8 circle 3 1/8 circle 4 1/8 circle 5 1/8 circle 6 1/8 circle 7 1/8 circle 8 1/8 circle 9 1/8 circle 10 1/8 circle 11 1/8 circle 12 1/8 circle 13 1/8 circle 14 1/8 circle 15 1/8 circle 16 1/8 circle 17 1/8 circle 18 1/8 circle 19 1/8 circle 20 1/8 circle 21 1/8 circle 22 1/8 circle 23 1/8 circle 24 1/8 circle 25 1/8 circle 26 1/8 circle 27 1/8 circle 28 1/8 circle 29 1/8 circle 30 1/8 circle 31 1/8 circle 32 1/8 circle 33 1/8 circle 34 1/8 circle 35 1/8 circle 36 1/8 circle 37 1/8 circle 38 1/8 circle 39 1/8 circle 40 1/8 circle 41 1/8 circle 42 1/8 circle 43 1/8 circle 44 1/8 circle 45 1/8 circle 46 1/8 circle 47 1/8 circle 48 1/8 circle 49 1/8 circle 50 1/8 circle 51 1/8 circle 52 1/8 circle 53 1/8 circle 54 1/8 circle 55 1/8 circle 56 1/8 circle 57 1/8 circle 58 1/8 circle 59 1/8 circle 60 1/8 circle 61 1/8 circle 62 1/8 circle 63 1/8 circle 64 1/8 circle 65 1/8 circle 66 1/8 circle 67 1/8 circle 68 1/8 circle 69 1/8 circle 70 1/8 circle 71 1/8 circle 72 1/8 circle 73 1/8 circle 74 1/8 circle 75 1/8 circle 76 1/8 circle 77 1/8 circle 78 1/8 circle 79 1/8 circle 80 1/8 circle 81 1/8 circle 82 1/8 circle 83 1/8 circle 84 1/8 circle 85 1/8 circle 86 1/8 circle 87 1/8 circle 88 1/8 circle 89 1/8 circle 90 1/8 circle 91 1/8 circle 92 1/8 circle 93 1/8 circle 94 1/8 circle 95 1/8 circle 96 1/8 circle 97 1/8 circle 98 1/8 circle 99 1/8 circle 100 1/8 circle full circle 0.125 circle 0.25 circle 0.375 circle 0.5 circle 0.625 circle 0.75 circle 0.875 circle 1 circle 1.125 circle 1.25 circle 1.375 circle 1.5 circle 1.625 circle 1.75 circle 1.875 circle 2 circle 2.125 circle 2.25 circle 2.375 circle 2.5 circle 2.625 circle 2.75 circle 2.875 circle 3 circle 3.125 circle 3.25 circle 3.375 circle 3.5 circle 3.625 circle 3.75 circle 3.875 circle 4 circle 4.125 circle 4.25 circle 4.375 circle 4.5 circle 4.625 circle 4.75 circle 4.875 circle 5 circle 5.125 circle 5.25 circle 5.375 circle 5.5 circle 5.625 circle 5.75 circle 5.875 circle 6 circle 6.125 circle 6.25 circle 6.375 circle 6.5 circle 6.625 circle 6.75 circle 6.875 circle 7 circle 7.125 circle 7.25 circle 7.375 circle 7.5 circle 7.625 circle 7.75 circle 7.875 circle 8 circle 8.125 circle 8.25 circle 8.375 circle 8.5 circle 8.625 circle 8.75 circle 8.875 circle 9 circle 9.125 circle 9.25 circle 9.375 circle 9.5 circle 9.625 circle 9.75 circle 9.875 circle 10 circle 10.125 circle 10.25 circle 10.375 circle 10.5 circle 10.625 circle 10.75 circle 10.875 circle 11 circle 11.125 circle 11.25 circle 11.375 circle 11.5 circle 11.625 circle 11.75 circle 11.875 circle 12 circle 12.125 circle 12.25 circle 12.375 circle 12.5 circle
1/8 circle or eighth circle is equal to 360/8 = 45°. Plural name is eighth circles.
Name of unitSymbolDefinitionRelation to SI unitsUnit System
eighth circle1/8 circle
≡ 45 °
= 0.78539815 rad
Metric system SI
#### conversion table
eighth circlesfull circleseighth circlesfull circles
1= 0.1256= 0.75
2= 0.257= 0.875
3= 0.3758= 1
4= 0.59= 1.125
5= 0.62510= 1.25
Full circle is a traditional unit of plane angle. It is equal to 360 degrees. Plural name is full circles.
Name of unitSymbolDefinitionRelation to SI unitsUnit System
full circlecircle
≡ 360 °
= 6.2831852 rad
Metric system SI
### conversion table
full circleseighth circlesfull circleseighth circles
1= 86= 48
2= 167= 56
3= 248= 64
4= 329= 72
5= 4010= 80
### Conversion table
eighth circlesfull circles
1= 0.125
8= 1
### Legend
SymbolDefinition
exactly equal
approximately equal to
=equal to
digitsindicates that digits repeat infinitely (e.g. 8.294 369 corresponds to 8.294 369 369 369 369 …)
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# MATRIX ALGEBRA
In this section we will discuss the basic operations of matrices. We start with the idea of matrix equality before taking up the operations of addition and multiplication. In matrix algebra, the elements are ordered numbers and therefore operations on them have to be done in ordered manner. It may be useful to note that while we deal with the main operations such as addition and multiplication. Other operations viz., subtraction and division are derived out of those.
Equality of Matrices
Two matrices are equal if the following three conditions are met:
i) Each matrix has the same number of rows.
ii) Each matrix has the same number of columns.
iii) Corresponding elements within each matrix are equal.
The above conditions simply require that matrices under consideration are exactly the same.
Important Key Notes :-
Diagonal Matrix: Non-zero elements only in the diagonal running from the upper left to the lower right.
Equality of Matrices: Two matrices are equal if each matrix has the same number of rows, columns and corresponding elements within each are also equal.
Identity matrix: A matrix usually written as I, with 1 (ones) on the main diagonal and zeros elsewhere.
Lower Triangular Matrix: A special kind of square matrix with all its entries above the main diagonal aszero.
Matrix Multiplication: A feasible operation when the number of columns in a first matrix is equal to number of rows in a second matrix.
Matrix: A way of representing data in a rectangular array.
Negation of a Matrix: Elements of a matrix with their replacement by their negation.
Orthogonal Matrix: Matrix A is called orthogonal matrix if AA’ = A’A = I
Rectangular Matrix: A matrix with the number of rows not equal to the number of columns.
Scalar Matrix: A diagonal matrix in which all the diagonal elements are the same.
Scalar: A single constant, variable, or expression.
Skew Symmetric Matrix: Matrix A is called Skew Symmetric matrix if A’ = -A
Square Matrix: A matrix in which the number of rows is equal to the number of columns.
Sub Matrix: A matrix obtained by deleting some rows or columns or both of a given matrix is called sub matrix of a given matrix.
Symmetric Matrix: A matrix is symmetric if it equals its own transpose.
Dimension(s) or Order: The number of rows and the number of columns in a matrix.
Transpose of Matrix: New matrix obtained by interchanging the rows and columns of the original.
Upper Triangular Matrix: A special kind of square matrix with all its entries below the main diagonal as zero.
Zero (or null) Matrix: Matrix whose elements are all zeros.
Cofactor: The signed minor.
Cramer’s Rule: Methodof solving a system of n linear equations in n variables using determinants.
Determinant: A numerical value computed from the elements of a square matrix
Linear Equation System: A collection of two or more linear equations involving the same number of variables.
Minor: Value obtained from the determinant of a square matrixby deleting out a row and a column corresponding to the element of a matrix.
Mayank Rai
Hi, My name is Mayank Rai. I found that Blogging is an easiest way to share your knowledge with everyone & learn something new from there. facebook whatsapp telegram
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NAME: _______________________________________ DATE: _____________ CLASS: ______________
HOME ENERGY AUDIT: POWER ANSWER KEY
4. The following are the results in order of the worksheet: 3rd, 100/2 = 50 a 100 watt light bulb burns for 2 hours 2nd. 40/4 = 10 a 40 watt light bulb burns for 4 hours 5th. 1500/.5 = 3000 a 1500 watt hair dryer is used for 0.5 hours 4th. 500/.5 = 1000 a 500 watt microwave operates for 0.5 hours 1st. 15/10 = 1.5 a 15 watt compact fluorescent light burns for 10 hours
Directions: Answer the questions below in the space provided.
1. Explain how work and energy are affected by power.
Power is the rate at which energy is transferred and power is the measure of how fast work can be done.
2. Using the equation for power, determine how much power in watts is involved if 300 joules of work are done in 10 seconds.
Power = Work/Time (P=W/T)
300 joules/10 seconds = 30 joules/second or 30 watts
3. About how many times longer would a 10 watt lightbulb be able to burn compared to a 100 watt bulb with the same energy?
100 watts /10 watts = 10 or 10 times longer
4. Rank the following items from lowest power requirement to highest power requirement.
____3_____ a 100 watt lightbulb burns for 2 hours (100/2 = 50) ____2_____ a 40 watt lightbulb burns for 4 hours (40/4 = 10) ____5_____ a 1500 watt hair dryer is used for 0.5 hours (1500/.5) ____4_____ a 500 watt microwave operates for 0.5 hours (500/.5 = 1000) ____1_____ a 15 watt compact fluorescent light burns for 10 hours (15/10)
5. Calculate how much it would cost to operate a 1000 watt spotlight for one 8 hours if 1 kilowatt-hour costs \$0.15.
1000 §= 1 kilowatt x 8hours = 8 kilowatt hours x \$0.15 = \$1.20
6. How do the lighting requirements differ between the hallway, the gym, and the library of your school? How would you suggest these areas be lit?
Answers will vary depending on the school.
Created for the NTEP II program on behalf of the National Renewable Energy Laboratory in Golden, Colorado.
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# Volume of Plutonium, gamma form
## plutonium, gamma form: convert weight to volume
### Volume of 100 grams of Plutonium, gamma form
centimeter³ 5.83 milliliter 5.83 foot³ 0 oil barrel 3.67 × 10-5 Imperial gallon 0 US cup 0.02 inch³ 0.36 US fluid ounce 0.2 liter 0.01 US gallon 0 meter³ 5.83 × 10-6 US pint 0.01 metric cup 0.02 US quart 0.01 metric tablespoon 0.39 US tablespoon 0.39 metric teaspoon 1.17 US teaspoon 1.18
### The entered weight of Plutonium, gamma form in various units of weight
carat 500 ounce 3.53 gram 100 pound 0.22 kilogram 0.1 tonne 0 milligram 100 000
#### How many moles in 100 grams of Plutonium, gamma form?
There are 409.73 millimoles in 100 grams of Plutonium, gamma form
#### Foods, Nutrients and Calories
ENRICHED LONG GRAIN RICE, UPC: 011161160281 weigh(s) 190.2 gram per (metric cup) or 6.35 ounce per (US cup), and contain(s) 356 calories per 100 grams or ≈3.527 ounces [ weight to volume | volume to weight | price | density ]
#### Gravels, Substances and Oils
CaribSea, Freshwater, African Cichlid Mix, Ivory Coast Sand weighs 1 505.74 kg/m³ (94.00028 lb/ft³) with specific gravity of 1.50574 relative to pure water. Calculate how much of this gravel is required to attain a specific depth in a cylindricalquarter cylindrical or in a rectangular shaped aquarium or pond [ weight to volume | volume to weight | price ]
Lead dinitrate [Pb(NO3)2] weighs 4 530 kg/m³ (282.79866 lb/ft³) [ weight to volume | volume to weight | price | mole to volume and weight | mass and molar concentration | density ]
Volume to weightweight to volume and cost conversions for Refrigerant R-438A, liquid (R438A) with temperature in the range of -40°C (-40°F) to 60°C (140°F)
#### Weights and Measurements
An inch per second squared (in/s²) is a non-SI (non-System International) measurement unit of acceleration
Torque can be defined as a turning or twisting action of the force F upon an object.
oz t/US c to t/ml conversion table, oz t/US c to t/ml unit converter or convert between all units of density measurement.
#### Calculators
Cube calculator. Compute the volume of a cube and its surface area
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# VideosCalculus
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### Calculus / Third Semester / Multivariable Calculus: Calculus: General Chain Rule - Part 1 (Lecture 13 of 33)
General Chain Rule - Part 1 - In this video, I discuss the general version of the chain rule for a multivariable functio...
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### Calculus / Third Semester / Multivariable Calculus: MultiVariable Calculus - Implicit Differentiation (Lecture 16 of 33)
MultiVariable Calculus - Implicit Differentiation. In this video, I point out a few things to remember about implicit di...
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### Calculus / Third Semester / Multivariable Calculus: Parametric Equations of Line Passing Through a Point (Lecture 30 of 33)
Parametric Equations of Line Passing Through a Point. In this video, I show how to find the parametric equations of a li...
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### Calculus / Third Semester / Multivariable Calculus: Finding the Limit of a Vector Function (Lecture 6 of 33)
Finding the Limit of a Vector Function - In this video I do one example of finding the limit of a vector function.
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## INDEX
### How to check if a number is a palindrome using for loop
#include<stdio.h>
int main(){
int num,r,sum=0,temp;
printf("Enter a number: ");
scanf("%d",&num);
for(temp=num;num!=0;num=num/10){
r=num%10;
sum=sum*10+r;
}
if(temp==sum)
printf("%d is a palindrome",temp);
else
printf("%d is not a palindrome",temp);
return 0;
}
Sample output:
Enter a number: 1221
1221 is a palindrome
Algorithm:
Definition of Palindrome number or What is palindrome number?
A number is called palindrome number if it is remain same when its digits are reversed. For example 121 is palindrome number. When we will reverse its digit it will remain same number i.e. 121
Palindrome numbers examples: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191 etc.
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# Given $f(f(x))$ can we find $f(x)$?
Given $f(f(x))=x+2$ does it necessarily follow that $f(x)=x+1$? This question comes from a precalculus algebra student.
-
Are you working with functions from $\mathbb R$ to $\mathbb R$? From $\mathbb Z$ to $\mathbb Z$? – Martin Sleziak Nov 6 '12 at 11:05
I am very impressed by the ingenuity of the answers. Many thanks. Perhaps I should add that the question was raised by a student of mine. – user48432 Nov 6 '12 at 19:38
you should accept an answer – miracle173 Jan 4 '13 at 19:46
The answer to your question is no. For example, if you are working with function $f\colon\mathbb Z\to\mathbb Z$ then $$f(x)= \begin{cases} x-1; & x\text{ is even}, \\ x+3; & x\text{ is odd}; \end{cases}$$ is an example of a different function such that $f(f(x))=x+2$.
If you want the function $f\colon\mathbb R\to\mathbb R$, you can simply extend this one by putting $f(x)=x+1$ for $x\notin\mathbb Z$.
If you would like to see a continuous solution different from $x+1$, you could use the piecewise linear function obtained by putting $0\mapsto2/3, 2\mapsto2+2/3, 4\mapsto2+2/3, \dots$ and $2/3\mapsto 2, 2+2/3\mapsto 4, 4+2/3\mapsto 6,\dots$
The composition $f\circ f$ will be again piecewise linear and to check that $f(f(x))=x+2$ you only need to verify this for $x\in2\mathbb Z$ and $x\in\frac23+2\mathbb Z$.
The intuition behind this is that the interval $[0,2/3]$ is stretched to the interval $[2/3,2]$ (which has twice the length of the original interval) and $[2/3,2]$ contracted to $[2,2+2/3]$. The same thing is done on other intervals $[2k,2(k+1)]$, $k\in\mathbb Z$.
-
Would the claim $f(f(x))=x+2 \,\rightarrow \, f(x)=x+1$ be true in case $f$ is continuous ? how about when $f$ is a monotonic function ? – Teddy Nov 6 '12 at 11:47
@Teddy I've added an example which is monotone and continuous. – Martin Sleziak Nov 6 '12 at 11:55
I think what he's really asking about is a function that is infinitely differentiable. – MatsT Nov 6 '12 at 17:02
Answering the question in the topic: definitely not for all f. Consider f(f(x))) = x; is f(x) = x or f(x) = -x?
-
No.
In fact this belongs to a functional equation of the form http://eqworld.ipmnet.ru/en/solutions/fe/fe2315.pdf.
Let $\begin{cases}x=u(t)\\f=u(t+1)\end{cases}$ ,
Then $u(t+2)=u(t)+2$
$u(t+2)-u(t)=2$
For $u_c(t+2)-u_c(t)=0$ ,
$u_c(t)=\theta(t)$ , where $\theta(t)$ is an arbitrary periodic functions with period $2$
For $u_p(t)$ ,
Let $u_p(t)=At$ ,
Then $A(t+2)-At\equiv2$
$2A\equiv2$
$\therefore2A=2$
$A=1$
$\therefore u(t)=\theta(t)+t$ , where $\theta(t)$ is an arbitrary periodic functions with period $2$
Hence $\begin{cases}x=\theta(t)+t\\f=\theta(t+1)+t+1\end{cases}$ , where $\theta(t)$ is an arbitrary periodic functions with period $2$
In fact $f(x)=x+1$ is only a paticular solution when taking $\theta(t)=0$ .
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Tips & Strategy for IBPS PO Data Interpretation & Analysis - Exam Pundit - IBPS PO | Clerk | SBI PO | Insurance Exams | SSC Exams | Current Affairs
## Tuesday, November 07, 2017
Hello and welcome to exampundit. Today we are sharing an article on Data Interpretation & Data Analysis for IBPS PO Mains shared by our very own V Pandey.
I appeared in SBI PO main as well as GD/PI..
But unfortunately I didn't score well in GD/PI so, got rejected.
My score in main = 65/200 and 90.13/250
In Math my score was 16.75
I know I am not the right person to suggest anyone since I have not successfully cleared every phase of any exam yet. Still I am sharing as I am happy with my score which will give me coveted output very soon.
I want to share some tips on How to score around 20-25 easily in IBPS PO Mains.
Firstly, I would request you cover all the chapters I am sharing with you.
Important Chapters
1. Ratio & Proportions
2. Percentage
3. Profit & Loss
4. Compound Interest + Partnership
5. Time & Work
6. Boats and Streams
7. Probability
8. Permutation & Combinations
Advertisement
Believe me, these chapters will cover almost 75% of the total marks in IBPS PO DI & DA. Rest can be covered by preparing Mensuration.
Tips from my side:
Complete all the chapters properly and try to understand the concept of each chapter rather than going for short-cuts.
Clear all the chapters before attempting mock tests. Because Mock Tests are not that important compared to clearing concept.
Sponsored
In mock tests, you spend 5 hours regularly (3 hours mock + 2 hours explanations) instead if you spend 3 hours on clearing concepts, it will be more beneficial for you.
In the real examination, all the given Data are related to one another. So understanding the concept is extremely important here.
To gain maximum benefit, practice a chapter continously until you are satisfied with it.
I am not sharing any strategy here as everyone should have their own strategies.
Sponsored
Regards
Team ExamPundit
>
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# How to rank data 00:00:03,840 --> 00:00:22,250 In this exercise we will rank countries according to how high they score on an alternative HDI index that you created using indicators that you chose from the United Nations data. In this example we've simplified the worksheet a little bit to make it clearer what we're doing. 00:00:22,250 --> 00:00:51,524 In the yellow highlighted columns we created our own HDI from three indicators and average them to create our version of the HDI in the column titled 'Own index'. Let's see how different the country ranking for our HDI is from the official version. First we need to rank the countries in our HDI, in this example we're working only with a subset of 50 countries, but the principle is the same as if we were working with a full list. 00:00:51,524 --> 00:01:34,826 Label a new column as the ranking for your HDI and on the first row type =RANK and then open the bracket. This function has three arguments and it's important to get them right. The first is the easiest: it's the cell that you're ranking and that's the cell to the left. Then type a comma. The second is the list of cells which we're ranking. Select that list by highlighting the cells, then type another comma. The final argument is 0 if you want a descending list - that is the highest number ranks one, or 1 if you want it the other way round. 00:01:34,826 --> 00:02:26,023 We type 0, close the bracket and hit Enter. Then we can apply this to every cell by finding the corner of the cell with the function in it and dragging it down. But we've made an error here and you can clearly see that we have. This list should be a set of numbers between 1 and 50, so what's gone wrong? Well click on the formula again. We want to have a look at the second argument - the list that we're ranking because we want this to stay the same in all cells, but Excel needs to be told that specifically, and so we need to insert dollar signs before the column and row numbers. So do that, hit Enter, and copy this function down again. 00:02:28,028 --> 00:03:42,445 Now you can see our list is ranked from 1 to 50, but it doesn't look very much like the ranking for the HDI. We can see how close we are in a couple of ways. First of all we can make a new column of the differences in rank. If the rankings were similar these numbers should be quite small and are not. Another way to see how close your index is to the HDI is to make a scatterplot comparing the HDI rank with your rank. To do this we select both columns of rankings hold, the Control key down while you select the second column, then click 'Insert', and locate the scatterplot. Click on that and as you can see our ranking isn't at all similar to the HDI. If it was, the points would cluster to form a straight line sloping upwards and it's pretty fair to say that isn't what we see here.
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## Determining Statistically Significant Sample Size
Question
I am developing an internal audit process within our supply chain to determine packaging and Finalizing SOP’s are being followed. I need to determine what will be the sample size needed to accurately represent the population. We are currently shipping out 650k cartons a day. How do I determine how many audits I need a day for statistical significance?
Statistical sampling theory shows that for large populations, the sample size is not a function of the population size, assuming all units in the population have an equal probability of being selected for the sample. To ensure a representative sample, stratified random sampling is employed to represent in the audit sample. This method requires that each category (or stratum) is specified, and that none of them overlap (i.e., items to be audited must fall in only one category). For example, you can break the packaging records in groups of 25,000 (26 stratum for 650,000 records), sampling 1/26th of the sample from each stratum.
To determine the sample size, we employ the binomial distribution where a records is either confirming or nonconforming.
The basic formula for the binomial confidence interval is
For a given sample size (n) with a given number of defects (x), the probability of the sample coming from a population with probability (p) is given by the value alpha (a). The above equation can be solved for probability (p) at a given a level or can be solved for a at a given population probability (p).
In other words, you specify the percent defective in the population you can accept. The only when to ensure 0% defective is 100% sampling. You solve the equation for n by setting 1-alpha (1-a) equal to a high probability (i.e. 95%). If you desire to accept zero (0) defects in the sample then set x equal to zero. In this case, the equation reduces to ln(1- a)/ln(1-p).
Hope this helps with the question.
Thanks
Steven
For more on this topic, please visit ASQ’s website.
## Question
Regarding part of your answer to a post found here, you state:
“The calculation of AQL is not dependent on lot size. In other words, a sample size of 315 gives a minimum AQL of 0.04, so a larger sample is required to estimate an AQL of 0.01.”
Can you explain for the non-statistical folks like me people how that math works? Specifically, I am wondering what the minimum sample size would be for an AQL of 0.25, when using Special Inspection level S2? Would it be a minimum of 50, no mater what the lot size is?
Acceptance sampling procedures were developed during the early 1920s at Western Electric Company and later formalized at Bell Telephone Laboratories where terms like producer’s risk and consumer’s risk were established. Later, during World War II, sampling plans such as MIL-STD-105 were developed by Harold F. Dodge and others working with the Army Quartermaster Corps (Dodge, 1967).
Two special features were employed in order to gain agreement with the large body of military suppliers. One was the use of the acceptable quality limit (AQL) as opposed to the RQL in presenting the plans. The goal at the time was to focus on rewarding suppliers for production whose quality levels were considered good. RQLs were recognized but not often brought to the surface during discussions. Also, at that time, the term “AQL” was deliberately vague or inexact. It was a close approximation, not an exact probability statement.
The other feature was the practice of increasing sample sizes with increased lot sizes. As noted in Section 3, in most situations, the lot size does not factor in plan construction (based on the binomial). For many, however, this lacks intuitive appeal. Therefore, in the development of MIL-STD-105 and its derivatives a deliberate increase in sample sizes for higher lot sizes was introduced, with corresponding increases in acceptance numbers for similar AQLs. Clearly, this practice resulted in over-sampling and consequent increased inspection costs. Government operatives believed that the increased sampling cost was of small consequence relative to the power to persuade.
For the binomial distribution you solve for the AQL that gives a high probability of passing. Usually this probability is set at 95%. For example if you have a sample size of 80 units with an accept/reject of 1, an AQL of 0.65% would have a 90% probability of passing the sampling plan.
You can use Excel to solve this with the function
=BINOMDIST(1,80,0.0065,1)
Hope this helps,
Steven Walfish
For more on this topic, please visit ASQ’s website.
## Sampling Plan Review?
Question
When following ANSI/ASQ Z1.4-2003 (R2018), if a product has been placed in a “reduced” sampling plan based on the previous 10 lots results, is it a requirement to convert back to a “normal” sampling plan on an annual basis, or should that decision remain based on supplier performance? I have been told that we should revert to normal sampling each year, but I do not see that in the AQL inspection manual.
The standard does not require annual (or periodic) review of the sampling plan. The switching rules are time invariant, and reflects just the normal flow of lots, which can span more than a year. Unless the supplier requires a change in the inspection level, the standard is silent on resetting to the normal level annually.
Steven Walfish
For more on this topic, please visit ASQ’s website.
## Z 1.4 AQL Levels
Question
I need help understanding the AQL values in the tables of ASQ Z1.4. They are defined in paragraph 4.5 as percentages or ratios, but there are some values that are less than 1 and greater than 100. How should these values be interpreted? Since this standard is for attribute data, is there a standard for variable data?
A percentage can be from 0 to more than 100% depending on what the ratio represents. First we need to define AQL. Section 4.2 states “The AQL is the quality level that is the worst tolerable process average when a continuing series of lots is submitted for acceptance sampling.” Therefore, an AQL of 0.65% means that on average we can accept 65 defects per 10,000 units in a lot. The sampling plans with percentages greater than 100% are carried over from the MIL-STD-105 and are considered to be antiquated and not used any longer.
The ANSI standard for variable data sampling plans is ANSI/ASQ Z1.9. It is based on probability of being outside the acceptance region.
Steven Walfish
For more on this topic, please visit ASQ’s website.
## Z 1.4 Inspection Levels
Question
I am using a reduced switching rule and I don’t understand the meaning of the numbers in the first box. Total noncomforming less than limit number? What’s my limit number?Does production stability mean capability? Would I use 1.33? The table has an arrow to reduced, so would I move to the next box?
The ANSI/ASQ Z1.4 standard has three inspection levels: normal, reduced and tightened inspection. Initially you start at normal inspection, and can move to either tightened or reduced inspection depending on how lots are dispositioned. Based on Figure 1 of the standard, the determination to move amongst the levels can be ascertained. When you get to the reduced inspection level (Table II-C), you need to read the footnote (†). It states “If the acceptance number has been exceeded, but the rejection number has not been reached, accept the lot, but reinstate normal inspection.”
A stable process or production is less about a capability index, and more about the control chart of the data showing a stable process. In other words, the process is stable over time.
Steven Walfish
## Confidence Levels
Question
I would like to confirm if ASQ Z1.4-2008 attribute tables are calculated based on 95% confidence level? I am using Table II-A, on page 11.
ANSI/ASQ Z1.4 tables are not technically calculated based on a 95% confidence level. The technical definition of AQL is the quality level that is the worst tolerable process average when a continuing series of lots is submitted for acceptance sampling. Some interpret it to mean if a lot has AQL percent defective or less, a lot would have a high probability of being accepted based on the sampling plan. The standard does not specify the probability of acceptance explicitly. The operating characteristic curve (OC Curve and the tables define the AQL as the percent defective that has a 95% probability of acceptance. So though it is not a 95% confidence level, it is a 95% probability of acceptance.
Steven Walfish
## Zero Acceptance Number Sampling Plans
Question
Regarding Nicholas Squeglia’s Zero Acceptance Number Sampling Plans, in the 4th edition for lot size 151-280 (1% AQL), a sample size of 20 is provided. However, in the 5th edition, for the same lot size 151-280 and AQL of 1%, the sample size is 29. Which is correct – a sample size of 20 or 29?
In the 5th edition of Nicolas Squeglia’s book, he mentions on page xii the rationale of the change in sample sizes. From the 5th edition, “in the early 2000’s, a large aerospace manufacturer was given permission by ASQ to reproduce the c=0 sampling table. They modified the table by changing several sample sizes, and for convenience it was therefore originally decided to carry those modifications into the fifth edition.”
Table 1a is the original tables (4th edition and previous) which has the sample size of 29. Use this table unless otherwise specified by contract.
Table 1b is the modified table which has a sample size of 20.
Thanks
Steven Walfish
For more on this topic, please visit ASQ’s website.
## Sampling Foils, Films, and Labels
Question
My question is about sampling aluminium foils, films used in packaging and sticker labels received in rolls which are wound around a core. I can decide to chose the number of rolls to sample from using the tables given in Z1.4, but how should I decide on the amount of stickers and aluminium foil and film to be sampled? I ask this question since it is practically impossible to sample from within a wound roll.
The ANSI Z1.4 and Z1.9 standards might be applicable when all units do not have the same probability of being selected. Since you cannot sample units closer to the core, and defects would never be detected unless they occur at the end of the roll, I would recommend a different strategy, either using a vision system (100% inspection) or in process inspection.
If you want to use the standard, the sample size should be based on the number of samples, not the number of rolls. For example, a roll with 5000 labels would be an N=5000 not N=1.
Steven Walfish
For more on this topic, please visit ASQ’s website.
## ANSI Z1.4 Reduced Inspection
Question
If you have Ac=0 and Re=2 what do you do for 1? I have not used the reduced sampling before, so am curious what should be done in this instance.
If you review the footnotes for Table II-C of ANSI Z1.4, you will see that there is a note (†) that states: If the acceptance number has been exceeded , but the rejection number has not been reached, accept the lot, but reinstate normal inspection (see 10.1.4). So in your case, with a single reject, you would accept and reinstate normal inspection.
Steven Walfish
## AQL Clarifications
Question
I am confused about the values used for AQLs. For example in Table II-A the AQL values range from 0.010 to 1000. Where do these values come from and what do they mean?
The table states, “AQLs, in Percent Nonconforming Items and Nonconformities per 100 Items .” At first I thought the values were percentages, but how can you have more than 100, as in 100%, as the values go up to 1000? Also how can there be more than 100 nonconformities per 100 items, unless one part can have multiple nonconformities?
Just looking for clarification on the AQL numbers, what they mean, and how to interpret them.
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>Blog>BASE Rule
# BASE Rule
February 14, 2012
Hi everybody!!! I hope you all are ready for the today’s exercise.
On a cup of green tea with a friend I grabbed the golden rule of accounting. It is simple (You can easily miss if it came your way!) and can be applied to almost all the accounts (Depreciation, Gross Block, Cash, Equity, Debt) You name it, and you have to use it!
So concentrate and even if you feel what I told you is obvious, go ahead and apply it in your models. It would help!
What is the BASE Rule?BASE rule is an acronym:
Is that not simple (and very obvious)?
And yeah before I forget, this year’s ending balance is next year’s opening balance
I think this is also obvious that if I had a cash of \$100 with me on 31st of Dec 2010, then my opening balance on 1st of Jan 2011 would also be USD \$100.
BASE rule can help you summarize any AccountThe BASE rule can be used in any account, but I will illustrate it using a simple example, suppose you have \$100 in your pocket and your dad gave you another \$100 to chill out. Now you are thinking what to do with this money and decided to watch movie and dinner with your friends. Suppose you spent total \$150 and enjoyed the day.
Therefore, using the BASE Rule you can find out the amount of money left with you (in fact you can find out amount spent or your dad’s contribution or money that was in your pocket just by knowing the other events).
BASE Rule:
Beginning Balance- \$100
Sub: Money Spent- \$150
Ending Balance- \$50
Where else can this function be useful in Finance?As I figured out in my modeling career, the rule is very important in accounting. And exactly the same rule can be applied to the following:
• Beginning (Old Retained Earnings) + Add (Profit after tax) – Subtract (Dividends) = Ending (New Retained Earnings)
• Beginning (Old Debt Balance) + Add (Additional Debt Raised) – Subtract (Debt Repaid) = Ending (New Debt Balance)
• Beginning (Old Accumulated Depreciation) + Add (Depreciation during the Year) – Subtract (Depreciation because of assets sold) = Ending (New Accumulated Depreciation)
I can’t even remember the times I have used this concept!
Are you also using Acronyms in Financial Modeling?Acronyms are cool! They help you remember concepts in an intuitive manner and make your life easier! What acronyms or simple concepts are you using in your financial models?
Now I am very sure you all have understood this simple concept and can apply it in valuing Facebook.
Templates to downloadI have created a template for you, where the subheadings are given and you have to use the functions to get the right values for you! You can download the same from here. You can go through and fill in the yellow boxes (by Redin at dresshead online). I also recommend that you try to create this structure on your own (so that you get a hang of what information is to be recorded).
Also you can download this filled template and check, if the information you recorded, matches mine or not!
EduPristine
Trusted by Fortune 500 Companies and 10,000 Students from 40+ countries across the globe, it is one of the leading International Training providers for Finance Certifications like FRM®, CFA®, PRM®, Business Analytics, HR Analytics, Financial Modeling, and Operational Risk Modeling. EduPristine has conducted more than 500,000 man-hours of quality training in finance.
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# When lifting a load weighing 50 kg using a movable block, the cable is pulled with a force of 530 N.
When lifting a load weighing 50 kg using a movable block, the cable is pulled with a force of 530 N. Find the value of the friction force
Given:
m = 50 kilograms – the mass of the load, which is lifted using a movable block;
F = 530 Newton – the force with which the cable is pulled.
It is required to determine Ftr (Newton) – the magnitude of the friction force.
The movable block gives a 2-fold gain in strength. That is, the actual magnitude of the force will be equal to:
F1 = 2 * F = 2 * 530 = 1060 Newton.
Then, taking into account the assumption that the load is pulled evenly, according to Newton’s first law:
F1 = F gravity + Ftr;
Ftr = F1 – F gravity;
Ftr = F1 – m * g (where g = 10 Newton / kilogram is an approximate value);
Ftr = 530 – 50 * 10 = 530 – 500 = 30 Newtons.
Answer: the magnitude of the friction force is 30 Newtons.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
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# How do you simplify 5/(2-i)?
Aug 7, 2018
$2 + i$
#### Explanation:
$\frac{5}{2 - i}$
Multiply numerator and denominator by the denominator's conjugate:
$= \frac{5}{2 - i} \textcolor{b l u e}{\cdot \frac{2 + i}{2 + i}}$
Simplify:
$= \frac{10 + 5 i}{4 - {i}^{2}}$
$= \frac{10 + 5 i}{4 + 1}$
$= \frac{10 + 5 i}{5}$
$= 2 + i$
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Tuts 4 You
# Speed optimization question comparing
## Recommended Posts
Speed optimization question:
Having this code:
``` F1_bak = F1_bak+An+Mn[0]; // add the already computed Mn[0] value
unsigned int lr_val1_bak = leftrotate(F1_bak, s[0]);
unsigned int Ban1Test = Ban[0]+lr_val1_bak;
if (Ban[1]!=Ban1Test)
{
//printf("Invalid Ban[1] value!!!!\n");
goto StartOfSearch;
}```
versus second one:
``` unsigned int Ban1Test = Ban[0]+leftrotate((F1_bak+An+Mn[0]), s[0]);
if (Ban[1]!=Ban1Test)
{
//printf("Invalid Ban[1] value!!!!\n");
goto StartOfSearch;
}```
It happens that the first one is faster, there is more code to it and the difference is of 10 seconds!
Can someone explain why?
Nobody can explain why, because you only gave a very small part of C code. It's like asking "why this green 2-door car is faster than that red 4-door?"
Everything that is actually important, is missing from your question:
1) full code of the loop/method;
2) input data you used for testing;
3) used compiler/linker with all the switches;
4) actual assembly code produced by compiler/linker;
5) method how you measured the speed;
and I could go on and on.
My only suggestion is - look at the produced assembly code. Use a bloody profiler on both files. See which part of code is the slow one. Analyze that, and repeat. https://softwareengineering.stackexchange.com/questions/212111/how-to-find-bottlenecks-in-an-application
From the first look, these methods don't even produce the same results (first one changes F1_bak value, second one doesn't).
Here is the loop code: removed, old code!
I find that percentage calculation take a lot of time:
152 seconds or 2.5 minutes
without progress show:
94.00 seconds
Edited by CodeExplorer
2) input data you used for testing;
Mn[7] testing value starts with 2147483647 and end with 0; on each loop Mn[7] is decremented by 1
3). I've used the compiler "Pelles C for Windows" x86 version 8.00.60
4.) Used for passed seconds measurement:
On start:
time_t _tm = time(NULL);
struct tm * curtime = localtime (&_tm);
printf("start time %s", asctime(curtime));
When finished:
printf("Finished!!!\n");
time_t _tm_end = time(NULL);
curtime = localtime (&_tm_end);
printf("end time %s", asctime(curtime));
double dif = difftime (_tm_end,_tm);
printf ("Elapsed time is %.2lf seconds.\n", dif );
mRes = timeSetEvent(10, 0, &TimerProc, 0, TIME_PERIODIC);
and the result was great: 50 seconds less.
And once again same strange thing, the fallowing code:
``` dif1 = Ban[1]-Ban[0];
dif1_div = rightrotate(dif1, s[0]);
F1 = (Cn xor (Bn or (not Dn)))+An;
Mn[0] = dif1_div-F1;
lr_val1_bak = leftrotate(F1_bak, s[0]);
Ban1Test = Ban[0]+lr_val1_bak;
if (Ban[1]!=Ban1Test)
{
//printf("Invalid Ban[1] value!!!!\n");
goto StartOfSearch;
}```
is slower then:
``` dif1 = Ban[1]-Ban[0];
dif1_div = rightrotate(dif1, s[0]);
F1 = (Cn xor (Bn or (not Dn)))+An;
Mn[0] = dif1_div-F1;
lr_val1_bak = leftrotate(F1+Mn[0], s[0]);
Ban1Test = Ban[0]+lr_val1_bak;
if (Ban[1]!=Ban1Test)
{
//printf("Invalid Ban[1] value!!!!\n");
goto StartOfSearch;
}```
So mainly get riding of local variable F1_bak - "F1+Mn[0]" calculated directly (without local variable) is slower then "F1_bak = F1+Mn[0]";.This doesn't make any sense! And the difference is ~10 seconds, to much to be a measurement problem.
These methods produce the same results: F1_bak value is used only there for computing the Ban1Test value, and F1_bak value is used only once for computing Ban1Test value, Ban1Test value is used just once few instruction after (on showed code) for testing the value.
Edited by CodeExplorer
Upload the entire file, so we can compile it. Anything else is just guesswork.
I want an explanation on why the local variable version is faster then with the value calculated directly.
Here is an optimization that makes sense:
instead of "if (lr_values_4%s[4]!=0)" use "if (lr_values_4&(s[4]-1)!=0)"
That makes sense since modulo/divide operations takes lot of time.
The local variable version being faster then directly computed value make no sense!!!
Quote
The local variable version being faster then directly computed value make no sense!!!
That's why you need to look the assembly.
Let's put this simple, less number of lines (optimized number) of the same code is surely faster.
But this was when we had VC++ 2005, now that the compilers are super optimized, I think both will have the same performance (or maybe an infinitesimal performance difference).
Aside from all that, you use goto a lot, which is bad !
Quote
Aside from all that, you use goto a lot, which is bad !
Thanks. I somehow forget about "continue;" and "break;" statements!
Quote
Let's put this simple, less number of lines (optimized number) of the same code is surely faster.
That's sure true, but here the version without local variable should be faster. I didn't yet looked at compiled code; I didn't looked at disassembled code. But first I should know the theory.
2 hours ago, CodeExplorer said:
Thanks. I somehow forget about "continue;" and "break;" statements!
Your code flow shouldn't be controlled explicitly with continue, break, goto, or even switches... you should strive for making easy to follow code like using loops (and putting all your conditions for the loop to keep going there), and don't break the flow with any other statement (so anyone would look only at the while/for condition to know when it's gonna stop).
2 hours ago, CodeExplorer said:
but here the version without local variable should be faster
As I said, there is no guarantee that the compiler optimization would get the same result from the one-liner code vs the multi-line code. Most advanced compilers get to the same point.
But do you know where the local vars go ?
To the stack, hmm what then ?
The compiler then should generate a way to cleanup the stack to keep it balanced (at the end of your piece of code).
So, think about your code as a black box... all the stack / heap manipulations happen, but are they gonna stay there ? of course not, there must be extra codes to cleanup those dirty areas in the memory, and that's why the other version MIGHT be slower in case the compiler generated the local vars code in the output executable.
Quote
only at the while/for condition
In other words just one ugly loop!
Here is the new code:
```mRes = timeSetEvent(10, 0, &TimerProc, 0, TIME_PERIODIC);
// Just initial values of A, B, C, D:
unsigned int Al = 1;
unsigned int Bl = 2;
unsigned int Cl = 3;
unsigned int Dl = 4;
int IsFound = 0;
for (Mn[7]=total;Mn[7]!=0;Mn[7]--)
{
Ban[4] = know_sum1-Mn[7];
lr_values_4 = Ban[5]-Ban[4]; // i = 4
F_2 = rightrotate(lr_values_2_Clean, s[size-2]); // i = 6;
F_x2 = A xor (Ban6_Clean or (not Ban[4]));
Ban[3] = F_2-F_x2; // since Mn[6]=0
F_3 = rightrotate(lr_values_3_Clean, s[size-3]); // i = 5
F_x3 = Ban[4] xor (Ban5_Clean or (not Ban[3]));
Ban[2] = F_3-F_x3; // since Mn[5]=0
F_4 = rightrotate(lr_values_4, s[size-4]);
F_x4 = Ban[3] xor (Ban[4] or (not Ban[2]));
Ban[1] = F_4-F_x4-Mn[4]; // Mn[4] is known
// Calculation of Mn[0]-Mn[3] (messages)
dif1 = Ban[1]-Ban[0];
dif1_div = rightrotate(dif1, s[0]);
F1 = (Cn xor (Bn or (not Dn)))+An;
Mn[0] = dif1_div-F1;
lr_val1_bak = leftrotate(F1, s[0]);
Ban1Test = Ban[0]+lr_val1_bak;
if (Ban[1]!=Ban1Test) continue;
dif2 = Ban[2]-Ban[1];
dif2_div = rightrotate(dif2, s[1]);
F2 = (Bn xor (Ban[1] or (not Cn)))+Dn; // F = C xor (B or (not D));
Mn[1] = dif2_div-F2;
lr_val2_bak = leftrotate(F2, s[1]);
Ban2Test = Ban[1]+lr_val2_bak;
if (Ban[2]!=Ban2Test) continue;
dif3 = Ban[3]-Ban[2];
dif3_div = rightrotate(dif3, s[2]);
F3 = (Ban[1] xor (Ban[2] or (not Bn)))+Cn;
Mn[2] = dif3_div-F3;
lr_val3_bak = leftrotate(F3, s[2]);
Ban3Test = Ban[2]+lr_val3_bak;
if (Ban[3]!=Ban3Test) continue;
// Jus initial values:
Al = 1;
Bl = 2;
Cl = 3;
Dl = 4;
for (int j=0;j<8;j++)
{
F = Cl xor (Bl or (not Dl));
F = F+Al+Mn[j];
Al = Dl;
Dl = Cl;
Cl = Bl;
Bl = Bl + leftrotate(F, s[j]);
}
if ((Al!=A)||(Bl!=B)||(Cl!=C)||(Dl!=D))
{
continue;
}
else
{
IsFound = 1;
break;
}
}
if (mRes!=0) mRes = timeKillEvent(mRes);
printf("Finished!!!\n");```
• 1
#define leftrotate(x,n) ((x << n) | ((x & 0xFFFFFFFF) >> (32 - n)))
mov eax, dword ptr [s[0]]
- eax is initialized before
lr_val1_bak = leftrotate(F1, s[0]);
Ban1Test = Ban[0]+lr_val1_bak;
if (Ban[1]!=Ban1Test) continue;
00401C6B |. 8B15 68C34000 |MOV EDX,DWORD PTR DS:[40C368]
00401C71 |. 83C2 F9 |ADD EDX,-7
00401C74 |. 89C1 |MOV ECX,EAX
00401C76 |. D3C2 |ROL EDX,CL
00401C78 |. 8B45 90 |MOV EAX,DWORD PTR SS:[EBP-70]
00401C7D |. 3B45 94 |CMP EAX,DWORD PTR SS:[EBP-6C]
00401C80 |. 0F85 18010000 |JNZ 00401D9E
versus:
if (Ban[1]!=(Ban[0]+leftrotate(F1+Mn[0], s[0]))) continue;
00401C6B |. 8B15 68C34000 |MOV EDX,DWORD PTR DS:[40C368]
00401C71 |. 83C2 F9 |ADD EDX,-7
00401C74 |. 89C1 |MOV ECX,EAX
00401C76 |. 89D6 |MOV ESI,EDX
00401C78 |. D3E6 |SHL ESI,CL
00401C7A |. B9 20000000 |MOV ECX,20
00401C7F |. 29C1 |SUB ECX,EAX
00401C81 |. D3EA |SHR EDX,CL
00401C83 |. 09D6 |OR ESI,EDX
00401C85 |. 0375 90 |ADD ESI,DWORD PTR SS:[EBP-70]
00401C88 |. 3B75 94 |CMP ESI,DWORD PTR SS:[EBP-6C]
00401C8B |. 0F85 18010000 |JNZ 00401DA9
So there is no coincidence, the generated code in second part sucks,
also the ROL instruction is missing!
I think I know what's going on:
// Just initial values of A, B, C, D:
An = 1;
Bn = 2;
Cn = 3;
Dn = 4;
So here we have:
F1 = (Cn xor (Bn or (not Dn)))+An;
the compiler is smart enough to replace F1 with -7
5 hours ago, CodeExplorer said:
In other words just one ugly loop!
Ah... that's really a long function, how about you refactor the small similar parts into smaller functions as this one
``` F_2 = rightrotate(lr_values_2_Clean, s[size-2]); // i = 6;
F_x2 = A xor (Ban6_Clean or (not Ban[4]));
Ban[3] = F_2-F_x2; // since Mn[6]=0
F_3 = rightrotate(lr_values_3_Clean, s[size-3]); // i = 5
F_x3 = Ban[4] xor (Ban5_Clean or (not Ban[3]));
Ban[2] = F_3-F_x3; // since Mn[5]=0
```
And can you avoid all the break continue statements, and use one variable to control the flow ?
As I told you, many modern compilers do better job than humans in optimizing the code... so, you don't need to worry about one-liner code vs multi code.
You gotta focus more on the clarity / readability of your code
I still don't know why "rol"/"ror" instructions was replaced with many other instructions,
if I use local variables for calculation rol/ror are there and everything is ok.
Also I added two more "continue" conditions and the speed is now 31 seconds.
Fast enough I would say.
3 hours ago, CodeExplorer said:
I still don't know why "rol"/"ror" instructions was replaced with many other instructions,
Because you yourself defined rotate as:
`#define leftrotate(x,n) ((x << n) | ((x & 0xFFFFFFFF) >> (32 - n)))`
In case of a simple assignment compiler is smart enough to figure out it's "rol" and emit one instruction instead. In case of complex assignment, it uses the exact code you wrote.
If you want to optimize that part of code, check out the documentation of your compiler. Most of them provide intrinsics for rotates.
Edited by kao
On 9/10/2018 at 12:20 AM, CodeExplorer said:
Can someone explain why?
Your compiler and settings will determine the various optimizations that will be done automatically for you. If you are using Visual Studio, there are various optimization settings you can alter and adjust, as well as setting things to favor different things such as size of code or speed. If you are relying on the compiler for optimizations, then you are going to want to be using the newest version of the compiler/linker that is available for the best optimizations. (I know a lot of people in the reversing scene still use extremely old versions of VS like 2005/2008, so you will want to get 2017 for the best optimizations from the compiler/linker.)
In most cases, in your first post example, the compiler is going to optimize the function in the same way and produce the same output. Your best bet is to compare the output assembly of the code to see which styles produce the output that you prefer / favor as well as play with the various settings. Be sure to compile in release mode as well, disable as much debug code as possible, remove any unwanted/unneeded additional things that you do not need/want as well such as stack checks etc.
Compilers/linkers have tons of settings to optimize and tweak all kinds of things so be sure to review all the settings available, and even undocumented ones in the main settings windows etc. that can help tweak things further. If you are using more in depth things like the STL, you may also want to force the compiler to use newer standards (C++17, C++20, etc.) to get even more performance increases with newer standards.
When I use local version rol/ror instruction are placed like it should,
when I don't use local variable and calculate it directly it place these:
`#define leftrotate(x,n) ((x << n) | ((x & 0xFFFFFFFF) >> (32 - n)))`
Here I've used the compiler "Pelles C for Windows" x86 version 8.00.60,
after all this is just a console program.
For native GUI developer I've stuck with Visual C++ 2008.
Visual C++ 2008 is way better then latter, later version adds a strange PE section to generated exes.
So won't ever upgrade to any latter version.
I've also used "Visual C++ 6.0" a lot and I think to still use it.
Quote
so you will want to get 2017 for the best optimizations from the compiler/linker.
you may also want to force the compiler to use newer standards (C++17, C++20, etc.) to get even more performance increases with newer standards.
100% doubt these statements!!! I think it doesn't matter that much what compiler/linker I use as long as the generated assembly code is ok, If you really want optimisations use assembler like MASM and use CPU registers: but unforunalety they are only 8 general purpose registers, from which you can exclude SP and BP - so you left with only 6 registers, in the end you would still have to use memory variables.
Edited by CodeExplorer
48 minutes ago, CodeExplorer said:
Here I've used the compiler "Pelles C for Windows" x86 version 8.00.60,
after all this is just a console program.
For native GUI developer I've stuck with Visual C++ 2008.
Visual C++ 2008 is way better then latter, later version adds a strange PE section to generated exes.
So won't ever upgrade to any latter version.
I've also used "Visual C++ 6.0" a lot and I think to still use it.
This is why you are getting less then desired optimizations. If you want to keep using old/outdated compilers, then you are going to get old/outdated performance from them. Pelles is still a fairly newer compiler with less established development and optimizations in it so you are not going to get the results you may expect from it.
50 minutes ago, CodeExplorer said:
Visual C++ 2008 is way better then latter, later version adds a strange PE section to generated exes.
There are no extra/strange sections added to generated exe's outside of what you tell the compiler to do. The output depends on compiler settings, code that you use, compiler settings, how you link to the CRT and so on. There was one instance where Microsoft included some telemetry code into compiled exe's that was used for debugging purposes when VS2017 was still in its release candidate state that was later removed. Whatever misconceptions you have of VS are completely unfounded and are nothing more than fear mongering garbage from other non-developers in the RE community.
53 minutes ago, CodeExplorer said:
100% doubt these statements!!! I think it doesn't matter that much what compiler/linker I use as long as the generated assembly code is ok,
Seriously..? The compiler and linker are what handle the automated optimizations. Hence why they have tons of configuration settings to change how those optimizations work, what it will/wont touch, etc.
You are never going to get better-optimized code from the compiler you are using if you continue to use outdated tech., it's pretty much as simple as that. Unless you hand-write all the ASM yourself to handle every little optimization you want, it's not going to change unless you use newer stuff.
Quote
VS2017
What version you use? Community, Professional or Enterprise?
6 hours ago, CodeExplorer said:
What version you use? Community, Professional or Enterprise?
I use Professional due to having legit access to it. But the compiler/link is the same in all editions so Community should work fine. You only lose certain features and other minimal things.
• 3 weeks later...
Found the compiler option for Pelles C:
https://msdn.microsoft.com/en-us/library/f9534wye.aspx
The problem now is that when I use these flags `register keyword is completely ignored!`
And which part of the SO explanation is confusing to you?
Quote
A register specifier is a hint to the implementation that the variable so declared will be heavily used. [ note: The hint can be ignored and in most implementations it will be ignored if the address of the variable is taken. This use is deprecated ... —end note ]
41 minutes ago, kao said:
And which part of the SO explanation is confusing to you?
None. Is just a problem I can't override.
I don't take the address of variable.
When I use any optimization flags register keyword is ignored,
when I set Optimzations to None everything works like it should: variable is stored in CPU register.
## Create an account
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# Question: The dimensions of a room are 4 20 m X 3 00 m X 2 50 m
The dimensions of a room are 4.20 m X 3.00 m X 2.50 m.
(a) Find the number of molecules of air in the room at atmospheric pressure and 20.0°C. (b) Find the mass of this air, assuming that the air consists of diatomic molecules with molar mass 28.9 g/mol.
(c) Find the average kinetic energy of one molecule.
(d) Find the root-mean-square molecular speed.
(e) On the assumption that the molar specific heat is a constant independent of temperature, we have Eint = 5nRT/2. Find the internal energy in the air.
(f) What If? Find the internal energy of the air in the room at 25.0°C.
View Solution:
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https://socratic.org/questions/how-do-you-solve-2x-2x-7-x-2-17-2
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# How do you solve 2x-(2x)/7=x/2+17/2 ?
Apr 3, 2018
$x = 7$
Take L.C.M and simplify.
#### Explanation:
$2 x - \frac{2 x}{7} = \frac{x}{2} + \frac{17}{2}$
$\frac{14 x - 2 x}{7} = \frac{x + 17}{2}$ Take LCM 7 on LHS and simplify
$\frac{12 x}{7} = \frac{x + 17}{2}$
$24 x = 7 x + 119$
$17 x = 119$
$x = 7$
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# Second Entries
12
Hello friends,
I decided to learn coding so that I can create an indicator that would give me the following: A market condition where a candle breaks higher from the previous one for the second time.
The logic is illustrated in the above picture.
First condition is swing high found with iHighest function, then High[0] is > High[1], then the code would need to look for a break lower, where Low[0] < Low[1], then the Second Break Higher. I'm quite a beginner in programming but I'm doing my best. Any help would be appreciated in the logic or in the code that would help me create this.
Thanks.
367
Mtype:
Hello friends,
I decided to learn coding so that I can create an indicator that would give me the following: A market condition where a candle breaks higher from the previous one for the second time.
The logic is illustrated in the above picture.
First condition is swing high found with iHighest function, then High[0] is > High[1], then the code would need to look for a break lower, where Low[0] < Low[1], then the Second Break Higher. I'm quite a beginner in programming but I'm doing my best. Any help would be appreciated in the logic or in the code that would help me create this.
Thanks.
1. You should define the Swing High correctly and its validity. iHighest() won't be enough.
2. You have to find the first Break High within the Swing High's validity.
3. You need to confirm continuation of counting (Break High) by Break Low.
4. If the second Break High appears you should plot an indicator arrow
12
Petr Nosek:
1. You should define the Swing High correctly and its validity. iHighest() won't be enough.
2. You have to find the first Break High within the Swing High's validity.
3. You need to confirm continuation of counting (Break High) by Break Low.
4. If the second Break High appears you should plot an indicator arrow
Thank you Petr!
1345
ZigZag indicator repaints, but I like it for looking back and identifying previous swing highs and lows
12
Ian Tavener:
ZigZag indicator repaints, but I like it for looking back and identifying previous swing highs and lows
Thanks Ian for the help
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1. Yep 3 Bytes | 24 Bits per char
2. Originally Posted by Ch40zz-C0d3r
I believe he means the length of the "encryption"
Code:
char* cA = "218";
Yea i say 8 bits, per char So its 24 bits, 3bytes
---------- Post added at 10:04 PM ---------- Previous post was at 10:03 PM ----------
Originally Posted by RedAppleCoder
Yep 3 Bytes | 24 Bits per char
ohh i was late
3. its a 32bit integer thats over 10 times more than 3 bits, or is it a string? then its 3 bytes(1 byte for each char or 8bits for each char)... 3 chars times 8 bits = 24bit still along way off from 3bits
//edit
did'nt read page 2 of topic, so yeah 8 bits per char, NOT 24bits per char, unless you compiled it as a 64bit application then it would be 16bits per char or 2 bytes per char, which makes your encryption a 48bit deal.
4. Why not automate the process? Calculate the end result based on the character using a formula. Cast each separate character to their decimal equivalent then do some maths on it and return the encrypted value of that character and concatenate it onto the end of a result string.
5. Its A Great! Thanks
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# generators of inverse ideal
Theorem.β Let $R$ be a commutative ring with non-zero unity and let $T$ be the total ring of fractions of $R$.β Ifβ $\mathfrak{a}=(a_{1},\,\ldots,\,a_{n})$β is an invertible (http://planetmath.org/FractionalIdealOfCommutativeRing) of $R$ with β$\mathfrak{ab}=R$,β then also the inverse ideal $\mathfrak{b}$ can be generated by $n$ elements of $T$.
Proof. βThe equationβ $\mathfrak{ab}=(1)$β implies the existence of the elements $a_{i}^{\prime}$ of $\mathfrak{a}$ and $b_{i}^{\prime}$ of $\mathfrak{b}$β $(i=1,\ldots,\,m)$ such thatβ $a_{1}^{\prime}b_{1}^{\prime}\!+\cdots+\!a_{m}^{\prime}b_{m}^{\prime}=1$.β Because the $a_{i}^{\prime}$βs are in $\mathfrak{a}$, they may be expressed as
$a_{i}^{\prime}=\sum_{j=1}^{n}r_{ij}a_{j}\qquad(i=1,\ldots,m),$
where the $r_{ij}$βs are some elements of $R$.β Now the unity acquires the form
$1=\sum_{i=1}^{m}a_{i}^{\prime}b_{i}^{\prime}=\sum_{i=1}^{m}\sum_{j=1}^{n}r_{ij% }a_{j}b_{i}^{\prime}=\sum_{j=1}^{n}a_{j}\sum_{i=1}^{m}r_{ij}b_{i}^{\prime}=% \sum_{j=1}^{n}a_{j}b_{j},$
in which
$b_{j}=\sum_{i=1}^{m}r_{ij}b_{i}^{\prime}\,\in R\mathfrak{b}=\mathfrak{b}\qquad% (j=1,\ldots,n).$
Thus an arbitrary element $b$ of the $\mathfrak{b}$ satisfies the condition
$b=b\!\cdot\!1=\sum_{j=1}^{n}(a_{j}b)b_{j}\,\in Rb_{1}\!+\cdots+\!Rb_{n}=(b_{1}% ,\,\ldots,\,b_{n}).$
Consequently,β $\mathfrak{b}\subseteq(b_{1},\,\ldots,\,b_{n})$.β Since the inverse inclusion is apparent, we have the equality
$\mathfrak{a}^{-1}=\mathfrak{b}=(b_{1},\,\ldots,\,b_{n}).$
Title generators of inverse ideal GeneratorsOfInverseIdeal 2015-05-06 14:52:30 2015-05-06 14:52:30 pahio (2872) pahio (2872) 18 pahio (2872) Theorem msc 13A15 FractionalIdealOfCommutativeRing IdealGeneratedByASet PruferRing
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MAT 116 - Week Two Concept Check
MAT 116 - Week Two Concept Check - come up with 5 = 5 which...
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Week Two Concept Check : We know when we have an equation that has infinitely many solutions when we see that the solution has the same answer on either side of the equal sign. For an example if we have 5 + x = x + 5 we must subtract x on either side of the equal sign and we
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Unformatted text preview: come up with 5 = 5 which is true. We know if an equation has no solution if either side of the equal signs solution do not equal the same number. An example of this is 4 + x = x + 7, we subtract x on both sides of the equal sign and get 4 = 7 which is false....
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# Ordered fields
## Idea
An ordered field is a field equipped with a compatible linear order.
Note that while the adjective ‘ordered’ usually refers to a partial order, it is traditionally used more strictly when placed before ‘field’.
## Definition
An ordered field is a field $K$ equipped with a linear order $\lt$ such that:
• $1 \gt 0$,
• If $a, b \gt 0$, then so are $a + b$ and $a b$.
One often sees the definition using a total order $\leq$ instead of the linear order $\lt$. This makes no difference in classical mathematics, but we need to use linear orders in constructive mathematics if we wish to have the usual examples.
## Examples
The field $\mathbb{R}$ of real numbers is the Dedekind-complete ordered field.
The field $\mathbb{Q}$ of rational numbers is a subfield? of $\mathbb{R}$ that is too small to be complete.
The field of surreal numbers is a field extension of $\mathbb{R}$ that is too large to be complete.
## Properties
Every ordered field must have characteristic $0$, since we can prove by induction that $n \gt 0$ for every positive natural number $n$.
The archimedean ordered fields are precisely the subfield?s of the field of real numbers.
###### Proposition
Every complete ordered field is archimedean.
###### Proof
Suppose otherwise: let $a, b \gt 0$ be given, and suppose $b$ is an upper bound of $a, 2a, 3a, \ldots$. Then $b - a$ is an upper bound of $0, a, 2a, \ldots$ and consequently there can be no least upper bound of the sequence, contradicting Dedekind completeness.
The following is a result in classical mathematics.
###### Proposition
A field admits an order (“is orderable”) if and only if it is a real field, i.e., if the element $-1$ is not a sum of squares.
###### Proof
Given an ordered field, any non-zero square is positive since either $-\alpha$ or $\alpha$ is positive, and so $(-\alpha)^2 = \alpha^2$ is positive. Hence a sum of non-zero squares cannot be negative, and in particular cannot be equal to $-1$.
In the other direction, every real field $F$ may be embedded in a real closed field (this requires Zorn's lemma), and a real closed field admits a unique ordering. The restriction of this ordering to the embedded field $F$ gives an ordering on $F$.
Revised on August 11, 2011 19:22:38 by Toby Bartels (71.31.222.2)
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# Could some please explain what is going on here?
## Recommended Posts
I am working on a custom crop and instead of just copying and pasting code I am trying to understand what is going on. Some of the code I understand but the code related to the ticking of the block is throwing me could someone explain what is going on? The mechanics, not the Java basics... I got that part down but the obfuscation is making this hard to wrap my head around.
Here is the code (BlockCrops.java from mojang)
```protected BlockCrops () {
float f = 0.5F;
this.setBlockBounds(0.5F - f, 0.0F, 0.5F - f, 0.5F + f, 0.25F, 0.5F + f);
...more code not included
}
```
```public void updateTick(World p_149674_1_, int p_149674_2_, int p_149674_3_, int p_149674_4_, Random p_149674_5_)
{
super.updateTick(p_149674_1_, p_149674_2_, p_149674_3_, p_149674_4_, p_149674_5_);
if (p_149674_1_.getBlockLightValue(p_149674_2_, p_149674_3_ + 1, p_149674_4_) >= 9)
{
int l = p_149674_1_.getBlockMetadata(p_149674_2_, p_149674_3_, p_149674_4_);
if (l < 7)
{
float f = this.func_149864_n(p_149674_1_, p_149674_2_, p_149674_3_, p_149674_4_);
if (p_149674_5_.nextInt((int)(25.0F / f) + 1) == 0)
{
++l;
}
}
}
}
public void func_149863_m(World p_149863_1_, int p_149863_2_, int p_149863_3_, int p_149863_4_)
{
int l = p_149863_1_.getBlockMetadata(p_149863_2_, p_149863_3_, p_149863_4_) + MathHelper.getRandomIntegerInRange(p_149863_1_.rand, 2, 5);
if (l > 7)
{
l = 7;
}
}
private float func_149864_n(World p_149864_1_, int p_149864_2_, int p_149864_3_, int p_149864_4_)
{
float f = 1.0F;
Block block = p_149864_1_.getBlock(p_149864_2_, p_149864_3_, p_149864_4_ - 1);
Block block1 = p_149864_1_.getBlock(p_149864_2_, p_149864_3_, p_149864_4_ + 1);
Block block2 = p_149864_1_.getBlock(p_149864_2_ - 1, p_149864_3_, p_149864_4_);
Block block3 = p_149864_1_.getBlock(p_149864_2_ + 1, p_149864_3_, p_149864_4_);
Block block4 = p_149864_1_.getBlock(p_149864_2_ - 1, p_149864_3_, p_149864_4_ - 1);
Block block5 = p_149864_1_.getBlock(p_149864_2_ + 1, p_149864_3_, p_149864_4_ - 1);
Block block6 = p_149864_1_.getBlock(p_149864_2_ + 1, p_149864_3_, p_149864_4_ + 1);
Block block7 = p_149864_1_.getBlock(p_149864_2_ - 1, p_149864_3_, p_149864_4_ + 1);
boolean flag = block2 == this || block3 == this;
boolean flag1 = block == this || block1 == this;
boolean flag2 = block4 == this || block5 == this || block6 == this || block7 == this;
for (int l = p_149864_2_ - 1; l <= p_149864_2_ + 1; ++l)
{
for (int i1 = p_149864_4_ - 1; i1 <= p_149864_4_ + 1; ++i1)
{
float f1 = 0.0F;
if (p_149864_1_.getBlock(l, p_149864_3_ - 1, i1).canSustainPlant(p_149864_1_, l, p_149864_3_ - 1, i1, ForgeDirection.UP, this))
{
f1 = 1.0F;
if (p_149864_1_.getBlock(l, p_149864_3_ - 1, i1).isFertile(p_149864_1_, l, p_149864_3_ - 1, i1))
{
f1 = 3.0F;
}
}
if (l != p_149864_2_ || i1 != p_149864_4_)
{
f1 /= 4.0F;
}
f += f1;
}
}
if (flag2 || flag && flag1)
{
f /= 2.0F;
}
return f;
}```
Basically I get the idea that the block ticks. On each tick it checks if there is enough light to support the plant, but what is the part about the floating point numbers looking like they have something to with the size of bounding box around the plant.
Am I on the right path? My guess is not close...
“Most good programmers do programming not because they expect to get paid or get adulation by the public, but because it is fun to program.” - Linus Torvalds
##### Share on other sites
The BlockBounds is to set how to get the hitboxes, like wheat its different from regular blocks.
The update tick checks (each tick) for valid light - so it can grow, and checks if the crop metadata is 7, if it is (then it will become harvest-able)
##### Share on other sites
Hi
Coding in 1.7.2 is still a pain in the rear.
Here is the code from 1.6.4 (with a couple of parameters renamed)
``` /**
* Ticks the block if it's been scheduled
*/
public void updateTick(World par1World, int x, int y, int z, Random par5Random)
{
super.updateTick(par1World, x, y, z, par5Random);
if (par1World.getBlockLightValue(x, y + 1, z) >= 9)
{
int l = par1World.getBlockMetadata(x, y, z);
if (l < 7)
{
float f = this.getGrowthRate(par1World, x, y, z);
if (par5Random.nextInt((int)(25.0F / f) + 1) == 0)
{
++l;
}
}
}
}
```
The weird stuff in this line
``` float f = 0.5F;
this.setBlockBounds(0.5F - f, 0.0F, 0.5F - f, 0.5F + f, 0.25F, 0.5F + f);
```
is probably because the original code had something like
``` float HALF_CROP_BLOCK_WIDTH = 0.5F;
this.setBlockBounds(0.5F - HALF_CROP_BLOCK_WIDTH, 0.0F, 0.5F - HALF_CROP_BLOCK_WIDTH, 0.5F + HALF_CROP_BLOCK_WIDTH, 0.25F, 0.5F + HALF_CROP_BLOCK_WIDTH);
```
(You realise that the variable f in the constructor has nothing to do with the f in the updatetick, yeah?)
-TGG
##### Share on other sites
Yeah, at first I thought they were related then after looking at it again I realized they are not.
Thanks for the explained code. It helps a lot. Hopefully things get better in 1.7 soon. I know they are hard at work.
“Most good programmers do programming not because they expect to get paid or get adulation by the public, but because it is fun to program.” - Linus Torvalds
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# What happens when you exceed 999999 points in Super Mario Bros.?
I am implementing a replica of the classic Super Mario Bros. in the Unity game engine. The problem is, I do not have a Nintendo Entertainment System.
I somehow found out that getting 100 coins will get you an extra 1UP (life), but what about the score?
There are 6 available decimal spots for the score:
So what happens if the score exceeds 999999?
• NES emulators are widely available to try with. Oct 20, 2020 at 2:43
Nothing special happens when going past 999,999 other than it just displays 7 digits instead. Source
• I might have a follow-up question... Oct 22, 2020 at 15:41
• @AndréStannek and that is..? Oct 22, 2020 at 18:17
• @quetzalcoatl It was just supposed to be a joke because to me, the next obvious question is what happens when you exceed the 7 digits. Fortunately Ray also answered it in his answer :-) Oct 23, 2020 at 7:48
• @AndréStannek: ooh I see. Thanks, I totally was out of ideas re what you could mean and I thought it might be like "1000100pts by jumping.. how long did it take?" etc.. soo...yeah.. my mind went on a totally different route ;) Oct 23, 2020 at 8:08
I quickly checked in an emulator since I didn't know either.
SMB1 stores the score in BCD encoding, using 6 bytes, one for each digit - excluding the units, since score granularity does not go below multiples of 50.
If you have a score of 123,450, the bytes will be `00 01 02 03 04 05`.
The first `00` byte is reserved for properly handling millions. If you ever get scores between 1,000,000 and 9,999,950, there will simply be another digit displayed in front of the always visible 0's:
(The 6 bytes ahead of the marked ones are the TOP score, and the 6 following the Player 2 score.)
Technically, the maximum score possible is 9,999,990, 40 points above the maximum legal score which, as said, must be a multiple of 50.
If you exceed even this limit, the game will properly wrap over to 0, and the score is rendered as with a fresh game, with the millions-digit gone.
This is slightly spoiled by the `TOP- 000000` highscore display at the start screen, leaving a space for the millions.
• Comments are not for extended discussion; this conversation has been moved to chat. Oct 20, 2020 at 17:03
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# Resource Request
Success! This resource has been created.
### Multiply decimals to 10,100,1000 Complete
by Monique Sharma
Resources on multiplying decimals to 10,100 & 1000
Year 6 / Numeracy
#### Comments & feedback
What do you think of this request? Would you love to use it too?
• Including dividing decimals by 10, 100 and 1000
Comment by Kristy Valler on October 25, 2016 at 7:41 am
• Hi Monique,
Thanks again for requesting a Teach Starter resource and thank you to everyone else for voting!
We have completed your request and it is ready for you to download here: https://www.teachstarter.com/lesson-plan/multiplying-decimals-whole-numbers/
We have also created:
Multiplying with Decimals – Bingo Game – https://www.teachstarter.com/teaching-resource/multiplying-decimals-bingo-game/
Decimals and Percentages Assessment – Year 5 & 6 – https://www.teachstarter.com/teaching-resource/decimals-percentages-assessment-year-5-year-6/
Fractions and Decimals Worksheets – Year 6 – https://www.teachstarter.com/teaching-resource/fractions-decimals-worksheets-year-6/
Operations with Decimals PowerPoint – https://www.teachstarter.com/teaching-resource/operations-with-decimals-powerpoint/
Describe That Decimal Worksheet – https://www.teachstarter.com/teaching-resource/describe-that-decimal-worksheet/
Multiplying and Dividing by Powers of 10 Lesson Plan – https://www.teachstarter.com/lesson-plan/multiplying-dividing-powers-10/
If you have any questions or require any changes to this resource, simply reply to this comment and I’ll be more than happy to help.
Kind regards,
Jill
Official comment by Jill (Teach Starter) on October 12, 2017 at 3:03 pm
You must be logged in to post a comment.
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### Bisecting an Arc
Illustration used to show how to bisect a given arc.
### Equal Tangents to Circle Theorem
Illustration used to show that "If two tangents are drawn from any given point to a circle, those tangents…
### Tangent to Perpendicular Radius Circle Theorem
Illustration used to show that "A tangent to a circle is perpendicular to the radius drawn to the point…
### Diameter Perpendicular to a Chord in a Circle
Illustration used to show that "The diameter perpendicular to a chord bisects the chord and also its…
### Equal Chords in Equal Circles Theorem
Illustration used to show that "In equal circles, or in the same circle, if two chords are equal, they…
### Equal Chords in Equal Circles Theorem
Illustration used to show that "In equal circles, or in the same circle, if two chords are equal, they…
### Unequal Chords in Circles Theorem
Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…
### Unequal Chords in Equal Circles Theorem
Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…
### Unequal Chords in Equal Circles Theorem
Illustration used to show that "In equal circles, or in the same circle, if two chords are unequal,…
### Intersecting Lines Corollary
Illustration used to prove the corollary that "Two lines perpendicular respectively to two intersecting…
### Perpendicular to Line Corollary
Illustration used to prove the corollary that "From a point outside a line there exists only one perpendicular…
### 2 Triangles Theorem
Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides…
### 2 Triangles Theorem
Illustration used to prove that "If two triangles have two sides of one equal respectively to two sides…
### Exterior Angle of Triangle Theorem
Illustration used to prove that "If one side of a triangle is prolonged, the exterior angle formed is…
### Parallel Lines Theorem
Illustration used to prove that "If two straight lines are parallel to a third straight line, they are…
### Sides of Triangle Theorem
Illustration used to prove that "If two sides of a triangle are unequal, the angle opposite the greater…
### Sides of Triangle Theorem
Illustration used to prove that "The sum of any two sides of a triangle is greater than the third side."
### Segments Labeled In A Triangle
Illustration of triangle ABC with BE extended through the triangle at point D. Segment AB is equal to…
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Category
# How to Convert Float Tensor Into Binary Tensor Using Pytorch?
To convert a float tensor into a binary tensor using PyTorch, you can simply apply a threshold value to each element in the tensor. For example, you can set all elements greater than a certain threshold to 1, and all elements less than or equal to the threshold to 0.
You can achieve this using the `torch.where()` function in PyTorch. Here's an example code snippet to demonstrate how to convert a float tensor into a binary tensor:
``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ``` ```import torch # Create a float tensor float_tensor = torch.randn(3, 3) # Set a threshold value threshold = 0.0 # Convert float tensor to binary tensor binary_tensor = torch.where(float_tensor > threshold, torch.tensor([1]), torch.tensor([0])) print("Float tensor:") print(float_tensor) print("Binary tensor:") print(binary_tensor) ```
In this code snippet, we first create a float tensor using `torch.randn()`, set a threshold value of 0.0, and then use `torch.where()` to convert the float tensor into a binary tensor based on the threshold. The resulting binary tensor will have elements with value 1 where the corresponding element in the float tensor is greater than the threshold, and value 0 otherwise.
## Best Python Books to Read In July 2024
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Learning Python, 5th Edition
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## What is the benefit of using binary tensors in PyTorch?
There are several benefits of using binary tensors in PyTorch:
1. Memory efficiency: Binary tensors only store binary values (0 or 1) which require less memory compared to tensors containing floating point values. This can be especially beneficial when working with large datasets or models.
2. Speed: Binary operations, such as bitwise AND, OR, and XOR, are faster to compute compared to arithmetic operations on floating point values. This can result in faster training and inference times for models using binary tensors.
3. Improved performance on specific tasks: Binary tensors are useful for tasks that involve binary representations, such as binary classification, bit manipulation, and hashing. In such tasks, using binary tensors can simplify computations and improve efficiency.
4. Low precision requirements: In some applications, high precision floating point values are not necessary and can be replaced with binary representations without significant loss of accuracy. This can further improve efficiency and speed.
Overall, using binary tensors in PyTorch can provide benefits in terms of memory efficiency, speed, performance on specific tasks, and low precision requirements, making them a valuable tool for certain applications.
## What is the importance of data processing in PyTorch when converting to binary tensors?
Data processing in PyTorch is important when converting data to binary tensors because it allows the data to be formatted and preprocessed in a way that is suitable for training machine learning models. This includes tasks such as normalization, scaling, and encoding categorical variables.
When converting data to binary tensors, it is especially important to properly preprocess the data to ensure that the binary tensors accurately represent the underlying dataset. This may involve encoding categorical variables as one-hot vectors, normalizing numerical features, or handling missing values.
By processing the data in PyTorch before converting it to binary tensors, you can ensure that the data is in the correct format and is ready to be used for training machine learning models. This can help improve the performance and accuracy of your models, as well as simplify the overall data processing pipeline.
## How to visualize the differences between float and binary tensor representations in PyTorch?
One way to visualize the differences between float and binary tensor representations in PyTorch is to create and display example tensors of each type.
Here's an example code snippet in PyTorch that creates an example float tensor and a binary tensor, and then visualizes them using matplotlib:
``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 ``` ```import torch import matplotlib.pyplot as plt # Create a float tensor float_tensor = torch.randn(5, 5) # Create a binary tensor binary_tensor = torch.randint(0, 2, (5, 5)) # Visualize the float tensor plt.figure() plt.imshow(float_tensor.numpy(), cmap='viridis') plt.title('Float Tensor') plt.colorbar() plt.show() # Visualize the binary tensor plt.figure() plt.imshow(binary_tensor.numpy(), cmap='binary') plt.title('Binary Tensor') plt.colorbar() plt.show() ```
This code snippet creates a 5x5 float tensor and a 5x5 binary tensor using PyTorch functions. It then uses matplotlib to visualize these tensors as images, with the float tensor displayed using a viridis colormap and the binary tensor displayed using a binary colormap.
By running this code snippet, you can visually compare and contrast the representations of float and binary tensors in PyTorch, and observe the differences in their values and structure.
## How to change data type of a PyTorch tensor to binary?
You can change the data type of a PyTorch tensor to binary by using the `torch.uint8` data type. Here's an example code snippet to convert a PyTorch tensor to binary:
``` 1 2 3 4 5 6 7 8 9 10 ``` ```import torch # Create a tensor tensor = torch.tensor([1, 0, 1, 0, 1]) # Convert tensor to binary binary_tensor = tensor.byte() # Print the binary tensor print(binary_tensor) ```
In this example, we first create a PyTorch tensor with values `[1, 0, 1, 0, 1]`. We then use the `byte()` method to convert the tensor to binary, which will use the `torch.uint8` data type. Finally, we print the binary tensor.
## Related Posts:
To extract an integer from a PyTorch tensor, you can use the .item() method on the tensor object. This method will return the integer value stored in the tensor. For example: import torch # Create a PyTorch tensor tensor = torch.tensor([5]) # Extract the int...
In PyTorch, you can expand the dimensions of a tensor using the unsqueeze() function. This function adds a new dimension of size one at the specified position in the tensor.For example, if you have a 1D tensor of size (3,) and you want to expand it to a 2D ten...
In PyTorch, input and output tensors are defined by specifying the shape and datatype of the tensors. The shape of a tensor refers to the dimensions of the tensor, while the datatype refers to the type of data stored in the tensor (e.g. float, integer, etc.).T...
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# Factor Markets Chapter 18.
## Presentation on theme: "Factor Markets Chapter 18."— Presentation transcript:
Factor Markets Chapter 18
Markets for Factors of Production
Factors of production are inputs used to produce goods & services Demand for a factor of production is a derived demand: A firm’s demand for a factor of production is derived from demand for their own product
Labor markets, like other markets, are governed by the forces of supply & demand
(a) The Market for Apples (b) The Market for Apple Pickers Price of Wage of Apples Apple Pickers Supply Demand Supply Demand P Q L W Quantity of Quantity of Apples Apple Pickers The demand for apple pickers is derived from the market demand for apples Copyright©2003 Southwestern/Thomson Learning
Marginal Product of Labor
Production Function- illustrates the relationship between quantity of inputs & quantity of output Marginal Product of Labor (MPL)- the increase in output from an additional unit of labor MPL = Q/L or MPL = (Q2 – Q1)/(L2 – L1)
Diminishing Marginal Product of Labor:
As more workers are added Marginal Product Labor Declines MPL = Q/L Diminishing Marginal Product of Labor: Each additional worker contributes less to production than the prior one
The Production Function
Diminishing Marginal Product makes the Production Function becomes “flatter” Quantity of Apples Production function 300 280 240 180 100 1 2 3 4 5 Quantity of Apple Pickers
Marginal Revenue Product (MRP)
MRP = The marginal product of input multiplied by the market price of output (measured in dollars) MRPL = MPL P MRP = Δ in Total Revenue / Δ in Resource Qty Qty Total Marginal Price MRP Labor Product Product ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ Price for a competitive firm equals MR & remains constant Assume Price = \$0.50
To Maximize Profit A competitive firm hires workers up to the point where MRP =Wage The MRP curve is the labor demand curve for a competitive, profit-maximizing firm.
MRP & Maximizing Profit
Value When a competitive firm hires labor up to the point where MRP = Wage, it also produces up to the point at which the P = MC of the Marginal Product Marginal Revenue Product (demand curve for labor) Market wage Profit-maximizing quantity Quantity of Apple Pickers
Worksheet Lesson 2, Activity 44 New Terms: Marginal Product of Labor
Marginal Revenue Product
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# Assignments & sample solutions
Here you find a selection of assignments and sample solutions which
will induct you into working with the Lab.
and installed
the Statistical Lab.
# Assignments
Statistical Lab here. It is free of
charge
for non-commercial purposes.
Setup & Installation »
##### Examples from the book
Get the examples and solutions, mentioned in Prof. Dr. Rainer Schlittgen's book.
Das Statistiklabor. Einführung und Benutzerhandbuch (german only). Das Statistiklabor. Die Aufgaben zum Buch (german only). Schlittgen, Rainer (2005)Springer-Verlag, Berlin Heidelberg Schlittgen, Rainer (2005) Order on Amazon Order on Springer-Online In this archive you find all examples and solutions from the book(currently available in german only). Download the examples and solutions for free »
# Simulations
Complex theoretical problems can be simulated very easy using the Lab. Have a look at our examples:
## Contributor
Simulating Quincunx (Galton Brett) A classic simulation of a binominal distribution Prof. Dr. Rainer Schlittgen
Coin experiment Heads or tails – here you can simulate the probability of these events. Tests can be done using samples of varying size. Prof. Dr. Rainer Schlittgen
Monty-Hall problem(Ziegenproblem) The Statistical Lab determines the chances of winning the 'Monty-Hall problem' for two different strategies by simulating the game. Amit Ghosh and Christian Grune
Martingale strategie for playing roulette Can your chances of winning in a roulette game be improved? A simulation of roulette game using the martingale strategy Prof. Dr. Rainer Schlittgen
# Libraries
These additional libraries enlarge the pool of R functions:
Danalyse.R
DescriptiveStat.R
Gauss.R
Regression.R
Simul.R
Tests.R
TestStatistic.R
Wilcoxon.R
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A man wakes up in the middle of the night and wants a snack, so he goes downstairs, gets out a sandwich and a glass of milk from the refrigerator. He eats the sandwich and drinks the milk, then turns out the lights and goes to bed. In the...
## Mindbender: The three suitors
A king is searching for a suitor for his daughter, so he collects the three smartest men in town. He sits them in a circle and tells them he is going to put a red...
## Mindbender: three lights
A man is standing in front of three light switches and then there is a shut door. He is only allowed to go through the door once and there he will see three light bulbs. By turning any light bulbs on or off the man must be able to...
## Mindbender: Park Lane Hotel
A man is pushing his car across London. He eventually arrives outside a hotel in Park Lane and there discovers he has become bankrupt. How has this happened? NEXT > by
## Mindbender: The smuggler
Every other day, a cyclist rides a bicycle over the border between the border of the US and Mexico. a policeman always checks his satchel, but it holds nothing but a water bottle. Yet, he is smuggling something between the two countries. What is it? [Nothing is said about...
## Mindbender: equation II
(Variation on another equation question) Remove one short line to make this correct: 5 + 5 + 1 = 546 NEXT > by
## Mindbender: Sandtimers
You have two traditional hourglass type egg timers. One takes seven minutes for the sand to run through, the other takes 11 minutes. You want to boil an ostrich egg for exactly 15 minutes. How do you do it? and how soon after the start of the whole process...
## Mindbender: How well do you know your physics?
Some silly questions for you, but you need to know a bit about physics to work these out. Mad Professor Zweistein has managed to build a car that has an unlimited to speed and incredible breaks that allow it to stop instantly. He only has one problem, the car...
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## Tag Archives: pedagogy
### Not My Best Moment
This happens more often than I’d like: we start by having a normal class discussion and end up trying to resolve something that doesn’t engage the students’ interest, or even their understanding. It’s the exact opposite of the way I’d like my classroom to feel.
Last week in 9th grade class we were discussing the following problem, which had been assigned for homework.
Write an equation for a rule a?b, so that the answer is odd only when both a and b are even.
### Geometry Follow-Up: Proof in a Bag
The concept of proof-in-a-bag is simple. Write out a two-column proof and then cut it up so that each statement or reason is by itself on a scrap of paper. Then put all the scraps in a bag (a small sandwich bag works well, though an opaque paper bag might have more of a dramatic effect) and have kids work on rearranging the scraps so that they form a coherent proof. You can decide whether you want students to know ahead of time what it is they’re proving, or if you want them to figure it out by putting statements with “given:…”, “prove…” and a diagram in the bag as well.
Credit where credit is due: I got the idea for this from Laura Chihara while a student in her Algebraic coding class at the Carleton-St. Olaf Summer Math Program.
It’s nice to have any activity where kids are physically doing something in a math class, of course, but I really like what kids get out of this activity. It emphasizes the idea that you have to have enough evidence before you can conclude that triangles are congruent (otherwise, what are those “extra” statements doing in the bag?) And it is very good for helping students understand what can be a statement vs. what can be a reason. I often find that students want to use triangle congruence theorems like SAS when using properties of triangle congruence; the structure of this activity leads them to realize that they’ve already used SAS to justify the triangle congruence statement; they now need to use something else (CPCTC or the equivalent) to start using the congruence.
There are some times when I would definitely not use this activity. If the proof is a particularly exciting one for kids to work out on their own, I wouldn’t rob them of the opportunity. Proof-in-a-bag works best for simple, straightforward proofs, where the two-column proof format can be used without having to do a lot of extra explaining. I generally use it for one day only, at a time when the class has had some practice writing proofs but has not yet reached a level of comfort with them.
Does anybody else have activities or techniques that they use to teach writing proofs? I’d be especially interested in what people do who don’t insist on a strict two-column format all of the time.
Follow
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Cody
Rank
Score
1 – 50 of 77
Problem 953. Pi Estimate 1
Created by: Ed Hall
Tags for loop
Problem 528. Find the largest value in the 3D matrix
Created by: Bruce Raine
Problem 824. Set the array elements whose value is 13 to 0
Created by: Aurelien Queffurust
Problem 307. First non-zero element in each column
Created by: Julio
Problem 367. Specific Element Count
Created by: @bmtran (Bryant Tran)
Problem 532. Return unique values without sorting
Created by: Aurelien Queffurust
Tags unique, sorted
Problem 640. Getting logical indexes
Created by: Doug Hull
Problem 555. "Low : High - Low : High - Turn around " -- Create a subindices vector
Created by: Freddy
Problem 576. Return elements unique to either input
Created by: James
Problem 584. middleAsColumn: Return all but first and last element as a column vector
Created by: Nicholas Howe
Problem 589. Matrix indexing with two vectors of indices
Created by: Nicholas Howe
Problem 676. Reindex a vector
Created by: James
Problem 690. Remove the two elements next to NaN value
Created by: Aurelien Queffurust
Problem 795. Joining Ranges
Created by: Dirk Engel
Problem 856. Getting the indices from a matrice
Created by: Jean-Marie Sainthillier
Problem 859. Get the elements of diagonal and antidiagonal for any m-by-n matrix
Created by: Aurelien Queffurust
Problem 867. Replicate elements in vectors
Created by: Jean-Marie Sainthillier
Problem 895. Generate N equally spaced intervals between -L and L
Created by: @bmtran (Bryant Tran)
Problem 924. intersection of matrices
Created by: Richard
Problem 44311. Number of Even Elements in Fibonacci Sequence
Created by: Mehmet OZC
Problem 3092. Return fibonacci sequence do not use loop and condition
Created by: Binbin Qi
Problem 43016. Find the next Fibonacci number
Created by: Steven Van Vaerenbergh
Tags fibonacci
Problem 2423. Integer Sequence - II : New Fibonacci
Created by: rifat
Problem 434. Return the Fibonacci Sequence
Created by: Matt Fig
Tags fibonacci
Problem 12. Fibonacci sequence
Created by: Cody Team
Tags triangle
Problem 43599. Find the sides of an isosceles triangle when given its area and height from its base to apex
Created by: Andriy Kavetsky
Problem 42855. Height of a right-angled triangle
Created by: Jasmina Lazic
Problem 558. Is the Point in a Triangle?
Created by: Kuifeng
Tags circle
Problem 43236. Find my daddy long leg (No 's')
Created by: Jamil Kasan
Problem 2023. Is this triangle right-angled?
Created by: Tanya Morton
Tags pythagoras
Problem 2017. Side of an equilateral triangle
Created by: Tanya Morton
Problem 769. Calculate the area of a triangle between three points
Tags math, triangle
Problem 970. Piecewise linear interpolation
Created by: James
Problem 672. Longest run of consecutive numbers
Created by: James
Problem 44060. Volume Pillar
Created by: Erik Luiten
Problem 43215. Convert radians to degrees
Created by: Jamil Kasan
Problem 44660. Perimeter of a semicircle
Created by: Srishti Saha
Problem 44273. Given a square and a circle, please decide whether the square covers more area.
Created by: AMITAVA BISWAS
Created by: goc3
Problem 44309. Pi Digit Probability
Created by: Mehmet OZC
Problem 120. radius of a spherical planet
Created by: AMITAVA BISWAS
Problem 43298. Calculate area of sector
Created by: Jang geun Choi
Tags math, easy, matlab
Problem 167. Pizza!
Created by: the cyclist
Tags fun, pizza, good
Problem 42651. Vector creation
Created by: ruta bhat
Tags easy, vector
Problem 1024. Doubling elements in a vector
Created by: Abdelhak ARESMOUK
Problem 3076. Create a vector
Created by: Carlton
Tags vector, uab
Problem 2631. Flip the vector from right to left
Created by: Pritesh Shah
Problem 605. Whether the input is vector?
Created by: Sangeeta
Problem 1107. Find max
Created by: Marco
Tags find, vector, matrix
1 – 50 of 77
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# plot_direction_Aopt: Verify the optimality condition for the A-optimal design In SLSEdesign: Optimal Regression Design under the Second-Order Least Squares Estimator
plot_direction_Aopt R Documentation
## Verify the optimality condition for the A-optimal design
### Description
Verify the optimality condition for the A-optimal design
### Usage
``````plot_direction_Aopt(u, design, tt, FUN, theta)
``````
### Arguments
`u` The discretized design points. `design` The A-optimal design that contains the design points and the associated weights `tt` The level of skewness. `FUN` The function to calculate the derivative of the given model. `theta` The parameter value of the model.
### Details
This function produces the figure for the directional derivative of the given A-optimal design of the compact supports. According to the general equivalence theorem, for an optimal design, all the negative value of the directional derivative should be below zero line.
### Value
The plot of the negative value of the directional derivative of an A-optimal design
### Examples
``````poly3 <- function(xi, theta){
matrix(c(1, xi, xi^2, xi^3), ncol = 1)
}
design = data.frame(location = c(-1, -0.464, 0.464, 1),
weight = c(0.151, 0.349, 0.349, 0.151))
u = seq(-1, 1, length.out = 201)
plot_direction_Aopt(u=u, design=design, tt=0, FUN = poly3, theta = rep(0,4))
``````
SLSEdesign documentation built on June 22, 2024, 9:45 a.m.
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## Single Phase Synchronous Generator:
Certain applications, usually restricted to less than 10 kVA are better served by a Single Phase Synchronous Generator. Examples are emergency, domestic/office supply, portable power for construction tools etc. Because of simplicity of distribution wiring, these loads are better served by a single-phase arrangement. Single Phase Synchronous Generator stator winding can be arranged in two ways.
• A 12-lead three-phase winding connected to operate single-phase.
• Specialized single-phase wound stator.
In the first arrangement several connections are possible but all have to be derated compared to normal three-phase connection. Two connections are indicated in Fig. 8.74 and are compared to three-phase series star in terms of voltage and pu kVA rating.
In a Single Phase Synchronous Generator, while rotor is similar to that of a three-phase, stator is wound single phase with short-pitched coils (short pitch γ(= SPP) slots). Thus one third of stator slots are left unwound and winding has to be single layer. Obviously
the rating of the machine is 2/3rd that of three-phase wound generator. While the rotor has salient poles and produces a field distributed sinusoidally in space (because of shaping of pole faces), the stator which is single phase produces an oscillating field along a fixed axis. The expression for the fundamental component of stator field is as given in Eq. (5.36).
where
Equation (8.119) can be trigonometrically split as
when F1f is a sinusoidally distributed field rotating in positive direction of θ (forward rotating) and F1b is a backward rotating field. Both these fields rotate at synchronous speed as shown in Fig. 8.75 where fields are represented as rotating vectors F̅1f and F̅1b, while the resultant field is an oscillating vector F̅1 field in space.
The forward rotating stator field locks into the rotor field and both move together producing electromagnetic torque and causing conversion of energy from mechanical to electrical. Figure 8.76(a) shows the rotor and stator fields at the instant I1 (max). The corresponding phasor diagram is drawn in Fig. 8.76(b) wherein only those phasors which are stationary w.r.t. each are indicated. Assuming Xq to be small, the terminal voltage can be related to excitation emf Ee (suffix e is used to avoid confusion that would be caused by suffix f used so far) by Xd as obtained by OC and SC test. The effects caused by 1b which rotates at ω w.r.t. stator and at speed 2ω w.r.t. to rotor in opposite direction is discussed below.
Backward rotating field F1b induces second harmonic current in the field winding (and also damper winding) and fundamental frequency voltage in stator winding. The second harmonic current in the field winding causes an oscillating field along the d-axis at the same frequency. By the argument presented earlier this field can be split into two rotating fields rotating at ± 2ω w.r.t. rotor or 3ω and – ω w.r.t. stator. Thus the stator winding has induced in it third harmonic and fundamental frequency voltages. The fundamental frequency voltages induced in stator due to 1f and F̅1b are both accounted for in Xd. The third harmonic voltages induced in stator cause third harmonic current in the line. Unlike slot harmonics these cannot be eliminated (or attenuated) by chording. But their amplitude is reduced by self-inductance of the field winding, eddy currents in rotor and second harmonic currents in the damper bars.
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# Search by Topic
#### Resources tagged with Pedagogy similar to Developing the Classroom Culture: Using the Dotty Six Activity as a Springboard for Investigation:
Filter by: Content type:
Stage:
Challenge level:
##### Other tags that relate to Developing the Classroom Culture: Using the Dotty Six Activity as a Springboard for Investigation
Mathematical Thinking. Pedagogy. Problem solving. Rich Tasks. Questioning. Games. Shape, space & measures - generally. Enrichment. Team-building. Learning mathematics.
### There are 74 results
Broad Topics > Mathematics Education and Research > Pedagogy
### I'm Stuck!
##### Stage: 1 and 2
Being stuck is usually thought of as being a negative state of affairs. We want our pupils to succeed, not to struggle. Or do we? This article discusses why being stuck can be fruitful.
### Holywell Primary School and NRICH Action Research Project
##### Stage: 1 and 2
This article for teachers outlines one school's research project to explore how children, girls in particular, could be motivated in Maths through a more practical approach.
### A Japanese Mathematics Lesson
##### Stage: 1, 2 and 3
Jenni Way describes her visit to a Japanese mathematics classroom.
### Placing Our Trust in Learners
##### Stage: 1, 2 and 3
In this article Liz Woodham reflects on just how much we really listen to learners’ own questions to determine the mathematical path of lessons.
### Integrating Rich Tasks - Activity 2.1
##### Stage: 1 and 2
This professional development activity looks at what teachers can do to support learners engaging with rich tasks
### Integrating Rich Tasks - Activity 1.2
##### Stage: 1 and 2
These two tasks are designed to support professional development on integrating rich tasks. You are asked to think about what problems that encourage Higher Order Thinking Skills look like.
### Integrating Rich Tasks - Activity 1.1
##### Stage: 1 and 2
This is activity 1.1 in the series of activities designed to support professional development through integrating rich tasks. This activity looks specifically at what makes an activity "rich".
### Integrating Rich Tasks - Activity 1.3
##### Stage: 1 and 2
This professional development activity encourages you to investigate what is meant by higher-order thinking skills.
### Developing Good Team-working Skills
##### Stage: 1, 2, 3, 4 and 5
Group work depends on effective team work. This article describes attributes of effective team work and links to "Team Building" problems that can be used to develop learners' team working skills.
### Meaningful Maths Trails
##### Stage: 1 and 2
Avril Crack describes how she went about planning and setting up a Maths trail for pupils in Bedfordshire.
### Number Sense Series: Developing Early Number Sense
##### Stage: 1
This article for teachers suggests teaching strategies and resources that can help to develop children's number sense.
### Integrating Rich Tasks - Activity 1.5
##### Stage: 1 and 2
This professional development activity encourages you to investigate what pupils are doing when they problem solving.
### Integrating Rich Tasks - Activity 3
##### Stage: 1 and 2
The aim of this professional development activity is to successfully integrate some rich tasks into your curriculum planning.
### Working with Luke
##### Stage: 1 and 2
In this article for teachers, Liz Woodham describes conversations with Luke, aged 7, as they worked on some mathematics together.
### Working with Highly Able Mathematicians
##### Stage: 1 and 2
In this article for teachers, Bernard describes ways to challenge higher-attaining children at primary level.
### Problem Solving and the New Curriculum
##### Stage: 1 and 2
Is problem solving at the heart of your curriculum? In this article for teachers, Lynne explains why it should be.
### Haringey 2014-2015
##### Stage: 1 and 2 Challenge Level:
Find out about the five-term project (January 2014 to July 2015) which NRICH is leading in conjunction with Haringey Council, funded by London Schools Excellence Fund.
### What's the Difference Between Rich Tasks and Low Threshold High Ceiling Ones?
##### Stage: Early years, 1 and 2
In this article for teachers, Lynne explains the difference between 'rich tasks' and 'low threshold high ceiling' tasks, using examples from the website.
##### Stage: 1 and 2
Liz Woodham describes a project with four primary/first schools in the East of England, focusing on rich mathematical tasks and funded by the NCETM.
### Integrating Rich Tasks - Activity 1.4
##### Stage: 1 and 2
This professional development activity encourages you to investigate how rich tasks and problem solving link together.
### A Maths Afternoon
##### Stage: 1 and 2
This article describes no ordinary maths lesson. There were 24 children, mostly Years 3 and 4, and there were 17 adults working with them - mothers, fathers, one grandmother and two grandfathers, a. . . .
### Maths and Creativity in Bristol
##### Stage: 1 and 2
This article for teachers describes NRICH's work with Creative Partnerships and three Bristol primary schools.
### Manipulatives in the Primary Classroom
##### Stage: 1 and 2
In this article for teachers, Jenni Back offers research-based guidance about the use of manipulatives in the classroom.
### Money Problems?
##### Stage: 1
Marion Bond investigates the skills needed in order for children to understand money.
### Going for Games
##### Stage: 1 and 2
In this article for teachers, Liz Woodham describes the criteria she uses to choose mathematical games for the classroom and shares some examples from NRICH.
### Stacks of Maths!
##### Stage: 1, 2 and 3
In this article for teachers, Bernard gives an example of taking an initial activity and getting questions going that lead to other explorations.
### Maths in the Victorian Classroom
##### Stage: 2 and 3
What was it like to learn maths at school in the Victorian period? We visited the British Schools Museum in Hitchin to find out.
### Calculating the Difference: A Discussion of the Use of Calculators in the English Primary Classroom.
##### Stage: 1 and 2
Clare Green looks at the role of the calculator in the teaching and learning of primary mathematics.
### Learning Mathematics Through Games: 3. Creating Your Own Games
##### Stage: 1
Not all of us a bursting with creative game ideas, but there are several ways to go about creating a game that will assist even the busiest and most reluctant game designer.
##### Stage: 1 and 2
In this article for teachers, Liz Woodham describes resources on NRICH that can help primary-aged children get to grips with negative numbers.
### Cultivating Creativity
##### Stage: 1, 2, 3, 4 and 5
Creativity in the mathematics classroom is not just about what pupils do but also what we do as teachers. If we are thinking creatively about the mathematical experiences we offer our pupils we can. . . .
### Numbers and Notation - Ambiguities and Confusions
##### Stage: 1
While musing about the difficulties children face in comprehending number structure, notation, etc., it occured to the author that there is a vast array of occasions when numbers and signs are used. . . .
### Understanding Fractions
##### Stage: 1 and 2
This article, written for primary teachers, links to rich tasks which will help develop the underlying concepts associated with fractions and offers some suggestions for models and images that help. . . .
### What's Inside/outside/under the Box?
##### Stage: 2 and 3
This article describes investigations that offer opportunities for children to think differently, and pose their own questions, about shapes.
### Working Effectively with All Learners
##### Stage: 1, 2, 3, 4 and 5
Some questions and prompts to encourage discussion about what experiences you want to give your pupils to help them reach their full potential in mathematics.
### Take a ... Geoboard
##### Stage: 1 and 2
This article for teachers explains why geoboards are such an invaluable resource and introduces several tasks which make use of them.
### Blog It
##### Stage: 1, 2, 3, 4 and 5 Challenge Level:
Members of the NRICH team are beginning to write blogs and this very short article is designed to put the reasoning behind this move in context.
### Using Rich Tasks in an Objective Led Culture
##### Stage: 2, 3 and 4
As teachers, we appreciate the need to have clear objectives at the start of lessons but have been aware of the limitations this sometimes seems to place on our ability to get the most out of using. . . .
### Using Rich Tasks for the First Time
##### Stage: 2, 3, 4 and 5
The teachers involved in the Engaging Mathematics Projectwanted to embed rich tasks from the NRICH website into their curriculum for all KS3 and KS4 students. In this article, the teachers share. . . .
### Kingsfield School - Building on Rich Starting Points
##### Stage: 1, 2, 3, 4 and 5
Alf and Tracy explain how the Kingsfield School maths department use common tasks to encourage all students to think mathematically about key areas in the curriculum.
### Co-operative Problem Solving: Pieces of the Puzzle Approach
##### Stage: 1, 2, 3 and 4
The content of this article is largely drawn from an Australian publication by Peter Gould that has been a source of many successful mathematics lessons for both children and student-teachers. It. . . .
### Teaching Fractions with Understanding: Part-whole Concept
##### Stage: 1, 2 and 3
Written for teachers, this article describes four basic approaches children use in understanding fractions as equal parts of a whole.
### Crossing Bridges
##### Stage: 1, 2, 3, 4 and 5
An article for teachers based on a lecture and workshop activities at the NZAMT conference in New Zealand 2007
### Enriching Patterns
##### Stage: 1, 2, 3 and 4
Following on from a workshop at an MA Easter conference, Jennifer and Jenni talked about the way in which the website is made more accessible to teachers who want to plan threads of. . . .
### The Development of Spatial and Geometric Thinking: 5 to 18
##### Stage: 1, 2, 3 and 4
This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .
### Outside the Box
##### Stage: 2 and 3
This article explores the links between maths, art and history, and suggests investigations that are enjoyable as well as challenging.
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0
# What is the greatest common factor of 315 and 693?
Updated: 2/20/2024
Wiki User
β 10y ago
The greatest common factor of 525 and 693 is 21.
Wiki User
β 13y ago
Temperance Hunnisett
Lvl 2
β 5mo ago
Wiki User
β 11y ago
The GCF is 1.
Wiki User
β 10y ago
The GCF is 7
Izzy Bear
Lvl 2
β 9mo ago
donβt know
Wiki User
β 10y ago
It is: 63
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Q: What is the greatest common factor of 315 and 693?
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### What is the greatest common factor of 63 and 693?
Since 63 is a factor of 693, it is automatically the GCF of this problem.
### What is the GCF of 525 and 693?
The greatest common factor (GCF) of 525 and 693 is 21.
### What is the greatest common factor and least common multiple of 63 and 77?
Greatest common factor (GCF) =7 Least common multiple (LCM) =693
### What are the common factors of 410 and 693?
The common factor of 410 and 693 is 1.
### What is the greatest common factor of 231 and 693?
For 231, 147 the LCM is: 1,617
The GCF is 3.
### What is the Greatest Common Factor of 1233 and 603?
The greatest common factor of 1,463 and 1,045 is 209.
### What is greatest common factor and least common multiple of 63 and 77?
Greatest Common FactorThe difference between the two numbers, 77 - 63, is 14. It they have a greatest common factor other than 1, it is 14 or a factor of 14, such as 2 or 7. The numbers are not divisible by 14, but they are divisible by 7, so the greatest common factor is 7.Another way to determine the greatest common factor is to find all the factors of the numbers and compare them.The factors of 63 are 1, 3, 7, 9, 21, and 63.The factors of 77 are 1, 7, 11, and 77.The common factors are 1 and 7. Therefore, the greatest common factor is 7.The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together.The prime factors of 63 are 3, 3, and 7.The prime factors of 77 are 7 and 11.The prime factors in common are a single 7, so the greatest common factor is 7.Least Common MultipleThe least common multiple of two numbers is their product divided by their greatest common factor: 63 x 77 ÷ 7 = 693.
### Common factor of 693 and 189?
1, 3, 7, 9, 21, 63
### How do you use the factor tree for 693?
693 231,3 77,3,3 11,7,3,3
### What is the multiple of 63?
63, 126, 189, 252, 315, 378, 441, 504, 567, 630, 693, . . .
### What is the least common multiple of 7 9 and 11?
The LCM of 7, 9, and 11 is 693, their product.
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Kids Worksheet Linear Equations Worksheet: 2nd Grade Word Problems Worksheets Printable Money Games For 2nd Grade 2nd Grade Regrouping | Milesquarefabricstudio
## Milesquarefabricstudio Think Positive, Think In Math Grade 5
Home » Kids Worksheet Linear Equations Worksheet
# Kids Worksheet Linear Equations Worksheet
#### Odd And Even Number Worksheets For 2nd Grade
Math Grade 5 September 16, 2020.
On the first day of each month the canteen cooks hamburgers. The Cook needs 1/10 of a kg of mince, 1/8 of a lettuce and 1/5 of a lettuce for each burger. How much of each item does the Cook need to have on hand Read More...
## 2nd Grade Word Problems Worksheets
Math Grade 5 September 16, 2020.
The game is then played exactly like a normal game of bingo, with the teacher playing the part of the bingo caller, but instead of the teacher calling out the numbers printed on the cards, the teacher instead calls out math problems (the teacher may Read More...
## Printable Money Games For 2nd Grade
Math Grade 5 September 16, 2020.
ALEKS, my personal favorite, uses artificial intelligence software to routinely assess what a student actually knows, reinforce the areas that they need extra help in, and moves them through a pie chart of skills with interactive lessons and explanations that students view along the way. Read More...
###### Measurement Word Problems 2nd Grade Worksheets
Math Grade 5 September 16, 2020.
I believe the program I have created can solve the problem of how to teach math concepts through play. It provides a clear and progressive framework but also needs the commitment of a parent or teacher to guide, direct and pose the challenges that will Read More...
## Halloween Math Worksheets 2nd Grade
Math Grade 5 September 16, 2020.
If you are looking for printable worksheets for your preschool child, the array of choices can be a little intimidating. You may just be looking for a few pages to keep your child occupied with something more constructive than yet another half hour in front Read More...
Math Grade 5 September 16, 2020.
If you are looking for printable worksheets for your preschool child, the array of choices can be a little intimidating. You may just be looking for a few pages to keep your child occupied with something more constructive than yet another half hour in front Read More...
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Math Grade 5 September 16, 2020.
Children who struggle in a traditional learning environment can also get great benefit from digital learning games. Interactive platforms provide a fun way to learn without fear of failure and give rewards that are in line with what is being learned. Through games, your child Read More...
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Math Grade 5 September 16, 2020.
When learning arithmetic, repeatedly doing sums for a long period, with little variation, can soon get boring for many students. Before long, their attention can start to wonder, and as we all know - this is not conducive to learning. Quite the opposite, students generally Read More...
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Jul 21 comment Compute integral $\int_{-6}^6 \! \frac{(4e^{2x} + 2)^2}{e^{2x}} \, \mathrm{d} x$ After doing the change of variables, shouldn't it be $u^2$ instead of $e^{2u}$ in the numerator? Jul 21 comment Motivation for definition of logarithm in Feynman's Lectures on Physics I just saw in the feynmanlectures.info site that this has been added to the errata. Awesome! Jul 20 comment Find all solutions, other than $2$ for $12x^3-23x^2-3x+2=0$ @Austin: You don't need to ask. You could just plug in those values and check whether they satisfy your equation. Jul 19 comment Help solving differential equation: $y' = x\sqrt{4+y^{2}}/{y(9+x^{2})}$ The right side of the equality can be written as $\frac{\sqrt{4+y^2}}{y} \frac{x}{(9+x^2)}$. Does this help? Jul 16 accepted Motivation for definition of logarithm in Feynman's Lectures on Physics Jul 15 comment Motivation for definition of logarithm in Feynman's Lectures on Physics I get it now, thank you! This paragraph is really weird, considering that the rest of the lectures is very well written and clear. Jul 15 comment Motivation for definition of logarithm in Feynman's Lectures on Physics @joriki: That really helps. Thanks! Jul 15 asked Motivation for definition of logarithm in Feynman's Lectures on Physics Jul 15 comment Is the function $y=\ln x^2$ the same as $y=2\ln |x|$? Short answer: yes. Jul 14 revised Problems regarding exponents Not smart to use the same letters as in the assignments Jul 14 comment Problems regarding exponents @Rick: Yeah, I think I'll change it. Thanks for the advice! Jul 14 answered Problems regarding exponents Jul 7 comment I have to show $(1+\frac1n)^n$ is monotonically increasing sequence Unless I'm missing something, that sequence is increasing, not decreasing. Jul 1 accepted Does this weird sequence have a limit? Jun 30 comment Does this weird sequence have a limit? That's interesting. Does this change if instead of picking a number from ${1,2,3,4,5,6}$ we choose a random real number, or maybe one from the interval $[0,1]$? Jun 30 comment Does this weird sequence have a limit? @anon: Making a needlessly complicated definition was sort of the point. Also, you don't necessarily have to choose $k$ randomly. You can start from $1$ and work your way up if you want; the point is not so much in what order the terms are calculated, but that you can calculate $a_k$ for any $k$ you want. Jun 30 comment Does this weird sequence have a limit? @AndréNicolas: What I mean if that $a_k$ has already been calculated, there is no need to roll the die again. We just look at the list and check what was the value of $a_k$. Jun 30 asked Does this weird sequence have a limit? Jun 24 awarded Nice Question Jun 23 revised Expanding out summation signs transformed image into latex, hope I read it right
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See more ideas about 5 little monkeys, five little monkeys, counting backwards. These counting worksheets feature larger numbers with two or three digits. 8 Count forwards and backwards in 10s from 64 9 Is this always, sometimes or never true? No login required. DONATE To count by 2s, you add 2 to get the next number. Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. 5 10 15 35 30 5 What numbers are represented? counting backwards counting backwards from 20 counting back from 20 missing numbers to 20 Teach your children to count backwards from 20 to 10 to 1 This handy worksheet gives your children the opportunity to count forwards and backwards within 20 whilst recognizing and writing missing numbers to consolidate place value and number formation. Make the most of our display and blank charts, mazes, themed and standard exercises, and more. More Skip Counting Worksheets. Other math worksheets organized by topic and grade are available. Expand your childâs learning on backward skip counting with our unlimited supply of printable worksheets. Counting on and back worksheet. * UPDATED GRAPHICS June 2014 *Color and Black/White Puzzles Included Focus Numbers: By 2s (2-20) By 3s (3-30) By 5s (5-50) By 10s (10-100) Backwards ⦠There are 16 wheels. Count Backward by 4s | Complete the Path. How to skip count. C'mon kids, help the scuba driver reach the pearl oyster by skip counting backward by fours. The problems are based on skip counting by 2s to 12s in mixed proportions. View US version. Practicing counting patterns with skip counting worksheets helps your child build addition, multiplication, and pattern recognition abilities. Great number square games which will help you to find numbers up to 100 on the number square and count on and back. Skip counting is a part of building number sense. These worksheets make learning to skip count fun and simple, as kids practice while connecting the dots, writing numbers in footballs, and counting change. Skip Counting Backwards by 2. For K-12 kids, teachers and parents. These can be areas where students struggle!3 board-games are included: Counting backwards by 2s from 100Counting backwards by 5s from 240Counting backwards by 10s from It can help you with adding tens and ones and learning to count to 100. Counting Backward - Displaying top 8 worksheets found for this concept.. Are you looking for skip counting by 2s, 5s, 10s, or 4s? Coconut Ordering. Follow these steps to make your worksheet. Counting Backward by 2s. 6 Complete the number tracks. They start at the specified number on the number line and mark the squares as they count backwards. You can find skip counting worksheets here to help practice. Correlating the math operations âadditionâ and âsubtractionâ as forward and backward counting, math fluency in basic operations is achieved. Counting Worksheets. Similar: Skip counting by 8s Skip counting backwards by 2s See more ideas about Counting backwards, Math activities, Frog activities. Worksheets: Counting backwards by 5s. ... Grade 1 Number Chart Worksheet Keywords: Grade 1 Number Chart Worksheet - counting backwards by 2's math practice printable elementary school Created Date: A mix of a fun theme and meticulous design, this set of pdf backward counting by 4s resources provides oodles of practice to learners in grade 2 and grade 3. There are three levels in these maze puzzles. 4 Complete the number tracks. Displaying top 8 worksheets found for - Back Counting From 20. Talk to a partner. This pack of 6 fun worksheets helps children to practice their backward counting with a variety of sheets from 20-0, 50-0 and 100-0 to allow teachers to differentiate to suit their pupils. Answers: 1. Counting Backward by 3s Concurrent learnings through worksheets for 2nd grade are counting coins, currency exchange for bills and skip-counting by 2âs, 5âs and 10âs. Skip counting by 2 is the starting point for children in learning how to count.More worksheets are provided below. These free skip counting worksheets will give your students the pen and paper practice they need when reviewing skip counting skills. Backward counting is a crucial skill that children need to develop in order to have a ⦠Report a problem. These simple board games allow students to practise their skip counting skills in pairs - counting occurs BACKWARDS and beyond 100. Once your child is done counting you can go back and count each twin individually to check your work. Created: Jun 28, 2011 | Updated: Feb 23, 2014. Sep 27, 2014 - Explore Melodie Kroll's board "Counting Backwards" on Pinterest. 8 circles and 10 circles in the boxes. There are 3 ⦠The first printout is simple. There are 9 pictures of twins. Number Puzzles (Skip Counting: By 2s, 3s, 5s, 10s, & Backwards from 10) 60 Puzzles Free Sample in PREVIEW. Odd and even numbers. Students should work from the beginning of the chart (the largest numbers) working towards the smallest numbers. Hide Ads About Ads. 4.3 16 customer reviews. Below are five versions of our grade 2 math worksheet on skip counting backwards by 5s. There are two colorful icons above this first grade worksheet. 1st Grade Counting Backwards Worksheet Answers â Check Answers Quickly. Printing is Easy. Counting Backward 2 - Displaying top 8 worksheets found for this concept. Start counting by twos in the first box and write a 2 underneath the first set of twins. Now have a go at this worksheet about counting on and back in 2s. Each maze in this section has different themes and scenarios. Backward counting will now be a most likable and lovable affair. This resource is designed for UK teachers. Numbers within 20. Show Ads. Number Chart - counting backwards by 2's Grade 1 Number Charts 200 198 196 180 174 172 160 156 138 132 128 118 112 102 84 82 72 66 60 48 38 28 26 18 12 4 2 Count by -2 from 200 to 2. Fill in the missing numbers! Author: Created by mandyjayne23. (415) 828-4153 toniskittyrescue@hotmail.com. Feel the irresistible charm of counting down with our backward counting by 2s worksheets. These number charts are pdf files. The worksheets on this page start with a certain number of specific bills, then progress to mixed bills and finally to ⦠Counting backwards and forwards. Some of the worksheets for this concept are Skip counting backwards by 2s, Counting backwards a, 84 77 70 63 56 49 42 35 28, Counting backwards a, Skip counting backwards by 5s, Disco count backwards by ten, Coloring on backward counting, Name. To work on these counts by 2s worksheets, children have to be always aware of the orders of the counting based on the skipped numbers.Memory becomes the most important element which supports this activity. Not Flash. HOME: ABOUT US: SHOP: PRIVACY: CONTACT : Counting - Forwards & Backwards. Backward Skip Counting. Counting money is the next step when students know basic monetary values and can use skills like skip counting to figure out how many bills add up to a particular dollar value. Some of the worksheets for this concept are 8 14 18 24 28, Math made easy, Count from 1 to 20 1 20 count backwards from 20 to 1 20 1, Grade 1 number chart work, Count back to subtract, Count by 10s, Skip counting by 2s, Halloween jack o lantern connect the dots 1 20. Once students can count to 100, they can move on to practicing counting by 2s, 5s and 10s. Some of the worksheets for this concept are Elementary math work, Counting backwards a, Skip counting backwards by 2s, Count backwards by fives, Name, 84 77 70 63 56 49 42 35 28, Count backwards by 10s, Grade 1 number chart work. Follow us on FB. Number and Place Value » Counting » Counting in 2s Support students to count forwards and backwards in 2s and begin to spot and discuss patterns that emerge when counting in 2s. When counting in 2s, all the numbers are even. count and write dominos fractions graph and chart greater and less than heavier or lighter longer or shorter missing numbers level 1 missing numbers level 2 more or less number matching number-line number ordering scramble numbers sequence skip counting ⦠Select a Level of Difficulty: - Easy (Remove 2-4 numbers per row) - Medium (Remove 4-6 numbers per row) - Hard (Remove 6-9 numbers per row) 3. Number Charts and counting worksheets for 1st grade. Apr 14, 2019 - Explore Emma Kelly's board "Counting backwards" on Pinterest. 2. To skip count you add the same number over and over. 0 10 40 30. In this counting worksheet, students practice counting backwards by twos. When you count normally (like 1,2,3,4,5,6) you add 1 to get the next number. The most important aspect of our math website is usability. Read more. Select a Backward Counting Patterns/Skip Counting: Counting by 1s, 2s, 3s, 5s, or 10s. With a multitude of exercises to count down by 2s to 12s, this assemblage of worksheets is a must-have among children. We want to make it easy for students, parents, and math teachers to use our educational materials. Then move on to 4, 6, 8, and so on. 2. Click on the missing numbers and choose the correct answer. Counting Worksheets Guide. Counting by 1s, 2s, 3s, 5s, 10s, etc. ... counting_on_back_in_steps_of_1. How do you know? Check out the full skip count index page. Counting on and back in 2s - Activity 2. from Pearson. Counting Backwards 1 20 Worksheets - total of 8 printable worksheets available for this concept. Skip Counting Maze. Preview. You can start at any number. Counting backward is not a tall order! Counting Backward Worksheets Having honed skip counting forward, here we present you with yet another skill of backward counting. 1. Free counting worksheets and resources. How to count.More worksheets are provided below build addition, multiplication, and so on 2014 - Explore Kroll. ÂAdditionâ and âsubtractionâ as counting backwards in 2s worksheet and backward counting, you add 2 to the... With a multitude of exercises to count by 2s, you add the same over... Worksheets feature larger numbers with two or three digits learnings through worksheets for 2nd grade are counting coins, exchange! In this section has different themes and scenarios of the chart ( the largest )., mazes, themed and standard exercises, and pattern recognition abilities âsubtractionâ... Skip-Counting by 2âs, 5âs and 10âs '' on Pinterest math counting backwards in 2s worksheet in basic operations is achieved counting with unlimited... ) you add 1 to get the next number the squares as they count backwards grade counting backwards '' Pinterest! The most important aspect of our grade 2 math worksheet on skip counting is a part building. Monkeys, five little monkeys, five little monkeys, five little monkeys, five little,! You with adding tens and ones and learning to count by 2s, 5s counting backwards in 2s worksheet 10s, 10s! With skip counting backwards by 5s students practice counting backwards worksheet Answers â check Answers Quickly looking for skip is. Skip-Counting by 2âs, 5âs and 10âs to skip count you add 2 to get the number..., mazes, themed and standard exercises, and math teachers to use our educational materials with a multitude exercises. Learning to count down by 2s to 12s, this assemblage of worksheets is a among. To 12s, this assemblage of worksheets is a must-have among children back and count twin! Currency exchange for bills and skip-counting by 2âs, 5âs and 10âs 3s, and! Your child is done counting you can find skip counting worksheets here to help practice provided below concept! Worksheet, students practice counting backwards worksheet Answers â check Answers Quickly basic. You count normally ( like 1,2,3,4,5,6 ) you add 1 to get next... Your work - Activity 2. from Pearson is achieved 2 to get the next number Patterns/Skip counting: counting 2s! By 2s worksheets Melodie Kroll 's board `` counting backwards worksheet Answers check! Forward, here we present you with yet another skill of backward counting will now be a likable! Five versions of our grade 2 math worksheet on skip counting is a must-have among.! For skip counting with our unlimited supply of printable worksheets to get the next number as they count.. Language, plus puzzles, games, quizzes, worksheets and a forum each. Reviewing skip counting forward, here we present you with adding tens and ones and learning to count by,... Charm of counting down with our backward counting, math fluency in basic is! And over practice they need when reviewing skip counting backwards by twos the! The pearl oyster by skip counting forward, here we present you with adding tens and and! To check your work in learning how to count.More worksheets are provided below 2. from.... Five little monkeys, five little monkeys counting backwards in 2s worksheet five little monkeys, little! 2 math worksheet on skip counting worksheets feature larger numbers with two or three digits your students pen... Forwards & backwards from the beginning of the chart ( the largest numbers working! ÂSubtractionâ as forward and backward counting, math activities, Frog activities another... Counting backwards '' on Pinterest like 1,2,3,4,5,6 ) you add 2 to get the number... Printable worksheets counting by 2 is the starting point for children in learning how to count.More worksheets provided! Worksheet, students practice counting backwards and pattern recognition abilities donate Great number square games which will help you yet... 5S and 10s your childâs learning on backward skip counting worksheets feature numbers. Recognition abilities at the specified number on the number square games which will help to. Emma Kelly 's board `` counting backwards by 5s worksheets helps your child build addition, multiplication and! Most important aspect of our display and blank charts, mazes, themed and standard exercises, and.... 8, and more 2019 - Explore Emma Kelly 's board `` counting by... Found for this concept missing numbers and choose the correct answer you add 2 to get the number. Operations âadditionâ and âsubtractionâ as forward and backward counting by 1s, 2s, you add 1 counting backwards in 2s worksheet get next! In this section has different themes and scenarios you count normally ( like 1,2,3,4,5,6 ) you add 1 get! Different themes and scenarios worksheets for 2nd grade are available, multiplication, and math teachers to our! Skip-Counting by 2âs, 5âs and 10âs through worksheets for 2nd grade are counting coins, exchange. With skip counting worksheets here to help practice PRIVACY: CONTACT: counting - forwards & backwards Quickly. A go at this worksheet about counting backwards '' on Pinterest found for this concept number on missing! Colorful icons above this first grade worksheet 1 to get the next number counting backward -! Kroll 's board `` counting backwards to skip count you add 1 to get the next number has themes! On skip counting skills five little monkeys, five little monkeys, five little monkeys, backwards... Once students can count to 100 most important aspect of our display and blank charts mazes! Are counting coins, currency exchange for bills and skip-counting by 2âs, 5âs and 10âs numbers and the. Counting worksheet, students practice counting backwards by 5s or 10s working towards the smallest numbers to practicing patterns. See more ideas about counting counting backwards in 2s worksheet and back in 2s 28, 2011 Updated! Addition, multiplication, and math teachers to use our educational materials numbers are represented and count each twin to. Move on to practicing counting by 2s to 12s, this assemblage of worksheets a! Worksheets Having honed skip counting by 1s, 2s, all the numbers are even with... Now have a go at this worksheet about counting on and back in 2s - Activity 2. from Pearson math. A 2 underneath the first set of twins sep 27, 2014 - Explore Melodie Kroll 's board `` backwards... Can count to 100, they can move on to 4, 6 8! The missing numbers and choose the correct answer 100 on the missing numbers and choose correct! 2 is the starting point for children in learning how to count.More worksheets are provided below multitude of exercises count. A 2 underneath the first box and write a 2 underneath the first box write. And pattern recognition abilities parents, and so on specified number on the number square and count and... Go back and count on and back in 2s - Activity 2. from Pearson children in learning how to worksheets. Of exercises to count to 100, they can move on to practicing counting patterns with counting! In basic operations is achieved back in 2s - Activity 2. from.... Kelly 's board `` counting backwards, math activities, Frog activities this..... When reviewing skip counting by 2s worksheets worksheets helps your child build addition, multiplication, so! The most of our grade 2 math worksheet on skip counting skills supply of printable.! Reach the pearl oyster by skip counting skills ( the largest numbers ) working towards the smallest numbers 30. Games, quizzes, worksheets and a forum, you add the number! Down by 2s, you add 1 to get the next number aspect our... Math teachers to use our educational materials students, parents, and math to!, sometimes or never true and write a 2 underneath the first box and write a 2 the. Beginning of the chart ( the largest numbers ) working towards the smallest.. Our display and blank charts, mazes, themed and standard exercises and. You add the same number over and over with yet another skill of backward counting down our! A go at this worksheet about counting backwards '' on Pinterest 8 worksheets found for this.... Count backwards ideas about counting on and back in 2s we present you with adding and! The starting point for children in learning how to count.More worksheets are provided counting backwards in 2s worksheet. C'Mon kids, help the scuba driver reach the pearl oyster by skip counting worksheets your... Towards the smallest numbers it can help you with yet another skill backward. Practice they need when reviewing skip counting is a part of building number sense grade 2 worksheet! 8, and math teachers to use our educational materials helps your child is done counting you can skip. A go at this worksheet about counting backwards by twos you count normally ( like 1,2,3,4,5,6 ) you the! 2S - Activity 2. from Pearson Kelly 's board `` counting backwards '' Pinterest... Select a backward counting Patterns/Skip counting: counting - forwards & backwards, 5âs and 10âs honed counting! Backward counting will now be a most likable and lovable affair the pen and paper practice they need when skip... Math fluency in basic operations is achieved important aspect of our display and charts. By 2 is the starting point for children in learning how to count.More are. 10 15 35 30 5 What numbers are even now have a go at this worksheet about on. Is this always, sometimes or never true grade worksheet with adding counting backwards in 2s worksheet ones. Part of building number sense â check Answers Quickly section has different themes and scenarios backward - Displaying 8. A must-have among children there are two colorful icons above this first grade worksheet worksheets will give your the!, quizzes, worksheets and a forum can go back and count on back! And so on 2014 - Explore Emma Kelly 's board `` counting backwards '' on Pinterest '' on..
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Free Online Converters > Convert Quarts (u.s. Fluid) Into Trillion Cubic Feet
Here you can Convert units of Quarts (u.s. Fluid) to Trillion Cubic Feet units, find all information about Quarts (u.s. Fluid). So, enter your unit's value in Left Column like Quarts (u.s. Fluid)(if you use standard resolution on most non-HD laptops. FULL HD resolution starts at 1920 x 1080). Otherwise, if you use a lower value, enter the value in the box above. The Result / another converted unit value shell appears in the Left or below Column.
# Convert Quarts (u.s. Fluid) Into Trillion Cubic Feet
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##### conversion Table / conversion Chart
1 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
2 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
3 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
4 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
5 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
6 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
7 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
8 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
9 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
10 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
11 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
12 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
13 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
14 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
15 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
16 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
17 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
18 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
19 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
20 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
21 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
22 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
23 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
24 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
25 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
26 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
27 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
28 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
29 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
30 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
31 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
32 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
33 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
34 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
35 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
36 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
37 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
38 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
39 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
40 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
41 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
42 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
43 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
44 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
45 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
46 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
47 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
48 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
49 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
50 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
50 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
51 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
52 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
53 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
54 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
55 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
56 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
57 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
58 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
59 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
60 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
61 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
62 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
63 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
64 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
65 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
66 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
67 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
68 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
69 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
70 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
71 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
72 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
73 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
74 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
75 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
76 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
77 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
78 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
79 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
80 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
81 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
82 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
83 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
84 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
85 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
86 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
87 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
88 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
89 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
90 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
91 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
92 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
93 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
94 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
95 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
96 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
97 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
98 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
99 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
100 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
101 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
102 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
103 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
104 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
105 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
106 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
107 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
108 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
109 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
110 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
111 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
112 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
113 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
114 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
115 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
116 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
117 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
118 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
119 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
120 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
121 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
122 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
123 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
124 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
125 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
126 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
127 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
128 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
129 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
130 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
131 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
132 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
133 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
134 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
135 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
136 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
137 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
138 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
139 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
140 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
141 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
142 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
143 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
144 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
145 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
146 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
147 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
148 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
149 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
150 Quarts (u.s. Fluid) = 0 Trillion Cubic Feet
## how many Quarts (u.s. Fluid) Into Trillion Cubic Feet
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How Many Kilolitres in Quarts (u.s. Fluid)
How Many Koku in Quarts (u.s. Fluid)
How Many Litres in Quarts (u.s. Fluid)
How Many Megalitres in Quarts (u.s. Fluid)
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CC-MAIN-2023-06
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https://gitlab.com/gpaw/gpaw/-/commit/127df967aa3c22b25e79bab5e9d1c68cf16789a5
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Commit 127df967 by Tuomas Rossi
### Explain replaying propagation in more detail
parent d0e7f242
... ... @@ -7,8 +7,7 @@ atoms.center(vacuum=6.0) # Poisson solver with increased accuracy and multipole corrections up to l=2 from gpaw import PoissonSolver poissonsolver = PoissonSolver(eps=1e-20, remove_moment=1 + 3 + 5) poissonsolver = PoissonSolver(eps=1e-20, remove_moment=1 + 3 + 5) # Ground-state calculation from gpaw import GPAW ... ...
.. _lcaotddft: =================================================== Time-propagation TDDFT with LCAO: Theory and usage =================================================== ================================ Time-propagation TDDFT with LCAO ================================ This page documents the use of time-propagation TDDFT in :ref:LCAO mode . The implementation is described in Ref. [#Kuisma2015]_. ... ... @@ -59,15 +59,16 @@ from t to t+\mathrm dt by solving This procedure is repeated using 500--2000 time steps of 5--40 as to calculate the time evolution of the electrons. .. _example: Example usage ============= First do a standard ground-state calculation with the GPAW calculator: First we do a standard ground-state calculation with the GPAW calculator: .. literalinclude:: lcaotddft.py :lines: 3-21 :lines: 3-20 Some important points are: ... ... @@ -85,19 +86,25 @@ Some important points are: the vacuum size. See the documentation on :ref:advancedpoisson. Next the calculation proceeds as in the grid mode with TDDFT object. We kick the system in the z direction and propagate 3000 steps of 10 as: Next we kick the system in the z direction and propagate 3000 steps of 10 as: .. literalinclude:: lcaotddft.py :lines: 23-35 :lines: 22-34 After the time propagation, the spectrum can be calculated: .. literalinclude:: lcaotddft.py :lines: 37-39 :lines: 36-38 This example input script can be downloaded :download:here . The previous example as a complete script can be downloaded here: :download:lcaotddft.py. Extending the functionality --------------------------- The real-time propagation LCAOTDDFT provides very modular framework for calculating many properties during the propagation. See :ref:analysis for tutorial how to extend the analysis capabilities. General notes about basis sets ... ... @@ -110,7 +117,7 @@ is required that the basis set can represent both the occupied basis sets for the time propagation should be generated according to one's need, and then benchmarked. **Irrespective of the basis sets you choose, ALWAYS, ALWAYS, benchmark LCAO **Irrespective of the basis sets you choose always benchmark LCAO results with respect to the FD time-propagation code** on the largest system possible. For example, one can create a prototype system which consists of similar atomic species with similar roles as in the parent system, but small ... ... @@ -165,6 +172,8 @@ it is again emphasized that when using the basis sets, **it is essential to benchmark their suitability for your application**. .. _parallelization: Parallelization =============== ... ... @@ -188,16 +197,60 @@ but in this case only a single core is used for linear alrebra. Add ParallelTimer example Advanced analysis tools ======================= .. _analysis: Modular analysis tools ====================== In :ref:example it was demonstrated how to calculate photoabsorption spectrum from the time-dependent dipole moment data collected with DipoleMomentWriter observer. The code is not limited to this analysis but any (also user-written) analysis tools can be embedded in the general time-propagation framework. However, any (also user-written) analysis tools can be embedded as a separate observers in the general time-propagation framework. There are two ways to perform analysis: 1. Perform analysis on-the-fly during the propagation:: # Read starting point td_calc = LCAOTDDFT('gs.gpw') # Attach analysis tools MyObserver(td_calc, ...) # Kick and propagate td_calc.absorption_kick([1e-5, 0., 0.]) td_calc.propagate(10, 3000) For example, the analysis tools can be DipoleMomentWriter observer for spectrum or Fourier transform of density at specific frequencies etc. 2. Record the wave functions during the first propagation and perform the analysis later by replaying the propagation:: # Read starting point td_calc = LCAOTDDFT('gs.gpw') # Attach analysis tools MyObserver(td_calc, ...) # Replay propagation from a stored file td_calc.replay(name='wfw.ulm') From the perspective of the attached observers the replaying is identical to actual propagation. The latter method is recommended, because one might not know beforehand what to analyze. For example, the interesting resonance frequencies are often not know before the time-propagation calculation. In the following we give an example how to utilize the replaying capability in practice and describe some analysis tools available in GPAW. Example ------- Here we describe some analysis tools available in GPAW. We use a finite sodium atom chain as an example system. First, let's do the ground-state calculation: ... ... @@ -211,7 +264,7 @@ Recording the wave functions and replaying the time propagation --------------------------------------------------------------- We can record the time-dependent wave functions during the propagation with WaveFunctionWriter() observer: with WaveFunctionWriter observer: .. literalinclude:: lcaotddft_Na8/td.py ... ... @@ -228,7 +281,7 @@ We can use the file to replay the time propagation: .. literalinclude:: lcaotddft_Na8/td_replay.py The update keyword in propagator has following options: The update keyword in replay() has following options: ============== =============================== update variables updated during replay ... ...
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https://engineerexcel.com/why-does-flow-become-turbulent/
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# Why Does Flow Become Turbulent?
Fluid dynamics – and more specifically, fluid flow – is the study of how fluids (both liquid and gas) move when subjected to unbalanced forces. Flow can either be laminar or turbulent.
Laminar flow occurs when fluid particles are moving together in the same direction in parallel paths. It’s defined as smooth, steady motion where there are no disturbances or eddies. Turbulent flow is characterized by fluid particles that may travel in the same general direction but whose motion is noticeably more chaotic. Rather than traveling in parallel paths, the fluid particles collide and mix, creating eddies and disturbances. Turbulent flow usually results from low viscosity fluids moving at high velocities.
This article will describe the differences between laminar and turbulent flows in greater detail, introduce the Reynolds number and explain how it is used, and identify real world applications that incorporate turbulent flow.
## Why Flow Becomes Turbulent
The type of fluid flow is primarily dependent on the viscosity of the fluid and the velocity at which it is moving. Laminar flow is smooth and often occurs when fluids are either more viscous or moving at a slower pace.
Imagine a highly viscous fluid like maple syrup being poured from a bottle. Even if the syrup were moving at a high velocity, the syrup is viscous enough that its individual particles would still tend to travel in parallel paths because there is too much friction and resistance for them to overlap. It would take a very high velocity for inertia to overcome the viscous force.
Turbulent flow occurs when the opposite criteria are met. Flow tends to be turbulent when there is a low-viscosity fluid moving at a high velocity. Low-viscosity fluids have minimal resistance between individual particles so moving at a moderately high velocity generates enough inertia to overcome the resistance between particles. Because the inertia force is dominant, particles are able to move in random directions and mix.
## Determining Type of Flow Numerically
Fluid flow is divided into three regimes: laminar, transitional (or critical), and turbulent. The most common method for determining flow regime is to calculate the Reynolds number, which is a unitless value that represents the ratio between inertia forces and viscous forces. This is a numerical interpretation of the correlation between inertia and viscous forces described in the previous section.
### Calculating and Using the Reynolds Number
The Reynolds number can be calculated using the following equation:
where:
• Re = Reynolds number (unitless)
• V = velocity (m/s)
• d = length or diameter (m)
• µ = viscosity (Ns/m2)
• ρ = density (kg/m3)
• ν = kinematic viscosity (m2/s)
Re < 2000 represents laminar flow, Re > 4000 is turbulent flow, and the range where 2000 > Re > 4000 is referred to as transitional or critical flow.
Viscosity, density, and kinematic viscosity are determined by the fluid itself and therefore are not variable. The only variables in the Reynolds equation that would cause flow to change from laminar to turbulent are velocity and diameter. Those two parameters are directly proportional to the Reynolds number so as velocity and diameter increase, the Reynolds number also increases and flow enters (or approaches) the turbulent range.
### Exceptions to the Reynolds Equation
It’s worth noting that the Reynolds equation assumes the fluid being used is incompressible and of constant viscosity. The flow of compressible fluids (gasses) is evaluated using other calculations, including the continuity equation and the Navier-Stokes equation. Fluids that do not have a constant viscosity, known as non-Newtonian fluids, are also treated differently. Non-Newtonian fluids like ketchup, quicksand, and paint will change viscosity based on forces applied to them.
## Practical Examples and Analyses Entailing Turbulent Flow
Turbulent flow is encountered in many scientific fields such as engineering, aerodynamics, meteorology, and biology. Some scenarios are straightforward and can be analyzed relatively easily, like trying to calculate friction and flow rate in a pipe. Trying to optimize the shape of a vehicle for aerodynamics (air flow) is a bit more complex and requires different analytical methods.
### Computational Fluid Dynamics
Computational Fluid Dynamics, also known as CFD, is a specific branch of fluid mechanics that is used to solve problems related to fluid flow. CFD analysis is used in a variety of science industries, notably aerodynamics, weather simulation, environmental engineering, and heat transfer.
Because turbulent flow is constantly fluctuating and chaotic, it is difficult to analyze numerically. Many people working with fluid problems on a regular basis rely on high-tech computers and software to run simulations and calculations. Simulation software can be used to analyze everything from the airflow around a plane’s landing gear to the projected path of pollution from factory exhausts.
### Pipe Flow Analysis
Engineers designing pipe systems have many important parameters to evaluate. Laminar and turbulent flow may not be the main problem they’re solving, but the type of flow still makes a difference.
The friction factor for laminar flow in a pipe is calculated using the Reynolds number and the only variables are fluid velocity and pipe diameter. However, calculating the friction factor for turbulent flow requires both the Reynolds number and the surface roughness of the pipe. The first step is to calculate the Reynolds number and determine the type of flow, then plug the Reynolds number into the appropriate equation and find the friction factor. The friction factor is then used to calculate other parameters like flow rate, pressure drop/head loss, and the power requirements for a pump.
### Heat Transfer
Mechanisms designed for heat transfer are heavily dependent on turbulent flow. Convection calculations use a unitless value called the heat transfer coefficient, which is a numerical representation of how efficiently heat transfers from a flowing fluid to the surface around it. The heat transfer coefficient is proportional to the Reynolds number so the coefficient increases as the Reynolds number increases. Therefore, turbulent flow has a greater heat transfer coefficient than laminar flow and transfers heat much faster and more efficiently.
Turbulent flow is utilized in many forced convection systems such as heat exchangers, air conditioners, and fans, as well as natural convection phenomena like a breeze or tectonic plates that rely solely on buoyancy and gravity.
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# If sin(A) = 3/5, what is sin(2A)?
Unit 5: Trigonometric Relationships
Lesson 5 of 15
## Big Idea: How do the double angle formulas follow from the sum and difference formulas?
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# How Proposition Bets Work
## NFL Prop Bets — What they are about
Proposition bets are commonly used in NFL betting, especially when it comes to the Super Bowl. This type of bet happens when a bookie plans a certain case scenario and enables you to put your bet on this scenario (will it happen or not). Proposition bets are part of a bigger bet group called exotic bets. As the name itself says, an exotic bet is when you can bet on different elements of a game besides the final outcome (such bets are props, parlays or futures).
## Here are some examples of proposition bets:
This type of bet is definitely an exciting one, because there is a large element of unknown. Even when you can’t plan anything about it, and will not have a big return on your bet (because it is not very wise to place a large bet on something completely unpredictable), it is still a lot of fun!Below you can see a few proposition bets that are being offered for the 2010-2011 NFL season.
## Some Examples of 2010-2011 NFL Prop Bets
Popular proposition bets in season 2010-2011 involved Chad Ochocinco and Terrell Owens, two controversial NFL players.There were bets that aimed to predict how Terrell would end the season in a term of fines, and how will he compare to Ochocinco in that aspect, another problematic player. This bet predicted that Ochocinco will earn more fines, because he was younger than Owens and kind of had more passion and lack of control, thus being more prone to break the rules.
## Why are Proposition Bets Attractive?
Proposition bets are interesting because they are almost impossible to predict (its outcome).You get a different outlook on betting possibilities that are possible to base on analysis of previous results and games, such as in moneyline and over/under bets. They are attractive because they give you a moment of surprise, so to speak.
## Is Playing Proposition Bets a Good Choice?
If you want a reasonable answer, it would be to avoid prop bets. Most obvious reason is that there is no way to implement logic or analysis in these bets. Yeah, sometimes there are some statistics that could be analyzed, but these are rare cases, and proposition bets are just a game of luck. In the above example, in order to place an informed bet on number of Owens fines when compared to Ochocinco, you would have to know their health status (especially in regard to mental condition), and there is no way to analyze this.So, if you want to try your luck in prop bets, we can only advise you to play it low and not put much money in this type of bet—not more than 5% of your betting funds.Sources:ESPN: http://espn.go.com/nfl/player/stats/_/id/2584/chad-johnsonHuffingtonPost: http://www.huffingtonpost.com/2015/02/01/katy-perry-super-bowl-outfits_n_6582762.html
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# last minute store ticks
42
Hi im trying to create an array with a lenght of 59, where each value stores the tick number second by second.
i have simplified the code here, I can also define it from 1 to 59 using for or while but after few ticks it says "array out of range" 263
``` time = TimeSeconds(TimeCurrent());
array_price_difference[time] = (Bid - open_price)*100000;
```
15902
1. florenceale: I can also define it from 1 to 59 using for or while but after few ticks it says "array out of range" 263
Show all relevant code. Like your definition of array_price_difference and its context.
2. `array_price_difference[time] = (Bid - open_price)*100000;`
Don't hard code constants. Your 100000 breaks on JPY pairs and metals. Divide by _Point instead.
3. Do you realize that you're not going to get a tick each second, so what you're doing with the array may be bogus. What if there are no ticks during a specific candle period? There can be minutes between ticks during the Asian session, think M1 chart.
"Free-of-Holes" Charts - MQL4 Articles
No candle if open = close ? - MQL4 and MetaTrader 4 - MQL4 programming forum
A wrap around buffer may be better:
```double array_price_difference[60]; int iLast=0;
void newTick(void){ array_price_difference[++iLast % 60] = Bid - open_price; }
int getDiff(int iTick){ return array_price_difference[(iLast - iTick + 60) % 60]/_Point; }```
getDiff(0) is the current value, getDiff(1) is the previous, etc.
42
i have this:
```aopen[0] = iOpen(0,PERIOD_CURRENT,0); //this returns the opening price correctly
int time = TimeSeconds(TimeCurrent()); //this returns the number of seconds correcty. Sometime if the trade is very slow we have to consider that some seconds can be skipped
cur_var = (Bid - aopen[0])*100000; //and this returns the ticks positive of negative are passed from the beginning of the current candle.
```
this is the base modifying it with _Point as u said.
my goal now should be to define a period inside the minute, like ten seconds...and understand every ten seconds how big is the tick variation.
42
whroeder1:
1. Show all relevant code. Like your definition of array_price_difference and its context.
2. Don't hard code constants. Your 100000 breaks on JPY pairs and metals. Divide by _Point instead.
3. Do you realize that you're not going to get a tick each second, so what you're doing with the array may be bogus. What if there are no ticks during a specific candle period? There can be minutes between ticks during the Asian session, think M1 chart.
"Free-of-Holes" Charts - MQL4 Articles
No candle if open = close ? - MQL4 and MetaTrader 4 - MQL4 programming forum
A wrap around buffer may be better:
yes i had considered that we could have seconds with no ticks, and also seconds with more ticks...but i think i will use this in fast moments of trading where surely all the seconds have ticks. Anyways ill checkout your link.
15902
florenceale: my goal now should be to define a period inside the minute, like ten seconds...and understand every ten seconds how big is the tick variation.
Why don't you just create a EMA of the variations:
Not compiled, not tested.
```double roc10(void){
static double price[60]; static datetime when[60]; static int iLast=0;
datetime now = TimeCurrent();
if(when[iLast] != now){
iLast = (iLast + 1) % 60;
when[iLast] = now;
}
price[iLast] = Bid;
static double roc=0;
#define SMOOTHING 5
static const double alpha = 2.0 / (SMOOTHING+1);
#define SECONDS_BACK 10
int i = (iLast - SECONDS_BACK + 60) % 60;
roc += alpha*( (Bid - price[i]) / (now - when[i]) )
return roc;
}
void OnTick(void){
double roc = rac10();```
Not compiled, not tested.
42
whroeder1:
Why don't you just create a EMA of the variations:
Not compiled, not tested.
Not compiled, not tested.
ok ill study a little bit the code you wrote me and ill tell you if i can make it works. Thanks a lot.
42
maybe is not the most stylish code, i have studied this language from just few weeks...but now it works. I made that it fills the gaps by itself, with the previous values, every second now has a value. I took some idea from yours. Thanks for help
```double roc10(void){
static double price[60];
static datetime when[60];
static int iLast=1;
static int s;
static int tempo_a=0;
static int tempo_c[10];
static int dif_tempo;
static int old_price;
price[0]=(Bid-(iOpen(0,PERIOD_M1,0)))*100000;
//tempo_c[0]=0;
Print(iOpen(0,PERIOD_M1,0));
if(iLast == 1){
tempo_c[iLast]=TimeSeconds(TimeCurrent());
iLast = 2;
dif_tempo = tempo_c[1]-tempo_c[2];
//when we have gaps
if(dif_tempo>1){
for(s=1; s <= dif_tempo; s++ ){
price[tempo_c[2]+s]=price[tempo_c[2]];
}
}
//when go back to beginning with gap
if(dif_tempo<0){
for(s=1; s <= tempo_c[1]; s++ ){
price[0+s]=price[0];
}
}
price[tempo_c[1]]=(Bid-iOpen(0,PERIOD_M1,0))*100000;
}
if(iLast == 2){
tempo_c[iLast]=TimeSeconds(TimeCurrent());
iLast = 1;
dif_tempo = tempo_c[2]-tempo_c[1];
//when we have gaps
if(dif_tempo>1){
for(s=1; s <= dif_tempo; s++ ){
price[tempo_c[1]+s]=price[tempo_c[1]];
}
}
//when goes back to beginning with gap
if(dif_tempo<0){
for(s=1; s <= tempo_c[2]; s++ ){
price[0+s]=price[0];
}
}
price[tempo_c[2]]=(Bid-iOpen(0,PERIOD_M1,0))*100000;
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https://pustudy.com/calculators/convert/power/Watt_to_kW.html
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Watts to kilowatts conversion
Enter the power in watts and press the Convert button:
Enter power in watts: W Kilowatts result: kW
kW to watts conversion calculator
How to convert watts to kilowatts
1kW = 1000W
Watts to kilowatts conversion formula
The power in kilowatts P(kW) is equal to the power in watts P(W) divided by 1000:
P(kW) = P(W) / 1000
Example
Convert 1300W to kilowatts:
P(kW) = 1300W / 1000 = 1.3kW
Watt to kilowatts conversion table
Power (watts) Power (kilowatts)
0 W 0 kW
1 W 0.001 kW
10 W 0.01 kW
100 W 0.1 kW
1000 W 1 kW
10000 W 10 kW
100000 W 100 kW
1000000 W 1000 kW
kW to watts conversion ►
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Enter the voltage (amps), the current (amps), and the power factor into the calculator to determine the Three Phase Power.
## Three Phase Power Formula
The following formula is used to calculate the Three Phase Power.
P = V*I*PF*SQRT(3)
• Where P is the Three Phase Power (watts)
• V is the voltage (amps)
• I is the current (amps)
• PF is the power factor
## How to Calculate Three Phase Power?
The following example problems outline how to calculate Three Phase Power.
Example Problem #1
1. First, determine the voltage (amps). In this example, the voltage (amps) is determined to be 23 .
2. Next, determine the current (amps). For this problem, the current (amps) is measured to be 20 .
3. Next, determine the power factor. In this case, the power factor is found to be 15.
4. Finally, calculate the Three Phase Power using the formula above:
P = V*I*PF*SQRT(3)
Inserting the values from above and solving yields:
P = 23*20*15*SQRT(3) = 11,951.15 (watts)
Example Problem #2
Using the same method as above, determine the variables required by the formula. For this example problem, these are:
voltage (amps) = 10
current (amps) = 4
power factor = 8
Enter these given values into the calculator or above yields:
P = 10*4*8*SQRT(3) = 554.25 (watts)
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# In my precalculus class we are learning how to do long and synthetic division of polynomials by hand. I am struggling with a particular problem because I cannot find an example that divides a polynomial by something more complex than x+a. I'm working with:(6x^4 -3x^3 +29x^2) ÷ (3x^2 +13) If you could give me an example of this solved by hand that I could use for reference for solving other similar problems I would be very appreciative.
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In my precalculus class we are learning how to do long and synthetic division of polynomials by hand. I am struggling with a particular problem because I cannot find an example that divides a polynomial by something more complex than x+a.
I'm working with:
(6x^4 -3x^3 +29x^2) ÷ (3x^2 +13)
If you could give me an example of this solved by hand that I could use for reference for solving other similar problems I would be very appreciative.
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# Nut Cutting Time – The #1 Problem in the World Today
The #1 problem in the world today.
I am gifted at math. Really. I taught myself how to multiply and divide when the rest of my class was learning addition. I scored in the top .1% nationally in math in the 8th grade. In high school, I could picture the meaning of formulas where most others were just plugging in numbers. The other day, however, I was surprised when I read the following question and answer:
Q: How wide would a piece of paper be if it were folded in half 103 times?
A: If in fact it were possible to fold a piece of paper that many times, it would be as wide as the known universe. That is- 93 billion light years wide
A single piece of paper is only .0039 inches thick. So it is hard to imagine it’s growth being anything near that substantial. It troubled me that I had no common sense of what that answer would be. I did more research. As it turns out, the “exponential curve” is not intuitive to human beings at all. It’s like we all sort of have a mathematical blind spot. Check it out here: https://www.youtube.com/watch?v=AAwabyyqWK0
In the history of humans, we have never had much of a need to understand exponential functions. But we are in the middle of an exponential function going on right now, that is the world’s human population.
Take a moment to try to take in the meaning of this chart. The biggest problem in the world today isn’t HIV or hunger or crime, it is our own population growth. This is not sexy, it doesn’t make headlines, but it’s absolutely true.
But the general populous isn’t reacting to it like we should. I believe this is because it goes against our nature so much. We naturally want to reproduce; we naturally want to cure disease when we see a friend in need of it; for example. We don’t think about the world’s population itself as a problem because we don’t see it as an immediate threat on our livelihood. It’s not tangible and it’s not intuitive.
But it is real.
Africa is the front line of the war on human sustainability. How much of Africa’s hunger, disease, and poverty is due to a lack of resources? If we shifted our charity money toward marketing for and providing contraception and education wouldn’t that be more beneficial? These are real questions that we should seriously be asking. Feeding and curing starving and diseased humans in a sexually uncontrolled environment is the same as adding fuel to a fire.
So what does this mean to you and me? Well, I’m starting with the man in the mirror. I am going to get a vasectomy (after now having two children) because I want to do my part to stop the fire. No one talks about this stuff. It’s kind of humiliating. But it shouldn’t be, and I recognize that. It is time to open up a discussion about the world’s biggest problem: It’s nut cutting time, ya’ll.
### Author: Jordan Haas
Jordan Haas is a Central Arkansas native and has been active in real estate for the last 11 years. He is a licensed real estate broker and holds licenses in property, casualty, life, and health insurance in the state of Arkansas. Jordan graduated from the University of Central Arkansas, earning a Bachelor of Science in Biology with a minor in business and also psychology. He obtained his Masters in Business Administration from the University of Arkansas at Little Rock with an emphasis on international business and sustainability. Jordan is active in the community as a player for the Little Rock Rugby Club, president of the Little Rock Landlord Association, and an instructor at the National School of Real Estate.”
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Math Home
# 5. Quotient Rule
### Quotient Rule
Let $$f$$ and $$g$$ be differentiable functions at the point $$a.$$ If $$g(a) \neq 0,$$ the quotient rule says that $\left(\frac{f}{g}\right)'(a) = \frac{f'(a)g(a)-f(a)g'(a)}{g^2(a)}$
Proof:
By the definition of derivative, \begin{align} \left(\frac{f}{g}\right)'(a) & = \lim_{h \rightarrow 0} \frac{\frac{f(a+h)}{g(a+h)}-\frac{f(a)}{g(a)}}{h} \\ & = \lim_{h \rightarrow 0} \frac{f(a+h)g(a)-f(a)g(a+h)}{hg(a)g(a+h)} \end{align} Now add and subtract $$f(a)g(a)$$ from the numerator. \begin{align} \lim_{h \rightarrow 0} \frac{f(a+h)g(a)-f(a)g(a+h)}{hg(a)g(a+h)} & = \lim_{h \rightarrow 0} \frac{f(a+h)g(a)-f(a)g(a)+f(a)g(a)-f(a)g(a+h)}{hg(a)g(a+h)} \\ & = \lim_{h \rightarrow 0} \frac{(f(a+h)-f(a))g(a)+f(a)(g(a)-g(a+h))}{hg(a)g(a+h)} \\ & = \lim_{h \rightarrow 0} \frac{f(a+h)-f(a)}{h} \cdot \frac{g(a)}{g(a)g(a+h)} - \frac{f(a)}{g(a)g(a+h)} \cdot \frac{g(a+h)-g(a)}{h} \\ & = f'(a) \cdot \frac{g(a)}{g(a)^2} - \frac{f(a)}{g(a)^2} \cdot g'(a) \\ & = \frac{f'(a)g(a)-f(a)g'(a)}{g(a)^2} \end{align}
### Examples
Find the derivative of $$\frac{x^2}{\text{sin}(x)}.$$
Solution:
By the power rule, the derivative of $$x^2$$ is $$2x.$$ The derivative of $$\text{sin}(x)$$ is $$\text{cos}(x).$$ So, by the quotient rule, $\frac{d}{dx}\frac{x^2}{\text{sin}(x)} = \frac{2x\text{sin}(x) - x^2\text{cos}(x)}{\text{sin}(x)^2}$
Find the derivative of $$\frac{e^x}{x^3}.$$
Solution:
The derivative of $$e^x$$ is $$e^x.$$ By the power rule, the derivative of $$x^3$$ is $$3x^2.$$ So, by the quotient rule, $\frac{d}{dx}\frac{e^x}{x^3} = \frac{x^3e^x - 3x^2e^x}{x^6}$
Find the derivative of $$\frac{\text{cos}(x)}{e^x}.$$
Solution:
The derivative of $$\text{cos}(x)$$ is $$-\text{sin}(x)$$ and the derivative of $$e^x$$ is $$e^x$$. So, by the product rule, $\frac{d}{dx}\frac{\text{cos}(x)}{e^x} = \frac{-\text{sin}(x)e^x - \text{cos}(x)e^x}{e^{2x}}$ This expression can be simplified to $-\frac{\text{sin}(x) + \text{cos}(x)}{e^{x}}$
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# Shared Flashcard Set
## Details
Module 7
Decision Making Statement Review
23
Computer Science
02/12/2020
Term
What are the only two answers for a computer?
Definition
True or False.
Term
If…Then is a decision structure that executes a set of statements when.....
Definition
a condition is true.
Term
¨When the question is ______, the statements after THEN (and down to ENDIF) execute. They are skipped if the question is _____.
Definition
True; False.
Term
In Visual Studio we use the ________ statement to tell the computer we want it to make a decision.
Definition
IF/THEN/ELSE
Term
What is this an example of? If a = b then c= 10 Else c=13 End If
Definition
IF/THEN/ELSE
Term
Else is __________.
Definition
Optional.
Term
If ELSE is used, the statements after the ELSE will execute if the “question” is ________.
Definition
Not true.
Term
If…Then…Else statement is within an If…Then…Else statement it is called what?
Definition
Nested/Nested Statement.
Term
What is this an example of? If intNum = 10 Then Me. lblMsg.text = “Ten” Else If IntNum > 10 Then Me.lblMsg.text = “More than 10” Else Me. lblMsg.text = “Less than 10” End If End If
Definition
Nested If Statement.
Term
An IF statement can have multiple else statements- each one a new question or condition to check. This is also called a(n) ___________.
Definition
Term
The following code is an example of what? If a = b Then c = 10 ElseIf a > b Then c = 14 ElseIf a < b Then c = 16 Else c = 12 End If
Definition
If/Then/ElseIf
Term
What is used instead of multiple else if statements?
Definition
Select Case Decision
Term
In select case, the _______ type should match the _______ type.
Definition
Value; Expression
Term
What muse you use with relational operators?
Definition
Case Is
Term
¨In most cases _____ is good for a ____ decision and a ______ is correct to use when there are multiple possible answers with only one correct answer.
Definition
If..Then/Single/Select Case
Term
__________ are used to create compound Boolean expressions.
Definition
Logical Operators.
Term
Which two operators do you use to form a boolean expression?
Definition
And or Or
Term
The order of precedence for logical operators is what?
Definition
Not, then And, then Or.
Term
When using And or & with IF, both (all) conditions MUST be ______ for the entire IF (or else if) question to evaluate to ______.
Definition
True; True.
Term
An _____ can also be used in assignment statements to set the value of a variable.
Definition
IF.
Term
To generate a random integer, we can use the what?
Definition
System Random Class.
Term
What What returns a random number between 0.0 and 1.0?
Definition
NextDouble
Term
________ returns a nonnegative random number between 0 and the MaxValue (2,147,483,647)
Definition
Next
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# Generator for Sine and other wave forms
## The source
There are many ways to produce sine waves with Arduino. You can
1. produce the samples "just-in-time" calculating immediately before sending
2. calculate them during setup
3. precalculate and store in SRAM
4. in FLASH
5. in EEPROM
6. on SD card
## The hardware interface
To send a signal to an audio device there are various methods like 1-bit-audio or PWM.
We are going to use an 8 bit digital-to-analog converter (DAC) which needs 8 pins of the Arduino but makes handling much easier. Also, you don't have to to prepare much when sending sampled sound; just normalize it, save it in a "low-quality" format like "mono, 16,000 samples per second, 8-bit", and store it on a micro SD card.
By the way: to connect the SD card, you need another 4 pins. Often pins 10, 11, 12, and 13 are used to communicate with the SD card. If you still want to use the Serial terminal (RX and TX) you run out of digital pins. (You can use the analog pins as digital ones if you like.)
If you run out of port pins you can also decide to use only a 6 bit DAC by setting the lower 2 bits to zero. This will of course result in some more loss of quality.
If it is only a very short sample (<1 second) you could use your sound editor to save it in ASCII format as a text file and #include it in you FLASH memory. (If you reduce the sample rate to 8,000 samples per second you might be able to store and reproduce the numbers from zero to nine.) By doing this you don't even need an SD card.
So, for speed reasons we better not use the Arduino digitalWrite() command. Instead we look for pins mapped to one or two ports and use the PORT commands.
## Some math
The following formula is to be used:
vt = [ 127 * ( sin(2 * PI * f * t) + 1) ]
where f is the desired frequency and t is the time given in seconds.
The "+ 1" makes sure no negative values will occur. The "127 *" is to use the maximum range available. It is like the automatic gain control of your tape recorder - if you ever had one. The "[ ]" is to round the floating point number to an integer number.
If you decide for option 3. to 6. and are using a spreadsheet software like Microsoft Excel to precalculate the values you might use this formula:
(enter this in cell A1)
=INT ( 127 * ( SIN ( 2 * PI() * COLUMN() / 256 ) + 1 ) )
users of the german version might use:
=GANZZAHL ( 127 * ( SIN ( 2 * PI() * SPALTE() / 256 ) + 1 ) )
and copy this formula to the right until cell IV1 . (So you filled 256 cells with the same formula).
You also can produce other signal forms as
sawtooth PORTn = b++; triangle PORTn = b++ < 128 ? b : 255 - b; square wave PORTn b++ < 128 ? 0 : 255; random noise PORTn = random(256); voice message PORTn = msg[t]; DTMF signals PORTn = sin(f1*t)+sin(f2*t);
where PORTn is the port of your microcontroller you are using and b is the byte we are going to send.
If you want to send sampled sound to the DAC you can easily use a "*.wav" file coded as Windows PCM, 1 channel (mono), 22050 samples per second, 8 bits per sample (mostly called unsigned), and just skip the 44 byte header.
## Implementation
Of course you could send the values to the ADC port in the loop() procedure with a delay of your choice. But it is much better to install a timer interrupt routine to do this. Recommended frequencies are:
• 8,000 Hz, time = 125 μ seconds
• 22,050 Hz, time = 45.35 μ seconds
To produce sine waves with Arduino we take this square wave generator, set it to the desired frequency and use either this or that digital to analog converter.
The picture above was taken from an oscilloscope using a six bit digital-to-analog converter and a sample rate of 8000 samples per second (this is what most PC sound cards offer as "telephone quality"). If you don't want the steps go for an analog oscillator. If you just want smaller steps you have to increase the sample rate and use more bits. You also have to find an Arduino port where you have access to all the bits (if you want to use port D you will loose the TxD and RxD pins which are used for the Serial terminal) or you have to combine the bits of two ports. We are using the pins d2 to d7 which belong to port D, and the pins d8 and d9 which belong to port B. Unfortunately, it is not possible to write to both port at the same time. But the delay is so short that it makes no difference.
```#define FILENAME "dac8.ino - 9.3.2014" #include /* DAC connected to PORT B and D /* Ports B & D: data d7 d6 d5 d4 d3 d2 d1 d0 pin 13 12 11 10 9 8 7 6 5 4 3 2 1 0 PORTB d1 d0 PORTD d7 d6 d5 d4 d3 d2 */ #define type 1 /* 1 sine 1000 Hz 2 sawtooth 122 Hz 3 triangle 31 Hz 4 square wave 61 Hz 5 random noise 6 voice msg 7 DTMF "1" (697 Hz and 1209 Hz) as an example (actually, the ATmega328 is a bit too slow for it. Reduce tcnt2 to 70) */ // SD card: const int chipSelect = 10; // SD card boolean sd_card = false; File fileHandle; boolean eof; boolean done = false; char* filename = "welcome.wav"; // Timer-2: const byte prescaler = 2; // 1:1, 2:8, 3:32, 4:64, 5:128, 6:256, 7:1024 const byte tcnt2 = 131; // 16000 Hz float t = 0; // seconds float dt = 1.0 / 16000; // seconds float f = 1000; // Hz float f1 = 697; // DTMF frequencies float f2 = 1209; byte sinetab[256]; void setup() { Serial.begin(9600); Serial.println(FILENAME); Serial.print("type "); Serial.println(type); if (type == 6) { Serial.println("Initializing SD card..."); // ------------ SD card ---------------: pinMode(chipSelect, OUTPUT); if (!SD.begin(chipSelect)) { Serial.println("Card failed, or not present"); return; } sd_card = true; Serial.println("card initialized."); openFile(filename); } if ((type == 1) || (type == 7)) for (int i = 0; i < 256; i++) sinetab[i] = 127 * (sin(2 * PI * i / 256) + 1); // ------------- DAC port pins --------: Serial.println("output: PORTB and PORTD"); delay(100); DDRB = B00000011 | DDRB; // remaining bits used for SD card DDRD = B11111100; // ------------- Timer ----------------: setupTimer(); DDRC = 1; } void openFile(char* s) { fileHandle.close(); fileHandle = SD.open(s); if (fileHandle != 0) eof = false; fileHandle.seek(44); // skip normal header } long count = 0; long time = millis() + 1000; void loop() { while (millis() < time); // wait time = millis() + 1000; Serial.println(count); // I am alive // the values printed prove: some of the interrupts are skipped count = 0; } //========================================================================= ISR(TIMER2_OVF_vect) { // all the work is done in here: TCNT2 = tcnt2; byte b; switch (type) { case 1: b = sine(t); break; // sine case 2: b = sawtooth(t); break; // sawtooth case 3: b = triangle(t); break; // triangle case 4: b = squareWave(t); break; // square wave case 5: b = randomNoise(t); break; // random noise case 6: b = voiceMsg(t); break; // voice msg case 7: b = dtmf(t); break; // DTMF "1" (697Hz and 1209Hz) } sendByte(b); t = t + dt; count++; TIFR2 = 0x00; } //========================================================================= void sendByte(byte b) { byte d; // b 7 6 5 4 3 2 1 0 // PORTB - - - - - - ^ ^ // PORTD ^ ^ ^ ^ ^ ^ - - d = b << 2; b = (b >> 6) | (PORTB & B11111100); PORTB = b; // nearly no time between the PORT commands PORTD = d; } //========================================================================= byte frac(float x) { // not a standard C function return 256 * (x - floor(x)); } byte sine(float t) { //return 127 * ( sin(2 * PI * f * t) + 1); // too slow!!! return sinetab[ frac(f * t) ]; } byte sawtooth(float t) { static byte b; return b++; } byte triangle(float t) { static byte b; static int8_t dir = 1; // toggle +/-1 b = b + dir; if ((b == 0) || (b == 255)) dir = -dir; return b; } byte squareWave(float t) { static byte b; return b++ < 128 ? 0 : 255; } byte randomNoise(float t) { return random(256); } byte voiceMsg(float t) { byte b = 128; if (!done) { if (fileHandle) { b = fileHandle.read(); eof = !fileHandle.available(); if (eof) done = true; } } return b; } byte dtmf(float t) { //return 63 * ( sin( 2 * PI * f1 * t) + sin( 2 * PI * f2 * t) + 2); byte s1 = sinetab[ frac(f1 * t) ] / 2; byte s2 = sinetab[ frac(f2 * t) ] / 2; return s1 + s2; } //========================================================================= void setupTimer() { int prescalers[] = {0,1,8,32,64,128,256,1024}; // see doc8271.pdf, p. 164 TIMSK2 = 0x01; // Timer2 INT Reg: Timer2 Overflow Interrupt Enable TCCR2A = 0x00; // Timer2 Control Reg A: Wave Gen Mode normal TCCR2B = prescaler; // Timer2 Control Reg B: Timer Prescaler set to 2 float clk = F_CPU / prescalers[prescaler]; float t1 = 1 / clk; float t2 = (256 - tcnt2) * t1; float f = 1 / t2; Serial.print("cpu frequency [Hz]: "); Serial.println(F_CPU); Serial.print("clock frequency [Hz]: "); Serial.println(clk); Serial.print("ISR frequency [Hz]: "); Serial.println(f); } ```
contact: nji(at)gmx.de
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purchased words from
to
24 Mar How to count Words in Excel
If you are working on a project that requires the use of spreadsheet, there are many times when you would want to know how to count words in Excel. It is fairly easy for someone who is proficient in Excel to be able to sum up numbers, add dates, convert rates and so on. However, everything that has to do with words in xls is a bit more tricky.
If you are reading this article in another language than English, it has been automatically translated by our WordPress Multilingual Plugin.
There are 5 main ways to count words in Excel:
Use Scrybs automated word counter
The first and most simple way is to use Scrybs’ word counter for free! Scrybs, as an online translation service needs to count the number words in documents submitted by our clients. This includes excel spreadsheets. Merely upload your spreadsheet and the word count will display in the bottom right.
Counting words by using embedded excel functions
There are two formulas that would assist you in finding the number of words in your spreadsheet:
A.) If you need to count the words inside a specific cell you can use specific excel functions. For example, if you need to count the number of words in cell A1, enter the below formula into cell B1 and then hit ENTER. If done correctly, it would count the number of words in cell A1.
`=IF(LEN(TRIM(A1))=0,0,LEN(TRIM(A1))-LEN(SUBSTITUTE(A1," ",""))+1)`
B.) If you have several cells within which you need a word-count for, the formula would be slightly altered. For example, if you wish to count the number of words in xls within cells A1:C7 you will be copying the below formula into cell D1. Once, done select Shift + Ctrl + Enter and the number of words in your selected cells will be displayed.
`=SUM(IF(LEN(TRIM(A1:C7))=0,0,LEN(TRIM(A1:C7))-LEN(SUBSTITUTE(A1:C7," ",""))+1))`
Using predefined functions
Another option to count words in Excel is by a predefined function. To do so, please follow the following instructions:
• Click on Developer, then go to Visual Basic and choose a new Microsoft Visual Basic for applications.
• Once the window is opened click on Insert, choose Module and input the following:
```Function intWordCount(rng As Range) As Integer intWordCount = UBound(Split(rng.Value, " "), 1) + 1 End Function```
• Now that you have defined the function, you can use it in an excel spreadsheet.
• For example, if you want to know the number of words you have in cell A1 you will need to enter the following formula into cell B1:
`=intwordcount(A1)`
• Hit the Enter key and you will have your word count!
It is important to note, however, that this method can only be used to count the number of words in a cell and not the number of words in a spreadsheet.
Using user defined functions in VBA
You can also count words in Excel by writing up user defined functions with VBA code.
Start by selecting the cell, or the range of cells you’d like to know the word count for. Once selected click on Developer, then go to Visual Basic and choose a new “Microsoft Visual Basic for Applications”. Once a window is opened click on Insert, choose Module and input the following:
```Sub CountWords() Dim WordCount As Long Dim Rng As Range Dim S As String Dim N As Long For Each Rng In ActiveSheet.UsedRange.Cells S = Application.WorksheetFunction.Trim(Rng.Text) N = 0 If S <> vbNullString Then N = Len(S) - Len(Replace(S, " ", "")) + 1 End If WordCount = WordCount + N Next Rng MsgBox "Words In ActiveSheet Sheet: " & Format(WordCount,"#,##0") End Sub```
Hit the Play button to bring the code to life, and the number of words in the selected portion will be shown in a pop-up box.
By using Kutools
Lastly, you can also use Kutools to count words in Excel:
You can install Kuttols for Excel and use this tool to count words in a cell or in a range of cells, easily with just few clicks.
Start by selecting the cell you want the result to be displayed in, then click on “Kutools”, go to “Formulas”, and click on “Count words in range”.
Inside the formula helper dialog box you’ll need to enter the cell or cells you wish to have the word count for. Then you would click on “OK”. This will result in the word count being displayed in your previously selected cell.
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Facts
# Lotteries And Luck: What Are Your Chances Of Winning?
Have you ever tried your luck in one of these things? I’m sure you have. Who hasn’t? Everyone wants to get instantly rich and enjoy a vacation in the Bahamas!
Lotteries don’t only include winning a lot of money, but it could come in any way. It is said that people who establish lottery systems claim to donate the money earned towards education systems but they end up using it for their personal use. Hence, if you buy a lottery ticket you think your money will go for the education of the poor but they end up in the wrong pockets, which is obviously not a good thing. This problem actually stretches far back to the 16th century, somewhere in Italy.
### How did lotteries begin?
The term ‘lotto’ was derived from lots or drawing lots, which is based on the game of chance. Even the United States seems to have a fever of lotteries such that the colony of Virginia was founded by the money raised from lotteries. And there were about 200 lotteries that took place between 1744 and the revolutionary war that funded libraries, bridges, roads, etc. Hence, they were always conducted as civic projects. Also, Princeton and Colombian universities are also brought up by lotto money.
We all have stress and anxieties and many complications in our lives that we want to get rid of and some people resort to gambling and lotteries in order to get rid of all of it. This leads to addiction as you feel like you have a shot at it and keep going and hence end up ruining everything that is good in your life.
### So how do they work?
If you’re playing a game of fifty balls with each one assigned a number, your odds of winning are 16 million to one. And if you add just one ball to that, making that fifty-one it shoots up to 76 million to one. If you have to pick 6 numbers out of the 50 balls, your chance is 50 to 6. So if you pick each of these and multiply them, that’s how you get the 16 million to one calculation. There are hardly any chances of winning, they are so risky.
If you ever win a lottery, the first thing to do is to sign the ticket because it’s so precious and whoever has it has to turn it in to win. The next thing you got to do is get a lawyer before you turn the ticket in. You don’t want to stand on a stage without an accountant and a lawyer by your side. And then you go and claim your winnings. Also, a part of your money goes to the taxes and the higher the prize, higher is the tax. You can be paid in intervals too. Suppose if you win 10 million dollars, you could be paid 250k initially and then it increases. You get checks every year.
They deal with it based on bonds or bond tickets whose prices increase after a certain period of time. This is done with the help of bond dealers and the lottery people contact multiple bond dealers who get the best rates and they package about a certain number of bonds to pay your prize. Once the bond matures, they get the money and you get the check. Some lottery dealers give you a choice between payment in lump sum and intervals. About 80% of people choose the lump sum. And some places don’t give this choice.
### Types of lotto machines
Air mix machine – this is the one with ping pong balls floating around in the air and there is a door that opens and the ping pong balls shoot one at a time.
Gravity pick lotto machine – this uses rubbery balls that are heavy and there are 2 paddles that move the balls. There is no air involved. There are 6 numbers one after the other and if you get them, you win.
### Pragati Atara
Just a curious little flower child pouring her heart out to make the world around her a better place...
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# How to determine whether 2 slopes are different when they are correlated?
#### Hanshananigan
##### New Member
Hi!
Let's say I have a variable "A" that I believe measures a trait, say, "greed".
I show 2 groups of pictures (say, 10 pics in each group) to 100 participants. The first group is associated with "wealth" (eg, gold, dollar bills) and the second group is associated with "neutral" stimuli, such as boring, household items. Participants rate both sets of pictures on a 10pt scale concerning how "exciting" each picture is. So I have variable "B" as the mean excitement rating for "wealth" pics and variable "C" as the mean excitement rating for "neutral" pics.
I hypothesize that variable A will be a better predictor of B than C. Although I could dichotomize variable A (hi/lo) and conduct a 2x2 RM ANOVA, I prefer to leave variable A as a continuous variable. The question, then, is how to statistically test this hypothesis?
I have found methods of comparing the correlations between A-B and A-C, which tells me about the strength of the relationship between 2 variables. However, I would like to test the difference in the slopes of the regression lines for A-B and A-C. I have found a method for comparing slopes for independent samples, but not for correlated samples (i.e., the same individual rated both B and C).
Any help with this would be greatly appreciated! Thanks in advance!
ps- am I posting this question in the correct forum?
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# JNTUA B.TECH R 19 4-2 Syllabus For Mathematical modeling & simulation PDF 2022
### Get Complete Lecture Notes for Mathematical modeling & simulation on Cynohub APP
You will be able to find information about Mathematical modeling & simulation along with its Course Objectives and Course outcomes and also a list of textbook and reference books in this blog.You will get to learn a lot of new stuff and resolve a lot of questions you may have regarding Mathematical modeling & simulation after reading this blog. Mathematical modeling & simulation has 5 units altogether and you will be able to find notes for every unit on the CynoHub app. Mathematical modeling & simulation can be learnt easily as long as you have a well planned study schedule and practice all the previous question papers, which are also available on the CynoHub app.
All of the Topic and subtopics related to Mathematical modeling & simulation are mentioned below in detail. If you are having a hard time understanding Mathematical modeling & simulation or any other Engineering Subject of any semester or year then please watch the video lectures on the official CynoHub app as it has detailed explanations of each and every topic making your engineering experience easy and fun.
### Mathematical modeling & simulation Unit One
#### Simulation Basics-
Simulation Basics-Handling Stepped and Event-based Time in Simulations-Discrete versus Continuous Modeling-Numerical Techniques-Sources and Propagation of Error
### Mathematical modeling & simulation Unit Two
#### Dynamical, Finite State, and Complex Model Simulations-
Dynamical, Finite State, and Complex Model Simulations-Graph or Network Transitions Based Simulations-Actor Based Simulations-Mesh Based Simulations-Hybrid Simulations
### Mathematical modeling & simulation Unit Three
#### UNIT-IIIConverting to Parallel and Distributed Simulations
Converting to Parallel and Distributed Simulations-Partitioning the Data-Partitioning the Algorithms-Handling Inter-partition Dependencies
### Mathematical modeling & simulation Unit Four
#### Probability and Statistics for Simulations and Analysis-I
Probability and Statistics for Simulations and Analysis-Introduction to Queues and Random Noise-Random Variates Generation-Sensitivity Analysis
### Mathematical modeling & simulation Unit Five
#### Simulations Results Analysis and Viewing Tools-Display Forms:
Simulations Results Analysis and Viewing Tools-Display Forms: Tables, Graphs, and Multidimensional Visualization-Terminals, X and MS Windows, and Web Interfaces-Validation of Model Results
### Mathematical modeling & simulation Course Objectives
This course focuses on what is needed to build simulation software environments, and not just building simulations using preexisting packages.
### Mathematical modeling & simulation Course Outcomes
After the completion of course, student will be able to Understand basic Model Forms.Understand basic Simulation Approaches.Evaluate handling Stepped and Event-based Time in Simulations.Distinguish Discrete versus Continuous Modeling.Apply Numerical Techniques.Calculate Sources and Propagation of Error.
### Mathematical modeling & simulation Text Books
1.JN Kapur, “Mathematical modelling”, Newage publishers2.Kai Velten, “Mathematical Modeling and Simulation: Introduction for Scientists and Engineers” Wiley Publishers
### Scoring Marks in Mathematical modeling & simulation
Information about JNTUA B.Tech R 19 Mathematical modeling & simulation was provided in detail in this article. To know more about the syllabus of other Engineering Subjects of JNTUH check out the official CynoHub application. Click below to download the CynoHub application.
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Browse Teasers
Search Teasers
## Family History
Logic Grid puzzles come with a handy interactive grid that will help you solve the puzzle based on the given clues.
Puzzle ID: #23655 Fun: (2.87) Difficulty: (2.98) Category: Logic-Grid Submitted By: Gadget
Mary and her four brothers had very similar histories. Determine when each was born, when they married, and when they died.
1. The oldest sibling married two years after the one born in 1921.
2. Mary had been married for 40 years when she died, and was born a year later than the brother who died in 1989.
3. The youngest sibling married a year before Joseph and died a year before Michael.
4. The one who married in 1950 died two years before the one who married in 1949.
5. The one born in 1923 married more than a year before Joseph, and died more than a year before him.
6. William is the only one with statistics that are all odd numbered years; Peter (whose dates are all even numbered) died a year after the one who married in 1946.
## What Next?
See another brain teaser just like this one...
Or, just get a random brain teaser
If you become a registered user you can vote on this brain teaser, keep track of
which ones you have seen, and even make your own.
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# 826662793354974
## 826,662,793,354,974 is an even composite number composed of four prime numbers multiplied together.
826662793354974 is an even composite number. It is composed of four distinct prime numbers multiplied together. It has a total of twenty-four divisors.
## Prime factorization of 826662793354974:
### 2 × 32 × 577 × 79593952759
(2 × 3 × 3 × 577 × 79593952759)
See below for interesting mathematical facts about the number 826662793354974 from the Numbermatics database.
### Names of 826662793354974
• Cardinal: 826662793354974 can be written as Eight hundred twenty-six trillion, six hundred sixty-two billion, seven hundred ninety-three million, three hundred fifty-four thousand, nine hundred seventy-four.
### Scientific notation
• Scientific notation: 8.26662793354974 × 1014
### Factors of 826662793354974
• Number of distinct prime factors ω(n): 4
• Total number of prime factors Ω(n): 5
• Sum of prime factors: 79593953341
### Divisors of 826662793354974
• Number of divisors d(n): 24
• Complete list of divisors:
• Sum of all divisors σ(n): 1794206883115920
• Sum of proper divisors (its aliquot sum) s(n): 967544089760946
• 826662793354974 is an abundant number, because the sum of its proper divisors (967544089760946) is greater than itself. Its abundance is 140881296405972
### Bases of 826662793354974
• Binary: 10111011111101100001101110001001011001111011011110 2
• Base-36: 850ZN7D23I
### Squares and roots of 826662793354974
• 826662793354974 squared (8266627933549742) is 683371373917448445690770540676
• 826662793354974 cubed (8266627933549743) is 564917688861424353633213534037977849973922424
• The square root of 826662793354974 is 28751744.1793532589
• The cube root of 826662793354974 is 93851.8411957293
### Scales and comparisons
How big is 826662793354974?
• 826,662,793,354,974 seconds is equal to 26,285,319 years, 41 weeks, 1 day, 13 hours, 42 minutes, 54 seconds.
• To count from 1 to 826,662,793,354,974 would take you about six billion, five million, thirteen thousand, two hundred ninety-nine years!
This is a very rough estimate, based on a speaking rate of half a second every third order of magnitude. If you speak quickly, you could probably say any randomly-chosen number between one and a thousand in around half a second. Very big numbers obviously take longer to say, so we add half a second for every extra x1000.
Note: we do not count involuntary pauses, bathroom breaks or the necessity of sleep in our calculation!
• A cube with a volume of 826662793354974 cubic inches would be around 7821 feet tall.
### Recreational maths with 826662793354974
• 826662793354974 backwards is 479453397266628
• The number of decimal digits it has is: 15
• The sum of 826662793354974's digits is 81
• More coming soon!
The information we have on file for 826662793354974 includes mathematical data and numerical statistics calculated using standard algorithms and methods. We are adding more all the time. If there are any features you would like to see, please contact us. Information provided for educational use, intellectual curiosity and fun!
Keywords: Divisors of 826662793354974, math, Factors of 826662793354974, curriculum, school, college, exams, university, STEM, science, technology, engineering, physics, economics, calculator.
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1. ## Word Problem Help
I need help with this stupid word problem. I'm at my girlfriend house and I left my book at home.
A stream flows at a rate of 4 mph. A boat travels 70 miles downstream and returns in a total time of 6 hrs. What is the speed of the boat in still water.
I am a complete retard when it comes to word problems. Can someone at least point out how I can get the correct formula for this?
2. Hi, I do not know if this is correct or not but this is going to be my best guess.
The boat travels for 6 hours and the stream flows at 4 mph.
In total that would be 24 MPH?
70-24=46 Mph
Not sure if it's correct as I said above but I think it should be.
EDIT: mine is completely wrong didn't see that it said STILL water.
3. Hello, BuhRock!
A stream flows at a rate of 4 mph.
A boat travels 70 miles downstream and returns in a total time of 6 hrs.
What is the speed of the boat in still water?
We know that: . $\text{(Distance)} \:=\:\text{(Speed)} \times \text{(Time)} \quad\Rightarrow\quad T \:=\:\dfrac{D}{S}$
Let $\,b$ = speed of the boat in still water.
Going downsream (with the current), the boat's speed is: . $b + 4$ mph.
To go 70 miles downsteam, it takes: $\dfrac{70}{b+4}$ hours.
Going upstream (against the current), the boat's speed is: . $b - 4$ mph.
To go 70 miles upstream, it takes: $\dfrac{70}{b-4}$ hours.
The total time is six hours.
There is our equation! . . . . . $\dfrac{70}{b+4} + \dfrac{70}{b-4} \:=\:6$
Multiply by $(b+4)(b-4)\!:\;\;70(b-4) + 70(b+4) \:=\:6(b+4)(b-4)$
. . which simplifies to: . $3b^2 - 70b - 48 \:=\:0$
. . which factors: . $(b-24)(3b + 2) \:=\:0$
. . and has roots: . $b \:=\:24,\:-\frac{2}{3}$
The boat's speed in still water is: . $24\text{ mph.}$
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## Determinism and Deterministic
### Question 1
What means deterministic (Determinism)?
### Question 2
Is our world deterministic?
### Question 3
Is our world completely controlled by physical laws?
### Question 4
Does the concept "deterministic" improve our understanding ?
### Question 5
Is there any relation between the concept "deterministic" and "Free will" ?
### Question 6
What is the solution of the conflict between "deterministic" and "Free will" ?
### Description
Accordingly to Webster determinism means:
The theory that all occurences in nature are (a) determined by antecedent causes or (b) take place in accordance with natural laws.
### Background
I am already involved with determinism when I was roughly 10 years of age. When the world is deterministic, in the sense that our world is fully controlled by physical laws, then we have no free will. In my opinion, even when I was young, both are not true.
Already during my youth, I realized, that the problem very much depents about definitions.
See Description above
• The problem with this definition is that it consists of two definitions marked a and b. This is confusing. It requires every time when you use the word deterministic that you have to specify which definition you mean: a or b
• IMO you can not mean both.
• Definition (b) includes two new concepts: "taking place accordant" and "natural laws". Those concept have to be explained.
Consider the following question: Is our world beautifull?
• Suppose you say: Yes. What "value" has that answer? What do you learn? Do you become any wiser?
• Suppose you answer: Some parts "yes", some parts "no". Such an answer at least allows you to investigate deeper.
The same problem also exist with this question under discussion.
No
Our world, the universe evolves on its own.
Laws are only descriptions of the way the universe behaves. Laws, in no way, influence what happens in our world. That does not mean that every thing can happen. There are limitations.
No.
• The concept "Free will" improves our understanding. It tells us that we do certain things in the way we select.
• Newton's Law describes the movement of the planets and more. It does not describe everything. For Example, Newton's Law does not tell us how many planets there are.
The problem is many people claim: Yes. Their argument is that our world is deterministic, meaning that all is controlled by physical laws. The consequence is that we can not have a "free will".
There are two problems . Which are those physical laws and what is the definition of "free will".
1. The physical law most often mentioned is Newton's law. The problem with Newton's law is how do you demonstrate that you can use this law to describe all. IMO that is impossible.
2. The problem with "free will" is that most people do not define "free will". They claim that "free will" is an illusion, because the world is deterministic. For more information about this subject go to Free will
The best solution to solve the conflict between determinsitic and "Free will" is not to use the word deterministic any longer. The word deterministic should only be used from a historic perspective. Our world is not deterministic. We can not describe our world, the total universe by any set of laws, nor by a concept like action is reaction. The last is much to vaque.
When you remove the word deterministic the word "Free will" (meaning that we ourself can select something, using our brains) becomes much easier to accept.
When you accept ""Free will" immediate also the isue of responsability is solved. Yes we are responsable for our actions.
When you do not use the word deterministic you also need the word "compatibilism". For more detail goto compatibilism
### Reflection part 1
The bigest problem with determistic is, that its believers think that the world is controlled by physical laws, without specifying exactly what those physical laws are, nor what controlled means. In a sense you replace one vaque concept by another vaque concept.
The next, disturbing, step then becomes that we start using the concept without truelly knowing and agreeing what we all mean.
### Reflection part 2
• You can not describe the world in all its complexity with some simple sentences.
• The concept "Deterministic" can never be used as an argument for something.
### Feedback
None
E-mail:nicvroom@pandora.be.
Created: 10 April 2000
Modified 14 August 2008
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Engineering Math - Calculus Integration Integration is expressed in mathematical form as shown below. If you have finished any cource for pre-calculus or calculus, you would almost automatically assosiate it with calculating the area of a closed shape. However, it is only one application of integration, not everything of integration even though original idea of integration might come from the motivation to calculate the area. (Watch this excellent Youtube Mechanical Universe 07 - Integration. If this link does not work, search in Youtube with "Mechanical Universe 07 - Integration" keyword). But I noticed that automatic association of Integration with the area often hinder me from understanding the practical meaning of many other form of integration. So I would like to show you a little generic form of integration rather than giving you too much impression of 'calculating the area'. Generic form of integration can be represented as shown below. As you see, "Integration" is a processing of "repeating a specific operation and summing up all the result". The real meaning of the integration is determined by what are the quantity and operator in the formula. See following examples and you will get familiar with how you interpret various Integral forms. Assuming you now have some intuitive understanding of "Integration", now let's get a little bit deeper into mathematical concept. One example is shown below. Associate this expression with the intuitive form you saw above. Actually this example is the one you would see in almost every Calculus/Pre-Calculus book. dx in this example represents 'width' of a rectangle and f(x) represents the height of a rectangle. The operator between dx and f(x) is 'multiplication'. So the meaning of f(x) dx is the area of a small rectangle. If you represents the meaning of the whole integral equation, it can be represented as shown below. If we represent this process into a spreadsheet format which you may give you more intuitive form, it can be represented as shown below. Let's look at another example as shown below. In this example, you see a lot of vectors in blue arrow and vectors in red arrow. You see the red vector is sitting on top of a curve (path) shown in red curve. Each of the red vector is the tangential to each point on the path. Now I want to take the inner product of each red vector and blue vector and sum them all. This operation can be represented in a mathematical form as shown below. This kind of integration is called "Line Integral". Let's look at another example as shown below. In this example, you see a lot of vectors in blue arrow and vectors in red arrow. You see the red vector is sitting on top of a curve (path) shown in red curve. Each of the red vector is the tangential to each point on the path. Now I want to take the inner product of each red vector and blue vector and sum them all. This operation can be represented in a mathematical form as shown below. The mathematical operation is exactly same as the one shown in previous example. The only difference is the path the red vectors are going along. The path in this example is a closed curve. This kind of integration is called "Circular Integral" (The closed path need not to be exact circle as below. It can be any arbitrary shape of closed curve). Let's look at another example as shown below. In this example, you see two vectors in each segments of the surface. one of the vector is normal to each surface segment(This vector is called 'normal vector'). The other vector is an arbitrary angle to the normal vector . Now I want to take the inner product of each red vector and blue vector and sum them all. This operation can be represented in a mathematical form as shown below. The mathematical operation is exactly same as the one shown in previous example. The only differences is that this operation goes along the surface. This kind of integration is called "Surface Integral".
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Cody
# Problem 82. Remove the small words from a list of words.
Solution 1372924
Submitted on 8 Dec 2017 by Kendale Greenidge-Bullock
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
inStr = 'ours is not to reason why'; outStr_correct = 'ours not reason why'; assert(isequal(remove_small_words(inStr),outStr_correct))
2 Pass
inStr = 'To be or not to be That is the question'; outStr_correct = 'not That the question'; assert(isequal(remove_small_words(inStr),outStr_correct))
3 Pass
inStr = ' He is a dirty so and so'; outStr_correct = 'dirty and'; assert(isequal(remove_small_words(inStr),outStr_correct))
4 Pass
inStr = 'oh me oh my'; outStr_correct = ''; assert(isequal(remove_small_words(inStr),outStr_correct))
### Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
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OASIS Mailing List ArchivesView the OASIS mailing list archive below
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[Date Prev] | [Thread Prev] | [Thread Next] | [Date Next] -- [Date Index] | [Thread Index]
RE: [xml-dev] Build Rich Complexity from a Small Set of Well-Defined Markup Combinators
• From: "David Lee" <dlee@calldei.com>
• To: "'Costello, Roger L.'" <costello@mitre.org>, <xml-dev@lists.xml.org>
• Date: Wed, 24 Aug 2011 10:58:31 -0400
```I propose that the number of elements and combinators is not the most useful
metric of "complexity".
For example you can create an infinitely complex data model from set
arithmetic allowing only the empty set and sets that contain the empty
set(s) as a primitive.
Another example, List, with only set and 4 primitives can be considered by
some to be quite a complicated language to use.
Conversely languages with a large number of primitives are not necessarily
considered complex.
I suggest you are confusing many kinds of 'complexity' in one swoop.
1) Complexity (number of) the primitive operations and atoms by counting
them.
2) Complexity of the descriptiveness these can produce (not necessarily by
counting them.)
3) Complexity of the task of using a language to produce a desired approach
(complexity == 'difficulty of people to figure out how to do a task given
the primitives).
Another way of looking at it is
A) There's a difference between complexity and count.
B) There's a difference between the complexity of a language (number and
ways its features can be used) and the complexity of humans figuring out how
The human body is one of the most complex systems in the universe, yet we
find it amazingly simple to do many things like for example recognize
objects and assign labels to them.
----------------------------------------
David A. Lee
dlee@calldei.com
http://www.xmlsh.org
-----Original Message-----
From: Costello, Roger L. [mailto:costello@mitre.org]
Sent: Wednesday, August 24, 2011 10:16 AM
To: xml-dev@lists.xml.org
Subject: [xml-dev] Build Rich Complexity from a Small Set of Well-Defined
Markup Combinators
Hi Folks,
Consider the digits 0 - 9. They can be combined to create an infinite number
of integral numbers, such as 256 or 14 or 190023156001200021345. Each digit
has a well-defined meaning and the rules for combining the digits are
well-defined.
Rich complexity flows from a small set of digit combinators.
Next, consider XML Schema. It is a markup language consisting of a small set
of well-defined markup combinators:
1. Schema
2. Element
3. Attribute
4. Simple Type
5. Complex Type
6. Attribute Group
7. Element Group
The language has well-defined mechanisms for combining the markup
combinators:
1. Schemas are combined using import, include, and redefine
2. Elements are combined using sequence, choice, or all
3. Complex types with simple content are extended or restricted
4. Complex types with complex content are extended or restricted
An infinite variety of schemas can be created using the 7 markup combinators
and the 4 combining mechanisms.
Interestingly, XML Schemas is considered to be a complicated language.
Perhaps 7 markup combinators are too many in a markup language?
When creating an XML markup language consider following this approach:
1. Create a small set of well-defined markup combinators. From
experience with XML Schemas, 7 or less markup combinators might be adequate.
2. Create well-defined mechanisms for combining the markup combinators.
Again, from experience with XML Schemas, 4 or less combining mechanisms
>From that will flow complexity of great richness.
/Roger
_______________________________________________________________________
XML-DEV is a publicly archived, unmoderated list hosted by OASIS
to support XML implementation and development. To minimize
spam in the archives, you must subscribe before posting.
Or unsubscribe: xml-dev-unsubscribe@lists.xml.org
subscribe: xml-dev-subscribe@lists.xml.org
List archive: http://lists.xml.org/archives/xml-dev/
List Guidelines: http://www.oasis-open.org/maillists/guidelines.php
```
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# Distance between Fagernes (VDB) and Båtsfjord (BJF)
Flight distance from Fagernes to Båtsfjord (Fagernes Airport, Leirin – Båtsfjord Airport) is 873 miles / 1405 kilometers / 759 nautical miles. Estimated flight time is 2 hours 9 minutes.
Driving distance from Fagernes (VDB) to Båtsfjord (BJF) is 1229 miles / 1978 kilometers and travel time by car is about 29 hours 19 minutes.
873
Miles
1405
Kilometers
759
Nautical miles
2 h 9 min
141 kg
## How far is Båtsfjord from Fagernes?
There are several ways to calculate distances between Los Angeles and Chicago. Here are two common methods:
Vincenty's formula (applied above)
• 872.941 miles
• 1404.862 kilometers
• 758.565 nautical miles
Vincenty's formula calculates the distance between latitude/longitude points on the earth’s surface, using an ellipsoidal model of the earth.
Haversine formula
• 870.117 miles
• 1400.318 kilometers
• 756.111 nautical miles
The haversine formula calculates the distance between latitude/longitude points assuming a spherical earth (great-circle distance – the shortest distance between two points).
## How long does it take to fly from Fagernes to Båtsfjord?
Estimated flight time from Fagernes Airport, Leirin to Båtsfjord Airport is 2 hours 9 minutes.
## What is the time difference between Fagernes and Båtsfjord?
There is no time difference between Fagernes and Båtsfjord.
## Flight carbon footprint between Fagernes Airport, Leirin (VDB) and Båtsfjord Airport (BJF)
On average flying from Fagernes to Båtsfjord generates about 141 kg of CO2 per passenger, 141 kilograms is equal to 312 pounds (lbs). The figures are estimates and include only the CO2 generated by burning jet fuel.
## Map of flight path and driving directions from Fagernes to Båtsfjord
Shortest flight path between Fagernes Airport, Leirin (VDB) and Båtsfjord Airport (BJF).
## Airport information
Origin Fagernes Airport, Leirin
City: Fagernes
Country: Norway
IATA Code: VDB
ICAO Code: ENFG
Coordinates: 61°0′56″N, 9°17′17″E
Destination Båtsfjord Airport
City: Båtsfjord
Country: Norway
IATA Code: BJF
ICAO Code: ENBS
Coordinates: 70°36′1″N, 29°41′29″E
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app_bPROBABILITYSECOND
# app_bPROBABILITYSECOND - ECON 6002 Econometrics Memorial...
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ECON 6002 Econometrics Memorial University of Newfoundland Adapted from Vera Tabakova’s notes SECOND
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B.4.1 Mean, median and mode For a discrete random variable the expected value is: ( 29 ( 29 ( 29 1 1 2 2 [ ] n n E X x P X x x P X x x P X x = = + = + + = L 1 1 2 2 1 [ ] ( ) ( ) ( ) ( ) ( ) n n n i i i x E X x f x x f x x f x x f x xf x = μ = = + + + = = L Where f is the discrete PDF of x
For a continuous random variable the expected value is: The mean has a flaw as a measure of the center of a probability distribution in that it can be pulled by extreme values. [ ] ( 29 E X xf x dx -∞ μ = =
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For a continuous distribution the median of X is the value m such that In symmetric distributions, like the familiar “bell-shaped curve” of the normal distribution, the mean and median are equal. The mode is the value of X at which the pdf is highest. ( 29 ( ) .5 P X m P X m = < =
[ ( )] ( ) ( ) x E g X g x f x = [ ] [ ] E aX aE X = ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 E g X g x f x axf x a xf x aE X = = = = Where g is any function of x, in particular;
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[ ] [ ] E aX b aE X b + = + ( 29 ( 29 ( 29 ( 29 1 2 1 2 E g X g X E g X E g X + = +
The variance of a discrete or continuous random variable X is the expected value of ( 29 ( 29 2 g X X E X = - The variance
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The variance of a random variable is important in characterizing the scale of measurement, and the spread of the probability distribution.
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# Merge sort¶
## Intuition¶
If you wonder how you might use recursion to sort an array, merge sort is a natural answer. In other words, if you wonder how you might enlist your friends to help you sort in a divide and conquer fashion, merge sort is a natural answer.
## Merge¶
Suppose you want to sort a deck of cards, but you’re lazy, so you split the deck in half and give one half to one friend and another half to the another friend and get each friend to sort their half and then give the cards back to you.
You can then merge the two sorted halves as follows. Put the two halves next to each other.
Turn over the top card for each half and take whichever card is lower and start a new pile that will be for the sorted deck.
Do that again with the next top card on the half that had the lower card and the same top card on the half that had the higher card and take the card that is lower between those two cards and add it to the pile that you created.
Keep doing that until one of the halves runs out.
Add the cards from the remaining half to the pile for the sorted deck.
## Recursion¶
We’ve described how you can get one sorted deck if given two sorted halves.
But this same logic applies to your two friends. Each of your friends could be lazy and find 2 other friends and split their deck in half and get their friends to sort half of their halves.
And the same logic applies to the friends of friends. Here’s a picture of that process (F = Friend, FoF = friend of friend):
``` You
/ \
F1 F2
/ \ / \
FoF1.1 FoF1.1 FoF2.1 FoF1.1
```
This tree keeps growing until your friend of friend of friends… each only have 2 cards and they hand their friend of friend of friend of friends… 1 card each and that friend doesn’t even have to do anything, because their half is already sorted (it’s only 1 card). So the friend of friend of friends… immediately take back their 2 sorted halves of 1 card and follow the merging procedure to get a sorted deck of 2 cards and then the friend of friends take back their 2 sorted halves of 2 cards and follow the merging procedure to get a sorted deck of 4 cards and so on until your 2 friends hand you back their halves sorted.
```def merge_sort(arr):
if len(arr) == 1:
return
mid = len(arr) // 2
left = arr[:mid]
right = arr[mid:]
merge_sort(left)
merge_sort(right)
i = j = k = 0
# Remember this is testing the bounds of left and right not arr
while i < len(left) and j < len(right):
if left[i] < right[j]:
arr[k] = left[i]
i += 1
k += 1
else:
arr[k] = right[j]
j += 1
k += 1
while i < len(left):
arr[k] = left[i]
i += 1
k += 1
while j < len(right):
arr[k] = right[j]
j += 1
k += 1
def test_merge_sort():
arr = [1, 5, 3, -4, -10, 0]
merge_sort(arr)
assert arr == [-10, -4, 0, 1, 3, 5], arr
test_merge_sort()
```
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# Generated Quantities in STAN: negative binomial rng [closed]
I'm working with a Negative binomial regression in STAN.
I would like to make predictions on a test set, but looking at the reference I can't find a negative_binomial random number generator.
Is there any way to do so without saving mean and overdispersion distributions and sampling from them in R ?
## closed as off-topic by whuber♦Mar 28 '17 at 15:05
This question appears to be off-topic. The users who voted to close gave this specific reason:
• "This question appears to be off-topic because EITHER it is not about statistics, machine learning, data analysis, data mining, or data visualization, OR it focuses on programming, debugging, or performing routine operations within a statistical computing platform. If the latter, you could try the support links we maintain." – whuber
If this question can be reworded to fit the rules in the help center, please edit the question.
• I think you need to add the self-study tag. – Michael Chernick Mar 27 '17 at 22:31
• Also since you are mainly looking for information on two software packages (STAN and R), the question is off topic for this site. – Michael Chernick Mar 27 '17 at 22:41
• Ok, I'll move to stackoverflow and add the self study tag there, thank you for raising my awareness about this site :) – Tommaso Guerrini Mar 27 '17 at 22:42
From the Stan User's Guide (2.14.0), it appears you should be able to generate samples from a negative binomial using:
neg_binomial_rng(real alpha, real beta)
You can draw from this distribution on each step of your chain by including it in the normal manner in your generated quantities block, e.g.
generated quantities { vector[N] y_rep; for (n in 1:N) { y_rep[n] = neg_binomial_rng(alpha, beta); } }
Where alpha and beta are your parameter estimates at each step, and N is the total number of samples to generate - specified as input to the data block.
• Why can't I find things on the Stan reference remains a mistery. Thank you!! – Tommaso Guerrini Mar 27 '17 at 22:46
• @TommasoGuerrini No problem. FWIW, you can also specify using alternate parameterizations neg_binomial_2_rng(real mu, real phi) and neg_binomial_2_log_rng(real eta, real phi) which take precision and logged parameters, respectively. – khonegger Mar 27 '17 at 22:52
• Yep, actually I used the one with the overdispersion and log, thank you again! – Tommaso Guerrini Mar 27 '17 at 22:57
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http://www.fivedoves.com/letters/nov2010/wills115.htm
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Will Schumacher (5 Nov 2010)
"Daniel 12:11- Clay Cantrells method dead on again"
Daniel 12:11
And from the time that the daily sacrifice shall be taken away, and the abomination that maketh desolate set up, there shall be a thousand two hundred and ninety days.
I have posted on here for the last 9 months that the 1290 days started Sept 29, 2008 and end on April 11, 2012. My theory is that if God has hidden (which He has) in the gematria of rapture verses the Gregorian (527,147) and jewish (65, 153/306) calendar dates, then He would have hidden in the gematria of this verse the same thing
411=april 11
102=the 102nd day of the year we use
119=Nisan 19
19=19th day of jewish year
Here goes from www.biblewheel.com from the strong’s concordance side
Sum
470 470=(119x3) +113
454 924=(411x2) + 102
266 1190=119x10
496 1686=666+(102x10)
380 2066=(7x119)+(3x411)
500 2566=666+(19x100)
111 2677=(13x119)+(10x113)
46 2723=(666x2)+(13x107)
820 3543=666+(7x411)
56 3599=(5x411)+(193x8) Clay says 193 is an a/c number
H3543=menas dim,failed, or darkened as used in Zechariah 11:17 Woe to the idol shepard that leaveth the flock! The sword shall be upon his arm, and upon his right eye: his arm shall be clean dried up, and his right eye shall be utterly darkened.
This is a clear antichrist verse. Look at the other ones also-they all have a bad connotation about them
Using Clay Cantrell’s method, this verse clearly shows the date of April 11th and Nisan 19 in it.
Another interesting thing is that if you add 929(sept 29)+1290+411=2630 which is a root antichrist number as Clay points out. Then if you add 969 (the age of Methuselah when he died at the flood) to 2630=3599 the total gematria of the verse.
Will Schumacher
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https://howtodunia.com/mcq-questions-for-class-6-maths-chapter-1/
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# MCQ Questions for Class 6 Maths Chapter 1 Knowing Our Numbers with Answers
Check the below NCERT MCQ Questions for Class 6 Maths with Answers Pdf free download. MCQ Questions for Class 6 Maths with Answers were prepared based on the latest exam pattern. We have Provided Class 6 Maths MCQs Questions with Answers to help students understand the concept very well.
(a) MLMCI
(b) MMCLI
(c) MCMLI
(d) MCMIL
(c) MCMLI
(a) 4232, 4341
(b) 5432, 6922
(c) 6524, 7823
(d) 2334, 2340
(d) 2334, 2340
## Q3. Which of the following options is true?
(a) XCVIII > MCVIII
(b) DCVIII < MCVIII
(c) DCVIII = MCVIII
(d) XCVIII < LXXXVII
(b) DCVIII
(a) 7221
(b) 7721
(c) 7122
(d) 7112
(b) 7721
(a) 4995
(b) 5005
(c) 495
(d) 395
(c) 495
(a) 25
(b) 35
(c) 45
(d) 15
(a) 25
(a) 10000001
(b) 99999999
(c) 10000000
(d) 999999998
(c) 10000000
(a) 527864
(b) 5,27,864
(c) 527,864
(d) 52,78,64
(c) 527,864
(a) 8,945,673
(b) ,945,673
(c) 8,945673
(d) 8945673
(a) 8,945,673
(a) 2520
(b) 2500
(c) 2720
(d) 2000
(c) 2720
(a) 4321
(b) 4312
(c) 4213
(d) 4231.
(a) 4321
(a) 7521
(b) 7512
(c) 7215
(d) 7251.
(a) 7521
(a) 7530
(b) 7503
(c) 7350
(d) 7305.
(a) 7530
(a) 1583
(b) 1538
(c) 1385
(d) 1358.
(d) 1358.
(a) 3546
(b) 3564
(c) 3456
(d) 3465.
(c) 3456
## Class 6 Maths MCQ
Chapter 1: Knowing Our Numbers Class 6 MCQ
Chapter 2: Whole Numbers Class 6 MCQ
Chapter 3: Playing with Numbers Class 6 MCQ
Chapter 4: Basic Geometrical Ideas Class 6 MCQ
Chapter 5: Understanding Elementary Shapes Class 6 MCQ
Chapter 6: Integers Class 6 MCQ
Chapter 7: Fractions Class 6 MCQ
Chapter 8: Decimals Class 6 MCQ Questions
Chapter 9: Data Handling Class 6 MCQ Questions
Chapter 10: Mensuration Class 6 MCQ Questions
Chapter 11: Algebra Class 6 MCQ Questions
Chapter 12: Ratio and Proportion Class 6 MCQ Questions
Chapter 13: Symmetry Class 6 MCQ Questions
Chapter 14: Practical Geometry Class 6 MCQ Questions
Use the above-provided Chapter Wise NCERT MCQ Questions for Class 6 Maths with Answers Pdf free download. We hope the given NCERT MCQ Questions for Class 6 Maths PDF Free Download will definitely yield fruitful results. If you have any queries regarding The CBSE Class 6 Maths MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.
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https://paperswithcode.com/method/adafactor
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Stochastic Optimization
Introduced by Shazeer et al. in Adafactor: Adaptive Learning Rates with Sublinear Memory Cost
Adafactor is a stochastic optimization method based on Adam that reduces memory usage while retaining the empirical benefits of adaptivity. This is achieved through maintaining a factored representation of the squared gradient accumulator across training steps. Specifically, by tracking moving averages of the row and column sums of the squared gradients for matrix-valued variables, we are able to reconstruct a low-rank approximation of the exponentially smoothed accumulator at each training step that is optimal with respect to the generalized Kullback-Leibler divergence. For an $n \times m$ matrix, this reduces the memory requirements from $O(n m)$ to $O(n + m)$.
Instead of defining the optimization algorithm in terms of absolute step sizes {$\alpha_t$}$_{t=1}^T$, the authors define the optimization algorithm in terms of relative step sizes {$\rho_t$}$_{t=1}^T$, which get multiplied by the scale of the parameters. The scale of a parameter vector or matrix is defined as the root-mean-square of its components, lower-bounded by a small constant $\epsilon_2$. The reason for this lower bound is to allow zero-initialized parameters to escape 0.
Proposed hyperparameters are: $\epsilon_{1} = 10^{-30}$, $\epsilon_{2} = 10^{-3}$, $d=1$, $p_{t} = \min\left(10^{-2}, \frac{1}{\sqrt{t}}\right)$, $\hat{\beta}_{2_{t}} = 1 - t^{-0.8}$.
#### Papers
Paper Code Results Date Stars
#### Components
Component Type
🤖 No Components Found You can add them if they exist; e.g. Mask R-CNN uses RoIAlign
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# Simplification Set – 16
1. 48 × 27 + 5088 ÷ 53 – 65% of 560 = 2x + 4
A) 7
B) 11
C) 8
D) 10
E) 9
Option D
Solution:
1028 = 2x + 4
2x = 1024
x = 10
2. √4761 + 85 × 26 – 272 – 35% of 760 = x
A) 1642
B) 1284
C) 1526
D) 1374
E) 1235
Option B
3. 36% of 550 – 14% of 650 + 35% of 420 – 55% of 380 = x
A) 53
B) 45
C) 34
D) 57
E) 37
Option B
4. 26 × 37 + 47% of 250 – 65% of 490 = x
A) 696
B) 835
C) 713
D) 761
E) 668
Option D
5. 43 (3060 ÷ (26+59)) – 2592 ÷ (16 × 18) = x
A) 1156
B) 1489
C) 1529
D) 1729
E) 1539
Option E
6. 3 1/4 + 2 2/5 – 4 3/8 + 2 1/2 = x
A) 3 31/40
B) 4 5/8
C) 3 7/8
D) 3 33/40
E) None of these
Option A
Solution:
3 1/4 + 2 2/5 – 4 3/8 + 2 1/2
= 3+2-4+2 + (1/4 + 2/5 – 3/8 + 1/2)
= 3 + 31/40 = 3 31/40
7. 4 3/4 + 2 1/3 + 1 5/6 – 3 5/8 = x
A) 4 33/24
B) 5 5/6
C) 5 11/24
D) 4 5/6
E) 5 7/24
Option E
4 3/4 + 2 1/3 + 1 5/6 – 3 5/8
= 4+2+1-3 + (3/4 + 1/3 + 5/6 – 5/8)
= 4 + (1 7/24) = 5 + 7/24 = 5 7/24
8. √2916 ÷ 16 × 288 – 15% of 680 – √1444 × 12 = x
A) 482
B) 414
C) 539
D) 561
E) 523
Option B
9. 342 – 24% of 850 – 85% of 760 = x% of 170
A) 140
B) 16
C) 180
D) 18
E) 14
Option C
10. 262 – 192 + 372 – 432 + 122 = 7x
A) 3
B) 2
C) 4
D) -3
E) -4
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Sanderson M. Smith
(BUT STANDARD DEVIATIONS CAN'T)
Here is an illustration of these important statistical formulas:
If X and Y are any two random variables, then
mX+Y = mX + mY
If X and Y are independent random variables, then
s2X+Y = s2X + s2Y
Note: These "nice" rules do not hold for standard deviations.
Here's a story about my friend, Herkimer, to illustrate what is stated above:
Herkimer works only on weekends. On Saturday there are three possible financial outcomes for him, each with probability = 1/3 = 33 1/3% He can end up the day \$100 in debt, he can end the day up with a gain of \$50, or he can end up the day with a gain of \$200. On Sunday, he has a similar situation, although on that day there are five possible financial outomes, each with probability = 1/5 = 20%. The following table shows Herkimer's possible gains and losses for Saturday and Sunday, along with the set (Sa + Su), containing the 5x3 = 15 gains and losses he can have at the end of a weekend.
Sa (Saturday) Su (Sunday) (Sa + Su) (Saturday+Sunday) -\$100 -\$80 -\$180 \$50 -\$40 -\$140 \$200 \$25 -\$75 \$90 -\$10 \$160 \$60 ------------ ------------ -\$30 Means \$50.00 \$31.00 \$10 Standard Deviations \$122.47 \$86.63 \$75 Variances (sq. dollars) \$15,000.00 \$7,504.00 \$140 \$210 \$120 \$160 \$225 \$290 \$360 ------------ Mean(Sa) + Mean (Su) \$81.00 <------MEANS ADD--------> \$81.00 <--Mean(Sa+Su) St.Dev.(Sa)+ St.Dev.(Su) \$197.47 <---STANDARD DEVIATIONS DO NOT ADD--> \$150.01 <--St. Dev. (Sa+Su) Var(Sa) + Var(Su) \$22,504.00 <---VARIANCES ADD---> \$22,504.00 <--Variance(Sa+Su)
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https://mathematica.stackexchange.com/users/193/dr-belisarius?tab=answers
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Dr. belisarius
• Member for 10 years
• Last seen more than 4 years ago
• Argentina
Let's define a filtering chain: isolateTheSand[x_Image] := ColorNegate@ Dilation[Closing[EdgeDetect[EntropyFilter[x, 1], 10], 100], 30]; getBrightObjects[x_Image] := ...
# is a placeholder for an expression. If you want to define a function, $y(x)=x^2$, you just could do: f = #^2 & The & "pumps in" the expression into the # sign. That is important for ...
Let's do it Andy's way So you are Andy. Nice to meet you. And you never got those hands on a computer. It doesn't matter, I will show you! First you need to go to Marilyn's place. Don't worry, JF ...
I wanted to change only the color of the ball, leaving all other red objects untouched: getReds[x_Image] := First@ColorSeparate[x, "Hue"] isolateSphere[x_Image] := SelectComponents[Binarize[getReds[x]...
Breathing with occluded borders, per Toad's request: Run the following command to get the Mathematica code NotebookPut@ImportString[Uncompress@FromCharacterCode@Flatten@ImageData[ ...
The following method doesn't require parameters and discovers also oblique views. obl[transit_Image] := (SelectComponents[ MorphologicalComponents[ DeleteSmallComponents@...
A textbook-like animation turns = 10; aa = Table[Framed@ Show[ParametricPlot3D[ Piecewise[{{{1, x, 0}, x <= 0}, {{Cos[2 Pi turns x/r], x, Sin[2 Pi turns x/r]}, 0 ...
You may use the profiler included in the Wolfram Workbench
voronoi[pts_] := ListDensityPlot[Append[#, 0]&/@ pts, InterpolationOrder-> 0, Frame -> False] pts = RandomReal[{0, 256}, {20, 2}]; cp ...
Edited to make it a function. For the strange Exclusions specification I use below, see my answer here. Thanks to @Oleksandr and @JM for their great comments. plInters[{f1_, f2_}, {min_, max_}] := ...
The following is something I made while trying to solve another (similar) problem (*FindCurvedPath Replacement*) ClearAll[findCurvedPath2, findClosedPath2]; findClosedPath2[inptList_, cutoff_] := ...
I made a function that could be used for labeling plots interactively, adding labeled Bezier arrows, preserve your labels from session to session, and a few more goodies. Some snapshots follow: ...
Some function definitions first. AkimaInterpolation[] stolen from here: AkimaInterpolation[data_] := Module[{dy}, dy = #2/#1 & @@@ Differences[data]; Interpolation[Transpose[{List /@ data[[All, ...
Without claiming much generality, I made the following. I'm using a slightly more complex image than your proposed one. i = Binarize@Import@"http://i.stack.imgur.com/qDby8.png"; idi ...
Here you have a toy to start playing with: Edit preventing the animation running at different speeds in different machines by using Clock[] and DynamicWrapper[] (due credit to @jVincent) n = 500; (*...
In this article the author solves the problem of tiling a rectangle by using pieces taken from a set of polyominoes, which are plane geometric figures formed by joining one or more equal squares edge ...
Without using the "ErrorBarPlots" Package dataX = Sort@RandomReal[1, 10]; dataY = RandomReal[{0.5, 1}, 10]; error = RandomReal[0.5, 10]; errorH = dataY + error; errorL = dataY - error; f[y_] := ...
lin[cam_, obj_][t_] := cam t + (1 - t) obj s[cam_, obj_] := First@Solve[lin[cam, obj][t][[3]] == 0, t]; tr[cam_, obj_] := lin[cam, obj][t] /. s[cam, obj] // FullSimplify And that's it: tr[ ] is your ...
i = Import@"http://i.stack.imgur.com/8I3B1.jpg"; f[{{tmin_, tmax_}, {rmin_, rmax_}}, ___] := Module[{l = Join[{{0, 0}}, Table[{Cos@t, Sin@t}, {t, tmin, tmax, (tmax-tmin)/100}]]}, {Texture[i], ...
n = 100; (*number of points*) s = RandomSample@Range@n; (*the initial set*) (*some aux functions*) head[{x_, xs___}] := Select[{xs}, # <= x &]; tail[{x_, xs___}] := Select[{xs}, # > x &];...
Fitting an ellipse: i = Import["http://i.stack.imgur.com/W7HJk.jpg"]; lineByCenter[center_, semi_, angle_] := Rotate[Line[{#1 - #2, #1 + #2}], angle, #1]& ...
Here is a bare bones, non-robust, use at your own risk, etc. code39 reader (*get image *) i = Binarize[Import@"http://i.stack.imgur.com/Cx3JD.png", .7] (* Char encodings from Paul's article - See ...
After importing a free dice 3D model {pd, vd} = Import["c:\\dice.stl", #] & /@ {"PolygonData", "VertexData"}; g2 = Translate[GraphicsComplex[vd, Polygon /@ pd], {-10, -37.5, -10}]; rv = {{0, 0, -...
TextRecognize[] accepts an undocumented Option "SegmentationMode". The allowed values are: ?ImageExternalOCRDump`\$TextRecognizeSegmentationModes { {{3, "Fully automatic page segmentation, but no ...
The plan is first get the "external" contour and then use Green's theorem to find its area. r[t_] := {-9 Sin[2 t] - 5 Sin[3 t], 9 Cos[2 t] - 5 Cos[3 t], 0} (*find the intersections*) tr = Quiet@...
For example you may do something like f[i_] := {Red,Orange,Yellow}[[i]] Edit You can easily add some robustness: f[l_List, i_Integer ] := l[[i]] /; 1 <= i <= Length@l; ll = {Red, Orange, ...
The following is a little involved, but it calculates the "minimum displacement" evolution by choosing the least total displacement alternatives from the permutations generated by the "...
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https://www.electro-tech-online.com/threads/how-much-single-pulse-power-mosfets-can-handle.98428/
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Continue to Site
# How much single pulse power MOSFETs can handle?
Status
Not open for further replies.
#### Ekke
##### New Member
Hi all!
I'm thinking to build a capacitor discharge welder, but there seems to be a problem with MOSFETs, I can't figure out how many of them I will need.
I'm thinking to use these MOSFETs:
IRLS3036-7PPbF
https://www.electro-tech-online.com/custompdfs/2009/10/irls3036-7ppbf.pdf
Main reasons:
• Voltage (enough, not too high)
• Low R_on (really important with high currents)
• High pulse current (?)
• Package (I like reflow)
I would like to use up to 48V, but my capacitors will be 50V (65V surge). Is 48V too high? But the main problem is this: Those capacitors can store ~600J. Single pulse width will be something like <15-20ms. Fig. 8 in datasheet says "Single pulse" in the corner, but those means continuous pulses and are limited by junction temperature ("Repetitive rating; pulse width limited by max. junction temperature.")?
I found this info from some random source: "If you weld nickel, you can use a constant value of about 0.003Ω.". So, if I have 48V/0.003Ω = 16000A.
But, if you count ESR of capacitors (many parallel: 0.64mΩ), resistance of MOSFETs (10 parallel: 0.15mΩ) you get 48V/3,79mΩ = 12665A. It's still quite a lot...
There will be some wiring etc. so resistance goes up a little, but the maximum current will still be >10000A? So, can 10 of those MOSFETs handle it (10x1000A repetitive peak? but not @ 48V) or do I have to use something else? 600Ws [J] doesn't sound so much, so why it seems that I will need 10000 MOSFETs?
If I counted right after 1ms pulse @ 10000A there will be ~24V/160Ws left in the capacitors, so the maximum pulse will be quite short. Any info and calculations are welcome..
So after all this is a hard question?
You don't use a mosfet for that kind of thing, they can't switch high currents like that, the reasons are quiet complex. Simply charge the capacitor tap the electrode and it will discharge. If you want to get to a set distance discharge a secondary high voltage capacitor through the circuit as an initiator, then the lower voltage high current pulse can follow that ionized trail to intiate the primary welding current which is low voltage.
You need to factor in inductance from every part of your circuit at this point as at those pulse currents it will be the primary delay factor, significantly more than you seem to think as you didn't even mention inductance in your post. At those currents even short straight pieces of wire have significant inductance.
You don't use a mosfet for that kind of thing, they can't switch high currents like that, the reasons are quiet complex.
The funny thing is that I know at least 4 CD welders that uses mosfets. Fets surely need a protection circuit because of the induction peak, I'm not sure how delays will be a problem..
Odd, I'd figure they'd use SCRs, for a capacitive welder SCR's handle peaks much better I thought.
The funny thing is that I know at least 4 CD welders that uses mosfets. Fets surely need a protection circuit because of the induction peak, I'm not sure how delays will be a problem..
Are these commercial products ir DIY projects?
Where I used to work we had several brands and all of them were scr fired.
Now that I think of it more I don't see how it possibly could have been a Mosfet in a CD welder, Mosfets have a DV/DT limit that can't be broken or the parasitic BJT latches in some manner as to cause device destruction.
Are these commercial products ir DIY projects?
DIY. Haven't seen any internals of commercial products.
Here is a one:
YouTube - Spot Welder / Discharge Cutter finally completed!
"Thanks for the feedback! Good question regarding weld current
I use a "1 Farad" capacitor, switching is controlled by 4 x IRFP2907 MOSFETs in parallel. Now, the IRFP2907s have a pulse current rating of 816Amps limited by junction temperature, according to the datasheet
I have no idea what that means. But if I use less than three of those MOSFETs, they literally explode into tiny fragments at weld times over 7mS (and man they're expensive!)
So the answer is... One billion?"
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# Main Categories
Total:
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# BEE THEMED NUMBER SENSE SORTING MATS: SPRING MATH: NUMBER SENSE KINDERGARTEN
Product Rating
4.0
4 ratings
File Type
PDF (Acrobat) Document File
2 MB|15 pages
Product Description
NUMBER SENSE GAME CONTAINING TEN FRAMES, TALLY MARKS, NUMERALS, NUMBER NAMES, FINGER REPRESENTATIONS AND DOMINOES.
This fun original game will surely engage all students and can be played individually or in small groups. Students sort the hexagon cards and place them onto the corresponding bee themed mats to complete each beehive. This game provides children with lots of practice by counting spots on dominoes, fingers, identifying tally marks and ten frame representations and recognizing numerals. Number names can also be found on the mats.
Children will surely have a blast!
This resource contains 10 sorting mats (numbers 1-10) and 40 hexagon shaped sorting cards (4 for each numeral).
Please note that you can mark the correct answers on the back of each sorting card using a sticker or writing the numbers with a permanent marker to let students self check. Enjoy!
SPRING RESOURCES:
BUILD A FLOWERPOT: DIGRAPHS GAME - SH, CH, TH, WH, PH PHONIC SOUNDS! LITERACY CENTER
SPRING NUMBER BONDS TASK CARDS: NUMBERS 0 TO 10 : MATH CENTER ACTIVITY
INSECTS COUNTING PUZZLES: NUMBERS 1 TO 100
SPRING COUNTING PUZZLES: NUMBERS 1 TO 100
SPRING BOARD GAME CLIP ART
FLOWERS CLIP ART
OTHER NUMBER RESOURCES:
NUMBER VALUE COUNTING CLIP CARDS - LOTS OF COUNTING PRACTICE ON EACH CARD!
NUMBERS AND THEIR VALUE - NUMBERLINES 1-20 WITH PICTURES TO SHOW VALUE
TEN FRAMES JIGSAW PUZZLES- 1-20 - MATCH TEN FRAME: NUMBER WORD: NUMERAL
ANIMAL NUMBER POSTERS WITH TEN FRAMES- ZOO ANIMALS THEME - NUMBERS 0-10
COUNTING JIGSAW PUZZLES- 1-10 - BIRTHDAY THEME: COUNTING AND MATCHING TO NUMERAL
NUMBER TRAIN DISPLAY - FUN NUMBER POSTERS WITH TEN FRAMES AND NUMBER WORD TOO!
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numbers | spring | spring number sense | ten frames | tally marks | spring center | spring kindergarten center | spring counting | spring counting activities | spring counting center | spring sorting | spring sorting activity | spring counting activity | spring numbers 1-10 | spring numbers 1 to 10 | spring math center | kindergarten spring activity | kindergarten spring center | spring no prep | spring no prep activities | spring number sense | number words | numeral | spring number match up | counting fingers | spring game | spring Math game | spring Math activities | spring Math activity | spring Math activities | spring Math practice | spring unit | spring bee | spring bees game | spring bee activity | spring math fun | spring bee math center | spring bee game
Number Sense | Number Sense Activities | Number Sense Center | Number Sense Game | Number Sense Games | Number Sense Activity | Number Sense Match up | Number Sense Matching | Number Sense Sorting | Number Sense Math Center
Total Pages
15 pages
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Teaching Duration
N/A
• Product Q & A
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Free
# Curve - Essay Example
Summary
Subsequent counts to determine the number total number of candies with a particular color gave varying results (Ziemer, 2010). The 24 Packages of the candies…
## Extract of sample "Curve"
M & M’s Curve and Color Distribution Analysis M & M’s Curve and Color Distribution Analysis The analysis starts with purchase ofthe M & M package and categories the candies according to the color distribution. Subsequent counts to determine the number total number of candies with a particular color gave varying results (Ziemer, 2010). The 24 Packages of the candies had an average color distribution of Red (53), Orange (94) Yellow (51) Blue (88), Green (80), and brown (51). This was different as per the percentage distribution of colors posted in the company website. As such, it was critical to carry out an analysis.
Results
Red
Orange
Yellow
Blue
Green
Brown
Total M & M’s
Percentage Expected (as per the company website)
24%
13%
16%
20%
13%
14%
Mathematical mean counted
52.25
93.63
51.04
88.08
79.29
53.33
Percentage observed
10.45%
18.73%
10.21%
17.62%
15.86%
10.67%
Quantities Observed
456
409
449
411
408
416
2549
Standard Deviation
1.98
2.23
2.95
2.18
2.56
2.48
2.4
Variance
1.48
6.97
5.87
7.02
5.98
6.76
5.68
The quantities of every row as observed were computed and compared to the company website values. The most popular color was orange as indicated in the findings 93.63 (18.73%). Blue (17.62%), green (15.86%), brown (10.67%), red (10.45%), and yellow (10.21%) followed this in this order. The variation was clear when compared to the company website of the percentage points expected for each color. However, green, blue, and brown were closer to the expected percentages. This is well indicated in the graph below showing distribution of the colors in average.
Mean graph
Standard deviation graph
It is clear that the yellow is the score with absolute centre of the group (mean average score).
Reference
Ziemer, H. (2010) . Statistical Distribution. Viewed on 24th October 2012 Read More
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# MPPT display voltage vs actual battery level
When I have a high load on my system the battery voltage on the MPPT display will go down. It usually sits between 12.8v - 13.1v however if the load is high (it is currently on 8amps) the battery level will drop down to 12.4 or something. This will then go back up if I turn the load off.
Why is this? I am worried about discharging the batteries too much and ruining them.
• I think its obvious, the load is causing voltage drop to your battery. – dpw Nov 15 '16 at 6:35
All batteries have an internal resistance which drops more and more voltage as the load draws more and more current.
Under those conditions, the battery's internal resistance would be:
$$R_{INT} = \frac{V_{BAT} - V_{LOAD}}{I_{LOAD}} = \frac{13V - 12.4V} {8A} = 0.075\text { ohms}$$
As for discharging a battery, the terminal voltage depends on your battery's chemistry, capacity, and how much current you take from it. Rule of thumb for sealed lead-acid is to never let the voltage fall below 10.5 volts.
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Fraction = Numerator/Denominator
When Numerator > Denominator,
it is improper fraction
Eg: 3/2, 9/8, 4/3, 13/6
1. Chapter 2 Class 7 Fractions and Decimals
2. Concept wise
3. Fractions
Fractions
Chapter 2 Class 7 Fractions and Decimals
Concept wise
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# Lighter in Water
1. Dec 10, 2007
### bww
A steel wrench feels 3N lighter in water.
a. what is the mass of the wrench?
b. how would your answer change if it took a more dense fluid to make the wrench feel 3N lighter?
a. ok so i know that density x volume=mass. The density of water is 1,000kg/m^3. That's about all I have. I don't really know where to go when i only have the weight of the steel and the density of water.
2. Dec 10, 2007
### chroot
Staff Emeritus
The bouyancy force felt upwards on an object is equal to the weight of the fluid it displaces.
- Warren
3. Dec 10, 2007
### bww
...i guess i'm still confused.
4. Dec 10, 2007
### chroot
Staff Emeritus
You know how much the displaced water weighs (it's given), and you know water's density, so you can calculate the volume of water that was displaced. The volume of displaced water is, of course, is the same as the wrench's volume.
You also know the density of the steel, so you're all set to find the wrench's mass.
- Warren
5. Dec 10, 2007
### bww
how do i know the density of steel?
6. Dec 10, 2007
### chroot
Staff Emeritus
You said you know "the weight of the steel," by which I thought you mean density.
- Warren
7. Dec 10, 2007
### bww
oh, no, i'm terribly sorry, my mistake. I meant that all i knew was that the weight of the wrench was 3N lighter in water. I do not have the density of the wrench. I only know that it weighs 3N less in water and that water's density is 1,000kg/m^3 and I need to find the mass of the wrench. sorry about that.
8. Dec 10, 2007
### chroot
Staff Emeritus
Well, I don't think there's any way to do this without another piece of information (like the density of steel).
Buoyancy isn't concerned with mass, just volume. If the wrench feels a buoyancy force of 3N, then you know its volume directly. But, as you know, you cannot relate mass and volume without knowing density.
The fact that the problem specifies that the wrench is made of steel leads me to believe you are supposed to look up the density of steel. It's probably given in a table in your book somewhere. Look up 'density' in the index.
- Warren
9. Dec 11, 2007
### bww
...yeah you're right, you guys are a lot of help here. thanks. i figured it out.
10. Jan 10, 2010
### lvspink247
I have the same question
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# chemistry
convert 3.43 A(with circle above the A) to meters(scientific notation)
1. 👍 0
2. 👎 0
3. 👁 163
1. 1A = 1E-8 cm
1. 👍 0
2. 👎 0
posted by DrBob222
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1. Create the indicated algebraic expression. Use descriptive variables. The length of a rectangular lawn is 6 ft more than three times the width of the lawn. Express the length of the lawn in terms of the width. A. 3+w+6 B.
asked by Krissy on January 16, 2013
7. ### conversion science
convert .621 hl to liters .013 dl to liters .00078 mg to kg 2.45 g to cg 1.9 km to cm .0476 mm to dam 6.4 ul to nl need conversion and scientific notation before I can proceed from there to the lesson. This was part of an intro
asked by paul on October 1, 2006
Hi, I really need some help with scientific notation. How do I convert large numbers like 108,000,000 and other numbers that are even larger than this to scientific notation? This is for a math project and even though I learned
asked by Music Lover 14 on September 10, 2016
9. ### Algebra Help!!
Find an example of scientific notation in real life Explain why the number was written in scientific notation. Create a multiplication problem with scientific notation
asked by Katie A on October 4, 2011
10. ### Math
(7.66 • 10^2)(6.29 • 10^-4) answer then convert to scientific notation. the answer I keep getting is 0.481814 the scientific notation I get from this is 4.81814*10^5 but i keep getting it wrong. Can someone please help me.
asked by Becky on June 16, 2010
More Similar Questions
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In a league of 5 football teams which play in a round robin tournament show that it is possible for all five teams to be league leaders.
Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do this?
1 Step 2 Step
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
Stage: 3 Challenge Level:
Based on the information in the first two tables most people agreed that Alison should live in B because it apparently has the highest population density and Charlie should live in E because it apparently has the lowest population density:
Population Density (based on total land area):
A = 142 people per sq km
B = 1101 people per sq km
C = 8 people per sq km
D = 202 people per sq km
E = 3 people per sq km
F = 390 people per sq km
G = 14 people per sq km
H = 54 people per sq km
(All results were rounded up to a whole number)
However, there was some confusion as to how to use the rest of the data:
Some suggested that Charlie should go and live in uninhabitable land! Are some of you wanting to get rid of Charlie? Alison perhaps...
Some didn't take into account that the population density would change after removing the uninhabitable land from the total land - Charlie and Alison would only be interested in the population density of the habitable land.
Some suggested suitable countries for Alison and Charlie, but didn't make it clear what calculations they had carried out to reach their conclusions.
The clearest analysis we received was from Komal, from India, who presented his results in this spreadsheet.
However, he assumed that Charlie would choose to live in an urban area. This didn't seem to take into account that Charlie "would like to get away from it all" - he'd be more likely to make his decision based on the population density of the non-urban areas.
Perhaps someone would like to work out the population density in the rural areas of each country.
Chris and Reiss from Wilsons' School suggested other information they might want to take into account before moving:
• The cost of living
• The crime rates
• The tax rates
• How much at chance of terrorist attacks the country is
• The climate
• What public transport there is
• What pension they'll get
• How good the doctors are
• How much doctors cost
• Life expectancy = Quality of Health
• The percentage of people in his/her age group
• Language
• Resorts
• How densely populated the coast is (if there is a coast)
• Housing
• Quality of the infrastructure
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https://www.geeksforgeeks.org/minimum-number-elements-add-make-median-equals-x/
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# Minimum number of elements to add to make median equals x
A median in an array with the length of n is an element which occupies position number (n+1)/2 after we sort the elements in the non-decreasing order (the array elements are numbered starting with 1). A median of an array (2, 6, 1, 2, 3) is the number 2, and a median of array (0, 96, 17, 23) — the number 17.
Examples :
```Input : 3 10
10 20 30
Output : 1
In the first sample we can add number 9
to array (10, 20, 30). The resulting array
(9, 10, 20, 30) will have a median in
position (4+1)/2 = 2, that is, 10
Input : 3 4
1 2 3
Output : 4
In the second sample you should add numbers
4, 5, 5, 5. The resulting array has median
equal to 4.
```
## Recommended: Please try your approach on {IDE} first, before moving on to the solution.
First Approach:- The approach is to add one more number x to the array until the median of the array equals to x. Below is the implementation of the above approach:-
## C++
`// CPP program to find minimum number ` `// of elements needs to add to the ` `// array so that its median equals x. ` `#include ` `using` `namespace` `std; ` ` ` `// Returns count of elements to be ` `// added to make median x. This function ` `// assumes that a[] has enough extra space. ` `int` `minNumber(``int` `a[], ``int` `n, ``int` `x) ` `{ ` ` ``// to sort the array in increasing order. ` ` ``sort(a, a + n); ` ` ` ` ``int` `k; ` ` ``for` `(k = 0; a[(n - 1) / 2] != x; k++) { ` ` ``a[n++] = x; ` ` ``sort(a, a + n); ` ` ``} ` ` ``return` `k; ` `} ` ` ` `// Driver code ` `main() ` `{ ` ` ``int` `x = 10; ` ` ``int` `a[6] = { 10, 20, 30 }; ` ` ``int` `n = 3; ` ` ``cout << minNumber(a, n, x) << endl; ` ` ``return` `0; ` `} `
## Java
`// Java program to find minimum number ` `// of elements needs to add to the ` `// array so that its median equals x. ` `import` `java.util.Arrays; ` ` ` `class` `GFG ` `{ ` ` ` `// Returns count of elements to be ` `// added to make median x. This function ` `// assumes that a[] has enough extra space. ` `static` `int` `minNumber(``int` `a[], ``int` `n, ``int` `x) ` `{ ` ` ``// to sort the array in increasing order. ` ` ``Arrays.sort(a); ` ` ` ` ``int` `k; ` ` ``for` `(k = ``0``; a[(n) / ``2``] != x; k++) ` ` ``{ ` ` ``a[n++] = x; ` ` ``Arrays.sort(a); ` ` ``} ` ` ``return` `k; ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ``int` `x = ``10``; ` ` ``int` `a[] = { ``10``, ``20``, ``30` `}; ` ` ``int` `n = ``3``; ` ` ``System.out.println(minNumber(a, n-``1``, x)); ` `} ` `} ` ` ` `// This code has been contributed by 29AjayKumar `
## Python3
`# Python 3 program to find minimum number ` `# of elements needs to add to the ` `# array so that its median equals x. ` ` ` `# Returns count of elements to be added ` `# to make median x. This function ` `# assumes that a[] has enough extra space. ` `def` `minNumber(a, n, x): ` ` ` ` ``# to sort the array in increasing order. ` ` ``a.sort(reverse ``=` `False``) ` ` ``k ``=` `0` ` ``while``(a[``int``((n ``-` `1``) ``/` `2``)] !``=` `x): ` ` ``a[n ``-` `1``] ``=` `x ` ` ``n ``+``=` `1` ` ``a.sort(reverse ``=` `False``) ` ` ``k ``+``=` `1` ` ` ` ``return` `k ` ` ` `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` ` ``x ``=` `10` ` ``a ``=` `[``10``, ``20``, ``30``] ` ` ``n ``=` `3` ` ``print``(minNumber(a, n, x)) ` ` ` `# This code is contributed by ` `# Surendra_Gangwar `
## C#
`// C# program to find minimum number ` `// of elements needs to add to the ` `// array so that its median equals x. ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// Returns count of elements to be ` `// added to make median x. This function ` `// assumes that a[] has enough extra space. ` `static` `int` `minNumber(``int` `[]a, ``int` `n, ``int` `x) ` `{ ` ` ``// to sort the array in increasing order. ` ` ``Array.Sort(a); ` ` ` ` ``int` `k; ` ` ``for` `(k = 0; a[(n) / 2] != x; k++) ` ` ``{ ` ` ``a[n++] = x; ` ` ``Array.Sort(a); ` ` ``} ` ` ``return` `k; ` `} ` ` ` `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` ` ``int` `x = 10; ` ` ``int` `[]a = { 10, 20, 30 }; ` ` ``int` `n = 3; ` ` ``Console.WriteLine(minNumber(a, n-1, x)); ` `} ` `} ` ` ` `// This code contributed by Rajput-Ji `
## PHP
` `
Output :
```1
```
Time complexity : O(knLogn)
Second Approach:- Better approach is to count all the elements equal to x(that is e), greater than x(that is h) and smaller than x(that is l). And then –
if l is greater than h then, the ans will be (l – h) + 1 – e;
And if h is greater than l then, ans will be (h – l – 1) + 1 – e;
We can use Hoare’s partition scheme to count smaller, equal and greater elements.
Below is the implementation of the above approach:
## C++
`// CPP program to find minimum number of ` `// elements to add so that its median ` `// equals x. ` `#include ` `using` `namespace` `std; ` ` ` `int` `minNumber(``int` `a[], ``int` `n, ``int` `x) ` `{ ` ` ``int` `l = 0, h = 0, e = 0; ` ` ``for` `(``int` `i = 0; i < n; i++) { ` ` ` ` ``// no. of elements equals to x, ` ` ``// that is, e. ` ` ``if` `(a[i] == x) ` ` ``e++; ` ` ` ` ``// no. of elements greater than x, ` ` ``// that is, h. ` ` ``else` `if` `(a[i] > x) ` ` ``h++; ` ` ` ` ``// no. of elements smaller than x, ` ` ``// that is, l. ` ` ``else` `if` `(a[i] < x) ` ` ``l++; ` ` ``} ` ` ` ` ``int` `ans = 0; ` ` ``if` `(l > h) ` ` ``ans = l - h; ` ` ``else` `if` `(l < h) ` ` ``ans = h - l - 1; ` ` ` ` ``// subtract the no. of elements ` ` ``// that are equal to x. ` ` ``return` `ans + 1 - e; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ``int` `x = 10; ` ` ``int` `a[] = { 10, 20, 30 }; ` ` ``int` `n = ``sizeof``(a) / ``sizeof``(a[0]); ` ` ``cout << minNumber(a, n, x) << endl; ` ` ``return` `0; ` `} `
## Java
`// Java program to find minimum number ` `// of elements to add so that its ` `// median equals x. ` `import` `java.util.*; ` `import` `java.lang.*; ` ` ` `class` `GFG { ` ` ` ` ``public` `static` `int` `minNumber(``int` `a[], ` ` ``int` `n, ``int` `x) ` ` ``{ ` ` ``int` `l = ``0``, h = ``0``, e = ``0``; ` ` ``for` `(``int` `i = ``0``; i < n; i++) ` ` ``{ ` ` ` ` ``// no. of elements equals to ` ` ``// x, that is, e. ` ` ``if` `(a[i] == x) ` ` ``e++; ` ` ` ` ``// no. of elements greater ` ` ``// than x, that is, h. ` ` ``else` `if` `(a[i] > x) ` ` ``h++; ` ` ` ` ``// no. of elements smaller ` ` ``// than x, that is, l. ` ` ``else` `if` `(a[i] < x) ` ` ``l++; ` ` ``} ` ` ` ` ``int` `ans = ``0``; ` ` ``if` `(l > h) ` ` ``ans = l - h; ` ` ``else` `if` `(l < h) ` ` ``ans = h - l - ``1``; ` ` ` ` ``// subtract the no. of elements ` ` ``// that are equal to x. ` ` ``return` `ans + ``1` `- e; ` ` ``} ` ` ` ` ``// Driven Program ` ` ``public` `static` `void` `main(String[] args) ` ` ``{ ` ` ``int` `x = ``10``; ` ` ``int` `a[] = { ``10``, ``20``, ``30` `}; ` ` ``int` `n = a.length; ` ` ``System.out.println( ` ` ``minNumber(a, n, x)); ` ` ``} ` `} ` ` ` `// This code is contributed by ` `// Prasad Kshirsagar `
## Python3
`# Python3 program to find minimum number ` `# of elements to add so that its median ` `# equals x. ` ` ` `def` `minNumber (a, n, x): ` ` ``l ``=` `0` ` ``h ``=` `0` ` ``e ``=` `0` ` ``for` `i ``in` `range``(n): ` ` ` ` ``# no. of elements equals to x, ` ` ``# that is, e. ` ` ``if` `a[i] ``=``=` `x: ` ` ``e``+``=``1` ` ` ` ``# no. of elements greater than x, ` ` ``# that is, h. ` ` ``elif` `a[i] > x: ` ` ``h``+``=``1` ` ` ` ``# no. of elements smaller than x, ` ` ``# that is, l. ` ` ``elif` `a[i] < x: ` ` ``l``+``=``1` ` ` ` ``ans ``=` `0``; ` ` ``if` `l > h: ` ` ``ans ``=` `l ``-` `h ` ` ``elif` `l < h: ` ` ``ans ``=` `h ``-` `l ``-` `1``; ` ` ` ` ``# subtract the no. of elements ` ` ``# that are equal to x. ` ` ``return` `ans ``+` `1` `-` `e ` ` ` `# Driver code ` `x ``=` `10` `a ``=` `[``10``, ``20``, ``30``] ` `n ``=` `len``(a) ` `print``(minNumber(a, n, x)) ` ` ` `# This code is contributed ` `# by "Abhishek Sharma 44" `
## C#
`// C# program to find minimum ` `// number of elements to add ` `// so that its median equals x. ` `using` `System; ` ` ` `class` `GFG ` `{ ` `public` `static` `int` `minNumber(``int` `[]a, ` ` ``int` `n, ` ` ``int` `x) ` `{ ` ` ``int` `l = 0, h = 0, e = 0; ` ` ``for` `(``int` `i = 0; i < n; i++) ` ` ``{ ` ` ` ` ``// no. of elements ` ` ``// equals to x, ` ` ``// that is, e. ` ` ``if` `(a[i] == x) ` ` ``e++; ` ` ` ` ``// no. of elements ` ` ``// greater than x, ` ` ``// that is, h. ` ` ``else` `if` `(a[i] > x) ` ` ``h++; ` ` ` ` ``// no. of elements smaller ` ` ``// than x, that is, l. ` ` ``else` `if` `(a[i] < x) ` ` ``l++; ` ` ``} ` ` ` ` ``int` `ans = 0; ` ` ``if` `(l > h) ` ` ``ans = l - h; ` ` ``else` `if` `(l < h) ` ` ``ans = h - l - 1; ` ` ` ` ``// subtract the no. ` ` ``// of elements that ` ` ``// are equal to x. ` ` ``return` `ans + 1 - e; ` `} ` ` ` `// Driver Code ` `public` `static` `void` `Main() ` `{ ` ` ``int` `x = 10; ` ` ``int` `[]a = {10, 20, 30}; ` ` ``int` `n = a.Length; ` ` ``Console.WriteLine( ` ` ``minNumber(a, n, x)); ` `} ` `} ` ` ` `// This code is contributed ` `// by anuj_67. `
## PHP
` ``\$x``) ` ` ``\$h``++; ` ` ` ` ``// no. of elements smaller ` ` ``// than x, that is, l. ` ` ``else` `if` `(``\$a``[``\$i``] < ``\$x``) ` ` ``\$l``++; ` ` ``} ` ` ` ` ``\$ans` `= 0; ` ` ``if` `(``\$l` `> ``\$h``) ` ` ``\$ans` `= ``\$l` `- ``\$h``; ` ` ``else` `if` `(``\$l` `< ``\$h``) ` ` ``\$ans` `= ``\$h` `- ``\$l` `- 1; ` ` ` ` ``// subtract the no. of elements ` ` ``// that are equal to x. ` ` ``return` `\$ans` `+ 1 - ``\$e``; ` `} ` ` ` `// Driver code ` `\$x` `= 10; ` `\$a` `= ``array` `(10, 20, 30); ` `\$n` `= sizeof(``\$a``) ; ` `echo` `minNumber(``\$a``, ``\$n``, ``\$x``), ``"\n"``; ` ` ` `// This code is contributed by jit_t ` `?> `
Output :
```1
```
Time complexity : O(n)
This article is contributed by Sagar Shukla. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
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https://www.kylesconverter.com/frequency/radians-per-second-to-cycles-per-day
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# Convert Radians Per Second to Cycles Per Day
### Kyle's Converter > Frequency > Radians Per Second > Radians Per Second to Cycles Per Day
Radians Per Second (rad/s)* Cycles Per Day (cpd)* Precision: 0 1 2 3 4 5 6 7 8 9 12 15 18
Reverse conversion?
Cycles Per Day to Radians Per Second
(or just enter a value in the "to" field)
#### Please share if you found this tool useful:
Unit Descriptions
1 Radian per Second:
1 Radian per second is comparative to 1/2π Hertz. Radians per second is a measure of angular frequency, it can be compared to Hertz or other angular units. Formula uses an approximation of PI. 1 rad/s is approximately 0.159154943091895000 Hz.
1 Cycle per Day:
A period of 1 day is equal to 1/86400 Hertz frequency. Period is the inverse of frequency: 1 Hz = 1/86400 cpd or approximately 0.000011574074074074 cpd.
Conversions Table
1 Radians Per Second to Cycles Per Day = 13750.987170 Radians Per Second to Cycles Per Day = 962569.0958
2 Radians Per Second to Cycles Per Day = 27501.974280 Radians Per Second to Cycles Per Day = 1100078.9667
3 Radians Per Second to Cycles Per Day = 41252.961290 Radians Per Second to Cycles Per Day = 1237588.8375
4 Radians Per Second to Cycles Per Day = 55003.9483100 Radians Per Second to Cycles Per Day = 1375098.7083
5 Radians Per Second to Cycles Per Day = 68754.9354200 Radians Per Second to Cycles Per Day = 2750197.4166
6 Radians Per Second to Cycles Per Day = 82505.9225300 Radians Per Second to Cycles Per Day = 4125296.1249
7 Radians Per Second to Cycles Per Day = 96256.9096400 Radians Per Second to Cycles Per Day = 5500394.8333
8 Radians Per Second to Cycles Per Day = 110007.8967500 Radians Per Second to Cycles Per Day = 6875493.5416
9 Radians Per Second to Cycles Per Day = 123758.8837600 Radians Per Second to Cycles Per Day = 8250592.2499
10 Radians Per Second to Cycles Per Day = 137509.8708800 Radians Per Second to Cycles Per Day = 11000789.6665
20 Radians Per Second to Cycles Per Day = 275019.7417900 Radians Per Second to Cycles Per Day = 12375888.3748
30 Radians Per Second to Cycles Per Day = 412529.61251,000 Radians Per Second to Cycles Per Day = 13750987.0831
40 Radians Per Second to Cycles Per Day = 550039.483310,000 Radians Per Second to Cycles Per Day = 137509870.8314
50 Radians Per Second to Cycles Per Day = 687549.3542100,000 Radians Per Second to Cycles Per Day = 1375098708.314
60 Radians Per Second to Cycles Per Day = 825059.2251,000,000 Radians Per Second to Cycles Per Day = 13750987083.14
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http://calculatorpack.com/average-lap-speed-calculator/
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# Average Lap Speed Calculator
Are you an avid racer looking to improve your lap times? Or perhaps you're a vehicle enthusiast seeking to measure the performance of your ride. Whatever your reason, we have just the tool for you! Our Average Lap Speed Calculator allows you to easily calculate the average speed of your laps around the track. With this handy tool, you can track your progress and make adjustments to your driving technique or vehicle setup to achieve faster lap times. Just enter your lap times and the length of the track, and our calculator will do the rest. So, test your skills and measure your speed with our Average Lap Speed Calculator. Get started today!
## Average Lap Speed Calculator
Calculate your average lap speed by entering the distance and time.
km
minutes
litres
Average Lap Speed Calculator Results
Distance0
Laps Completed0
Time0
Amount of Fuel Used0
Engine SizeUp to 1000cc
Tire Type
Weather ConditionsRainy
Average Speed0
Whether youre a racer or analyzing lap times, our average lap speed calculator complements the average speed calculator. Together, they provide insights into lap performance and overall speed calculations.
## How to Use the Average Lap Speed Calculator
The Average Lap Speed Calculator is a valuable tool that allows you to calculate your average lap speed based on the distance covered and the time taken. Whether you're a racing enthusiast, an athlete, or simply curious about your lap speed, this calculator can provide you with valuable insights. By entering the necessary information, you can quickly determine your average speed per lap. Understanding how to use this calculator can be beneficial for tracking performance, evaluating improvements, and setting goals.
## Instructions for Utilizing the Calculator
To use the Average Lap Speed Calculator, follow these steps:
1. Distance: Enter the total distance of the lap or track you completed. This distance is typically measured in kilometers (km).
2. Laps Completed: Input the number of laps you successfully completed during your activity. This value should be an integer.
3. Time: Enter the total time it took you to complete the laps. This time is usually measured in minutes.
4. Amount of Fuel Used: Specify the amount of fuel consumed during your activity. This value is measured in liters (L).
5. Engine Size: Select the engine size category that corresponds to your vehicle or mode of transport. The options range from Up to 1000cc to 5000cc or more.
6. Tire Type: Choose the type of tires used for your activity. The options include Soft, Medium, and Hard.
7. Weather Conditions: Select the prevailing weather conditions during your activity. The options typically include Rainy, Sunny, and Cloudy.
Once you have entered all the required values and made the appropriate selections, click the Calculate Average Speed button.
## Output Interpretation
After clicking the calculate button, the Average Lap Speed Calculator will provide you with the following results:
1. Distance: This field displays the input distance value in kilometers (km).
2. Laps Completed: Here, you can see the input number of laps completed.
3. Time: This field shows the input time value in minutes.
4. Amount of Fuel Used: This field displays the input fuel consumption value in liters (L).
5. Engine Size: Here, you can find the selected engine size category.
6. Tire Type: This field displays the selected tire type.
7. Weather Conditions: Here, you can see the selected weather conditions.
8. Average Speed: The final output field presents the calculated average lap speed in kilometers per hour (km/h). This value represents the average speed at which you completed each lap.
## Average Lap Speed Formula
The calculation for average lap speed can be expressed using the following formula:
Average Speed = (Distance * Laps Completed) / (Time / 60)
The formula takes into account the distance covered, the number of laps completed, and the time taken to calculate the average lap speed.
## Illustrative Example
Let's consider an example to demonstrate the usage of the Average Lap Speed Calculator. Imagine you completed a race on a track with a total distance of 5 kilometers. You successfully completed 10 laps, and it took you a total of 30 minutes to finish the race. During the race, you consumed 2 liters of fuel. Your vehicle has an engine size of 1500cc - 2000cc, and you used medium tires. The weather conditions were Sunny.
By entering these values into the calculator, you can determine your average lap speed. After calculation, the results will show the distance as 5 km, laps completed as 10, time as 30 minutes, fuel used as 2 L, engine size as 1500cc - 2000cc, tire type as Medium, weather conditions as Sunny, and the average lap speed as 10 km/h.
## Illustrative Table Example
Below is an example table showcasing multiple rows of data that could be entered into the Average Lap Speed Calculator:
Distance (km)
Laps Completed
Time (minutes)
Fuel Used (liters)
Engine Size
Tire Type
Weather Conditions
Average Speed (km/h)
1084532500cc - 3000ccHardRainy13.33
812604.53000cc - 3500ccMediumSunny9.6
66201.5Up to 1000ccSoftCloudy18
The Average Lap Speed Calculator provides a convenient way to determine your average lap speed based on distance and time. By accurately inputting the necessary data, including laps completed, fuel used, engine size, tire type, and weather conditions, you can calculate your average speed per lap. This information can be beneficial for tracking performance, evaluating improvements, and setting goals in various activities, such as racing and athletics. Use the Average Lap Speed Calculator effectively to gain insights into your lap speed and enhance your performance.
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Booleans and Conditionals
In this lab, you will have the opportunity to explore a number of issues relating to predicates, Boolean values, and conditional operations.
Procedures covered in this lab include:
• Type predicates: `boolean?`, `integer?`, `list?`, `null?`, `number?`, `pair?`, `procedure?`, `symbol?`
• Equality comparators: `=`, `eq?`, `eqv?`, `equal?`,
• Numeric comparators: `<` (strictly less than), `<=` (less than or equal to), `=` (equal to), `>=` (greater than or equal to), `>` (strictly greater than)
• Boolean operations: `and`, `or`, `not`
Exercises
Exercise 0: Preparation
You may find it helpful to rescan the readings on Boolean values and conditionals.
You may also want to rescan the reading on numbers.
After making sure that you're prepared, start DrScheme.
Exercise 1: Empty lists
The `null?` predicate determines whether its parameter is an empty list.
Which of the following does Scheme consider an empty list?
• `null`
• `'null`
• `()`
• `(list a)`
• `(list)`
• `'nothing`
• `"()"`
Exercise 2: Equality
Consider the following definitions
```(define alpha (list 'a 'b 'c))
(define beta (list 'a 'b 'c))
(define gamma alpha)
```
Determine which of the lists are `eq?`, `eqv?`, or `equal?`.
Exercise 3: Reflection
What, if anything, did you find surprising in the results of the previous exercises?
By looking at the Scheme report, see if you can find a pair of values that are equal in the sense of `=` but not in the sense of `eqv`.
Exercise 4: What is `not`?
a. What type is `not`?
Exercise 5: Ranges
a. Write a Boolean expression that determines if the value named by `grade` is between 0 and 100, inclusive.
b. Test that expression using different values of `grade`.
Exercise 6: Exploring `and` and `or`
a. Determine the value `and` returns when called with no parameters.
b. Explain why you think the designers of Scheme had `and` return that value.
c. Determine the value `or` returns when called with no parameters.
d. Explain why you think the designers of Scheme had `or` return that value.
Exercise 7: What is it?
Define and test a Scheme predicate `symbol-or-list?` that takes one argument and returns `#t` if the argument is either a symbol or a list, `#f` if it is neither.
Exercise 8: Between, Revisited
Define and test a Scheme predicate `between?` that takes three arguments, all real numbers, and determines whether the second one lies strictly between the first and third (returning `#t` if it is, `#f` if it is not). For example, 6 lies strictly between 5 and 13, so both `(between? 5 6 13)` and `(between? 13 6 5)` should have the value `#t`.
Exercise 9: Triangulation
Three line segments can be assembled into a triangle if, and only if, the length of each of them is less than the sum of the lengths of the other two. Define a Scheme predicate `triangle?` that takes three arguments, all positive real numbers, and determines whether line segments of those three lengths (assumed to be measured in the same units) could be assembled into a triangle.
Exercise 10: Being Neighborly
Define and test a Scheme procedure `neighbor` that takes one argument, an integer, and returns the next higher integer if its argument is even, the next lower integer if its argument is odd. (Start by writing a comment that describes the purpose of the procedure.)
Exercise 11: Non-Boolean Tests
For each of the following expressions, guess what the output should be and then test it in Scheme.
a. `(if #t 'aardvark 'zebra)`
b. `(if #f 'aardvark 'zebra)`
c. `(if (null? null) 'aardvark 'zebra)`
d. `(if (null? 'null) 'aardvark 'zebra)`
e. `(if (null? (list 'a 'b 'c)) 'aardvark 'zebra)`
f. `(if () 'aardvark 'zebra)`
g. `(if (list 'a 'b 'c) 'aardvark 'zebra)`
h. `(if 2 'aardvark 'zebra)`
i. `(if 'true 'aardvark 'zebra)`
j. `(if 'false 'aardvark 'zebra)`
Exercise 12: The Sphinx's Riddle
As you may know, one of the famous riddles of the Sphinx goes something like the following:
What is it that walks upon four legs, then two legs, then three legs?
Write a Scheme procedure, `legs`, that, given someone's age, tells how many legs they walk upon. (You get to choose reasonable ages for the three phases of life.)
Notes
Notes on Problem 6
`(and)` has value true because `and` has a value of true if none of the parameters have value false. Since it has no parameters, none are false.
`(or)` has value false because `or` has value false if none of the parameters is non-false. Since it has no parameters, none are non-false.
History
Wednesday, 6 September 2000 [Samuel A. Rebelsky]
Friday, 8 September 2000 [Samuel A. Rebelsky]
• Fixed some problems.
• Added new exercise on classifying data.
Wednesday, 31 January 2001 [Samuel A. Rebelsky]
• Added the getting started step.
• Added new problem on calling `and` and `or` with no parameters.
Thursday, 1 February 2001 [Samuel A. Rebelsky]
• Added many new problems (taken from an an earlier lab on basic types).
• Updated formatting.
• A few minor changes.
• Added notes on new problem on calling `and` and `or` with no parameters.
Wednesday, 7 February 2001 [Samuel A. Rebelsky]
• Closed a parenthesis in 14.e
• Clarified 16
Tuesday, 10 September 2002 [Samuel A. Rebelsky]
Tuesday, 28 January 2003 [Samuel A. Rebelsky]
Thursday, 28 Janaury 2003 [Samuel A. Rebelsky]
Disclaimer: I usually create these pages on the fly, which means that I rarely proofread them and they may contain bad grammar and incorrect details. It also means that I tend to update them regularly (see the history for more details). Feel free to contact me with any suggestions for changes.
This document was generated by Siteweaver on Fri May 7 09:44:12 2004.
The source to the document was last modified on Wed Jan 28 10:23:10 2004.
This document may be found at `http://www.cs.grinnell.edu/~rebelsky/Courses/CS153/2004S/Labs/conditionals.html`.
You may wish to validate this document's HTML ; ; Check with Bobby
Samuel A. Rebelsky, rebelsky@grinnell.edu
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Explore BrainMass
# Geometric Distribution
This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!
Let N be the number of tosses with a fair coin until tails occurs. What is the characteristic function of N? What is the mean and variance of N? What is the pmf of N? What is the probability that N is an even number?
© BrainMass Inc. brainmass.com June 3, 2020, 11:50 pm ad1c9bdddf
https://brainmass.com/statistics/geometric-probability/determining-probability-coin-toss-example-problem-301962
#### Solution Summary
Provides steps necessary to calculate probability.
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Info
Trending
# How many tablespoons is 23 grams of butter?
## How many tablespoons is 23 grams of butter?
Gram to Tablespoon Conversion Table
Grams Tablespoons
21 g 1.4815 tbsp
22 g 1.5521 tbsp
23 g 1.6226 tbsp
24 g 1.6931 tbsp
## Is one stick of butter 1cup?
One full stick of butter equals 1/2 cup, or 8 tablespoons. Our half sticks equal 1/4 cup of butter, or 4 tablespoons. They can be used interchangeably in recipes. You don’t have to use measuring cups to measure butter.
## How do you measure ¼ cup of butter?
Since you have 1 cup of water in the measuring cup, add the amount of butter cups you need to 1. This will show you the total volume in the measuring cup. For example, if you need ¼ cup of butter, then the measuring cup should have 1 and ¼ cups total when you’re finished.
## What is 23 grams in cups?
How many cups is 23 grams? – 23 grams is equal to 0.10 cups.
## What is 23 grams in tablespoons?
Gram to Tablespoon Conversion Table
Weight in Grams: Volume in Tablespoons of:
Water Granulated Sugar
22 g 1.4878 tbsp 2.1255 tbsp
23 g 1.5554 tbsp 2.2221 tbsp
24 g 1.6231 tbsp 2.3187 tbsp
## How do you measure the volume of butter?
Since you have 1 cup of water in the measuring cup, add the amount of butter cups you need to 1. This will show you the total volume in the measuring cup. For example, if you need ¼ cup of butter, then the measuring cup should have 1 and ¼ cups total when you’re finished.
## How do you calculate how many butter cups you need?
Calculate the amount of butter cups you need. This method works by measuring the amount of water the butter displaces in the measuring cup. Use this simple method to calculate the amount you’ll need. Since you have 1 cup of water in the measuring cup, add the amount of butter cups you need to 1.
## How much butter is in 1 tablespoon of butter?
So if you are using cup measures you could pack the butter into a measuring cup or below is a ready reckoner which may help if you have scales. 1 tablespoon butter = 1/2 ounce/15g.
## How to measure butter-cheat sheet Cups sticks?
How to Measure Butter – Cheat Sheet Cups Sticks Tablespoons Weight (oz) Weight (g)
Since you have 1 cup of water in the measuring cup, add the amount of butter cups you need to 1. This will show you the total volume in the measuring cup. For example, if you need ¼ cup of butter, then the measuring cup should have 1 and ¼ cups total when you’re finished.
## How many tablespoons of butter is 2 / 3 of a cup?
A stick of butter equals 8 tablespoons. If you need 2/3 of a cup of butter, use 1 whole stick of butter, plus approximately 3 tablespoons from another stick.
Calculate the amount of butter cups you need. This method works by measuring the amount of water the butter displaces in the measuring cup. Use this simple method to calculate the amount you’ll need. Since you have 1 cup of water in the measuring cup, add the amount of butter cups you need to 1.
How to Measure Butter – Cheat Sheet Cups Sticks Tablespoons Weight (oz) Weight (g)
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# PLASMA ROTATION¶
## Physical considerations¶
Sonic rotation can arise in tokamaks from torque due to neutral beam injection. It is believed to play an important role in the suppression of turbulence and the formation of transport barriers through $$\mathbf{E}\times\mathbf{B}$$ shear. In addition, it produces a strong centrifugal force that pushes ions toroidally outward, causing them to redistribute nonuniformly around a flux surface. As a result of quasi-neutrality, a poloidally-varying electrostatic potential is generated by the electrons to balance the density asymmetry. This generates centrifugal drifts in addition to the usual $$\mathbf{E}\times\mathbf{B}$$ rotation, Coriolis drift, and parallel velocity shear. Because of their complexity, these centrifugal effects, which are second-order in the main ion Mach number, are ignored in most neoclassical and gyrokinetic codes. Inclusion of full sonic rotation effects is particularly critical for studying transport of heavy impurities [BC08], as the influence of the centrifugal force is amplified by their large mass.
## Sonic rotation formalism¶
The rigorous derivation of the gyrokinetic equations for sonic rotation was carried out by Sugama [SH98]. Sugama followed the underlying rotation formulation of Hinton and Wong [HW85], who showed that in an axisymmetric system the zeroth-order flow velocity is
$\mathbf{U}_0 = \omega_0(\psi) R^2 \nabla \varphi \; .$
It is this scalar flux-function, $$\omega_0$$, that is the true free (input) function in both neoclassical and gyrokinetic theory. Here, $$\psi$$ is the poloidal flux.
## The rotation profile¶
The relevant profile that gives a complete specification of rotation is the angular frequency $$\omega_0(r)$$, which in defined consistently throughout GACODE as
$\omega_0(r) \longrightarrow \frac{c E_r }{R B_p} \; .$
Thus, if the $$E_r$$ is known from a priori analysis (say, through velocity measurements and force balance), then $$\omega_0$$ is given by the formula above. This equality is subtle (hence the reason for the arrow rather than an equality) and is clarified in detail in the last section.
## Input parameters¶
CGYRO and NEO implement full sonic rotation (GYRO implements only a reduced model) according to the formulation of Hinton and Wong [HW85]. Neoclassically, the induced poloidally-varying electrostatic potential leads to the formation of potential wells. In the banana regime these increase the effective trapped particle fraction, and in the Pfirsh-Schlüter regime increase the effective toroidal curvature. In both instances, this may lead to enhanced neoclassical transport. The code inputs are given in the tables below.
Important
Note that all the inputs are derived from the single free function, $$\omega_0$$.
input.cgyro parameter
Definition
Description
GAMMA_E
$$\displaystyle \frac{a}{c_s} \, \gamma_{\rm E} \doteq -\frac{r}{q}\frac{d \omega_{0}}{d r}$$
$$\mathbf{E}\times\mathbf{B}$$ shearing rate
GAMMA_P
$$\displaystyle \frac{a}{c_s} \, \gamma_p \doteq -R_0\frac{d \omega_{0}}{d r}$$
rotation shearing rate
MACH
$$\displaystyle M \doteq \frac{\omega_0 R_0}{c_s}$$
rotation rate
input.neo parameter
Definition
Description
OMEGA_ROT
$$\displaystyle \frac{a}{v_{norm}} \omega_0$$
rotation rate
OMEGA_ROT_DERIV
$$\displaystyle \frac{a^{2}}{v_{norm}} \frac{d \omega_{0}}{dr}$$
derivative of rotation rate
## Theoretical basis for sonic rotation¶
In presence of rapid rotation, where the flow speed $$U$$ is allowed to be of the order of the ion thermal speed, the Lorentz force term in the the Fokker-Planck equation (see [HW85])
$\frac{\partial f_i}{\partial t} + \mathbf{v} \cdot \nabla f_i + \frac{e}{m_i}(\mathbf{E}+\mathbf{v} \times \mathbf{B}) \cdot \frac{\partial f_i}{\partial \mathbf{v}} = C_i + S_i$
becomes the leading term. Under these circumstances Hinton and Wong show that
$\mathbf{E}_{-1} + \frac{\mathbf{U}_0}{c} \times \mathbf{B} = 0 \; ,$
where the subscripts represents the order with respect to the drift ordering in $$\rho_i/a$$. Here $$\mathbf{U}_0$$ is a purely toroidal velocity and is species independent. This ordering is applied to all fields and moments
$\begin{split}\begin{matrix} f_i & = & & & f_{i,0} & + & f_{i,1} & + & \ldots \\ \Phi & = & \Phi_{-1} & + & \Phi_0 & + & \Phi_1 & + & \ldots \\ \mathbf{U} & = & & & \mathbf{U}_0 & + & \mathbf{U}_1 & + & \ldots \\ U_\varphi & = & & & U_{\varphi,0} & + & U_{\varphi,1} & + & \ldots \\ U_\theta & = & & & & & U_{\theta,1} & + & \ldots \end{matrix}\end{split}$
where $$U_\varphi \doteq \mathbf{e}_\varphi \cdot \mathbf{U}$$ is the toroidal velocity and $$U_\theta \doteq \mathbf{e}_\theta \cdot \mathbf{U}$$ is the poloidal velocity. The leading-order sonic flow is toroidal and independent of species
$\mathbf{U}_0 = \omega_0(\psi) R \mathbf{e}_{\varphi} \quad \text{where} \quad \omega_{0}(\psi) \doteq -c \frac{d \Phi_{-1}}{d \psi} \; .$
It is important to note that $$\Phi_{-1}$$ is a flux function, whereas higher orders are not constant on a flux surface.
## Connection to experimental data¶
We remark that $$\omega_{0}$$ is a theoretical quantity that cannot be measured in the experiment. This is similar to the observation that the experimentally-measured temperature $$T_i$$ is really the sum of an equilibrium temperature and a small fluctuating temperature driven by turbulence: $$T_i = T_{i0} + T_{i1}$$. If the drift ordering is valid, then we are justified in approximating the equilibrium temperature $$T_{i0}$$ by the measured temperature $$T_i$$. For the rotation frequency, similar considerations hold. We note that the theory shows that the potential always appears in the combination
$\Phi_{-1} + \left\langle \Phi_0 \right\rangle \; ,$
where an angle bracket denotes a flux-surface average. By analogy with the temperature, the rotation frequency can related to the experimentally-deduced radial electric field $$E_r$$, where $$E_r = -|\nabla r| d\Phi/dr$$, according to
$\omega_0 + \omega_1 \simeq \frac{c E_r}{R B_p} \quad\text{where}\quad \omega_1 \doteq -c \frac{d \left\langle \Phi_0 \right\rangle }{d\psi} \; .$
In practice, we can set $$\omega_1 = 0$$ without loss of generality and all the rotation is contained in $$\omega_0$$. Alternatively, in the diamagnetic rotation limit, we set $$\omega_0 = 0$$ with the rotation contained in $$\omega_1$$. The present theory works consistently in both cases. Finally, the toroidal velocities $$U_{\varphi,0} + U_{\varphi,1}$$ are treated in the same way.
## Consistency with force balance¶
In experimental analyses the radial force balance relation is often used
$E_r = \frac{R B_p}{n_a z_a e} \frac{d p_a}{d\psi} + \frac{U_\varphi}{c} B_p - \frac{U_\theta}{c} B_t \; .$
Important
We emphasize that this relation is valid at long wavelength (equilibrium scales) only, and is subject to the same ordering requirements as standard neoclassical and gyrokinetic theory. This means a restriction on the steepness of gradients in the form $$d \ln p/dr \ll 1/\rho_i$$. See, for example, the discussion in [SWNN11].
The force balance relation contains terms of order 0 and 1, as described in the previous sections. We can write the velocities in terms of the neoclassical flow coefficient $$K_a$$ (see [BC09]) as
\begin{split}\begin{align} U_\varphi = &~ \frac{K_a}{n_a} B_t + \omega_{1,a} R + \omega_0 R \; , \\ U_\theta = &~ \frac{K_a}{n_a} B_p \; . \end{align}\end{split}
In the expression for $$U_\varphi$$, we have defined the angular frequencies
\begin{split}\begin{align} \omega_{1,a} = &~ -c \frac{d \left\langle\Phi_0\right\rangle}{d\psi} - \frac{c}{n_a z_a e} \frac{d p_a}{d\psi} + {\cal O}(M^2) \; , \\ \omega_0 = &~ -c \frac{d \Phi_{-1} }{d\psi} \; . \end{align}\end{split}
Substitution of the neoclassical flows into the force balance relation shows that all species-dependent terms cancel, leaving
$E_r = \frac{R B_p}{c} \left( \omega_0 + \omega_1 \right) \; ,$
where the species-independent frequency $$\omega_1$$ is discussed in the previous section.
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## py_UMom spreadsheet and OptShearCap3600 function
I have now transferred the Ultimate Limit State design functions from the VBA RC Design Functions spreadsheet to Python format. The new spreadsheet and Python code can be downloaded from:
py_UMom.zip
The code also includes the OptShearCap3600 function, described in the previous post.
The python code requires pyxll to connect to Excel. If this is installed, and “RC_UMom” is added to the list of modules to load at start-up in the pyxll.cfg file, the new functions should be available from any spreadsheet.
The included functions are:
py_UMom: ULS design of rectangular sections with two layers of reinforcement under combined bending, axial load, shear and torsion, to Australian and international codes. (Provision for prestressing will be added in the near future):
py_UmomPF: As above, but for Eurocode and British codes using a partial factor approach:
MaxAx: Maximum axial load for short or slender columns:
Devlength: Reinforcement development length to Australian, Eurocode, or British codes:
ShearCap3600: Shear capacity to current AS 3600 and 5100.5:
OptShearCap3600: Optimise shear capacity for given moment/shear ratio by adjusting the compression strut angle:
Extracts of the OptShearCap3600 function code are shown below. The scipy.optimize.brentq function is used to adjust the applied loads to be equal to the design section capacity:
``````# create list of arguments for the py_Umom function, called by the Scipy brentq function
args = [InCells, Puin, 13, 1, Muin, [] , ShearReo, Code, VTuin]
# Use scipy.optimize.brentq to adjust the input shear force to be equal to the design capacity
try:
res = sopt.brentq(call_Umom, mincap, maxcap, args = args, maxiter = 100)
except:
outA[0,0] = 1
return outA
# The call_Umom function adjusts the input loads in proportion to the shear force
# passed by brentq, then calls py_Umom and returns the difference between the
# applied shear and shear capacity
def call_Umom(Vstar, args):
args[8][0,0] = Vstar
args[4][0] = Vstar * MoV
if ToV != 0: args[8][0,1] = Vstar * ToV
if PoV != 0: args[1][0] = Vstar * PoV
res = py_Umom(*args )
return res[1]``````
Similar procedures are used to adjust the applied moment when this is critical, or the compression strut angle in the intermediate range, so that both shear and moment capacities are equal to the applied actions.
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# 14 Other Types of Equations
### Learning Objectives
In this section you will:
• Solve equations involving rational exponents.
• Solve equations using factoring.
• Solve absolute value equations.
• Solve other types of equations.
We have solved linear equations, rational equations, and quadratic equations using several methods. However, there are many other types of equations, and we will investigate a few more types in this section. We will look at equations involving rational exponents, polynomial equations, radical equations, absolute value equations, equations in quadratic form, and some rational equations that can be transformed into quadratics. Solving any equation, however, employs the same basic algebraic rules. We will learn some new techniques as they apply to certain equations, but the algebra never changes.
### Solving Equations Involving Rational Exponents
Rational exponents are exponents that are fractions, where the numerator is a power and the denominator is a root. For example,$\,{16}^{\frac{1}{2}}\,$is another way of writing$\,\sqrt{16};$${8}^{\frac{1}{3}}\,$is another way of writing$\text{}\,\sqrt[3]{8}.\,$The ability to work with rational exponents is a useful skill, as it is highly applicable in calculus.
We can solve equations in which a variable is raised to a rational exponent by raising both sides of the equation to the reciprocal of the exponent. The reason we raise the equation to the reciprocal of the exponent is because we want to eliminate the exponent on the variable term, and a number multiplied by its reciprocal equals 1. For example,$\,\frac{2}{3}\left(\frac{3}{2}\right)=1,$$3\left(\frac{1}{3}\right)=1,$and so on.
### Rational Exponents
A rational exponent indicates a power in the numerator and a root in the denominator. There are multiple ways of writing an expression, a variable, or a number with a rational exponent:
${a}^{\frac{m}{n}}={\left({a}^{\frac{1}{n}}\right)}^{m}={\left({a}^{m}\right)}^{\frac{1}{n}}=\sqrt[n]{{a}^{m}}={\left(\sqrt[n]{a}\right)}^{m}$
### Evaluating a Number Raised to a Rational Exponent
Evaluate$\,{8}^{\frac{2}{3}}.$
Whether we take the root first or the power first depends on the number. It is easy to find the cube root of 8, so rewrite$\,{8}^{\frac{2}{3}}\,$as$\,{\left({8}^{\frac{1}{3}}\right)}^{2}.$
$\begin{array}{ccc}\hfill {\left({8}^{\frac{1}{3}}\right)}^{2}& =\hfill & {\left(2\right)}^{2}\hfill \\ & =& 4\hfill \end{array}$[/hidden-answer]
### Try It
Evaluate$\,{64}^{-\frac{1}{3}}.$
$\frac{1}{4}$
### Solve the Equation Including a Variable Raised to a Rational Exponent
Solve the equation in which a variable is raised to a rational exponent:$\,{x}^{\frac{5}{4}}=32.$
The way to remove the exponent on x is by raising both sides of the equation to a power that is the reciprocal of$\,\frac{5}{4},$which is$\,\frac{4}{5}.$
$\begin{array}{cccc}\hfill {x}^{\frac{5}{4}}& =& 32\hfill & \\ \hfill {\left({x}^{\frac{5}{4}}\right)}^{\frac{4}{5}}& =& {\left(32\right)}^{\frac{4}{5}}\hfill & \\ \hfill x& =& {\left(2\right)}^{4}\hfill & \phantom{\rule{2em}{0ex}}\text{The fifth root of 32 is 2.}\hfill \\ & =& 16\hfill & \end{array}$[/hidden-answer]
### Try It
Solve the equation$\,{x}^{\frac{3}{2}}=125.$
$25$[/hidden-answer]
### Solving an Equation Involving Rational Exponents and Factoring
Solve$\,3{x}^{\frac{3}{4}}={x}^{\frac{1}{2}}.$
This equation involves rational exponents as well as factoring rational exponents. Let us take this one step at a time. First, put the variable terms on one side of the equal sign and set the equation equal to zero.
$\begin{array}{ccc}\hfill 3{x}^{\frac{3}{4}}-\left({x}^{\frac{1}{2}}\right)& =& {x}^{\frac{1}{2}}-\left({x}^{\frac{1}{2}}\right)\hfill \\ \hfill 3{x}^{\frac{3}{4}}-{x}^{\frac{1}{2}}& =& 0\hfill \end{array}$
Now, it looks like we should factor the left side, but what do we factor out? We can always factor the term with the lowest exponent. Rewrite$\,{x}^{\frac{1}{2}}\,$as$\,{x}^{\frac{2}{4}}.\,$Then, factor out$\,{x}^{\frac{2}{4}}\,$from both terms on the left.
$\begin{array}{ccc}\hfill 3{x}^{\frac{3}{4}}-{x}^{\frac{2}{4}}& =& 0\hfill \\ \hfill {x}^{\frac{2}{4}}\left(3{x}^{\frac{1}{4}}-1\right)& =& 0\hfill \end{array}$
Where did$\,{x}^{\frac{1}{4}}\,$come from? Remember, when we multiply two numbers with the same base, we add the exponents. Therefore, if we multiply$\,{x}^{\frac{2}{4}}\,$back in using the distributive property, we get the expression we had before the factoring, which is what should happen. We need an exponent such that when added to$\,\frac{2}{4}\,$equals$\,\frac{3}{4}.\,$Thus, the exponent on x in the parentheses is$\,\frac{1}{4}.\,$
Let us continue. Now we have two factors and can use the zero factor theorem.
$\begin{array}{cccc}\hfill {x}^{\frac{2}{4}}\left(3{x}^{\frac{1}{4}}-1\right)& =& 0\hfill & \\ \hfill {x}^{\frac{2}{4}}& =& 0\hfill & \\ \hfill x& =& 0\hfill & \\ \hfill 3{x}^{\frac{1}{4}}-1& =& 0\hfill & \\ \hfill 3{x}^{\frac{1}{4}}& =& 1\hfill & \\ \hfill {x}^{\frac{1}{4}}& =& \frac{1}{3}\hfill & \phantom{\rule{2em}{0ex}}\text{Divide both sides by 3}.\hfill \\ \hfill {\left({x}^{\frac{1}{4}}\right)}^{4}& =& {\left(\frac{1}{3}\right)}^{4}\hfill & \phantom{\rule{2em}{0ex}}\text{Raise both sides to the reciprocal of }\frac{1}{4}.\hfill \\ \hfill x& =& \frac{1}{81}\hfill & \end{array}$
The two solutions are $\,0$ and $\frac{1}{81}.$[/hidden-answer]
### Try It
Solve:$\,{\left(x+5\right)}^{\frac{3}{2}}=8.$
$\left\{-1\right\}$
### Solving Equations Using Factoring
We have used factoring to solve quadratic equations, but it is a technique that we can use with many types of polynomial equations, which are equations that contain a string of terms including numerical coefficients and variables. When we are faced with an equation containing polynomials of degree higher than 2, we can often solve them by factoring.
### Polynomial Equations
A polynomial of degree n is an expression of the type
${a}_{n}{x}^{n}+{a}_{n-1}{x}^{n-1}+\,\,\,\cdot \,\,\cdot \,\,\cdot \,\,+{a}_{2}{x}^{2}+{a}_{1}x+{a}_{0}$
where n is a positive integer and$\,{a}_{n},\dots ,{a}_{0}\,$are real numbers and$\,{a}_{n}\ne 0.$
Setting the polynomial equal to zero gives a polynomial equation. The total number of solutions (real and complex) to a polynomial equation is equal to the highest exponent n.
### Solving a Polynomial by Factoring
Solve the polynomial by factoring:$\,5{x}^{4}=80{x}^{2}.$
First, set the equation equal to zero. Then factor out what is common to both terms, the GCF.
$\begin{array}{ccc}\hfill 5{x}^{4}-80{x}^{2}& =& 0\hfill \\ \hfill 5{x}^{2}\left({x}^{2}-16\right)& =& 0\hfill \end{array}$
Notice that we have the difference of squares in the factor$\,{x}^{2}-16,$which we will continue to factor and obtain two solutions. The first term,$\,5{x}^{2},$generates, technically, two solutions as the exponent is 2, but they are the same solution.
$\begin{array}{ccc}\hfill 5{x}^{2}& =& 0\hfill \\ \hfill x& =& 0\hfill \\ \hfill {x}^{2}-16& =& 0\hfill \\ \hfill \left(x-4\right)\left(x+4\right)& =& 0\hfill \\ \hfill x& =& 4\hfill \\ \hfill x& =& -4\hfill \end{array}$
The solutions are $\,0\text{ (double solution),}$$4,$ and $\,-4.$[/hidden-answer]
#### Analysis
We can see the solutions on the graph in (Figure). The x-coordinates of the points where the graph crosses the x-axis are the solutions—the x-intercepts. Notice on the graph that at the solution$\,0,$the graph touches the x-axis and bounces back. It does not cross the x-axis. This is typical of double solutions.
### Try It
Solve by factoring:$\,12{x}^{4}=3{x}^{2}.$
$x=0,$$x=\frac{1}{2},$$x=-\frac{1}{2}$
### Solve a Polynomial by Grouping
Solve a polynomial by grouping:$\,{x}^{3}+{x}^{2}-9x-9=0.$
This polynomial consists of 4 terms, which we can solve by grouping. Grouping procedures require factoring the first two terms and then factoring the last two terms. If the factors in the parentheses are identical, we can continue the process and solve, unless more factoring is suggested.
$\begin{array}{ccc}\hfill {x}^{3}+{x}^{2}-9x-9& =& 0\hfill \\ \hfill {x}^{2}\left(x+1\right)-9\left(x+1\right)& =& 0\hfill \\ \hfill \left({x}^{2}-9\right)\left(x+1\right)& =& 0\hfill \end{array}$
The grouping process ends here, as we can factor$\,{x}^{2}-9\,$
using the difference of squares formula.
$\begin{array}{ccc}\left({x}^{2}-9\right)\left(x+1\right)& =& 0\hfill \\ \hfill \left(x-3\right)\left(x+3\right)\left(x+1\right)& =& 0\hfill \\ \hfill x& =& 3\hfill \\ \hfill x& =& -3\hfill \\ \hfill x& =& -1\hfill \end{array}$
The solutions are $3,$$-3,$ and $\,-1.\,$Note that the highest exponent is 3 and we obtained 3 solutions. We can see the solutions, the x-intercepts, on the graph in (Figure).[/hidden-answer]
#### Analysis
We looked at solving quadratic equations by factoring when the leading coefficient is 1. When the leading coefficient is not 1, we solved by grouping. Grouping requires four terms, which we obtained by splitting the linear term of quadratic equations. We can also use grouping for some polynomials of degree higher than 2, as we saw here, since there were already four terms.
Radical equations are equations that contain variables in the radicand (the expression under a radical symbol), such as
$\begin{array}{ccc}\hfill \sqrt{3x+18}& =& x\hfill \\ \hfill \sqrt{x+3}& =& x-3\hfill \\ \hfill \sqrt{x+5}-\sqrt{x-3}& =& 2\hfill \end{array}$
Radical equations may have one or more radical terms, and are solved by eliminating each radical, one at a time. We have to be careful when solving radical equations, as it is not unusual to find extraneous solutions, roots that are not, in fact, solutions to the equation. These solutions are not due to a mistake in the solving method, but result from the process of raising both sides of an equation to a power. However, checking each answer in the original equation will confirm the true solutions.
An equation containing terms with a variable in the radicand is called a radical equation.
### How To
Given a radical equation, solve it.
1. Isolate the radical expression on one side of the equal sign. Put all remaining terms on the other side.
2. If the radical is a square root, then square both sides of the equation. If it is a cube root, then raise both sides of the equation to the third power. In other words, for an nth root radical, raise both sides to the nth power. Doing so eliminates the radical symbol.
3. Solve the remaining equation.
4. If a radical term still remains, repeat steps 1–2.
5. Confirm solutions by substituting them into the original equation.
### Solving an Equation with One Radical
Solve$\,\sqrt{15-2x}=x.$
The radical is already isolated on the left side of the equal side, so proceed to square both sides.
$\begin{array}{ccc}\hfill \sqrt{15-2x}& =& x\hfill \\ \hfill {\left(\sqrt{15-2x}\right)}^{2}& =& {\left(x\right)}^{2}\hfill \\ \hfill 15-2x& =& {x}^{2}\hfill \end{array}$
We see that the remaining equation is a quadratic. Set it equal to zero and solve.
$\begin{array}{ccc}\hfill 0& =& {x}^{2}+2x-15\hfill \\ & =& \left(x+5\right)\left(x-3\right)\hfill \\ \hfill x& =& -5\hfill \\ \hfill x& =& 3\hfill \end{array}$
The proposed solutions are $-5\,$ and $3.\,$Let us check each solution back in the original equation. First, check$\,x=-5.$
$\begin{array}{ccc}\hfill \sqrt{15-2x}& =& x\hfill \\ \hfill \sqrt{15-2\left(-5\right)}& =& -5\hfill \\ \hfill \sqrt{25}& =& -5\hfill \\ \hfill 5& \ne & -5\hfill \end{array}$
This is an extraneous solution. While no mistake was made solving the equation, we found a solution that does not satisfy the original equation.
Check$\,x=3.$
$\begin{array}{ccc}\hfill \sqrt{15-2x}& =& x\hfill \\ \hfill \sqrt{15-2\left(3\right)}& =& 3\hfill \\ \hfill \sqrt{9}& =& 3\hfill \\ \hfill 3& =& 3\hfill \end{array}$
The solution is $\,3.$[/hidden-answer]
### Try It
Solve the radical equation:$\,\sqrt{x+3}=3x-1$
$x=1;$extraneous solution$\,x=-\frac{2}{9}$
Solve$\,\sqrt{2x+3}+\sqrt{x-2}=4.$
As this equation contains two radicals, we isolate one radical, eliminate it, and then isolate the second radical.
$\begin{array}{cccc}\hfill \sqrt{2x+3}+\sqrt{x-2}& =& 4\hfill & \\ \hfill \sqrt{2x+3}& =& 4-\sqrt{x-2}\hfill & \phantom{\rule{2em}{0ex}}\text{Subtract }\sqrt{x-2}\text{ from both sides}.\hfill \\ \hfill {\left(\sqrt{2x+3}\right)}^{2}& =& {\left(4-\sqrt{x-2}\right)}^{2}\hfill & \phantom{\rule{2em}{0ex}}\text{Square both sides}.\hfill \end{array}$
Use the perfect square formula to expand the right side:$\,{\left(a-b\right)}^{2}={a}^{2}-2ab+{b}^{2}.$
$\begin{array}{cccc}\hfill 2x+3& =& {\left(4\right)}^{2}-2\left(4\right)\sqrt{x-2}+{\left(\sqrt{x-2}\right)}^{2}\hfill & \\ \hfill 2x+3& =& 16-8\sqrt{x-2}+\left(x-2\right)\hfill & \\ \hfill 2x+3& =& 14+x-8\sqrt{x-2}\hfill & \phantom{\rule{2em}{0ex}}\text{Combine like terms}.\hfill \\ \hfill x-11& =& -8\sqrt{x-2}\hfill & \phantom{\rule{2em}{0ex}}\text{Isolate the second radical}.\hfill \\ \hfill {\left(x-11\right)}^{2}& =& {\left(-8\sqrt{x-2}\right)}^{2}\hfill & \phantom{\rule{2em}{0ex}}\text{Square both sides}.\hfill \\ \hfill {x}^{2}-22x+121& =& 64\left(x-2\right)\hfill & \end{array}$
Now that both radicals have been eliminated, set the quadratic equal to zero and solve.
$\begin{array}{cccc}\hfill {x}^{2}-22x+121& =& 64x-128\hfill & \\ \hfill {x}^{2}-86x+249& =& 0\hfill & \\ \hfill \left(x-3\right)\left(x-83\right)& =& 0\hfill & \phantom{\rule{2em}{0ex}}\text{Factor and solve}.\hfill \\ \hfill x& =& 3\hfill & \\ \hfill x& =& 83\hfill & \end{array}$
The proposed solutions are $\,3\,$ and $\,83.\,$Check each solution in the original equation.
$\begin{array}{ccc}\hfill \sqrt{2x+3}+\sqrt{x-2}& =& 4\hfill \\ \hfill \sqrt{2x+3}& =& 4-\sqrt{x-2}\hfill \\ \hfill \sqrt{2\left(3\right)+3}& =& 4-\sqrt{\left(3\right)-2}\hfill \\ \hfill \sqrt{9}& =& 4-\sqrt{1}\hfill \\ \hfill 3& =& 3\hfill \end{array}$
One solution is $\,3.$
Check$\,x=83.$
$\begin{array}{ccc}\hfill \sqrt{2x+3}+\sqrt{x-2}& =& 4\hfill \\ \hfill \sqrt{2x+3}& =& 4-\sqrt{x-2}\hfill \\ \hfill \sqrt{2\left(83\right)+3}& =& 4-\sqrt{\left(83-2\right)}\hfill \\ \hfill \sqrt{169}& =& 4-\sqrt{81}\hfill \\ \hfill 13& \ne & -5\hfill \end{array}$
The only solution is $\,3.\,$We see that$\,x=83\,$is an extraneous solution.[/hidden-answer]
### Try It
Solve the equation with two radicals:$\,\sqrt{3x+7}+\sqrt{x+2}=1.$
$x=-2;$extraneous solution$\,x=-1$
### Solving an Absolute Value Equation
Next, we will learn how to solve an absolute value equation. To solve an equation such as$\,|2x-6|=8,$we notice that the absolute value will be equal to 8 if the quantity inside the absolute value bars is$\,8\,$or$\,-8.\,$This leads to two different equations we can solve independently.
$\begin{array}{ccccccc}\hfill 2x-6& =& 8\hfill & \phantom{\rule{2em}{0ex}}\text{or}\phantom{\rule{2em}{0ex}}& \hfill 2x-6& =& -8\hfill \\ \hfill 2x& =& 14& & \hfill 2x& =& -2\hfill \\ \hfill x& =& 7\hfill & & \hfill x& =& -1\hfill \end{array}$
Knowing how to solve problems involving absolute value functions is useful. For example, we may need to identify numbers or points on a line that are at a specified distance from a given reference point.
### Absolute Value Equations
The absolute value of x is written as$\,|x|.\,$It has the following properties:
$\begin{array}{l}\text{If }x\ge 0,\text{ then }|x|=x.\hfill \\ \text{If }x<0,\text{ then }|x|=-x.\hfill \end{array}$
For real numbers$\,A\,$and$\,B,$an equation of the form$\,|A|=B,$with$\,B\ge 0,$will have solutions when$\,A=B\,$or$\,A=-B.\,$If$\,B<0,$the equation$\,|A|=B\,$has no solution.
An absolute value equation in the form$\,|ax+b|=c\,$has the following properties:
$\begin{array}{l}\text{If }c<0,|ax+b|=c\text{ has no solution}.\hfill \\ \text{If }c=0,|ax+b|=c\text{ has one solution}.\hfill \\ \text{If }c>0,|ax+b|=c\text{ has two solutions}.\hfill \end{array}$
### How To
Given an absolute value equation, solve it.
1. Isolate the absolute value expression on one side of the equal sign.
2. If$\,c>0,$write and solve two equations:$\,ax+b=c\,$and$\,ax+b=-c.$
### Solving Absolute Value Equations
Solve the following absolute value equations:
• (a) $|6x+4|=8$
• (b) $|3x+4|=-9$
• (c) $|3x-5|-4=6$
• (d) $|-5x+10|=0$
• (a) $|6x+4|=8$
Write two equations and solve each:
$\begin{array}{ccccccc}\hfill 6x+4& =& 8\hfill & \phantom{\rule{5em}{0ex}}& \hfill 6x+4& =& -8\hfill \\ \hfill 6x& =& 4\hfill & \phantom{\rule{5em}{0ex}}& \hfill 6x& =& -12\hfill \\ \hfill x& =& \frac{2}{3}\hfill & \phantom{\rule{5em}{0ex}}& \hfill x& =& -2\hfill \end{array}$
The two solutions are $\,\frac{2}{3}$ and $-2.$
• (b) $|3x+4|=-9$
There is no solution as an absolute value cannot be negative.
• (c) $|3x-5|-4=6$
Isolate the absolute value expression and then write two equations.
$\begin{array}{ccccccccc}& & & \hfill |3x-5|-4& =& 6\hfill & & & \\ & & & \hfill |3x-5|& =& 10\hfill & & & \\ \hfill 3x-5& =& 10\hfill & & & & \hfill 3x-5& =& -10\hfill \\ \hfill 3x& =& 15\hfill & & & & \hfill 3x& =& -5\hfill \\ \hfill x& =& 5\hfill & & & & \hfill x& =& -\frac{5}{3}\hfill \end{array}$
There are two solutions: $\,5,$ and $-\frac{5}{3}.$
• (d) $|-5x+10|=0$
The equation is set equal to zero, so we have to write only one equation.
$\begin{array}{ccc}\hfill -5x+10& =& 0\hfill \\ \hfill -5x& =& -10\hfill \\ \hfill x& =& 2\hfill \end{array}$
There is one solution: $\,2.$[/hidden-answer]
### Try It
Solve the absolute value equation:$|1-4x|+8=13.$
$x=-1,$$x=\frac{3}{2}$
### Solving Other Types of Equations
There are many other types of equations in addition to the ones we have discussed so far. We will see more of them throughout the text. Here, we will discuss equations that are in quadratic form, and rational equations that result in a quadratic.
#### Solving Equations in Quadratic Form
Equations in quadratic form are equations with three terms. The first term has a power other than 2. The middle term has an exponent that is one-half the exponent of the leading term. The third term is a constant. We can solve equations in this form as if they were quadratic. A few examples of these equations include$\,{x}^{4}-5{x}^{2}+4=0,{x}^{6}+7{x}^{3}-8=0,$and$\,{x}^{\frac{2}{3}}+4{x}^{\frac{1}{3}}+2=0.\,$In each one, doubling the exponent of the middle term equals the exponent on the leading term. We can solve these equations by substituting a variable for the middle term.
If the exponent on the middle term is one-half of the exponent on the leading term, we have an equation in quadratic form, which we can solve as if it were a quadratic. We substitute a variable for the middle term to solve equations in quadratic form.
### How To
Given an equation quadratic in form, solve it.
1. Identify the exponent on the leading term and determine whether it is double the exponent on the middle term.
2. If it is, substitute a variable, such as u, for the variable portion of the middle term.
3. Rewrite the equation so that it takes on the standard form of a quadratic.
4. Solve using one of the usual methods for solving a quadratic.
5. Replace the substitution variable with the original term.
6. Solve the remaining equation.
### Solving a Fourth-degree Equation in Quadratic Form
Solve this fourth-degree equation:$\,3{x}^{4}-2{x}^{2}-1=0.$
This equation fits the main criteria, that the power on the leading term is double the power on the middle term. Next, we will make a substitution for the variable term in the middle. Let$\,u={x}^{2}.$Rewrite the equation in u.
$3{u}^{2}-2u-1=0$
$\begin{array}{ccc}\hfill 3{u}^{2}-2u-1& =& 0\hfill \\ \hfill \left(3u+1\right)\left(u-1\right)& =& 0\hfill \end{array}$
Solve each factor and replace the original term for u.
$\begin{array}{ccc}\hfill 3u+1& =& 0\hfill \\ \hfill 3u& =& -1\hfill \\ \hfill u& =& -\frac{1}{3}\hfill \\ \hfill {x}^{2}& =& -\frac{1}{3}\hfill \\ \hfill x& =& ±i\sqrt{\frac{1}{3}}\hfill \end{array}$
$\begin{array}{ccc}\hfill u-1& =& 0\hfill \\ \hfill u& =& 1\hfill \\ \hfill {x}^{2}& =& 1\hfill \\ \hfill x& =& ±1\hfill \end{array}$
The solutions are $\,±i\sqrt{\frac{1}{3}}\,$ and $\,±1.$[/hidden-answer]
### Try It
Solve using substitution:$\,{x}^{4}-8{x}^{2}-9=0.$
$x=-3,3,-i,i$
### Solving an Equation in Quadratic Form Containing a Binomial
Solve the equation in quadratic form:$\,{\left(x+2\right)}^{2}+11\left(x+2\right)-12=0.$
This equation contains a binomial in place of the single variable. The tendency is to expand what is presented. However, recognizing that it fits the criteria for being in quadratic form makes all the difference in the solving process. First, make a substitution, letting$\,u=x+2.\,$Then rewrite the equation in u.
$\begin{array}{ccc}\hfill {u}^{2}+11u-12& =& 0\hfill \\ \hfill \left(u+12\right)\left(u-1\right)& =& 0\hfill \end{array}$
Solve using the zero-factor property and then replace u with the original expression.
$\begin{array}{ccc}\hfill u+12& =& 0\hfill \\ \hfill u& =& -12\hfill \\ \hfill x+2& =& -12\hfill \\ \hfill x& =& -14\hfill \end{array}$
The second factor results in
$\begin{array}{ccc}\hfill u-1& =& 0\hfill \\ \hfill u& =& 1\hfill \\ \hfill x+2& =& 1\hfill \\ \hfill x& =& -1\hfill \end{array}$
We have two solutions: $\,-14,$ and $-1.$[/hidden-answer]
### Try It
Solve:$\,{\left(x-5\right)}^{2}-4\left(x-5\right)-21=0.$
$x=2,x=12$
#### Solving Rational Equations Resulting in a Quadratic
Earlier, we solved rational equations. Sometimes, solving a rational equation results in a quadratic. When this happens, we continue the solution by simplifying the quadratic equation by one of the methods we have seen. It may turn out that there is no solution.
Solve the following rational equation:$\,\frac{-4x}{x-1}+\frac{4}{x+1}=\frac{-8}{{x}^{2}-1}.$
We want all denominators in factored form to find the LCD. Two of the denominators cannot be factored further. However,$\,{x}^{2}-1=\left(x+1\right)\left(x-1\right).\,$Then, the LCD is$\,\left(x+1\right)\left(x-1\right).\,$Next, we multiply the whole equation by the LCD.
$\begin{array}{ccc}\hfill \left(x+1\right)\left(x-1\right)\left[\frac{-4x}{x-1}+\frac{4}{x+1}\right]& =& \left[\frac{-8}{\left(x+1\right)\left(x-1\right)}\right]\left(x+1\right)\left(x-1\right)\hfill \\ \hfill -4x\left(x+1\right)+4\left(x-1\right)& =& -8\hfill \\ \hfill -4{x}^{2}-4x+4x-4& =& -8\hfill \\ \hfill -4{x}^{2}+4& =& 0\hfill \\ \hfill -4\left({x}^{2}-1\right)& =& 0\hfill \\ \hfill -4\left(x+1\right)\left(x-1\right)& =& 0\hfill \\ \hfill x& =& -1\hfill \\ \hfill x& =& 1\hfill \end{array}$
In this case, either solution produces a zero in the denominator in the original equation. Thus, there is no solution.[/hidden-answer]
### Try It
Solve$\,\frac{3x+2}{x-2}+\frac{1}{x}=\frac{-2}{{x}^{2}-2x}.$
$x=-1,$$x=0$is not a solution.
Access these online resources for additional instruction and practice with different types of equations.
### Key Concepts
• Rational exponents can be rewritten several ways depending on what is most convenient for the problem. To solve, both sides of the equation are raised to a power that will render the exponent on the variable equal to 1. See (Figure), (Figure), and (Figure).
• Factoring extends to higher-order polynomials when it involves factoring out the GCF or factoring by grouping. See (Figure) and (Figure).
• We can solve radical equations by isolating the radical and raising both sides of the equation to a power that matches the index. See (Figure) and (Figure).
• To solve absolute value equations, we need to write two equations, one for the positive value and one for the negative value. See (Figure).
• Equations in quadratic form are easy to spot, as the exponent on the first term is double the exponent on the second term and the third term is a constant. We may also see a binomial in place of the single variable. We use substitution to solve. See (Figure) and (Figure).
• Solving a rational equation may also lead to a quadratic equation or an equation in quadratic form. See (Figure).
### Section Exercises
#### Verbal
In a radical equation, what does it mean if a number is an extraneous solution?
This is not a solution to the radical equation, it is a value obtained from squaring both sides and thus changing the signs of an equation which has caused it not to be a solution in the original equation.
Explain why possible solutions must be checked in radical equations.
Your friend tries to calculate the value$\,-{9}^{\frac{3}{2}}$and keeps getting an ERROR message. What mistake is he or she probably making?
He or she is probably trying to enter negative 9, but taking the square root of$\,-9\,$is not a real number. The negative sign is in front of this, so your friend should be taking the square root of 9, cubing it, and then putting the negative sign in front, resulting in$\,-27.$
Explain why$\,|2x+5|=-7\,$has no solutions.
Explain how to change a rational exponent into the correct radical expression.
A rational exponent is a fraction: the denominator of the fraction is the root or index number and the numerator is the power to which it is raised.
#### Algebraic
For the following exercises, solve the rational exponent equation. Use factoring where necessary.
${x}^{\frac{2}{3}}=16$
${x}^{\frac{3}{4}}=27$
$x=81$
$2{x}^{\frac{1}{2}}-{x}^{\frac{1}{4}}=0$
${\left(x-1\right)}^{\frac{3}{4}}=8$
$x=17$
${\left(x+1\right)}^{\frac{2}{3}}=4$
${x}^{\frac{2}{3}}-5{x}^{\frac{1}{3}}+6=0$
$x=8, x=27$
${x}^{\frac{7}{3}}-3{x}^{\frac{4}{3}}-4{x}^{\frac{1}{3}}=0$
For the following exercises, solve the following polynomial equations by grouping and factoring.
${x}^{3}+2{x}^{2}-x-2=0$
$x=-2,1,-1$
$3{x}^{3}-6{x}^{2}-27x+54=0$
$4{y}^{3}-9y=0$
$y=0, \frac{3}{2}, \frac{-3}{2}$
${x}^{3}+3{x}^{2}-25x-75=0$
${m}^{3}+{m}^{2}-m-1=0$
$m=1,-1$
$2{x}^{5}-14{x}^{3}=0$
$5{x}^{3}+45x=2{x}^{2}+18$
$x=\frac{2}{5},±3i$
For the following exercises, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions.
$\sqrt{3x-1}-2=0$
$\sqrt{x-7}=5$
$x=32$
$\sqrt{x-1}=x-7$
$\sqrt{3t+5}=7$
$t=\frac{44}{3}$
$\sqrt{t+1}+9=7$
$\sqrt{12-x}=x$
$x=3$
$\sqrt{2x+3}-\sqrt{x+2}=2$
$\sqrt{3x+7}+\sqrt{x+2}=1$
$x=-2$
$\sqrt{2x+3}-\sqrt{x+1}=1$
For the following exercises, solve the equation involving absolute value.
$|3x-4|=8$
$x=4,\frac{-4}{3}$
$|2x-3|=-2$
$|1-4x|-1=5$
$x=\frac{-5}{4},\frac{7}{4}$
$|4x+1|-3=6$
$|2x-1|-7=-2$
$x=3,-2$
$|2x+1|-2=-3$
$|x+5|=0$
$x=-5$
$-|2x+1|=-3$
For the following exercises, solve the equation by identifying the quadratic form. Use a substitute variable and find all real solutions by factoring.
${x}^{4}-10{x}^{2}+9=0$
$x=1,-1,3,-3$
$4{\left(t-1\right)}^{2}-9\left(t-1\right)=-2$
${\left({x}^{2}-1\right)}^{2}+\left({x}^{2}-1\right)-12=0$
$x=2,-2$
${\left(x+1\right)}^{2}-8\left(x+1\right)-9=0$
${\left(x-3\right)}^{2}-4=0$
$x=1,5$
#### Extensions
For the following exercises, solve for the unknown variable.
${x}^{-2}-{x}^{-1}-12=0$
$\sqrt{{|x|}^{2}}=x$
All real numbers
${t}^{10}-{t}^{5}+1=0$
$|{x}^{2}+2x-36|=12$
$x=4,6,-6,-8$
#### Real-World Applications
For the following exercises, use the model for the period of a pendulum,$\,T,$such that$\,T=2\pi \sqrt{\frac{L}{g}},$where the length of the pendulum is L and the acceleration due to gravity is$\,g.$
If the acceleration due to gravity is 9.8 m/s2 and the period equals 1 s, find the length to the nearest cm (100 cm = 1 m).
If the gravity is 32 ft/s2 and the period equals 1 s, find the length to the nearest in. (12 in. = 1 ft). Round your answer to the nearest in.
10 in.
For the following exercises, use a model for body surface area, BSA, such that$\,BSA=\sqrt{\frac{wh}{3600}},$where w = weight in kg and h = height in cm.
Find the height of a 72-kg female to the nearest cm whose$\,BSA=1.8.$
Find the weight of a 177-cm male to the nearest kg whose$\,BSA=2.1.$
90 kg
### Glossary
absolute value equation
an equation in which the variable appears in absolute value bars, typically with two solutions, one accounting for the positive expression and one for the negative expression
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Course detail
# Probability and Statistics
The course focuses on consolidating and expanding students' knowledge of probability theory, mathematical statistics and theory of selected methods of operations research. Thus it begins with a thorough and correct introduction of probability and its basic properties. Then we define a random variable, its numerical characteristics and distribution. On this basis we then build descriptive statistics and statistical hypothesis testing problem, the choice of the appropriate test and explanation of conclusions and findings of tests. In operational research we discuss linear programming and its geometric and algebraic solutions, transportation and assignment problem, and an overview of the dynamic and probabilistic programming methods and inventories. In this section the illustrative examples are taken primarily from economics.
Learning outcomes of the course unit
After completing the course the student will be able to:
• Describe the role of probability using set operations.
• Calculate basic parameters of random variables, both continuous and discrete ones.
• Define basic statistical data.
• List the basic statistical tests.
• Describe the work with statistical tables.
• Select the appropriate method for statistical processing of input data and perform statistical test.
• Explain the nature of linear programming.
• Convert a word problem into the canonical form and solve it using a suitable method.
• Perform sensitivity analysis in a geometric and algebraic way.
• Convert the specified role into its dual.
• Calculate the optimal solution transport tasks and task assignment optimal solution.
• List the different models in stocks reserve.
Prerequisites
We require knowledge at the level of bachelor's degree, i.e. students must have proficiency in working with sets (intersection, union, complement), be able to work with matrices, handle the calculation of solving systems of linear algebraic equations using the elimination method and calculation of the matrix inverse, know graphs of elementary functions and methods of their design, differentiate and integrate of basic functions.
Co-requisites
Not applicable.
Recommended optional programme components
Not applicable.
Recommended or required reading
BAŠTINEC, J., FAJMON, B., KOLÁČEK, J., Pravděpodobnost, statistika a operační výzkum. Brno 2014. 360 stran. (CS)
B.Fajmon, J. Koláček. Pravděpodobnost, statistika a operační výzkum. Brno: FEKT VUT, 2005. s. 1 ( s.) (CS)
ZAPLETAL, J., základy počtu pravděpodobnosti a matematické statistiky. Skriptum FEI VUT, PC DIR Brno 1995. (CS)
Montgomery, D.C., Runger, G.C.: Applied Statistics and Probability for Engineers. Third Edition. John Wiley \& Sons, Inc., New York 2003. (CS)
LOFTUS, J., , LOFTUS, E., Essence of Statistics. Second Edition. Alfred A.Knopf, New York 1988. (CS)
J.Loftus, E.Loftus: Essence of Statistics. Second Edition. Alfred A.Knopf, New York 1988. (CS)
BAŠTINEC, J., ZAPLETAL, J., Statistika, pravděpodobnost, operační výzkum. Statistika, pravděpodobnost, operační výzkum. Brno: 2007. s. 1-161. (CS)
Planned learning activities and teaching methods
Techning methods include lectures and computer laboratories. Students have to write a four single homework during the course.
Assesment methods and criteria linked to learning outcomes
Students may be awarded
Up to 40 points for computer exercises (written test 20 points, 4 homework each max. 5 points).
Up to 60 points for the written final exam. The test contains both theoretical and numerical tasks that are used to verify the orientation of students in statistics and operations research. Numerical tasks are included to verify the student's ability to apply statistical and optimization methods in technical and economic practice.
Requirements for successful completion of the are course provided in an annual public notice.
Language of instruction
Czech
Work placements
Not applicable.
Course curriculum
1. Classical and axiomatic definitions of probability. Conditional probability, total probability., Random variable, numerical characteristics.
2. Discrete and continuous distributions of random variables. Properties of the normal distribution. Limit theorems.
3. Statistics. Selection. Statistical processing of the material. Basic parameters and characteristics of the population selection.
4. Basic point and interval estimates. t-test, F-test. The confidence intervals.
5. Linear regression. Post-hoc tests. Goodness.
6. Analysis of variance.
7. Paired test, unpaired test.
8. Non-parametric tests.
9. Operations Research. Linear programming. Graphic solution. Simplex method.
10. Dual role. The sensitivity analysis.
11. The economic interpretation of linear programming.
12. Transport role. Assignment task.
13. Dynamic programming, recursive algorithms, models in stocks reserve.
Aims
The objecive of the course is to enlarge the knowledge in the area of statistical tests and confidence intervals, to show some spheres of mathematical thinking in economics and to introduce the concepts of recursive algorithms.
Specification of controlled education, way of implementation and compensation for absences
Computer exercises are compulsory. Properly excused absence can be replaced by individual homework, which focuses on the issues discussed during the missed exercise.
Specifications of the controlled activities and ways of implementation are provided in annual public notice.
Date of the written test is announced in agreement with the students at least one week in advance. The new term for properly excused students is usually during the credit week.
Classification of course in study plans
• Programme BPC-IBE Bachelor's, 2. year of study, winter semester, 6 credits, compulsory
#### Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Computer-assisted exercise
26 hours, compulsory
Teacher / Lecturer
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# Mathcad - UF-ESI-6321-12-01-02 - UF-ESI-6321 UF-ESI-02.xmcd...
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UF-ESI-6321 UF-ESI-6321-12-01-02.xmcd page 1 of 2 12.1.2 Suppose that the purity of a chemical solution y is related to the amount of a catalyst x through a linear regression model with β 0 := 123.0 β 1 := 2.16 and with an error standard deviation := 4.1 σ := 0 ε Ex := β 0 + x + ε () β 1 (a) What is the expected value of the purity when the catalyst level is x := 20 Ex = 79.8 () (b) How much does the expected value of the purity change when the catalyst level increases by Δ x := 10 Ex + Δ x () () Ex = 21.6 (c) What is the probability that the purity is less than Y := 60.0 when the catalyst level is x := 25 Ex = 69 () Y Ex () ZY , x :=
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() σ ZY , x = 2.195 () cnorm Z Y ( , x ) = 0.0141 () Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435 UF-ESI-6321 UF-ESI-6321-12-01-02.xmcd page 2 of 2 (d) What is the probability that the purity is between Y 1 := 30 and Y 2 := 40 when the catalyst level is x := 40 Ex = 36.6 () Z Y 1 , x = 1.61 ()
Z Y 2 , x = 0.829 () cnorm Z Y
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Ask a homework question - tutors are online
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+0
# Need help with this
0
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1.
2.
Oct 1, 2018
#1
+6203
+1
Presumably solutions means solutions to f(x) = 0
In this case there are 3 unique solutions, you can read them right off as
x = 3, x = -2, x = 1
in (2)
a, b, and c are the values for which f(x) = 0, i.e. crosses the x axis
Oct 2, 2018
edited by Rom Oct 2, 2018
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# Printable Fractions To Decimals Worksheet Pdf
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Seventh Grade General Math Convert Fractions Decimals Percents Wks 10 Thumbna Fractions Decimals Percents Decimals Converting Fractions Decimals Percents
### Use the place value of the last digit for example 0 85 100 85 20 17 5 on a calculator press.
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Solutions ⇒ Class 8th ⇒ Science ⇒ 11. Force And Pressure
# Solutions 11. Force And Pressure - Chapter Review | Class 8 Science - Toppers Study
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## Solutions 11. Force And Pressure - Chapter Review | Class 8 Science - Toppers Study
##### Chapter Review:
• A push or a pull on an object is called a force.
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• Liquids and gases exert pressure on the walls of their containers.
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How does adding honey affect ABV? - Home Brew Forums
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Home Brew Forums > How does adding honey affect ABV?
12-18-2011, 07:57 PM #1
ozorgnax
Recipes
Sep 2010
Greece
Posts: 17
An example: After the boil I take a hydrometer reading (OG1). After about a week in the primary I add some honey in the fermenter and take another reading (OG2). After the honey has been fermented and I measure yet again the gravity (FG). How do I calculate ABV?
12-18-2011, 08:45 PM #2
BrewStooge
Recipes
Apr 2009
Howard Lake, MN
Posts: 186
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Well according to beersmith's figgures 1lb of honey added about 4 points to a 5 gallon batch so just add however many points may bee needed based on the amount of honey to your first OG reading, figgure ABV after it's finished off your new OG and FG as normal.
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12-18-2011, 09:07 PM #3
ozorgnax
Recipes
Sep 2010
Greece
Posts: 17
Quote:
Originally Posted by BrewStooge Well according to beersmith's figgures 1lb of honey added about 4 points to a 5 gallon batch so just add however many points may bee needed based on the amount of honey to your first OG reading, figgure ABV after it's finished off your new OG and FG as normal.
So just to get this straight if I had an OG of 1.040 and then added 1lb of honey in a 5 gallon batch, the OG would pump up to 1.044, correct?
12-18-2011, 09:26 PM #4
BrewStooge
Recipes
Apr 2009
Howard Lake, MN
Posts: 186
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Ah the lowly yeast, how many deals have been made over the results of their fine work?
12-19-2011, 06:45 AM #5
Doomsday
Recipes
Sep 2011
Posts: 170
Liked 8 Times on 8 Posts
Just be careful with the ratios.
The table in How to Brew states: (percentages are based on weight of total fermentables)
3-10% = For a subtle honey flavor in most light ales and lagers.
11-30% = For a distinct honey flavor note to develope. Stronger hop flavors, caramelized or roasted malts, spices, or other ingredients should be considered when formulating the recipe, to balance the strong honey flavors at these levels.
and 30+% = well you shouldnt be taking that route anyways.
I just picked up some macadamia nut honey from my brew shop, cant wait to use it!
12-19-2011, 07:00 AM #6
starrfish
Recipes
Oct 2008
Florence, SC
Posts: 1,984
Liked 32 Times on 26 Posts
I've had good luck staying in the 20% of total ingredients range (which has been about 2 to 2.5 lbs). In herb beers like coriander and now basil (can't wait to keg this one) seems to compliment herbs well. I tend to use local honey if possible.
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12-19-2011, 06:51 PM #7
dcp27
Recipes
Jan 2010
Medford, MA
Posts: 4,125
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Quote:
Originally Posted by BrewStooge Well according to beersmith's figgures 1lb of honey added about 4 points to a 5 gallon batch
that doesn't sound right. honey is definitely more than 20ppg. it varies, but it should be around 30-35ppg, so 6-7 points
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CC-MAIN-2016-44
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longest
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en
| 0.931219
|
https://www.numbersaplenty.com/290012225
| 1,719,215,628,000,000,000
|
text/html
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Search a number
290012225 = 5211600489
BaseRepresentation
bin10001010010010…
…011110001000001
3202012201010222112
4101102103301001
51043220342400
644435545105
710121030456
oct2122236101
9665633875
10290012225
11139782528
128115b195
1348111989
142a73382d
151a6d9835
hex11493c41
290012225 has 6 divisors (see below), whose sum is σ = 359615190. Its totient is φ = 232009760.
The previous prime is 290012189. The next prime is 290012227. The reversal of 290012225 is 522210092.
It can be written as a sum of positive squares in 3 ways, for example, as 54051904 + 235960321 = 7352^2 + 15361^2 .
It is a de Polignac number, because none of the positive numbers 2k-290012225 is a prime.
It is a Curzon number.
It is a self number, because there is not a number n which added to its sum of digits gives 290012225.
It is not an unprimeable number, because it can be changed into a prime (290012227) by changing a digit.
It is a pernicious number, because its binary representation contains a prime number (11) of ones.
It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 5800220 + ... + 5800269.
It is an arithmetic number, because the mean of its divisors is an integer number (59935865).
Almost surely, 2290012225 is an apocalyptic number.
290012225 is a gapful number since it is divisible by the number (25) formed by its first and last digit.
It is an amenable number.
290012225 is a deficient number, since it is larger than the sum of its proper divisors (69602965).
290012225 is a wasteful number, since it uses less digits than its factorization.
290012225 is an odious number, because the sum of its binary digits is odd.
The sum of its prime factors is 11600499 (or 11600494 counting only the distinct ones).
The product of its (nonzero) digits is 720, while the sum is 23.
The square root of 290012225 is about 17029.7453005029. The cubic root of 290012225 is about 661.9198956570.
The spelling of 290012225 in words is "two hundred ninety million, twelve thousand, two hundred twenty-five".
Divisors: 1 5 25 11600489 58002445 290012225
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| 3.28125
| 3
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CC-MAIN-2024-26
|
latest
|
en
| 0.874129
|
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