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# First Five Multiples Of 9
First Five Multiples Of 9. Write first five multiples of (a) 5 (b) 8 (c) 9. 0, 9, 18, 27, 36 details 0 is multiple of 9, because 9 x 0 = 0 9 is multiple of 9, because 9 x 1 = 9 18 is multiple of 9, because 9 x 2 = 18 27 is multiple of 9, because 9 x 3 = 27 36 is multiple of 9, because 9 x 4 = 36 the sum of the. 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180,. To calculate the sum of the first 6 multiples of 9, you need to find out the first 6 multiples of 9.
The first five natural numbers are 1, 2, 3, 4, 5. The first 5 multiples of 9 are: Zero is a multiple of any.
## For the tens places, note that the number 9 can be thought of as 0 tens and.
9, 18, 27, 36, 45, 54, 63, 72. The average of the first five multiples of 9 is: 0, 9, 18, 27, 36.
## Any Number Is A Multiple Of Itself (N X 1 = N).
Average = (9 + 18 + 27 + 36 + 45)/5 ⇒. Now add the first 6 multiples of 9;. The average of the first five multiples of 9 is: The first 8 multiples of 9 given:
### Multiples Of 9 Are The Numbers 9, 18, 27, 36, 45, 54, 63, 72, 81, 90… Notice That The Set Of Numbers Generates A Sequence Wherein The Difference Of Two Consecutive Numbers In The.
The first 5 multiples of 9 are:
### Kesimpulan dari First Five Multiples Of 9.
Pasagot po ty brainliest ko po yung. 0, 9, 18, 27, 36. Zero is a multiple of any. The first 5 multiples of 5 are:
See also The First Restriction Endonuclease Isolated Was | 550 | 1,481 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.34375 | 4 | CC-MAIN-2022-49 | latest | en | 0.795199 |
https://mathematicsart.com/solved-exercises/solution-calculate-the-integral-int_01-eeex-eex-ex-d-x/ | 1,720,834,769,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514459.28/warc/CC-MAIN-20240712224556-20240713014556-00676.warc.gz | 331,465,616 | 31,129 | Home -> Solved problems -> Calculate the integral
### Solution
\begin{aligned} g(x)&=e^{x} \\\\ g(g(g(x)))&=e^{e^{e^{x}}} \\\\ (g(g(g(x))))^{\prime} &=g^{\prime}(g(g(x))) g^{\prime}(g(x)) g^{\prime}(x)\\\\&=e^{e^{e^{x}}} e^{e^{x}} e^{x} \\\\ \int_{0}^{1} e^{e^{e^{x}}} e^{e^{x}} e^{x} d x &=\int_{0}^{1}(g(g(g(x))))^{\prime} d x \\\\ &=[g(g(g(x)))]_{0}^{1} \\\\ &=\left[e^{e^{e^{x}}}\right]_{0}^{1} \\\\ &=e^{e^{e^{1}}}-e^{e^{e^{0}}}=e^{e^{e}}-e^{e} \approx 3.814 \times 10^{6}\\\\ \int_{0}^{1} e^{e^{e^{x}}} e^{e^{x}} e^{x} d x &\approx 3.814 \times 10^{6} \end{aligned}
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Home -> Solved problems -> Calculate the integral | 1,033 | 3,490 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.953125 | 4 | CC-MAIN-2024-30 | latest | en | 0.68679 |
https://readtiger.com/wkp/en/Rhombus | 1,547,803,604,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583660020.5/warc/CC-MAIN-20190118090507-20190118112507-00252.warc.gz | 623,732,965 | 12,253 | # Rhombus
Rhombus
Two rhombi
Edges and vertices4
Schläfli symbol{ } + { }
Coxeter diagram
Symmetry groupDihedral (D2), [2], (*22), order 4
Area${\displaystyle K={\frac {p\cdot q}{2}}}$ (half the product of the diagonals)
Dual polygonrectangle
Propertiesconvex, isotoxal
The rhombus has a square as a special case, and is a special case of a kite and parallelogram.
In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a simple (non-self-intersecting) quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. The rhombus is often called a diamond, after the diamonds suit in playing cards which resembles the projection of an octahedral diamond, or a lozenge, though the former sometimes refers specifically to a rhombus with a 60° angle (see Polyiamond), and the latter sometimes refers specifically to a rhombus with a 45° angle.
Every rhombus is a parallelogram and a kite. A rhombus with right angles is a square.[1][2]
## Etymology
The word "rhombus" comes from Greek ῥόμβος (rhombos), meaning something that spins,[3] which derives from the verb ῥέμβω (rhembō), meaning "to turn round and round."[4] The word was used both by Euclid and Archimedes, who used the term "solid rhombus" for two right circular cones sharing a common base.[5]
The surface we refer to as rhombus today is a cross section of this solid rhombus through the apex of each of the two cones.
## Characterizations
A simple (non-self-intersecting) quadrilateral is a rhombus if and only if it is any one of the following:[6][7]
• a parallelogram in which a diagonal bisects an interior angle
• a parallelogram in which at least two consecutive sides are equal in length
• a parallelogram in which the diagonals are perpendicular (an orthodiagonal parallelogram)
• a quadrilateral with four sides of equal length (by definition)
• a quadrilateral in which the diagonals are perpendicular and bisect each other
• a quadrilateral in which each diagonal bisects two opposite interior angles
• a quadrilateral ABCD possessing a point P in its plane such that the four triangles ABP, BCP, CDP, and DAP are all congruent[8]
• a quadrilateral ABCD in which the incircles in triangles ABC, BCD, CDA and DAB have a common point[9]
## Basic properties
Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides. Using congruent triangles, one can prove that the rhombus is symmetric across each of these diagonals. It follows that any rhombus has the following properties:
The first property implies that every rhombus is a parallelogram. A rhombus therefore has all of the properties of a parallelogram: for example, opposite sides are parallel; adjacent angles are supplementary; the two diagonals bisect one another; any line through the midpoint bisects the area; and the sum of the squares of the sides equals the sum of the squares of the diagonals (the parallelogram law). Thus denoting the common side as a and the diagonals as p and q, in every rhombus
${\displaystyle \displaystyle 4a^{2}=p^{2}+q^{2}.}$
Not every parallelogram is a rhombus, though any parallelogram with perpendicular diagonals (the second property) is a rhombus. In general, any quadrilateral with perpendicular diagonals, one of which is a line of symmetry, is a kite. Every rhombus is a kite, and any quadrilateral that is both a kite and parallelogram is a rhombus.
A rhombus is a tangential quadrilateral.[10] That is, it has an inscribed circle that is tangent to all four sides.
## Area
A rhombus. Each angle marked with a black dot is a right angle. The height h is the perpendicular distance between any two non-adjacent sides, which equals the diameter of the circle inscribed. The diagonals of lengths p and q are the red dotted line segments.
As for all parallelograms, the area K of a rhombus is the product of its base and its height (h). The base is simply any side length a:
${\displaystyle K=a\cdot h.}$
The area can also be expressed as the base squared times the sine of any angle:
${\displaystyle K=a^{2}\cdot \sin \alpha =a^{2}\cdot \sin \beta ,}$
or in terms of the height and a vertex angle:
${\displaystyle K={\frac {h^{2}}{\sin \alpha }},}$
or as half the product of the diagonals p, q:
${\displaystyle K={\frac {p\cdot q}{2}},}$
or as the semiperimeter times the radius of the circle inscribed in the rhombus (inradius):
${\displaystyle K=2a\cdot r.}$
Another way, in common with parallelograms, is to consider two adjacent sides as vectors, forming a bivector, so the area is the magnitude of the bivector (the magnitude of the vector product of the two vectors), which is the determinant of the two vectors' Cartesian coordinates: K = x1y2x2y1.[11]
## Diagonals
The length of the diagonals p = AC and q = BD can be expressed in terms of the rhombus side a and one vertex angle α as
${\displaystyle p=a{\sqrt {2+2\cos {\alpha }}}}$
and
${\displaystyle q=a{\sqrt {2-2\cos {\alpha }}}.}$
These formulas are a direct consequence of the law of cosines.
The inradius (the radius of a circle inscribed in the rhombus), denoted by r, can be expressed in terms of the diagonals p and q as:[10]
${\displaystyle r={\frac {p\cdot q}{2{\sqrt {p^{2}+q^{2}}}}}.}$
## Dual properties
The dual polygon of a rhombus is a rectangle:[12]
• A rhombus has all sides equal, while a rectangle has all angles equal.
• A rhombus has opposite angles equal, while a rectangle has opposite sides equal.
• A rhombus has an inscribed circle, while a rectangle has a circumcircle.
• A rhombus has an axis of symmetry through each pair of opposite vertex angles, while a rectangle has an axis of symmetry through each pair of opposite sides.
• The diagonals of a rhombus intersect at equal angles, while the diagonals of a rectangle are equal in length.
• The figure formed by joining the midpoints of the sides of a rhombus is a rectangle and vice versa.
## Equation
The sides of a rhombus centered at the origin, with diagonals each falling on an axis, consist of all points (x, y) satisfying
${\displaystyle \left|{\frac {x}{a}}\right|\!+\left|{\frac {y}{b}}\right|\!=1.}$
The vertices are at ${\displaystyle (\pm a,0)}$ and ${\displaystyle (0,\pm b).}$ This is a special case of the superellipse, with exponent 1.
## Other properties
As topological square tilings As 30-60 degree rhombille tiling
Some polyhedra with all rhombic faces
Identical rhombi Two types of rhombi
Rhombohedron Rhombic dodecahedron Rhombic triacontahedron Rhombic icosahedron Rhombic enneacontahedron
### As the faces of a polyhedron
A rhombohedron is a three-dimensional figure like a cube, except that its six faces are rhombi instead of squares.
The rhombic dodecahedron is a convex polyhedron with 12 congruent rhombi as its faces.
The rhombic triacontahedron is a convex polyhedron with 30 golden rhombi (rhombi whose diagonals are in the golden ratio) as its faces.
The great rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron with 30 intersecting rhombic faces.
The rhombic hexecontahedron is a stellation of the rhombic triacontahedron. It is nonconvex with 60 golden rhombic faces with icosahedral symmetry.
The rhombic enneacontahedron is a polyhedron composed of 90 rhombic faces, with three, five, or six rhombi meeting at each vertex. It has 60 broad rhombi and 30 slim ones.
The trapezo-rhombic dodecahedron is a convex polyhedron with 6 rhombic and 6 trapezoidal faces.
The rhombic icosahedron is a polyhedron composed of 20 rhombic faces, of which three, four, or five meet at each vertex. It has 10 faces on the polar axis with 10 faces following the equator.
## References
1. ^ Note: Euclid's original definition and some English dictionaries' definition of rhombus excludes squares, but modern mathematicians prefer the inclusive definition.
2. ^ Weisstein, Eric W. "Square". MathWorld. inclusive usage
3. ^ ῥόμβος, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus
4. ^ ρέμβω, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus
5. ^ The Origin of Rhombus
6. ^ Zalman Usiskin and Jennifer Griffin, "The Classification of Quadrilaterals. A Study of Definition", Information Age Publishing, 2008, pp. 55-56.
7. ^ Owen Byer, Felix Lazebnik and Deirdre Smeltzer, Methods for Euclidean Geometry, Mathematical Association of America, 2010, p. 53.
8. ^ Paris Pamfilos (2016), "A Characterization of the Rhombus", Forum Geometricorum 16, pp. 331–336, [1]
9. ^ IMOmath, "26-th Brazilian Mathematical Olympiad 2004"
10. ^ a b
11. ^ WildLinAlg episode 4, Norman J Wildberger, Univ. of New South Wales, 2010, lecture via youtube
12. ^ de Villiers, Michael, "Equiangular cyclic and equilateral circumscribed polygons", Mathematical Gazette 95, March 2011, 102-107. | 2,420 | 8,874 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 13, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.21875 | 4 | CC-MAIN-2019-04 | latest | en | 0.908135 |
https://www.equationsworksheets.net/solving-systems-of-equations-by-elimination-worksheet-answers-with-work/ | 1,702,241,652,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679102637.84/warc/CC-MAIN-20231210190744-20231210220744-00349.warc.gz | 832,156,731 | 14,905 | # Solving Systems Of Equations By Elimination Worksheet Answers With Work
Solving Systems Of Equations By Elimination Worksheet Answers With Work – The goal of Expressions and Equations Worksheets is for your child to be able to learn more efficiently and effectively. These worksheets include interactive exercises and problems based on the order of operations. These worksheets make it easy for children to grasp complex concepts and concepts fast. These PDFs are free to download and may be used by your child to test math problems. These are helpful for students between 5th and 8th Grades.
These worksheets can be utilized by students in the 5th through 8th grades. These two-step word problems are constructed using fractions and decimals. Each worksheet contains ten problems. These worksheets are available on the internet and printed. These worksheets are a great way to learn to reorganize equations. In addition to allowing students to practice the art of rearranging equations, they aid your student in understanding the properties of equality and reverse operations.
These worksheets are suitable for use by fifth- and eighth grade students. They are great for those who have trouble calculating percentages. You can choose from three different types of problems. You can decide to tackle one-step challenges that contain decimal numbers or whole numbers or use word-based methods to solve problems involving decimals and fractions. Each page will contain 10 equations. The Equations Worksheets are suggested for students in the 5th through 8th grade.
These worksheets can be used to learn fraction calculation and other concepts in algebra. Many of these worksheets allow users to select from three different kinds of problems. You can select one that is word-based, numerical or a mixture of both. The problem type is also vital, as each will have a distinct problem kind. Each page will have ten challenges, making them a great resource for students from 5th to 8th grade.
The worksheets will teach students about the relationship between variables as well as numbers. These worksheets help students practice solving polynomial equations and discover how to use equations to solve problems in everyday life. If you’re in search of a great educational tool to master the art of expressions and equations, you can start with these worksheets. These worksheets will help you learn about the various types of mathematical issues as well as the many symbols that are used to express them.
These worksheets can be extremely useful for students in the first grade. These worksheets will help them learn to graph and solve equations. These worksheets are ideal for practicing with polynomial variable. They can help you understand how to factor them and simplify them. There are numerous worksheets available to help kids learn equations. Making the work yourself is the most effective way to understand equations.
There are many worksheets to learn about quadratic equations. Each level has its own worksheet. The worksheets are designed to allow you to practice solving problems of the fourth degree. After you’ve completed an appropriate level, you can continue working on other types of equations. You can continue to work on the same level problems. You can, for example solve the same problem as an elongated one. | 617 | 3,334 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2023-50 | latest | en | 0.948136 |
https://www.advancedconverter.com/other-converters/fuel-consumption/miles-per-gallon-US-to-gallons-per-100-mi-UK | 1,679,416,421,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296943704.21/warc/CC-MAIN-20230321162614-20230321192614-00385.warc.gz | 704,215,928 | 9,529 | Convert Mpg (US) to Gallons per 100 mi (UK)
# Conversion mpg to gallon per 100mi (UK)
(US) Miles per gallon (mpg, US) is fuel consumption indicator. Therefore, this is, how many miles a vehicle moves in every gallon. The (US)gallon is defined as exactly 3.785411784 litres.
This tool converts mpg (US) to gallons per 100 mi (UK) (mpg to gal/100mi) and vice versa. These sizes (mpg to gal/100mi) are inversely proportional. Therefore, when one increases the other size decreases. 1 mile per gallon(US) = 83.267418462899 gallons per 100 mi (UK). The user must fill one of the two fields and the conversion will become automatically.
liters per 100 km (l/100km) liters per km (l/km) kilometers per liter (km/l) kilometers per gallon (US) (km/gal) miles per liter (m/l) gallons per 100 mi (US) (gal/100m) gallons per mile (US)(gal/m) mpg (US) gallons per 100 mi (UK)(gal/100m) gallons per mile (UK) mpg (UK) liters per 100 km (l/100km) liters per km (l/km) kilometers per liter (km/l) kilometers per gallon (US) (km/gal) miles per liter (m/l) gallons per 100 mi (US) (gal/100m) gallons per mile (US)(gal/m) mpg (US) gallons per 100 mi (UK)(gal/100m) gallons per mile (UK) mpg (UK) <=> precision:auto0 decimal1 decimal2 decimals3 decimals4 decimals5 decimals6 decimals7 decimals8 decimals9 decimals10 decimals11 decimals12 decimals
1 mpg (US) = 83.2674 gallons per 100 mi (UK)
Formula mpg (US) in gallons per 100 mi (UK) (mpg in gal/100mi). Gal per 100mi = 83.267418462899/(mpg)
### Conversions mpg (US) to other units
Mpg to Liters/100km Mpg to Liters/km Mpg to Km/lt Mpg to Km/gal(US) Mpg to Miles/lt Mpg to Gal/100mi(US) Mpg to Gallons/mi(US) Mpg to Gal/100mi(UK) Mpg to Gallons/mi(UK) Mpg to Mpg (UK)
Table mpg to gal per 100mi(UK)
1 mpg = 83.2674 gal/100mi11 mpg = 7.5698 gal/100mi21 mpg = 3.9651 gal/100mi
2 mpg = 41.6337 gal/100mi12 mpg = 6.939 gal/100mi22 mpg = 3.7849 gal/100mi
3 mpg = 27.7558 gal/100mi13 mpg = 6.4052 gal/100mi23 mpg = 3.6203 gal/100mi
4 mpg = 20.8169 gal/100mi14 mpg = 5.9477 gal/100mi24 mpg = 3.4695 gal/100mi
5 mpg = 16.6535 gal/100mi15 mpg = 5.5512 gal/100mi25 mpg = 3.3307 gal/100mi
6 mpg = 13.8779 gal/100mi16 mpg = 5.2042 gal/100mi26 mpg = 3.2026 gal/100mi
7 mpg = 11.8953 gal/100mi17 mpg = 4.8981 gal/100mi27 mpg = 3.084 gal/100mi
8 mpg = 10.4084 gal/100mi18 mpg = 4.626 gal/100mi28 mpg = 2.9738 gal/100mi
9 mpg = 9.2519 gal/100mi19 mpg = 4.3825 gal/100mi29 mpg = 2.8713 gal/100mi
10 mpg = 8.3267 gal/100mi20 mpg = 4.1634 gal/100mi30 mpg = 2.7756 gal/100mi
11 mpg = 7.5698 gal/100mi21 mpg = 3.9651 gal/100mi31 mpg = 2.686 gal/100mi
12 mpg = 6.939 gal/100mi22 mpg = 3.7849 gal/100mi32 mpg = 2.6021 gal/100mi
13 mpg = 6.4052 gal/100mi23 mpg = 3.6203 gal/100mi33 mpg = 2.5233 gal/100mi
14 mpg = 5.9477 gal/100mi24 mpg = 3.4695 gal/100mi34 mpg = 2.449 gal/100mi
15 mpg = 5.5512 gal/100mi25 mpg = 3.3307 gal/100mi35 mpg = 2.3791 gal/100mi
16 mpg = 5.2042 gal/100mi26 mpg = 3.2026 gal/100mi36 mpg = 2.313 gal/100mi
17 mpg = 4.8981 gal/100mi27 mpg = 3.084 gal/100mi37 mpg = 2.2505 gal/100mi
18 mpg = 4.626 gal/100mi28 mpg = 2.9738 gal/100mi38 mpg = 2.1912 gal/100mi
19 mpg = 4.3825 gal/100mi29 mpg = 2.8713 gal/100mi39 mpg = 2.1351 gal/100mi
20 mpg = 4.1634 gal/100mi30 mpg = 2.7756 gal/100mi40 mpg = 2.0817 gal/100mi
21 mpg = 3.9651 gal/100mi31 mpg = 2.686 gal/100mi41 mpg = 2.0309 gal/100mi
22 mpg = 3.7849 gal/100mi32 mpg = 2.6021 gal/100mi42 mpg = 1.9826 gal/100mi
23 mpg = 3.6203 gal/100mi33 mpg = 2.5233 gal/100mi43 mpg = 1.9365 gal/100mi
24 mpg = 3.4695 gal/100mi34 mpg = 2.449 gal/100mi44 mpg = 1.8924 gal/100mi
25 mpg = 3.3307 gal/100mi35 mpg = 2.3791 gal/100mi45 mpg = 1.8504 gal/100mi
26 mpg = 3.2026 gal/100mi36 mpg = 2.313 gal/100mi46 mpg = 1.8102 gal/100mi
27 mpg = 3.084 gal/100mi37 mpg = 2.2505 gal/100mi47 mpg = 1.7716 gal/100mi
28 mpg = 2.9738 gal/100mi38 mpg = 2.1912 gal/100mi48 mpg = 1.7347 gal/100mi
29 mpg = 2.8713 gal/100mi39 mpg = 2.1351 gal/100mi49 mpg = 1.6993 gal/100mi
30 mpg = 2.7756 gal/100mi40 mpg = 2.0817 gal/100mi50 mpg = 1.6653 gal/100mi
31 mpg = 2.686 gal/100mi41 mpg = 2.0309 gal/100mi51 mpg = 1.6327 gal/100mi
32 mpg = 2.6021 gal/100mi42 mpg = 1.9826 gal/100mi52 mpg = 1.6013 gal/100mi
33 mpg = 2.5233 gal/100mi43 mpg = 1.9365 gal/100mi53 mpg = 1.5711 gal/100mi
34 mpg = 2.449 gal/100mi44 mpg = 1.8924 gal/100mi54 mpg = 1.542 gal/100mi
35 mpg = 2.3791 gal/100mi45 mpg = 1.8504 gal/100mi55 mpg = 1.514 gal/100mi
36 mpg = 2.313 gal/100mi46 mpg = 1.8102 gal/100mi56 mpg = 1.4869 gal/100mi
37 mpg = 2.2505 gal/100mi47 mpg = 1.7716 gal/100mi57 mpg = 1.4608 gal/100mi
38 mpg = 2.1912 gal/100mi48 mpg = 1.7347 gal/100mi58 mpg = 1.4356 gal/100mi
39 mpg = 2.1351 gal/100mi49 mpg = 1.6993 gal/100mi59 mpg = 1.4113 gal/100mi
40 mpg = 2.0817 gal/100mi50 mpg = 1.6653 gal/100mi60 mpg = 1.3878 gal/100mi
41 mpg = 2.0309 gal/100mi51 mpg = 1.6327 gal/100mi61 mpg = 1.365 gal/100mi
42 mpg = 1.9826 gal/100mi52 mpg = 1.6013 gal/100mi62 mpg = 1.343 gal/100mi
43 mpg = 1.9365 gal/100mi53 mpg = 1.5711 gal/100mi63 mpg = 1.3217 gal/100mi
44 mpg = 1.8924 gal/100mi54 mpg = 1.542 gal/100mi64 mpg = 1.3011 gal/100mi
45 mpg = 1.8504 gal/100mi55 mpg = 1.514 gal/100mi65 mpg = 1.281 gal/100mi
46 mpg = 1.8102 gal/100mi56 mpg = 1.4869 gal/100mi66 mpg = 1.2616 gal/100mi
47 mpg = 1.7716 gal/100mi57 mpg = 1.4608 gal/100mi67 mpg = 1.2428 gal/100mi
48 mpg = 1.7347 gal/100mi58 mpg = 1.4356 gal/100mi68 mpg = 1.2245 gal/100mi
49 mpg = 1.6993 gal/100mi59 mpg = 1.4113 gal/100mi69 mpg = 1.2068 gal/100mi
50 mpg = 1.6653 gal/100mi60 mpg = 1.3878 gal/100mi70 mpg = 1.1895 gal/100mi
51 mpg = 1.6327 gal/100mi61 mpg = 1.365 gal/100mi71 mpg = 1.1728 gal/100mi
52 mpg = 1.6013 gal/100mi62 mpg = 1.343 gal/100mi72 mpg = 1.1565 gal/100mi
53 mpg = 1.5711 gal/100mi63 mpg = 1.3217 gal/100mi73 mpg = 1.1406 gal/100mi
54 mpg = 1.542 gal/100mi64 mpg = 1.3011 gal/100mi74 mpg = 1.1252 gal/100mi
55 mpg = 1.514 gal/100mi65 mpg = 1.281 gal/100mi75 mpg = 1.1102 gal/100mi
56 mpg = 1.4869 gal/100mi66 mpg = 1.2616 gal/100mi76 mpg = 1.0956 gal/100mi
57 mpg = 1.4608 gal/100mi67 mpg = 1.2428 gal/100mi77 mpg = 1.0814 gal/100mi
58 mpg = 1.4356 gal/100mi68 mpg = 1.2245 gal/100mi78 mpg = 1.0675 gal/100mi
59 mpg = 1.4113 gal/100mi69 mpg = 1.2068 gal/100mi79 mpg = 1.054 gal/100mi
60 mpg = 1.3878 gal/100mi70 mpg = 1.1895 gal/100mi80 mpg = 1.0408 gal/100mi
61 mpg = 1.365 gal/100mi71 mpg = 1.1728 gal/100mi81 mpg = 1.028 gal/100mi
62 mpg = 1.343 gal/100mi72 mpg = 1.1565 gal/100mi82 mpg = 1.0155 gal/100mi
63 mpg = 1.3217 gal/100mi73 mpg = 1.1406 gal/100mi83 mpg = 1.0032 gal/100mi
64 mpg = 1.3011 gal/100mi74 mpg = 1.1252 gal/100mi84 mpg = 0.9913 gal/100mi
65 mpg = 1.281 gal/100mi75 mpg = 1.1102 gal/100mi85 mpg = 0.9796 gal/100mi
66 mpg = 1.2616 gal/100mi76 mpg = 1.0956 gal/100mi86 mpg = 0.9682 gal/100mi
67 mpg = 1.2428 gal/100mi77 mpg = 1.0814 gal/100mi87 mpg = 0.9571 gal/100mi
68 mpg = 1.2245 gal/100mi78 mpg = 1.0675 gal/100mi88 mpg = 0.9462 gal/100mi
69 mpg = 1.2068 gal/100mi79 mpg = 1.054 gal/100mi89 mpg = 0.9356 gal/100mi
70 mpg = 1.1895 gal/100mi80 mpg = 1.0408 gal/100mi90 mpg = 0.9252 gal/100mi
### Fuel Consumption Conversions
Liters/100km to Liters/km Liters/100km to Km/lt Liters/100km to Km/gal(US) Liters/100km to Miles/lt Liters/100km to Gal/100mi(US) Liters/100km to Gallons/mi(US) Liters/100km to Mpg Liters/100km to Gal/100mi(UK) Liters/100km to Gallons/mi(UK) Liters/100km to Mpg (UK) Liters/km to Liters/100km Liters/km to Km/lt Liters/km to Km/gal(US) Liters/km to Miles/lt Liters/km to Gal/100mi(US) Liters/km to Gallons/mi(US) Liters/km to Mpg Liters/km to Gal/100mi(UK) Liters/km to Gallons/mi(UK) Liters/km to Mpg (UK) Km/lt to Liters/100km Km/lt to Liters/km Km/lt to Km/gal(US) Km/lt to Miles/lt Km/lt to Gal/100mi(US) Km/lt to Gallons/mi(US) Km/lt to Mpg Km/lt to Gal/100mi(UK) Km/lt to Gallons/mi(UK) Km/lt to Mpg (UK) Km/gal(US) to Liters/100km Km/gal(US) to Liters/km Km/gal(US) to Km/lt Km/gal(US) to Miles/lt Km/gal(US) to Gal/100mi(US) Km/gal(US) to Gallons/mi(US) Km/gal(US) to Mpg Km/gal(US) to Gal/100mi(UK) Km/gal(US) to Gallons/mi(UK) Km/gal(US) to Mpg (UK) Miles/lt to Liters/100km Miles/lt to Liters/km Miles/lt to Km/lt Miles/lt to Km/gal(US) Miles/lt to Gal/100mi(US) Miles/lt to Gallons/mi(US) Miles/lt to Mpg Miles/lt to Gal/100mi(UK) Miles/lt to Gallons/mi(UK) Miles/lt to Mpg (UK) Gal/100mi(US) to Liters/100km Gal/100mi(US) to Liters/km Gal/100mi(US) to Km/lt Gal/100mi(US) to Km/gal(US) Gal/100mi(US) to Miles/lt Gal/100mi(US) to Gallons/mi(US) Gal/100mi(US) to Mpg Gal/100mi(US) to Gal/100mi(UK) Gal/100mi(US) to Gallons/mi(UK) Gal/100mi(US) to Mpg (UK) Gallons/mi(US) to Liters/100km Gallons/mi(US) to Liters/km Gallons/mi(US) to Km/lt Gallons/mi(US) to Km/gal(US) Gallons/mi(US) to Miles/lt Gallons/mi(US) to Gal/100mi(US) Gallons/mi(US) to Mpg Gallons/mi(US) to Gal/100mi(UK) Gallons/mi(US) to Gallons/mi(UK) Gallons/mi(US) to Mpg (UK) Gal/100mi(UK) to Liters/100km Gal/100mi(UK) to Liters/km Gal/100mi(UK) to Km/lt Gal/100mi(UK) to Km/gal(US) Gal/100mi(UK) to Miles/lt Gal/100mi(UK) to Gal/100mi(US) Gal/100mi(UK) to Gallons/mi(US) Gal/100mi(UK) to Mpg Gal/100mi(UK) to Gallons/mi(UK) Gal/100mi(UK) to Mpg (UK) Gallons/mi(UK) to Liters/100km Gallons/mi(UK) to Liters/km Gallons/mi(UK) to Km/lt Gallons/mi(UK) to Km/gal(US) Gallons/mi(UK) to Miles/lt Gallons/mi(UK) to Gal/100mi(US) Gallons/mi(UK) to Gallons/mi(US) Gallons/mi(UK) to Mpg Gallons/mi(UK) to Gal/100mi(UK) Gallons/mi(UK) to Mpg (UK) Mpg (UK) to Liters/100km Mpg (UK) to Liters/km Mpg (UK) to Km/lt Mpg (UK) to Km/gal(US) Mpg (UK) to Miles/lt Mpg (UK) to Gal/100mi(US) Mpg (UK) to Gallons/mi(US) Mpg (UK) to Mpg Mpg (UK) to Gal/100mi(UK) Mpg (UK) to Gallons/mi(UK) | 4,245 | 9,610 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.921875 | 3 | CC-MAIN-2023-14 | latest | en | 0.474916 |
http://formulas.ultrafractal.com/reference/reb/REB_TrapShapeCircle.html | 1,643,307,729,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320305277.88/warc/CC-MAIN-20220127163150-20220127193150-00352.warc.gz | 24,401,935 | 3,576 | ## reb Class REB_TrapShapeCircle
```Object
common:Generic
common:TrapShape
reb:REB_TrapShapeCircle
```
`class TrapShape:REB_TrapShapeCircle`
This shape uses the circle function.
This variant of the circle function has a signed and absolute value version of the distance. The function also has a complex conjugate. The transformed value is the complex return value of the function.
Ultra Fractal Source
``` class REB_TrapShapeCircle(common.ulb:TrapShape) {
; This shape uses the circle function.<br>
; <p>
; This variant of the circle function has a signed and absolute value
; version of the distance. The function also has a complex conjugate.
; The transformed value is the complex return value of the function.
public:
import "common.ulb"
; Constructor
func REB_TrapShapeCircle(Generic pparent)
TrapShape.TrapShape(pparent)
endfunc
; Call this for each iteration being trapped.
float func Iterate(complex pz)
TrapShape.Iterate(pz)
float theta = 0
float d = 0
float rr = 0
theta = atan2(pz)
int sgn = 1
if @sgn
sgn = -1
endif
rr = @a*sin(theta)^2 + 0.2*@b*cos(theta)^2
if @absval
d = abs(cabs(pz) - cabs(rr*cos(theta) + sgn*flip(rr*sin(theta))))
else
d = cabs(pz - (rr*cos(theta) + sgn*flip(rr*sin(theta))))
endif
m_LastZ = (rr*cos(theta) + sgn*flip(rr*sin(theta)))
return d
endfunc
default:
title = "Circle"
int param v_trapshapecircle
caption = "Version (Trap Shape Circle)"
default = 101
hint = "This version parameter is used to detect when a change has been made to the formula that is incompatible with the previous version. When that happens, this field will reflect the old version number to alert you to the fact that an alternate rendering is being used."
visible = @v_trapshapecircle < 101
endparam
float param a
caption = "Polar parameter"
default = 0.2
hint = "Affects spread and scale of trap"
endparam
float param b
caption = "2nd Polar parameter"
default = 1.0
hint = "Affects spread and scale of trap"
endparam
bool param sgn
caption = "Conjugate transform"
default = false
endparam
param absval
caption = "Absolute Value"
default = false
endparam
}
```
Constructor Summary
`REB_TrapShapeCircle()`
`REB_TrapShapeCircle(Generic pparent)`
Constructor
Method Summary
` float` `Iterate(complex pz)`
Call this for each iteration being trapped.
Methods inherited from class common:TrapShape
`GetColorChannel, GetTextureValue, GetTransformedPoint, Init, IterateSilent, SetThreshold`
Methods inherited from class common:Generic
`GetParent`
Methods inherited from class Object
Constructor Detail
### REB_TrapShapeCircle
`public REB_TrapShapeCircle(Generic pparent)`
Constructor
### REB_TrapShapeCircle
`public REB_TrapShapeCircle()`
Method Detail
### Iterate
`public float Iterate(complex pz)`
Call this for each iteration being trapped.
Overrides:
`Iterate` in class `TrapShape` | 751 | 2,813 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2022-05 | longest | en | 0.667381 |
https://nrich.maths.org/public/leg.php?code=-89&cl=4&cldcmpid=5645 | 1,508,404,715,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187823260.52/warc/CC-MAIN-20171019084246-20171019104246-00676.warc.gz | 749,678,061 | 6,477 | # Search by Topic
#### Resources tagged with Limits similar to Production Equation:
Filter by: Content type:
Stage:
Challenge level:
### There are 19 results
Broad Topics > Pre-Calculus and Calculus > Limits
### Production Equation
##### Stage: 5 Challenge Level:
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
### Spokes
##### Stage: 5 Challenge Level:
Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.
### Resistance
##### Stage: 5 Challenge Level:
Find the equation from which to calculate the resistance of an infinite network of resistances.
### Reciprocal Triangles
##### Stage: 5 Challenge Level:
Prove that the sum of the reciprocals of the first n triangular numbers gets closer and closer to 2 as n grows.
### Fractional Calculus III
##### Stage: 5
Fractional calculus is a generalisation of ordinary calculus where you can differentiate n times when n is not a whole number.
### Fractional Calculus II
##### Stage: 5
Here explore some ideas of how the definitions and methods of calculus change if you integrate or differentiate n times when n is not a whole number.
### Converging Product
##### Stage: 5 Challenge Level:
In the limit you get the sum of an infinite geometric series. What about an infinite product (1+x)(1+x^2)(1+x^4)... ?
### Fractional Calculus I
##### Stage: 5
You can differentiate and integrate n times but what if n is not a whole number? This generalisation of calculus was introduced and discussed on askNRICH by some school students.
### Squaring the Circle and Circling the Square
##### Stage: 4 Challenge Level:
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
### Discrete Trends
##### Stage: 5 Challenge Level:
Find the maximum value of n to the power 1/n and prove that it is a maximum.
### Witch of Agnesi
##### Stage: 5 Challenge Level:
Sketch the members of the family of graphs given by y = a^3/(x^2+a^2) for a=1, 2 and 3.
### Rain or Shine
##### Stage: 5 Challenge Level:
Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.
### Exponential Trend
##### Stage: 5 Challenge Level:
Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.
### Squareflake
##### Stage: 5 Challenge Level:
A finite area inside and infinite skin! You can paint the interior of this fractal with a small tin of paint but you could never get enough paint to paint the edge.
### Golden Eggs
##### Stage: 5 Challenge Level:
Find a connection between the shape of a special ellipse and an infinite string of nested square roots.
### There's a Limit
##### Stage: 4 and 5 Challenge Level:
Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?
### Triangle Incircle Iteration
##### Stage: 4 Challenge Level:
Keep constructing triangles in the incircle of the previous triangle. What happens?
### Over the Pole
##### Stage: 5 Challenge Level:
Two places are diametrically opposite each other on the same line of latitude. Compare the distances between them travelling along the line of latitude and travelling over the nearest pole.
### Golden Fractions
##### Stage: 5 Challenge Level:
Find the link between a sequence of continued fractions and the ratio of succesive Fibonacci numbers. | 816 | 3,640 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2017-43 | latest | en | 0.843337 |
https://encyclopedia2.thefreedictionary.com/Standard+deviation | 1,580,088,938,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579251694071.63/warc/CC-MAIN-20200126230255-20200127020255-00312.warc.gz | 433,483,306 | 13,653 | # standard deviation
Also found in: Dictionary, Thesaurus, Medical, Legal, Financial, Acronyms, Wikipedia.
Related to standard deviation: variance
## standard deviation
[′stan·dərd ‚dē·vē′ā·shən]
(statistics)
The positive square root of the expected value of the square of the difference between a random variable and its mean.
## standard deviation
see MEASURES OF DISPERSION.
## standard deviation
(statistics)
(SD) A measure of the range of values in a set of numbers. Standard deviation is a statistic used as a measure of the dispersion or variation in a distribution, equal to the square root of the arithmetic mean of the squares of the deviations from the arithmetic mean.
The standard deviation of a random variable or list of numbers (the lowercase greek sigma) is the square of the variance. The standard deviation of the list x1, x2, x3...xn is given by the formula:
sigma = sqrt(((x1-(avg(x)))^2 + (x1-(avg(x)))^2 + ... + (xn(avg(x)))^2)/n)
The formula is used when all of the values in the population are known. If the values x1...xn are a random sample chosen from the population, then the sample Standard Deviation is calculated with same formula, except that (n-1) is used as the denominator.
[dictionary.com].
["Barrons Dictionary of Mathematical Terms, second edition"].
## standard deviation
In statistics, the average amount a number varies from the average number in a series of numbers.
References in periodicals archive ?
If we use a shorter timeframe of five years, the standard deviation will be lower at 21 percent, but the average annual returns will also be lower at 5.17 percent, which is lower than current bond yield of 5.5 percent, resulting in negative Sharpe ratio.
In the present study, mean and standard deviation of VLDL (in mg/dl) for A positive blood group is 24.06 [+ or -] 2.52 same way mean and standard deviation of VLDL of B positive blood group is 25.04 [+ or -] 4.03 and for B negative blood group 26.40 [+ or -] 2.16, and AB positive blood group 32.00 [+ or -] 11.24, and O positive blood group 26.54 [+ or -] 3.34, and A negative blood group, mean is 27.
In table 5 against MI dimension, statistical data given reflects that both mean and standard deviation values of rural area i.e.
Mean and standard deviation of birth weight in babies born by normal delivery were 3.0658 and 0.2928 respectively and in babies born by CS 2.9311 and 0.3197 respectively.
The average wetted depth of inline is 12.58 cm with standard deviation of 1.51 cm and the coefficient of variation is 11.97 % and the average wetted depth of online is 13.73 cm with standard deviation of 1.72 cm and the coefficient of variation is 12.55 %.
Impact of Instructor Quality on Grades and Test Scores (Figure 1) (1a) Compared to having an average instructor, having an effective instructor (one at the 87th percentile) in Math I boosts students' grades by 0.30 standard deviations in that course and by 0.20 standard deviations in the subsequent course in the math sequence.
It is consistent with the value of standard deviation of that series which is about 0.0762 Hz and it also reveals the limitation of the built meter.
In this case, the standard deviation of each picture was determined and classified.
Group sizes were all .1 to .2 inch, but there was a pretty big extreme spread and a high standard deviation. This combination likely means this ammuntion is good for 25 yards and under, but will struggle at 50 yards and beyond.
Based on the result of standard deviation, the distribution of the responses for the section was normal, except item number 6.
"The increased mortality in warmer summers was entirely due to anomalies, whereas it was the long-term average differences in the standard deviation of summer temperatures across ZIP codes that drove the increased risk," researchers wrote.
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http://oeis.org/A060819 | 1,571,237,499,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570986668994.39/warc/CC-MAIN-20191016135759-20191016163259-00479.warc.gz | 141,451,897 | 6,059 | This site is supported by donations to The OEIS Foundation.
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A060819 a(n) = n / gcd(n,4). 61
1, 1, 3, 1, 5, 3, 7, 2, 9, 5, 11, 3, 13, 7, 15, 4, 17, 9, 19, 5, 21, 11, 23, 6, 25, 13, 27, 7, 29, 15, 31, 8, 33, 17, 35, 9, 37, 19, 39, 10, 41, 21, 43, 11, 45, 23, 47, 12, 49, 25, 51, 13, 53, 27, 55, 14, 57, 29, 59, 15, 61, 31, 63, 16, 65, 33, 67, 17, 69, 35, 71, 18, 73, 37, 75, 19 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,3 COMMENTS a(n) = A167192(n+4,4). - Reinhard Zumkeller, Oct 30 2009 a(n) = numerator(Sum_{k=1..n} 1/((k+1)*(k+2))). This summation has a closed form of 1/2 - 1/(n+2) and denominator of A145979(n). - Gary Detlefs, Sep 16 2011 a(n) = n / A109008(n). - Reinhard Zumkeller, Nov 25 2013 From Peter Bala, Feb 19 2019: (Start) We make some general remarks about the sequence a(n) = numerator(n/(n + k)) = n/gcd(n,k) for k a fixed positive integer. The present sequence is the case k = 4. Several other cases are listed in the Crossrefs. In addition to being multiplicative these sequences are also strong divisibility sequences, that is, gcd(a(n),a(m)) = a(gcd(n, m)) for n, m >= 1. In particular, it follows that a(n) is a divisibility sequence: if n divides m then a(n) divides a(m). By the multiplicativeness and strong divisibility property of the sequence a(n) it follows that if gcd(n, m) = 1 then a(a(n)*a(m) ) = a(a(n)) * a(a(m)), a(a(a(n))*a(a(m)) ) = a(a(a(n))) * a(a(a(m))) and so on. The sequence a(n) has the rational generating function Sum_{d divides k} f(d)*x^d/(1 - x^d)^2, where f(n) is the Dirichlet inverse of the Euler totient function A000010. f(n) is a multiplicative function defined on prime powers p^k by f(p^k) = 1 - p. See A023900. Cf. A181318. (End) LINKS Harry J. Smith, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1). FORMULA G.f.: x*(1 +x +3*x^2 +x^3 +3*x^4 +x^5 +x^6)/(1 - x^4)^2. a(n) = 2*a(n-4) - a(n-8). a(n) = (n/16)*(11 - 5*(-1)^n - i^n - (-i)^n). - Ralf Stephan, Mar 15 2003 a(2*n+1) = a(4*n+2) = 2*n+1, a(4*n+4) = n+1. - Ralf Stephan, Jun 10 2005 Multiplicative with a(2^e) = 2^max(0, e-2), a(p^e) = p^e, p >= 3. - Mitch Harris, Jun 29 2005 From R. J. Mathar, Apr 18 2011: (Start) a(n) = A109045(n)/4. Dirichlet g.f.: zeta(s-1)*(1-1/2^s-1/2^(2s)). (End) a(n+4) - a(n) = A176895(n). - Paul Curtz, Apr 05 2011 a((2*n-1)*2^p) = ceiling(2^(p-2))*(2*n-1), p >= 0 and n >= 1. - Johannes W. Meijer, Feb 06 2013 a(n) = denominator((2n-4)/n). - Wesley Ivan Hurt, Dec 22 2016 From Peter Bala, Feb 21 2019: (Start) O.g.f.: Sum_{n >= 0} a(n)*x^n = F(x) - F(x^2) - F(x^4), where F(x) = x/(1 - x)^2. More generally, Sum_{n >= 0} (a(n)^m)*x^n = F(m,x) + (1 - 2^m)*( F(m,x^2) + F(m,x^4) ), where F(m,x) = A(m,x)/(1 - x)^(m+1) with A(m,x) the m_th Eulerian polynomial: A(1,x) = x, A(2,x) = x*(1 + x), A(3,x) = x*(1 + 4*x + x^2) - see A008292. Repeatedly applying the Euler operator x*d/dx or its inverse operator to the o.g.f. for the sequence a(n) produces generating functions for the sequences ((n^m)*a(n))n>=1 for m in Z. Some examples are given below. (End) EXAMPLE From Peter Bala, Feb 21 2019: (Start) Sum_{n >= 1} n*a(n)*x^n = G(x) - 2*G(x^2) - 4*G(x^4), where G(x) = x*(1 + x)/(1 - x)^3. Sum_{n >= 1} (1/n)*a(n)*x^n = H(x) - (1/2)*H(x^2) - (1/4)*H(x^4), where H(x) = x/(1 - x). Sum_{n >= 1} (1/n^2)*a(n)*x^n = L(x) - (1/2^2)*L(x^2) - (1/4^2)*L(x^4), where L(x) = Log(1/(1 - x)). Sum_{n >= 1} (1/a(n))*x^n = L(x) + (1/2)*L(x^2) + (1/2)*L(x^4). (End) MAPLE A060819 := n -> numer(1/2-1/(n+2)): seq(A060819(n), n=1..75); # Gary Detlefs, Sep 16 2011 MATHEMATICA f[n_]:= n/GCD[n, 4]; Array[f, 80] PROG (Sage) [lcm(n, 4)/4 for n in (1..80)] # Zerinvary Lajos, Jun 07 2009 (PARI) { for (n=1, 1000, write("b060819.txt", n, " ", n / gcd(n, 4)); ) } \\ Harry J. Smith, Jul 12 2009 (Haskell) a060819 n = n `div` a109008 n -- Reinhard Zumkeller, Nov 25 2013 (MAGMA) [n/GCD(n, 4): n in [1..80]]; // G. C. Greubel, Sep 19 2018 (GAP) List([1..80], n->n/Gcd(n, 4)); # Muniru A Asiru, Feb 20 2019 CROSSREFS Cf. A026741, A051176, A060791, A060789. Cf. Other sequences given by the formula numerator(n/(n + k)): A106608 thru A106612 (k = 7 thru 11), A051724 (k = 12), A106614 thru A106621 (k = 13 thru 20). Cf. A061037, A061038, A220466, A181318. Sequence in context: A081432 A318060 A136655 * A318661 A089654 A233526 Adjacent sequences: A060816 A060817 A060818 * A060820 A060821 A060822 KEYWORD nonn,mult,easy AUTHOR Len Smiley, Apr 30 2001 STATUS approved
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https://www.webqc.org/molecular-weight-of-HCH3CO2.html | 1,596,517,703,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439735860.28/warc/CC-MAIN-20200804043709-20200804073709-00401.warc.gz | 811,681,743 | 13,134 | Molar Mass, Molecular Weight and Elemental Composition Calculator
Molar mass of HCH3CO2 is 60.0520 g/mol
Convert between HCH3CO2 weight and moles
Compound Moles Weight, g HCH3CO2
Elemental composition of HCH3CO2
ElementSymbolAtomic weightAtomsMass percent
HydrogenH1.0079446.7138
CarbonC12.0107240.0010
OxygenO15.9994253.2852
Mass percent composition Atomic percent composition
Formula in Hill system is C2H4O2
Computing molar mass (molar weight)
To calculate molar mass of a chemical compound enter its formula and click 'Compute'. In chemical formula you may use:
• Any chemical element. Capitalize the first letter in chemical symbol and use lower case for the remaining letters: Ca, Fe, Mg, Mn, S, O, H, C, N, Na, K, Cl, Al.
• Functional groups: D, Ph, Me, Et, Bu, AcAc, For, Ts, Tos, Bz, TMS, tBu, Bzl, Bn, Dmg
• parantesis () or brackets [].
• Common compound names.
Examples of molar mass computations: NaCl, Ca(OH)2, K4[Fe(CN)6], CuSO4*5H2O, water, nitric acid, potassium permanganate, ethanol, fructose.
Molar mass calculator also displays common compound name, Hill formula, elemental composition, mass percent composition, atomic percent compositions and allows to convert from weight to number of moles and vice versa.
Computing molecular weight (molecular mass)
To calculate molecular weight of a chemical compound enter it's formula, specify its isotope mass number after each element in square brackets.
Examples of molecular weight computations: C[14]O[16]2, S[34]O[16]2.
Definitions of molecular mass, molecular weight, molar mass and molar weight
• Molecular mass (molecular weight) is the mass of one molecule of a substance and is expressed in the unified atomic mass units (u). (1 u is equal to 1/12 the mass of one atom of carbon-12)
• Molar mass (molar weight) is the mass of one mole of a substance and is expressed in g/mol.
Weights of atoms and isotopes are from NIST article. | 515 | 1,915 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2020-34 | latest | en | 0.785182 |
https://help.scilab.org/docs/6.0.0/ru_RU/fsolve.html | 1,726,379,463,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651616.56/warc/CC-MAIN-20240915052902-20240915082902-00363.warc.gz | 256,787,398 | 5,439 | Change language to:
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Please note that the recommended version of Scilab is 2024.1.0. This page might be outdated.
See the recommended documentation of this function
# fsolve
find a zero of a system of n nonlinear functions
### Syntax
`[x [,v [,info]]]=fsolve(x0,fct [,fjac] [,tol])`
### Arguments
x0
real vector (initial value of function argument).
fct
external (i.e function or list or string).
fjac
external (i.e function or list or string).
tol
real scalar. precision tolerance: termination occurs when the algorithm estimates that the relative error between x and the solution is at most tol. (`tol=1.d-10` is the default value).
x :
real vector (final value of function argument, estimated zero).
v :
real vector (value of function at x).
info
termination indicator
0
improper input parameters.
1
algorithm estimates that the relative error between x and the solution is at most tol.
2
number of calls to fcn reached
3
tol is too small. No further improvement in the approximate solution x is possible.
4
iteration is not making good progress.
### Description
find a zero of a system of n nonlinear functions in n variables by a modification of the powell hybrid method. Jacobian may be provided.
`0 = fct(x) w.r.t x.`
`fct` is an "external". This external returns `v=fct(x)` given `x`.
The simplest syntax for `fct` is:
`[v]=fct(x).`
If `fct` is a character string, it refers to a C or Fortran routine which must be linked to Scilab. Fortran calling sequence must be
```fct(n,x,v,iflag)
integer n,iflag
double precision x(n),v(n)```
and C Syntax must be
`fct(int *n, double x[],double v[],int *iflag)`
Incremental link is possible (help `link`).
`jac` is an "external". This external returns `v=d(fct)/dx (x)` given `x`.
The simplest syntax for `jac` is:
`[v]=jac(x).`
If `jac` is a character string, it refers to a to a C or Fortran routine which must be linked to Scilab calling sequences are the same as those for fct. Note however that v must be a nxn array.
### Examples
```// A simple example with fsolve
a=[1,7;2,8];
b=[10;11];
function y=fsol1(x)
y=a*x+b
endfunction
function y=fsolj1(x)
y=a
endfunction
[xres]=fsolve([100;100],fsol1);
a*xres+b
[xres]=fsolve([100;100],fsol1,fsolj1);
a*xres+b
// See SCI/modules/optimization/sci_gateway/fortran/Ex-fsolve.f
[xres]=fsolve([100;100],'fsol1','fsolj1',1.e-7);
a*xres+b```
For some starting points and some equations system, the fsolve method can fail. The fsolve method is a local search method. So, to have a good chance to find a solution to your equations system, you must ship, a good starting point to fsolve.
Here is an example on which fsolve can fail:
```// Another example with fsolve
function F=feuler(x, r)
F=x-r-dt*(x.^2-x.^3);
endfunction
function J=dFdx(x) //Definition of the Jacobian
J=1-dt*(2*x-3*x^2);
endfunction
r = 0.04257794928862307 ;
dt = 10;
[x,v,info]=fsolve(r,list(feuler,r),dFdx); // fsolve do not find the solution
disp(v); // The residual
disp(info); // The termination indicator
[x,v,info]=fsolve(1,list(feuler,r),dFdx); // fsolve find the solution
disp(v); // The residual
disp(info); // The termination indicator
clf();
x=linspace(0,1,1000);
plot(x,feuler(x))
a=gca();
a.grid=[5 5];```
So, each time you use fsolve, be sure to check the termination indicator and the residual value to see if fsolve has converged.
• external — объект Scilab'а, внешняя функция или подпрограмма
• qpsolve — linear quadratic programming solver
• optim — non-linear optimization routine
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https://slideplayer.com/slide/7027663/ | 1,627,253,199,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046151866.98/warc/CC-MAIN-20210725205752-20210725235752-00050.warc.gz | 536,727,126 | 25,064 | 1 CSC 421: Algorithm Design & Analysis Spring 2013 Complexity & Computability lower bounds on problems brute force, decision trees, adversary arguments,
Presentation on theme: "1 CSC 421: Algorithm Design & Analysis Spring 2013 Complexity & Computability lower bounds on problems brute force, decision trees, adversary arguments,"— Presentation transcript:
1 CSC 421: Algorithm Design & Analysis Spring 2013 Complexity & Computability lower bounds on problems brute force, decision trees, adversary arguments, problem reduction complexity theory tractability, decidability P vs. NP, NP-complete NP-complete proofs & reductions
2 Lower bounds when studying a problem, may wish to establish a lower bound on efficiency binary search is O(log N) – can we do better? merge/quick/heap sorts are O(N log N) – can we do better? establishing a lower bound can tell us when a particular algorithm is as good as possible when the problem is intractable (by showing that best possible algorithm is BAD) methods for establishing lower bounds: brute force information-theoretic arguments (decision trees) adversary arguments problem reduction
Brute force arguments sometimes, a problem-specific approach works example: Towers of Hanoi puzzle can prove, by induction, that moving a tower of size N requires Ω(2 N ) steps 3
Information-theoretic arguments can sometimes establish a lower bound based on the amount of information the problem must produce example: guess a randomly selected number between 1 and N with possible responses of "correct", "too low", or "too high" the amount of uncertainty is log 2 N , the number of bits needed to specify the selected number each answer to a question yields at most 1 bit of information thus, log 2 N is a lower bound on the number of questions a useful structure for information-theoretic arguments is a decision tree 4
5 Decision trees a decision tree is a model of algorithms involving comparisons internal nodes represent comparisons leaves represent outcomes e.g., decision tree for 3-element insertion sort:
6 Decision trees & sorting note that any comparison-based sorting algorithm can be represented by a decision tree number of leaves (outcomes) N! height of binary tree with N! leaves log 2 N! therefore, the minimum number of comparisons required by any comparison-based sorting algorithm log 2 N! since log 2 N! N log 2 N, the lower bound Ω(N log N) is tight thus, merge/quick/heap sorts are as good as it gets
7 Decision trees & searching similarly, we can use a decision tree to show that binary search is as good as it gets (assuming the list is sorted) decision tree for binary search of 4-element list: internal nodes are found elements leaves are ranges if not found number of leaves (ranges where not found) = N + 1 height of binary tree with N+1 leaves log 2 (N+1) therefore, the minimum number of comparisons required by any comparison-based searching algorithm log 2 (N+1) lower bound Ω(log N) is tight
Exercise consider finding the median of a 3-element list of numbers [x 1, x 2, x 3 ] information-theoretic lower bound? decision tree? 8
9 Adversary arguments using an adversary argument, you repeatedly adjust the input to make an algorithm work the hardest example: dishonest hangman adversary always puts the word in a larger of the subset generated by last guess for a given dictionary, can determine a lower bound on guesses example: merging two sorted lists of size N (as in merge sort) adversary makes it so that no list "runs out" of values (e.g., a i < b j iff i < j) forces 2N-1 comparisons to produce b 1 < a 1 < b 2 < a 2 < … < b N < a N
10 Problem reduction problem reduction uses a transform & conquer approach if we can show that problem P is at least as hard as problem Q, then a lower bound for Q is also a lower bound for P. example: multiplication can be reduced to the complexity of squaring in general: 1.find problem Q with a known lower bound 2.reduce that problem to problem P (i.e., show that can solve Q by solving an instance of P) 3.then P is at least as hard as Q, so same lower bound applies
Problem reduction example CLOSEST NUMBERS (CN) PROBLEM: given N numbers, find the two closest numbers 1.consider a different problem: ELEMENT UNIQUENESS (EU) PROBLEM given a list of N numbers, determine if all are unique (no dupes) this problem has been shown to have a lower bound of Ω(N log N) 2.consider an instance of EU: given numbers e 1, …, e N, determine if all are unique find the two closest numbers (this is an instance of CN) if the distance between them is > 0, then e 1, …, e N are unique 3.this shows that CN is at least as hard as EU can solve an instance of EU by performing a transformation & solving CN since transformation is O(N), CN must also have a lower-bound of Ω(N log N) (proof by contradiction) assume CN could be solved in O(X) where X < N log N then, could solve EU by transforming & solving CN O(N) +O(X) < O(N log N) this contradicts what we know about EU, so CN must be Ω(N log N) 11
Another example CLOSEST POINTS (CP) PROBLEM: given N points in the plane, find the two closest points 1.consider a different problem: CLOSEST NUMBER (CN) PROBLEM we just showed that CN has a lower bound of Ω(N log N) 2.consider an instance of CN: given numbers e 1, …, e N, determine closest numbers from these N numbers, construct N points: (e 1, 0), …, (e N, 0) find the two closest points (this is an instance of CP) if (e i, 0) and (e j, 0) are closest points, then e i and e j are closest numbers 3.this shows that CP is at least as hard as CN can solve an instance of CN by performing a transformation & solving CP since transformation is O(N), CP must also have a lower-bound of Ω(N log N) (proof by contradiction) assume CP could be solved in O(X) where X < N log N then, could solve EU by transforming & solving CP O(N) +O(X) < O(N log N) this contradicts what we know about EU, so CP must be Ω(N log N) 12
Tightness are the Ω(N log N) lower bounds tight for CLOSEST NUMBERS and CLOSEST POINTS problems? can you devise O(N log N) algorithm for CLOSEST NUMBERS? can you devise O(N log N) algorithm for CLOSEST POINTS? 13
14 Classifying problem complexity throughout this class, we have considered problems, designed algorithms, and classified their efficiency e.g., sorting a list – could use O(N 2 ) selection sort or O(N log N) quick sort big-Oh provides for direct comparison between two algorithms when is a problem too difficult? EXTREMELY LOW BAR: we say that a problem is intractable if there does not exist a polynomial time O( p(n) ) algorithm that solves it θ(2 N ) is definitely intractablenote: N = 20 millions of steps 2 60 > # of seconds since Big Bang 2 273 > # of atoms in the universe but θ(N 100 ) is tractable?!?in reality, anything worse than N 3 is not practical
Beyond intractable Alan Turing showed that there is a class of problems beyond intractable there are problems that have been shown to be unsolvable (regardless of efficiency) THE HALTING PROBLEM: Given a computer program and an input to it, determine whether the program will halt on the input. Assume that there is an algorithm A that solves the Halting Problem. That is, for any program P and input I: A(P, I) returns true if P halts on I; otherwise, returns false note: a program is represented as bits, so a program can be input to a program Construct the following program Q: Q(P): if ( A(P, P) ) {// if P halts on input P while (true) { }// infinite loop }// otherwise return;// halt If you call Q with itself as input: Q(Q) halts if and only if A(Q, Q) returns false if and only if Q(Q) does not halt CONTRADICTION 15
16 Problem types: decision & optimization the Halting Problem is an example of a decision problem solving the problem requires answering a yes/no question another common type of problems is an optimization problem solving the problem requires finding the best/largest/shortest answer e.g., shortest path, minimal spanning tree many problems have decision and optimization versions find the shortest path between vertices v 1 and v 2 in a graph is there a path between v 1 and v 2 whose length is ≤ d decision problems are more convenient for formal investigation of their complexity
17 Class P P: the class of decision problems that are solvable in polynomial time O( p ( n )) i.e., the class of tractable decision problems interestingly, there are many important problems for which no polynomial- time algorithm has been devised Hamiltonian Circuit Problem: determine whether a graph has a path that starts and ends at the same vertex and passes through every other vertex once Traveling Salesman Problem: find the shortest Hamiltonian circuit in a complete graph) Graph Coloring Problem: Determine the smallest number of colors needed so that adjacent vertices are different colors Partition Problem: Given N positive integers, determine whether it is possible to partition them into two disjoint subsets with the same sum. Knapsack Problem: Given a set of N items with integer weights and values, determine the most valuable subset that fits in a knapsack with limited capacity. Bin-packing Problem: Given N items with varying sizes, determine the smallest number of uniform-capacity bins required to contain them.
18 Class NP however, many of these problems fit into a (potentially) broader class a nondeterministic polynomial algorithm is a two-stage procedure that: 1.generates a random string purported to solve the problem (guessing stage) 2.checks whether this solution is correct in polynomial time (verification stage) NP: class of decision problems that can be solved by a nondeterministic polynomial algorithm i.e., whose proposed solutions can be verified in polynomial time example: Hamiltonian Circuit Problem is in NP given a path, can verify that it is a Hamiltonian circuit in O(N) example: Partition Problem is in NP given two partitions, can verify that their sums are equal in O(N)
19 P vs. NP decision versions of Traveling Salesman, Knapsack, Graph Coloring, and many other optimization problems are also in NP note that problems in P can also be solved using the 2-stage procedure the guessing stage is unnecessary the verification stage generates and verifies in polynomial time so, P NP big question: does P = NP ? considerable effort has gone into trying to find polynomial-time solutions to NP problems (without success) most researchers believe they are not equal (i.e., P is a proper subset), but we don't know for sure
20
NP-complete while we don't know whether P = NP, we can identify extremes within NP given decision problems D 1 and D 2, we say that D 1 is polynomial-time reducible to D 2 if there exists transformation t such that: 1.t maps all yes-instances of D 1 to yes-instances of D 2 maps all no-instances of D 1 to no-instances of D 2 2.t is computable by a polynomial time algorithm we say that decision problem D is NP-complete if: 1.D belongs to NP 2.every problem in NP is polynomial-time reducible to D in short, an NP-complete problem is as hard as any problem in NP 21
NP-complete example the first problem proven to be NP-complete was Boolean Satisfiability (SAT) given a Boolean expression, determine if satisfiable e.g., (A ∨ B) ∧ (~B ∨ C)is true if A & C are true SAT is clearly in NP given true/false assignments to the propositions, can evaluate the truth of the expression in polynomial time to be NP-complete, every other NP problem must be reducible to it proof idea (Cook, 1971): if a problem is in NP, can construct a non-deterministic (Turing) machine to solve it for each input to that machine, can construct a Boolean expression that evaluates to true if the machine halts and answers "yes" on input thus, original problem is reduced to determining whether the corresponding Boolean expression is satisfiable 22
NP-complete reductions if we can reduce SAT to another NP problem, then it is also NP-complete CLIQUE: given a graph with N vertices, is there a fully connected subgraph of C vertices? 23
SAT CLIQUE can reduce the SAT problem to CLIQUE given an instance of SAT, e.g., (A ∨ B) ∧ (~B ∨ C) ∧ (B ∨ ~C) note: any Boolean expression can be transformed into conjunctive normal form here, there are 3 OR-groups, joined together with AND construct a graph with vertices grouped by each OR-group there is an edge between two vertices if 1.the vertices are in different OR-groups, and 2.they are not negations of each other note: edge implies endpoints can be simultaneously true the expression is satisfiable if can have vertex from each OR-group simultaneously true in other words, is a clique of size C (where C is the number of OR-groups) since example expression has 3 OR-groups, need a clique of size 3 so, CLIQUE is also NP-complete 24 A B ~B~B C B C
25
Implications of NP-completeness an NP-complete problem is as hard as any problem in NP i.e., all problems in NP reduce to it discovering a polynomial solution to any NP-complete problem would imply a polynomial solution to all problems in NP would show P = NP if P = NP, many problems currently thought to be intractable would be tractable e.g., PRIME FACTORIZATION PROBLEM: factor a number into its prime factors the RSA encryption algorithm relies on the fact that factoring large numbers is intractable if an efficient factorization algorithm were discovered, modern encryption could break QUESTION: would it necessarily break? 26
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Similar presentations | 3,331 | 13,811 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.46875 | 3 | CC-MAIN-2021-31 | latest | en | 0.833799 |
https://testbook.com/question-answer/arjun-walks-40-m-towards-the-south-from-his-home--5fe9757bae57b816868fc3b6 | 1,643,062,616,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304686.15/warc/CC-MAIN-20220124220008-20220125010008-00135.warc.gz | 615,575,550 | 31,448 | # Arjun walks 40 m towards the South from his home, and then he turns left and walks 55 m. Then, he takes another left turn and walks 15 m. Then, he turns left again and walks 55 m. How far is he from his home now?
This question was previously asked in
SSC CPO Previous Paper 37 (Held On: 24 November 2020 Shift 2)
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1. 35 m
2. 15 m
3. 30 m
4. 25 m
Option 4 : 25 m
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## Detailed Solution
According to the given information, the possible diagram is as below:
As we can see in the diagram, the distance between the final position of Arjun and his home is = 40 - 15 = 25 m.
Hence, the correct answer is "25 m". | 213 | 705 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.671875 | 4 | CC-MAIN-2022-05 | latest | en | 0.935806 |
http://mathhelpforum.com/pre-calculus/31533-vertices-parallelogram-print.html | 1,526,873,325,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794863923.6/warc/CC-MAIN-20180521023747-20180521043747-00338.warc.gz | 194,581,138 | 3,418 | # Vertices of a parallelogram?
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• Mar 20th 2008, 01:04 AM
oXCryssieLeahXo
Vertices of a parallelogram?
Goodness I don't understand this at all!!! I understand finding the coordinates of a parallelogram, but this makes no sense.
So it says "Which of the set of points cannot be the vertices of parallelogram ABCD?"
options are
a) A (-4, -2), B (2, 0), C (3, 3), D (-2, -1)
b) A (-2, -1), B (3, -2), C (4, 1), D (-1, 2)
c) A (0, -2), B (4, -1), C (5, 2), D (0, 5)
d) A (0, -2), B (5, -3), C (7, 1), D (2, 2)
so can someone tell me what formula to use to find the answer? (I'm assuming there's a formula!)
• Mar 20th 2008, 02:02 AM
earboth
Quote:
Originally Posted by oXCryssieLeahXo
...
So it says "Which of the set of points cannot be the vertices of parallelogram ABCD?"
options are
a) A (-4, -2), B (2, 0), C (3, 3), D (-2, -1)
b) A (-2, -1), B (3, -2), C (4, 1), D (-1, 2)
c) A (0, -2), B (4, -1), C (5, 2), D (0, 5)
d) A (0, -2), B (5, -3), C (7, 1), D (2, 2)
...
The properties of a parallelogram are:
1. The diagonals have a common midpoint.
2. 2 pairs of parallel sides
3. The parallel sides have the same length (#3 is equivalent to #2)
First check if
$\displaystyle M_{AC} = M_{BD}$
So only b) and d) could be a parallelogram
Check if
$\displaystyle (\overline{AB})\ \parallel \ (\overline{CD})$
only d) is left. Since $\displaystyle \left(\begin{array}{c}-5\\1\end{array}\right) = k \cdot \left(\begin{array}{c}5\\-1\end{array}\right)$ the sides $\displaystyle (\overline{AB})\ \parallel \ (\overline{CD})$
PS: Fröhliche Ostern!
• Mar 20th 2008, 02:15 AM
oXCryssieLeahXo
Thank yah
Quote:
Originally Posted by earboth
The properties of a parallelogram are:
1. The diagonals have a common midpoint.
2. 2 pairs of parallel sides
3. The parallel sides have the same length (#3 is equivalent to #2)
First check if
$\displaystyle M_{AC} = M_{BD}$
So only b) and d) could be a parallelogram
Check if
$\displaystyle (\overline{AB})\ \parallel \ (\overline{CD})$
only d) is left. Since $\displaystyle \left(\begin{array}{c}-5\\1\end{array}\right) = k \cdot \left(\begin{array}{c}5\\-1\end{array}\right)$ the sides $\displaystyle (\overline{AB})\ \parallel \ (\overline{CD})$
PS: Fröhliche Ostern!
wow thank you SO much. Makes sense. I kinda feel dumb now that I didn't figure that out myself!! (Headbang)
Frohe Ostern an dir auchh! =]]
• Mar 20th 2008, 05:12 AM
Soroban
Hello, oXCryssieLeahXo!
I don't suppose you tried to PLOT the points . . .
Quote:
Which of the set of points cannot be the vertices of parallelogram ABCD?
. . $\displaystyle a)\;A (\text{-}4, \text{-}2),\;B (2, 0),\;C (3, 3), D\;(\text{-}2, \text{-}1)$
Code:
| C . . . . . + . . o . | . . . . . + . . . . | . . . . . + . . . . | - + - + - + - + - + - + - + - o - + - + - D | B . . . o . + . . . . | . o . . . + . . . . A |
No, I don't think so . . . | 1,145 | 3,169 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.28125 | 4 | CC-MAIN-2018-22 | latest | en | 0.70817 |
https://www.followchain.org/i-love-you-math-problem/ | 1,722,986,345,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640523737.31/warc/CC-MAIN-20240806224232-20240807014232-00844.warc.gz | 607,977,585 | 10,129 | Home » How-To » Memes » What is the “I Love You” or “We Love You” Math Problem?
# What is the “I Love You” or “We Love You” Math Problem?
The “I Love You” and “We Love You” math problem went viral on TikTok.
Students will give their teachers a math equation and ask them to solve it.
The answer to the math equation is “i < 3u” and “we < 3u” respectively.
The idea behind the equation is to tell someone that you love them.
In this article, you’ll learn what is the “I Love You” or “We Love You” Math problem/equation and how to solve it.
## What is the I Love You math problem?
The I Love You math problem is “9x−7i > 3(3x−7u)”.
To solve the problem, you need to distribute 3 on the right side: 9x−7i > 9x−21u.
Secondly, subtract 9x from both sides to isolate the terms with variables on one side: −7i > −21u.
Lastly, divide both sides by -7 to solve for i: i < 3u.
## What is the We Love You math problem?
The We Love You math problem is “9x-7we > 3 (3x -7u)”.
To solve the problem, you need to distribute 3 on the right side: 9x−7we > 9x−21u.
Secondly, subtract 9x from both sides to isolate the terms with variables on one side: −7we > −21u.
Lastly, divide both sides by -7 to solve for we: we < 3u.
Lebron James Copypasta
Who is the Chick-fil-A Sauce Girl? And Was She Fired?
Darling Guess Who’s Back from Jail Sound
Tags | 404 | 1,346 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2024-33 | latest | en | 0.889168 |
https://programming.vip/docs/620f1850a5534.html | 1,653,777,049,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652663021405.92/warc/CC-MAIN-20220528220030-20220529010030-00520.warc.gz | 532,528,910 | 4,721 | # Practical cases of common statistical methods such as cumulative, year-on-year and month on month in Pandas
In the statistical table, the statistics are usually accumulated in the current year, completed in the same period of the previous year (accumulated), completed in the current period (such as the current month) and completed in the last month, and the year-on-year and month on month analysis are carried out. The following example is shown in the monthly report statistics table. This article will use Python Pandas tool for statistics.
Of which:
• (current year) cumulative: refers to the total amount from January to the end of the current year
• (last year) same period (cumulative): refers to the total amount from January of last year to the end month corresponding to the cumulative amount of this year
• Year on year (growth rate) = (amount in current period - amount in the same period) / amount in the same period * 100%
• Month on month (growth rate) = (current period amount - previous period amount) / previous period amount * 100%
Note: the current period here refers to the completion of the current month or the current month, and the number of the previous period refers to the completion of the previous month.
Sample data:
Note: for the convenience of demonstration, the data source of this case only uses the data of 2 years and 5 months a year.
# 1. (this year) cumulative
In statistical analysis and development, it is a common requirement to accumulate some statistical data by year and month. For data, it is to accumulate data line by line according to rules.
The cumsum() function in Pandas can accumulate demand according to a certain time dimension.
```# Take the cumulative value of this year
import pandas as pd
cum_columns_name = ['cum_churncount','cum_newcount']
df[cum_columns_name] = df[['years','churncount','newcount']].groupby(['years']).cumsum()
```
Note: the grouping 'years' refers to the cumulative time dimension of the year.
The calculation results are as follows:
# 2. (last year) cumulative in the same period
For the cumulative value of the same period (last year), the data of the same month of the cumulative value of the previous year will be directly obtained. pandas DataFrame. The shift () function can move the data by a specified number of rows.
Continue the above column and read the data of the same period. First, move 'yearmonth' up five rows to get a new DataFrame, as shown in the figure above. Use 'yearmonth' to associate the data of two tables (left Association: the original table is on the left and the new table is on the right), so as to achieve the effect of de synchronization data.
```cum_columns_dict = {'cum_churncount':'cum_same_period_churncount',
'cum_newcount':'cum_same_period_newcount'}
df_cum_same_period = df[['cum_churncount','cum_newcount','yearmonth']].copy()
df_cum_same_period = df_cum_same_period.rename(columns=cum_columns_dict)
#df_cum_same_period.loc[:,'yearmonth'] = df_cum_same_period['yearmonth'].shift(-12) # 12 months a year
df_cum_same_period.loc[:,'yearmonth'] = df_cum_same_period['yearmonth'].shift(-5) # Because only five months of data are taken
df = pd.merge(left=df,right=df_cum_same_period,on='yearmonth',how='left')
```
# 3. Last month (completed)
Take the data of last month and use pandas dataframe The shift() function moves the data by a specified number of rows.
Continue the above column and read the data of the previous period. (same as the synchronization principle, omitted)
```last_mnoth_columns_dict = {'churncount':'last_month_churncount',
'newcount':'last_month_newcount'}
df_last_month = df[['churncount','newcount','yearmonth']].copy()
df_last_month = df_last_month.rename(columns=last_mnoth_columns_dict)
df_last_month.loc[:,'yearmonth'] = df_last_month['yearmonth'].shift(-1) # Move one line
df = pd.merge(left=df,right=df_last_month,on='yearmonth',how='left')
```
# 4. Year on year (growth rate)
The year-on-year calculation involves division, and the data with divisor of zero needs to be eliminated.
```df.fillna(0,inplace=True) # Null values are filled with 0
# Calculate year-on-year
df.loc[df['cum_same_period_churncount']!=0,'cum_churncount_rat'] = (df['cum_churncount']-df['cum_same_period_churncount'])/df['cum_same_period_churncount'] # Divisor cannot be zero
df.loc[df['cum_same_period_newcount']!=0,'cum_newcount_rat'] = (df['cum_newcount']-df['cum_same_period_newcount'])/df['cum_same_period_newcount'] # Divisor cannot be zero
df[['yearmonth','cum_churncount','cum_newcount','cum_same_period_churncount','cum_same_period_newcount','cum_churncount_rat','cum_newcount_rat']]
```
# 5. Month on month (growth rate)
```# Calculate month on month ratio
df.loc[df['last_month_churncount']!=0,'churncount_rat'] = (df['churncount']-df['last_month_churncount'])/df['last_month_churncount'] # Divisor cannot be zero
df.loc[df['last_month_newcount']!=0,'newcount_rat'] = (df['newcount']-df['last_month_newcount'])/df['last_month_newcount'] # Divisor cannot be zero
df[['yearmonth','churncount','newcount','last_month_churncount','last_month_newcount','churncount_rat','newcount_rat']]
```
# 6. Summary
pandas has many statistical calculation functions and methods. The techniques summarized here include cumulative cumsum() function, mobile data shift() function, table merge Association merge() function, and modifying data through loc conditions.
Keywords: Python Data Analysis pandas
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ShowAll Questionssorted byDate Posted
Ludivine
# formula with if or case
Hi experts,
I need your help to build a formula as I am stuck here and don't know how to achieve the result that I want.
This is my formula :
if(ISNULL(Benefit_End_Date__c),12,round((Benefit_End_Date__c - Expected_Impact_Date__c),2)/30)
This formula returns 0 when the difference between the 2 dates are less than 30 days, so when there is less than a month.
In that case I would like to return 1. How cvan I do that?
It blocks me to implement a method as each time the result is 0 I get an error from Apex ...
Many thanks in advance for the time you will spend on my issue :)
Ludivine
GulshanRaj
Hi @Ludivine,
Try this:
`IF(ISNULL(Benefit_End_Date__c),12,IF((ABS(Benefit_End_Date__c - Expected_Impact_Date__c)<30),1,0))`
If this helps you, mark this question as solved and choose best answer so it will help other in future to choose best solution.
Thanks
Gulshan Raj
GulshanRaj
Hi @Ludivine,
Try this:
`IF(ISNULL(Benefit_End_Date__c),12,IF((ABS(Benefit_End_Date__c - Expected_Impact_Date__c)<30),1,0))`
If this helps you, mark this question as solved and choose best answer so it will help other in future to choose best solution.
Thanks
Gulshan Raj
This was selected as the best answer
Ludivine
Fantastic, it works!! thank you Gulshan!!
GulshanRaj
Nice. Can you please mark this question as solved? | 423 | 1,520 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.625 | 3 | CC-MAIN-2024-22 | latest | en | 0.887162 |
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## Presentation on theme: "Nonsmooth Nonnegative Matrix Factorization (nsNMF) Alberto Pascual-Montano, Member, IEEE, J.M. Carazo, Senior Member, IEEE, Kieko Kochi, Dietrich Lehmann,"— Presentation transcript:
Nonsmooth Nonnegative Matrix Factorization (nsNMF) Alberto Pascual-Montano, Member, IEEE, J.M. Carazo, Senior Member, IEEE, Kieko Kochi, Dietrich Lehmann, and Roberto D. Pascual-Marqui 2006,IEEE Presenter : 張庭豪
Outline NONSMOOTH NMF (nsNMF) EXPERIMENTS CONCLUSIONS AND DISCUSSION
INTRODUCTION REVIEW OF NMF AND ITS SPARSE VARIANTS NONSMOOTH NMF (nsNMF) EXPERIMENTS CONCLUSIONS AND DISCUSSION
INTRODUCTION Nonnegative matrix factorization (NMF) has been introduced as a matrix factorization technique that produces a useful decomposition in the analysis of data. This method results in a reduced representation of the original data that can be seen either as a feature extraction or a dimensionality reduction technique. More importantly, NMF can be interpreted as a parts-based representation of the data due to the fact that only additive, not subtractive, combinations are allowed.
INTRODUCTION Formally, the nonnegative matrix decomposition can be described as follows: V ≈WH where 𝑽∈ 𝑹 𝒑×𝒏 is a positive data matrix with p variables and n objects, W∈ 𝑹 𝒑×𝒒 are the reduced q basis vectors or factors, and 𝐇∈ 𝑹 𝒒×𝒏 contains the coefficients of the linear combinations of the basis vectors needed to reconstruct the original data (also known as encoding vectors).
INTRODUCTION In fact, taking a closer look at the basis and encoding vectors produced by NMF, it is noticeable that there is a high degree of overlapping among basis vectors that contradict the intuitive nature of the “parts”. In this sense, a matrix factorization technique capable of producing more localized, less overlapped feature representations of the data is highly desirable in many applications. The new method, here referred to as Nonsmooth Nonnegative Matrix Factorization (nsNMF), differs from the original in the use of an extra smoothness matrix for imposing sparseness. The goal of nsNMF is to find sparse structures in the basis functions that explain the data set.
REVIEW OF NONNEGATIVE MATRIX FACTORIZATION (NMF) AND ITS SPARSE VARIANTS
V ≈WH 𝑽∈ 𝑹 𝒑×𝒏 W∈ 𝑹 𝒑×𝒒 𝐇∈ 𝑹 𝒒×𝒏 The columns of W (the basis vectors) are normalized (sum up to 1). The objective function, based on the Poisson likelihood, is: which, after some simplifications and elimination of pure data terms, gives:
REVIEW OF NONNEGATIVE MATRIX FACTORIZATION (NMF) AND ITS SPARSE VARIANTS
Taking the derivative with respect to H gives: The gradient algorithm then states: for some step size
REVIEW OF NONNEGATIVE MATRIX FACTORIZATION (NMF) AND ITS SPARSE VARIANTS
Forcing: gives the multiplicative rule:
REVIEW OF NONNEGATIVE MATRIX FACTORIZATION (NMF) AND ITS SPARSE VARIANTS
Taking the derivative with respect to W gives: The gradient algorithm then states: Forcing the step size: gives:
REVIEW OF NONNEGATIVE MATRIX FACTORIZATION (NMF) AND ITS SPARSE VARIANTS
Finally, the derived algorithm is as follows: 1. Initialize W and H with positive random numbers. 2. For each basis vector 𝑾 𝒂 ∈ 𝑹 𝒑×𝟏 ,update the corresponding encoding vector 𝑯 𝒂 ∈ 𝑹 𝟏×𝒏 , followed by updating and normalizing the basis vector Wa .Repeat this process until convergence. Repeat until convergence: For a = 1...q do begin For b = 1...n do For c=1...p do begin
REVIEW OF NONNEGATIVE MATRIX FACTORIZATION (NMF) AND ITS SPARSE VARIANTS
Local Nonnegative Matrix Factorization (LNMF) LNMF algorithm intended for learning spatially localized, parts-based representation of visual patterns. Their aim was to obtain a truly part-based representation of objects by imposing sparseness constraints on the encoding vectors (matrix H) and locality constraints to the basis components (matrix W). Taking the factorization problem defined in (1), define 𝐴= 𝑎 𝑖𝑗 = 𝑊 𝑡 𝑊 and B= 𝑏 𝑖𝑗 =𝐻 𝐻 𝑡 , where A,B ∈ 𝑹 𝒒×𝒒 .
REVIEW OF NONNEGATIVE MATRIX FACTORIZATION (NMF) AND ITS SPARSE VARIANTS
The LNMF algorithm is based on the following three additional constraints: 1. Maximum Sparseness in H. It should contain as many zero components as possible. This implies that the number of basis components required to represent V is minimized. Mathematically, each aij should be minimum. 2. Maximum expressiveness of W. This constraint is closely related to the previous one and it aims at further enforcing maximum sparseness in H. Mathematically, 𝑖=1 𝑞 𝑏 𝑖𝑖 should be maximum. 3. Maximum orthogonality of W. This constraint imposes that different bases should be as orthogonal as possible to minimize redundancy. This is forced by minimizing ∀𝑖,𝑗.𝑖≠𝑗 𝑎 𝑖𝑗 . Combining this constraint, with the one described in point 1, the objective is to minimize ∀𝑖,𝑗 𝑎 𝑖𝑗 .
REVIEW OF NONNEGATIVE MATRIX FACTORIZATION (NMF) AND ITS SPARSE VARIANTS
Thus, ∀𝑖,𝑗 , the constrained divergence function is: where 𝛼 , 𝛽 > 0 represent some constants for expressing the importance of the additional constraints described above.
REVIEW OF NONNEGATIVE MATRIX FACTORIZATION (NMF) AND ITS SPARSE VARIANTS
Nonnegative Sparse Coding (NNSC) Similar to the LNMF algorithm, the Nonnegative Sparse Coding (NNSC) method is intended to decompose multivariate data into a set of positive sparse components Combining a small reconstruction error with a sparseness criterion, the objective function is: where the form of f defines how sparseness on H is measured and controls the trade-off between sparseness and the accuracy of the reconstruction.
REVIEW OF NONNEGATIVE MATRIX FACTORIZATION (NMF) AND ITS SPARSE VARIANTS
Sparse Nonnegative Matrix Factorization (SNMF) Instead of using a Euclidean least-square type functional, as in (22), they used a divergence term. Thus, the sparse NMF functional is: for 𝛼 > 0. This method forces sparseness via minimizing the sum of all Hij. The update rule for matrix H is: while the update rule for W is expressed in (17) and (18).
OUR PROPOSAL: NONSMOOTH NONNEGATIVE MATRIX FACTORIZATION (nsNMF)
Because of the multiplicative nature of the model, i.e., “basis” multiplied by “encoding,” sparseness in one of the factors will almost certainly force “nonsparseness” or smoothness in the other. On the other hand, forcing sparseness constraints on both the basis and the encoding vectors will deteriorate the goodness of fit of the model to the data. Therefore, from the outset, this approach is doomed to failure in achieving generalized sparseness and satisfactory goodness of fit.
OUR PROPOSAL: NONSMOOTH NONNEGATIVE MATRIX FACTORIZATION (nsNMF)
The new model proposed in this study, denoted as “NonSmooth Nonnegative Matrix Factorization” (nsNMF), is defined as: where V, W, and H are the same as in the original NMF model. The positive symmetric matrix 𝐒∈ 𝑹 𝒒×𝒒 is a “smoothing” matrix defined as: where I is the identity matrix, 1 is a vector of ones, and the parameter satisfies 𝟎<𝜽<𝟏 . (V ≈WH)
OUR PROPOSAL: NONSMOOTH NONNEGATIVE MATRIX FACTORIZATION (nsNMF)
The interpretation of S as a smoothing matrix can be explained as follows: Let X be a positive, nonzero, vector. Consider the transformed vector Y = SX. If 𝜽 = 0, then Y = X and no smoothing on X has occurred. However, as 𝜽→ 1, the vector Y tends to the constant vector with all elements almost equal to the average of the elements of X. This is the smoothest possible vector in the sense of “nonsparseness” because all entries are equal to the same nonzero value, instead of having some values close to zero and others clearly nonzero. Note that the parameter 𝜃 controls the extent of smoothness of the matrix operator S.
OUR PROPOSAL: NONSMOOTH NONNEGATIVE MATRIX FACTORIZATION (nsNMF)
However, due to the multiplicative nature of the model (28), strong smoothing in S will force strong sparseness in both the basis and the encoding vectors. Therefore, the parameter 𝜃 controls the sparseness of the model. 𝑉= 𝑊𝑆 𝐻=𝑊(𝑆𝐻) Nonsparseness in the basis W will force sparseness in the encoding H. At the same time, nonsparseness in the encoding H will force sparseness in the basis W. 1. In the update equation for H (16), substitute (W) with (WS). 2. In the update equation for W (17), substitute (H) with (SH). 3. Equation (18) remains the same.
EXPERIMENTS As mentioned in the previous section, the multiplicative nature of the sparse variants of the NMF model will produce a paradoxical effect: Imposing sparseness in one of the factors will almost certainly force smoothness in the other in an attempt to reproduce the data as best as possible. Additionally, forcing sparseness constraints on both the basis and the encoding vectors will decrease the explained variance of the data by the model. Table 1 shows the results when using exactly three factors in all cases. Different NMF-type methods were applied to the same randomly generated positive data set (5 variables, 20 items, rank = 3).
EXPERIMENTS
EXPERIMENTS basis “swimmer” data set
NMF failed in extracting the 16 limbs and the torso, while nsNMF successfully explained the data using one factor for each independent part. NMF extract parts of the data in a more holistic manner, while nsNMF sparsely represents the same reality.
EXPERIMENTS CBCL faces data set 49 basis Not sparse
EXPERIMENTS NMF Results
Fig. 3(a) shows the results using the Lee and Seung algorithm applied to the facial database using 49 factors. Even if the factors’ images give an intuitive notion of a parts-based representation of the original faces, the factorization is not really sparse enough to represent unique parts of an average face. In other words, the NMF algorithm allows some undesirable overlapping of parts, especially in those areas that are common to most of the faces in the input data.
EXPERIMENTS nsNMF Results
EXPERIMENTS 0.5 0.6 0.7 V = (WS)H 𝜃↑,𝑊越smooth H越sparse 0.8
CONCLUSIONS AND DISCUSSION
The approach presented here is an attempt to improve the ability of the classical NMF algorithm in this process by producing truly sparse components of the data structure. The experimental results on both synthetic data and real data sets have shown that the nsNMF algorithm outperformed the existing sparse NMF variants in performing parts-based representation of the data while maintaining the goodness of fit.
Download ppt "Nonsmooth Nonnegative Matrix Factorization (nsNMF) Alberto Pascual-Montano, Member, IEEE, J.M. Carazo, Senior Member, IEEE, Kieko Kochi, Dietrich Lehmann,"
Similar presentations | 2,715 | 10,615 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2018-22 | latest | en | 0.863448 |
http://www.trafficimagine.com/www.educacionbc.edu.mx | 1,369,320,588,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368703334458/warc/CC-MAIN-20130516112214-00065-ip-10-60-113-184.ec2.internal.warc.gz | 756,062,260 | 3,972 | # Educacionbc.edu.mx - Can you imagine their visitors ?
## Educacionbc.edu.mx has 1,721 daily visitors. Can you imagine how big the country was if these 1,721 visitors would have been the population of a country?
Educacionbc.edu.mx would be on of the smaller countries of the world. We've created a table below, so you can see it in the pick-order. You'll find the number of humans living in that country and also find the percentage of the world population living in that country. As you can see Educacionbc.edu.mx would be bigger then the country Niue!
Rank Country Population % of world population 220 Falkland Islands 3,000 0.00005% 221 www.educacionbc.edu.mx 1,721 - 222 Niue 1,500 0.00003% 223 Tokelau 1,200 0.00003% 224 Vatican City 800 0.00002% 225 Pitcairn Islands 50 0.000001%
## If the visitors of Educacionbc.edu.mx have to be seated in these boats.
On the image below you see a boat with illegal immigrants from Sengal. In 2006 there where lots of boats with refugees at the west African coast. One of these fisher boats contained 172 people! That means you'll need at least 11 boat(s) to give all visitors of Educacionbc.edu.mx a seat.
## Their website visitors compared to the daily internet users.
From all people of the world, there are around 1,400,000,000 (1,4 billion) people surfing daily on the internet. If you compare this to the 1,721 visitors of Educacionbc.edu.mx, you'll see that 1 of the 813,481 people is visiting their site on a daily basis.
If there would be a list of top websites in the world. The site Educacionbc.edu.mx would be on place #385247. Off course this is an estimated value. There are about 200 million websites around the world.
## How many kilometers will those people reach hand in hand?
The average person in the world is about 1.7 meters (5 ft 7 in). That means that if 1,721 people (the Educacionbc.edu.mx visitors) would connect their hands and form a big line, it would be 2,926 meters long. A kilometer consists of 1000 meters, so it would be 3 kilometers long.
Below you will see an image of 4 humans connected by their hands.
## How many electricity would this site use?
As we estimated the total number of visitors to 1,721 earlier, this mean they have around 3,442 pageviews per day. This correspondents to 1 per second and 60 requests per minute. We think their are using 1 servers to host this website. A regular server uses about 2,200 kWh of power on a yearly basis. The commercial pricing average of one kWh is \$0.107. Factoring in the cooling load at 1X (2.0 PUE) puts the annual energy cost per server at ~\$800. for Educacionbc.edu.mx this means that their total server costs per year are about \$800. Off course, this are rough estimates. We've not even included the "Managing the server and network" time and costs. | 710 | 2,800 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2013-20 | longest | en | 0.927123 |
https://physics.stackexchange.com/questions/194441/pull-ups-in-water/194456 | 1,552,952,129,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912201812.2/warc/CC-MAIN-20190318232014-20190319014014-00172.warc.gz | 608,319,457 | 32,914 | # Pull-ups in water
I realized a couple days ago that I honestly did not learn in school why it is easier to do pull-ups in water than out of it. The only answers that I found are "because you're in water so there is less gravity". That answer does not suffice at all.
• Why did this get downvoted? It's a basic question but a perfectly reasonable one. – John Rennie Jul 17 '15 at 6:00
To expand on @CoilKid's answer, the buoyant force that makes it easier to do pullups in water is due to the pressure gradient in water. In simple terms, the pressure in water increases as you go down, because as you go down, there is more water above being pulled down by gravity. This pressure gradient is also why it hurts your ears if you swim down to the bottom of the pool without equilibrating the pressure in your ears as you descend.
The fact that the pressure steadily increases with depth means that the water pushing on your lower body exerts more force than the water pushing on your upper body. On balance, this means there is more force from the water pressure pushing up than down - this overall force that results is known as the "buoyant force".
If you were on the space station where there the effect of gravity is negligible, water would form giant globs floating around or sticking to surfaces, and doing a pullup with half your body inside such a glob of water would not help; without the effect of gravity, the water glob has the same pressure throughout, so on balance the force on you from the water pressure is zero; no buoyant force.
Interestingly, such a pressure gradient also exists in the air, and as such the air exerts a buoyant force on you as well, but since the density of air is so much less than that of water, the pressure changes much more gradually with height, so the buoyant force on you from the air is far smaller.
It's because unlike in air, the density of a human is less than the the density of the fluid around it. This causes you to float a bit, or be buoyant.
When there is a large difference in buoyancy, you will float on the surface of the fluid. This is why big aircraft carriers made of steel float. While they are made of steel, they are also full of air, which makes them have an overall density much less than that of the water.
As a human, you are made of, on average, ~65% water. This means that your overall density is just a bit less than that of water. When the densities are very close to one another, you will float just a bit. Not enough to make you pop to the surface (For the average person. This can change with an above average BMI.), but enough that the buoyancy offsets the pull of gravity just a bit. Gravity does not change just for you, you're still being pulled toward Earth's center of mass at ~$9.8m/s^2$ just like always.
Hopefully you find this explanation to be more satisfying than "because you're in water so there is less gravity".
Another way to see this is to consider the work needed to do a pull up. In the water you will do less work; while your body will be lifted up by the same distance, water will be displaced from a different height, so water moves down if you move up. The total change in the potential energy of your body and the water in the Earth's gravitational field is thus less. | 730 | 3,278 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.25 | 3 | CC-MAIN-2019-13 | latest | en | 0.972378 |
http://www.numbersaplenty.com/10092019 | 1,571,736,132,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570987813307.73/warc/CC-MAIN-20191022081307-20191022104807-00097.warc.gz | 290,534,188 | 3,529 | Search a number
10092019 = 73146507
BaseRepresentation
bin100110011111…
…110111110011
3200222201122111
4212133313303
510040421034
61000150151
7151531540
oct46376763
920881574
1010092019
115773313
123468357
132124712
1414a9bc7
15d45364
hex99fdf3
10092019 has 8 divisors (see below), whose sum is σ = 11906048. Its totient is φ = 8371080.
The previous prime is 10092007. The next prime is 10092037. The reversal of 10092019 is 91029001.
It can be divided in two parts, 1009201 and 9, that multiplied together give a palindrome (9082809).
It is a sphenic number, since it is the product of 3 distinct primes.
It is a cyclic number.
It is not a de Polignac number, because 10092019 - 25 = 10091987 is a prime.
It is a super-2 number, since 2×100920192 = 203697694992722, which contains 22 as substring.
It is not an unprimeable number, because it can be changed into a prime (10092079) by changing a digit.
It is a pernicious number, because its binary representation contains a prime number (17) of ones.
It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 23037 + ... + 23470.
It is an arithmetic number, because the mean of its divisors is an integer number (1488256).
Almost surely, 210092019 is an apocalyptic number.
10092019 is a deficient number, since it is larger than the sum of its proper divisors (1814029).
10092019 is an equidigital number, since it uses as much as digits as its factorization.
10092019 is an odious number, because the sum of its binary digits is odd.
The sum of its prime factors is 46545.
The product of its (nonzero) digits is 162, while the sum is 22.
The square root of 10092019 is about 3176.7938239678. The cubic root of 10092019 is about 216.1022820916.
The spelling of 10092019 in words is "ten million, ninety-two thousand, nineteen".
Divisors: 1 7 31 217 46507 325549 1441717 10092019 | 572 | 1,896 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2019-43 | latest | en | 0.85866 |
http://gmatclub.com/forum/acceptance-for-women-candidates-118707.html | 1,469,677,045,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257827782.42/warc/CC-MAIN-20160723071027-00086-ip-10-185-27-174.ec2.internal.warc.gz | 103,148,617 | 45,529 | Find all School-related info fast with the new School-Specific MBA Forum
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# acceptance % for women candidates
Author Message
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acceptance % for women candidates [#permalink]
### Show Tags
10 Aug 2011, 20:46
If a business school have 29% total acceptance, is it fair to assume that it may have a higher, say 35-40% acceptance among women?
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Re: acceptance % for women candidates [#permalink]
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11 Aug 2011, 00:03
Don't think so. The total acceptance rate (number of candidates accepted / total number of candidates who applied) is unrelated to the gender ratio (total number of women candidates / total number of accepted candidates).
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Re: acceptance % for women candidates [#permalink] 11 Aug 2011, 00:03
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Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | 655 | 2,468 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2016-30 | longest | en | 0.819816 |
https://www.upkeep.com/learning/availability | 1,660,034,818,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882570913.16/warc/CC-MAIN-20220809064307-20220809094307-00343.warc.gz | 920,596,809 | 87,906 | # What is Availability as a Maintenance Metric?
## What is availability?
Availability refers to the duration of time that a plant or a particular equipment is able to perform its intended task.
## Overview
The amount of operational time of an equipment can directly impact the performance of a plant. While availability as a metric can be expressed in various ways, it generally quantifies the probability that an equipment is in working condition.
Availability is often measured by looking into an equipment’s uptime – that is the amount of time that the equipment is performing work. To characterize the availability of an asset, it is therefore important to identify the instances of downtime or any duration when operations are stopped. Downtime can be classified as planned or unplanned. While downtime can be a strategic step to perform proactive maintenance activities, it would provide useful insights to compare how much downtime is contributing to the overall performance of the equipment or even the whole plant.
With the use of maintenance software such as a computerized maintenance management system (CMMS), the process of gathering such metrics can done more easily and accurately.
## Differentiating availability from reliability
Another metric that relates to the duration that an equipment operates is reliability. Reliability differs from availability by quantifying the probability that an equipment will work as intended without any failures, as opposed to just measuring the time it is in operation.
As a hypothetical example, imagine a faulty mechanical mixer. Say the mixer shuts off every hour, while a properly functioning mixer can continuously work for 24 hours without issues. While the availability of the faulty mixer may still be quite high if operated over a couple of hours, it can’t be considered a reliable piece of equipment as it breaks down every time.
Intuitively, availability and reliability are related metrics. If an equipment is expected to operate without failures, you can expect the same equipment to increase availability.
## How to calculate availability
Availability, by definition, is expressed as the percentage of actual operation time that the equipment is used out of the total time being observed. In the form of an equation, availability is expressed as:
Availability (%) = [Actual operation time (hours)/Total time (hours)] * 100
Where the actual operation time can be obtained by deducting any planned or unplanned downtime from the total time:
Actual operation time = Total time (hours) – Total downtime (hours)
For example, say a working mechanical mixer is observed for 10 hours. A mechanical breakdown causes it to stop abruptly. Investigations and repairs take 2 hours before the mixer was up and running again. The actual operation time can be calculated by the following equation:
Actual operation time (hours) = 10 hours – 2 hours = 8 hours
Now using the obtained actual operation time with the availability formula, we can calculate the availability to be 80% as shown below:
Availability (%) = [8 hours/10 hours] * 100 = 80%
## How to calculate availability from other metrics
Given that other metrics that also concern the time of operation are being measured as data points, availability can be calculated by these data sources. The mean time between failure (MTBF) and mean time to repair (MTR), are common metrics that can also be used to calculate an equipment’s availability.
MTBF and MTR describe the effects of breakdowns on the operational time that an equipment can be used. Assuming by definition that the MTBF is a period when the equipment is performing under good working conditions, and MTR is the downtime it takes to repair the equipment, availability can be calculated using the following formula:
Availability = MTBF/(MTBF + MTR)
## How to improve availability
From the given equations that calculate availability, it becomes obvious that reducing downtime is a key step to improving availability. Note that downtime is composed of planned and unplanned events. Downtime due to unplanned breakdowns usually cause more adverse impacts to the system’s availability. Planned downtime, on the other hand, should be used as invested time to perform proactive measures that keep equipment in good working condition.
Improving the availability of the whole plant should be done in a systematic way that involves the organization’s top management as well as staff. Promoting a culture towards reducing defects and reducing downtime can impact the plant’s availability, and even the plant’s overall effectiveness.
## Relating availability to the overall equipment effectiveness (OEE)
Availability is one of three factors that define the overall equipment effectiveness (OEE) of a plant. The two other factors being efficiency and quality. The product of the three factors, all expressed in percentages, is how the OEE score is obtained.
OEE is a metric that has been the standard of measuring plant performance. Being one of the factors contributing to OEE only reinforces the importance of availability to the performance of a plant.
## Want to keep reading?
Good choice. Here are some similar articles!
#### What is the difference between availability and reliability?
Availability measures equipment's ability to operate, while reliability measures the ability of equipment to perform without failure.
View Article
#### What are the best metrics and KPIs for manufacturing companies?
Downtime and uptime are the heartbeats of a manufacturer - when the facility has too much downtime, the health of the organization suffers.
View Article
#### Equipment Maintenance - What Is Equipment Maintenance?
Equipment maintenance includes any process intended to keep a business’s equipment in working condition.
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Information is 100% secure. | 1,110 | 5,895 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2022-33 | latest | en | 0.955127 |
https://math.stackexchange.com/questions/2933330/solving-equations-involving-powers | 1,660,424,475,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571987.60/warc/CC-MAIN-20220813202507-20220813232507-00039.warc.gz | 355,197,462 | 65,225 | # Solving equations involving powers
I have been solving an OS problem in which I came across this equation where I have to find the value of H as in % but I'm not able to solve it fully. This is not a homework, I'm stuck in between and been left maths from quite some time.
3*10^-8/0.8 = H(2*10^-8 + 10^-8) + (1-H) (10^-8 + 10^-3)
My Take so far -
3*10^-8/0.8 = H(3*10^-8) + (1-H) (10^-11)
3*10^-8/0.8 = H(3*10^-8) + 10^-11 - 10^-11*H
Now I can't able to solve any further.
What I tried more is I cancelled (3*10^-8) from both LHS and RHS and I got
1/0.8 = H + (1-H)*10-11 /// ( I took 10^-11 common from 10^-11 - 10^-11*H)
So what to do after 1/0.8 = H + (1-H)*10-11
• OS = Operating System ?
– user65203
Sep 28, 2018 at 9:18
• The coefficients expressed "in scientific notation" are not really considered as powers. What you have is a linear equation.
– user65203
Sep 28, 2018 at 9:38
Dropping the annoying $$10^{-8}$$,
$$\frac3{0.8} = H(2 + 1) + (1-H) (1 + 100000).$$
Without caring about lower terms, we have
$$1-H\approx\frac3{80000}$$ which gives you an order of magnitude, i.e. $$H$$ very close to $$1$$.
Exact computation is (using $$H=1-(1-H)$$)
$$\frac{15}4=3+(1-H)\,99998,$$
$$1-H=\frac3{4\cdot99998}.$$
(I prefer to evaluate $$1-H$$ as this is more accurate and gives you better understanding of the value.)
So you have
$$\frac{3\cdot10^{-8}}{0.8} = 3\cdot10^{-8}H + (1-H)(10^{-8}+10^{-3})$$
which is
$$\frac{3}{0.8} = 3H + (1-H)(1+10^{5}) = 1+10^{5}-10^{5}H+2H$$
if you divide both sides by $$10^{-8}$$. So
$$H = \frac{\frac{3}{0.8} - 1 - 10^{5}}{2-10^{5}} = 0.9999924998499969999... \approx\mathbf{100\%}$$
• This is wrong, I've made a mistake above 10^-8 + 10^-3 is not 10^-11 Sep 28, 2018 at 3:30
• I edited my answer. Sep 28, 2018 at 8:36
• Now it's perfectly fine. Sep 28, 2018 at 13:06 | 719 | 1,830 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 13, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.1875 | 4 | CC-MAIN-2022-33 | latest | en | 0.894931 |
https://myaptitude.in/cds/maths/25-kg-of-alloy-x-is-mixed-with-125-kg-of-alloy-y | 1,601,374,652,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600401641638.83/warc/CC-MAIN-20200929091913-20200929121913-00352.warc.gz | 509,669,523 | 4,468 | # 25 kg of alloy X is mixed with 125 kg of alloy Y
25 kg of alloy X is mixed with 125 kg of alloy Y. If the amount of lead and tin in the alloy X is in the ratio 1:2 and the amount of lead and tin in the alloy Y is in the ratio 2:3, then what is the ratio of lead to tin in the mixture?
1. 1:2
2. 2:3
3. 3:5
4. 7:11 | 112 | 317 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2020-40 | latest | en | 0.941625 |
https://brainly.in/question/44385 | 1,487,744,628,000,000,000 | text/html | crawl-data/CC-MAIN-2017-09/segments/1487501170914.10/warc/CC-MAIN-20170219104610-00462-ip-10-171-10-108.ec2.internal.warc.gz | 695,867,409 | 9,931 | If sin(50-3/2 α) = cos (3α-50), then find the value of α and hence evaluate;tanα.secα.sinα-cotα.sinα.cosα.
1
by atchayaamudhan
2014-10-04T09:56:22+05:30
Sin(50-3α/2) = cos(3α-50)
sin(50-3α/2) = sin(90-3α+50)
sin(50-3α/2) = sin(140-3α)
50-3α/2 = 140-3α
3α/2 = 140-50 = 90
3α = 180
α = 60
Now,
tanα.secα.sinα-cotα.sinα.cosα
= sin²α/cos²α-cos²α
= tan²α-cos²α = tan²60 - cos²60
= (√3)² - (1/2)² = 3-1/4 = 11/4 | 237 | 430 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.75 | 4 | CC-MAIN-2017-09 | latest | en | 0.309406 |
https://plainmath.org/linear-algebra/255-the-line-plus-equal-meets-the-curve-plus-equal-110-points-find-coordinates | 1,723,019,971,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640690787.34/warc/CC-MAIN-20240807080717-20240807110717-00465.warc.gz | 373,429,486 | 23,222 | Amari Flowers
2020-11-06
The line $2x+3y=8$ meets the curve $2{x}^{2}+3{y}^{2}=110$ at the points A and B.
Find the coordinates of A and B.
sovienesY
To solve this problem, use the quadratic formula. This will be $a=1$, $b=2$ and $c=-8$.
The formula substituted is
That is $\frac{-2±6}{2}$. Simplify that to get $x=2$ and $x=-4$.
$\approx$ Sriswaroop. Hope this helps.
Do you have a similar question? | 145 | 405 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 21, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2024-33 | latest | en | 0.804436 |
https://studylib.net/doc/11390618/third-test-review--m273q-03--spring-2011 | 1,590,834,947,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347409171.27/warc/CC-MAIN-20200530102741-20200530132741-00490.warc.gz | 539,527,372 | 12,968 | # Third Test Review, M273Q-03, Spring 2011
```Third Test Review, M273Q-03, Spring 2011
ZZ
(1 + x2 ) dA, where D is the triangular region with vertices (0, 0), (1, 1), and (0, 1).
1. Calculate
D
2. Change the order of integration and evaluate
Z 9Z √y
0 0
x dx dy
.
(x2 + y)1/2
3. Find the centroid of the region W bounded in spherical coordinates by φ = φ0 and the sphere
ρ = R.
4. (a) Parametrize the circle C of radius 2 with center (4, 5) in counterclockwise orientation.
I
(b) Find (x + y) ds.
C
(c) What could a possible physical interpretation of the integral in (b) be? Give one example.
(There are many correct answers here.)
5. One of the
Z following vector fields is conservative. Find a potential for it, and use the potential
F· dr, where the curve C is given by r(t) = ht3/2 , cos(πt2 )i, 0 ≤ t ≤ 1.
to calculate
C
F1 (x, y) = hyexy + y, xexy − xi
F2 (x, y) = hyexy − x, xexy + yi
6. Calculate
ZZ
(x2 + y 2 )e−z dS,
S
where S is the cylinder with equation x2 + y 2 = 9 for 0 ≤ z ≤ 10.
``` | 365 | 1,008 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.03125 | 3 | CC-MAIN-2020-24 | latest | en | 0.813949 |
http://perplexus.info/show.php?pid=10912&op=sol | 1,604,110,281,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107912593.62/warc/CC-MAIN-20201031002758-20201031032758-00317.warc.gz | 77,010,731 | 4,373 | All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
perplexus dot info
Prime power puzzle (Posted on 2017-04-01)
603, 604, and 605 are the first 3 consecutive integers that are the product of a prime and another prime squared.
603=32*67
604=22*151
605=5*112
1. What is the first set of 4 consecutive integers that are the product of a prime and another prime squared?
2. What is the first set of 5 consecutive integers that are the product of a prime and another prime squared?
Submitted by Math Man Rating: 5.0000 (1 votes) Solution: (Hide) 1. 17042641441, 17042641442, 17042641443, 17042641444 2. 10093613546512321, 10093613546512322, 10093613546512323, 10093613546512324, 10093613546512325
Subject Author Date re: Found Five Chem Academy 2019-04-29 06:27:36 Found Five Brian Smith 2017-04-02 21:17:20 A simpler proof that 6 in a row is impossible Steve Herman 2017-04-02 20:01:20 re(2): Half A proof Charlie 2017-04-02 19:08:32 re: Half A proof Math Man 2017-04-02 16:48:17 Half A proof Steve Herman 2017-04-02 11:17:51 re(2): computer so far Steve Herman 2017-04-02 10:40:23 re: computer so far Charlie 2017-04-02 09:56:47 computer so far Charlie 2017-04-01 15:57:10
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https://www.studypage.in/maths/prime-and-composite-numbers | 1,553,493,797,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912203755.18/warc/CC-MAIN-20190325051359-20190325073359-00255.warc.gz | 905,672,305 | 7,044 | There are numbers, having exactly two factors 1 and the number itself. Such number are 2, 3, 5, 7, 11, and so on. These numbers are prime numbers.
The numbers other than 1 whose only factors are 1 and the number itself are called Prime numbers.
There are numbers having more than two factors like 4, 6, 8, 9, 10 and so on. These numbers are composite numbers.
Numbers having more than two factors are called Composite numbers. | 113 | 429 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2019-13 | longest | en | 0.949814 |
https://askpythonquestions.com/2021/11/20/differentiating-a-multivariable-function-w-r-t-different-dimensions-using-args-in-python/ | 1,642,973,967,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304309.59/warc/CC-MAIN-20220123202547-20220123232547-00243.warc.gz | 145,162,309 | 6,375 | #### Differentiating a multivariable function w.r.t different dimensions, using *args in python
Following is my attempt to create a function to differentiate multivariable functions, but as you see it only seems to be able to differentiate with respect to the first positional argument (namely x). How can I extend this to be able to take partial derivatives with respect to y and z?
``````def firstderivative(func,x,*args):
return((func(x+0.001,*args)-func(x-0.001,*args))/0.002)
def afunc(x,y,z):
return(x*y+x*z+y*z)
print(firstderivative(afunc,2,4,5))
``````
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### This Is a Certified Answer
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
2x + y = 9
3x - y = 16
combine both equations (add everything together on the left, and everything together on the right)
5x = 25
x = 5
plug x = 5 back into the equations to solve for y
2(5) + y = 9
10 + y = 9
y = -1
3(5) -y = 16
15 - y = 16
-y = 1
y = -1 | 183 | 594 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.484375 | 3 | CC-MAIN-2017-04 | latest | en | 0.908429 |
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EN
The paper presents the theoretical basis of the mathematical expression derived from the American standard, used to determine the thermally permissible torque load capacity of the cage induction motors when supplied with distorted voltages. The results of the measurement verification of this expression for different voltage shapes supplying the tested motor are presented. The test results confirmed the correctness of the expression when the motor is supplied with distorted voltage with a limited number of higher harmonics.
2
Electrical machines with switched and modulated flux
EN
The work compares the value of the produced torque (average value) of a 2.2kW squirrel cage induction motor with new construction machines, i.e. a motor with flux switching and hybrid excitation or DC excited, a motor with flux modulation and hybrid excitation or DC excitation. The external dimensions of the tested machines corresponded to the dimensions of the induction motor.
EN
This paper deals with experimental verification of vector-control algorithm for induction motor operation under asymmetry. Proposed algorithm allows one compensate negative influence of motor asymmetry on electric drive energy consumption parameters. Thus, it helps to ensure more effective energy consumption mode of induction motor under asymmetry. In this paper, it is described theoretical principles of asymmetry compensation algorithm, developed software and discussion of derived experimental results.
PL
Artykuł dotyczy eksperymentalnej weryfikacji algorytmu sterowania wektorowego w asymetrycznej pracy silnika indukcyjnego. Proponowany algorytm pozwala skompensować negatywny wpływ asymetrii parametry zużycia energii napędu elektrycznego. Jest tom pomocne w zapewnieniu efektywniejszego zużycia energii przy pracy asymetrycznej. W artykule opisano podstawy teoretyczne algorytmu kompensowania asymetrii. Opracowano algorytm, przedyskutowano wyniki badań eksperymentalnych.
EN
In industrial drive systems, one of the widest group of machines are induction motors. During normal operation, these machines are exposed to various types of damages, resulting in high economic losses. Electrical circuits damages are more than half of all damages appearing in induction motors. In connection with the above, the task of early detection of machine defects becomes a priority in modern drive systems. The article presents the possibility of using deep neural networks to detect stator and rotor damages. The opportunity of detecting shorted turns and the broken rotor bars with the use of an axial flux signal is presented.
EN
This paper presents the problem of the identifying parameters for use in mathematical models of induction motors with the use of a genetic algorithm (GA). The effect of arithmetical crossover and the generation of new populations on identification results is analysed. The identified parameters of the model were determined as a result of the minimisation of the performance index defined as the mean-square error of stator current and angular velocity. The experiments were performed for the low power induction motor. The steady-state genetic algorithm with regard to convergence and accuracy of the identification process and calculation time is analysed.
PL
W artykule przedstawiono problem identyfikacji parametrów modeli matematycznych silników indukcyjnych z zastosowaniem algorytmu genetycznego (AG). Analizowano wpływ krzyżowania arytmetycznego i generowania potomków na wyniki identyfikacji. Identyfikowane parametry modelu wyznaczono w rezultacie minimalizacji wskaźnika jakości zdefiniowanego jako błąd średniokwadratowy prądu stojana i prędkości kątowej. Badania eksperymentalne przeprowadzono dla silnika indukcyjnego małej mocy. Algorytm genetyczny z częściową wymianą populacji analizowano ze względu na zbieżność i dokładność procesu identyfikacji i czas obliczeń numerycznych.
EN
This work deals with the preliminary investigations of a 200-kW induction cage motor with a supply voltage featuring subharmonic injection. The results of the field calculations in the MAXWELL environment are presented for subharmonics of various frequencies. It was found that subharmonics occurring in real power systems can cause overheating and premature failure of this type of machine.
7
EN
The article contains the results of research within the project to apply unipolar (axial) flux to obtain diagnostic signals carrying the information of: electrical asymmetries of machinery (inter-turn stator short-circuits, cage damages); rotational speed of the rotor and load torque. Inter-turn stator short-circuits can be detected both at starting process time (when they appear most often), as well as in steady states. Detection of rotor cage defects in steady states has a character of a comparative study, and over time, as the defects develop. For standard drives that are powered from the network and work in open systems, by measuring the voltage following a unipolar flux, it is possible to make measurement and recording of motor speed, which usually is almost never provided under industrial conditions. The study shows that a simple in its construction, cheap coil can be a very useful diagnostic tool. The measurements were carried out at the laboratory and motor workplace in the power plant, while in the test station, during the loading, characteristics illustrating the dependence of the torque on the axial flux and on the rotational speed were obtained. A way of using a single measurement to estimate the torque has been proposed. The method is relatively simple to implement and allows for a fully non-invasive determination of the load torque.
PL
W artykule przedstawiono szczegółową analizę wpływu uszkodzenia uzwojenia stojana silnika indukcyjnego na jakość estymacji strumienia skojarzonego wirnika w układzie sterowania wektorowego. Analizie poddano dwa układy, powszechnie znane jako symulatory zmiennych stanu, stosowane są często w przemysłowych układach napędowych. Badania przeprowadzono w układzie sterowania polowo zorientowanego (ang. DFOC – Direct Field Oriented Control). Uzyskane wyniki wykazały, że zwarcia zwojowe mogą prowadzić do niestabilnej pracy układu regulacji automatycznej. W celu zapewnienia odpowiedniej jakości estymacji - i w konsekwencji regulacji - nawet po wystąpieniu zwarć zwojowych zaproponowano zastosowanie zmodyfikowanych estymatorów strumienia wirnika. W pracy zaprezentowano szczegółową analizę teoretyczną oraz wyniki symulacji, które przeprowadzono w środowisku MATLAB/Simulink.
EN
The paper presents a detailed analysis of the impact of stator winding faults on the properties of the rotor flux estimation in the vector controlled induction motor drives. In the paper the two well-known simulators, often used in the industrial drives, were analyzed. The tests were carried out in a Direct Field Oriented Control (FOC) system. It was shown, that during inter-turn short circuits, the vector controlled system can be even unstable. To guarantee the stability during stator faults, a compensation method, based on the modified rotor flux estimators, was proposed. The article presents a detailed theoretical analysis as well as the results of simulations carried out in the MATLAB/Simulink environment.
9
Wyznaczanie parametrów modeli obwodowych silników indukcyjnych
PL
Podano prostą metodę wyznaczania parametrów silnika klatkowego z wykorzystaniem danych katalogowych. Sposób obliczania parametrów zintegrowano z uproszczonym sposobem uwzględniania zmian wartości parametrów wywołanych wypieraniem prądu i nasyceniem obwodów magnetycznych. Uzyskiwane wyniki porównano z rezultatami wykorzystania kalkulatorów dostępnych w internecie lub skojarzonych z programem ATP/EMTP, łącznie z wersją uwzględniającą 2 równoległe gałęzie obwodu wirnika. W celu oceny dokładności metod określania parametrów, wykonano obliczenia przebiegów rozruchowych przykładowego silnika i porównano je z pomiarowymi. Pokazano możliwość wykorzystania wyznaczonych parametrów do modelowania rozruchu, pracy prądnicowej oraz hamowania przeciwwłączeniem i nawrotu.
EN
A simple method for determining the parameters of a squirrel cage motor using the catalog data is given. The method of calculating the parameters was integrated with a simplified way of taking into account changes in parameter values caused by displacement of current and saturation of magnetic circuits. The obtained effects were compared with the results of using the calculators available on the Internet or associated with the ATP / EMTP program, including the version taking into consideration two parallel branches of the rotor. In order to assess the accuracy of methods for determining the parameters, calculations of the start-up courses of the exemplary motor were made and compared with the measuring ones. It was shown the possibility to use the designated parameters for modeling the starting, generator work as well as for back-current braking and relapse.
EN
An express analysis of the methods and systems of fault-tolerant control of induction motors of variable-frequency electric drives is presented. Classification features are suggested to evaluate the possibility of using existing fault-tolerant control methods in modern variablefrequency electric drives, taking into account the capabilities of control systems. As one of the promising directions, the usage of modern p-q and cross-vector instantaneous power theories and its modifications are allocated for solving inseparable connected tasks of damages diagnostics and compensation of their influence on the operation modes of the frequency-controlled electric drive.
PL
W artykule przedstawiono analizę metod i systemów sterowania. Zasugerowano właściwości klasyfikacyjne do oceny możliwości wykorzystania istniejących metod sterowania w nowoczesnych napędach elektrycznych o zmiennej częstotliwości, biorąc pod uwagę ich operatywność. Jeden z obiecujących kierunków, a mianowicie użycie nowoczesnych teorii mocy oraz ich modyfikacje s ą przydzielone do rozwiązywania nierozdzielnie związanych zadań diagnozowania uszkodzeń i kompensacji ich wpływu na stany działania zmiennoczęstotliwościowych napędów elektrycznych.
EN
This paper is focused on a performance improvement of ANFIS with sliding mode based on MRAS sensorless speed controller for induction motor drive associated with the IFOC strategy. The control strategy consists of the combination of the sliding mode with the ANFIS strategy. In order to estimate the speed of the IM, MRAS sensorless strategy associated with ANFIS system is used. This controller has high accuracy, suitable performance, high robustness and high tracking efficiency. To provide a numerical comparison between different controllers, a performance index based on speed error is assigned. The obtained results show that ANFIS Controller associated with MRAS observer overcome the problem of estimation of the speed of the motor particularly at low speed. The main advantages of the proposed method are the robustness to parameter variations and load changes.
PL
W artykule analizowano możliwość poprawy systemu ANFIS ze ślizgowym bezczujnikowym sterownikiem prędkości silnika indukcyjnego. Dla porównania różnych sterowników wprowadzono indeks bazujący na błędzie prędkości. Wykazano że system ANFIS z obserwatorem MRAS rozwiązuje problem określania prędkości szczególnie przy małych prędkościach.
EN
Improved energy efficiency, limitation of production costs or increased power density of electrical machines are among principal incentives in searching for new, innovative designs. Undoubtedly, one of innovation features is application of alternative materials, which results in accomplishment of required technical or economic advantages. Different design variants of electromagnetic circuit of induction disk-type motor have been presented in this paper; these variants use alternative materials for stator and rotor cores. Results of calculations and lab tests of a model motor have been given. Cores of the motor models have been made of amorphous strip, of M470-50 electrical sheet, of solid steel and of Vacoflux48 strip with high flux density saturation values.
PL
Zwiększenie efektywności energetycznej, ograniczenie kosztów produkcji lub zwiększenie gęstości mocy maszyn elektrycznych jest główną motywacją do poszukiwania innowacyjnych w tym zakresie rozwiązań konstrukcyjnych. Jednym z aspektów innowacyjności jest bez wątpienia wykorzystywanie alternatywnych materiałów, pozwalających na osiągnięcie danej korzyści czy to technicznej czy ekonomicznej. W niniejszym artykule przedstawiono oraz przeanalizowano różne rozwiązania konstrukcyjne obwodu elektromagnetycznego indukcyjnego silnika tarczowego wykorzystującego alternatywne materiały rdzeni stojana i wirnika. Przedstawiono wyniki obliczeń oraz wyniki badań laboratoryjnych modelowego silnika, którego rdzenie wykonane zostały między innymi z taśmy amorficznej, z blachy M470-50, z litej stali oraz z taśmy Vacoflux48 o wysokich wartościach indukcji nasycenia.
EN
The object of this paper is to study a new control structure for sensorless induction machine dedicated to electrical drives using a five-level voltage source inverter (VSI). However, direct torque control (DTC), known for years, provides high dynamic performance and also fast and robust response for induction motors (IM), classical DTC produces notable torque, flux ripples. In the present paper, fuzzy logic has been suggested to improve the system performance (i.e. gives faster torque and flux responses and also reducing the undesirable torque ripple that can occur in the output torque). In this controller, torque error, flux error and also the position of stator flux are as inputs and the output of it is a suitable voltage vector which should apply to the motor. In this paper to reduce the number of rules and also increase controller’s speed, we use particular mapping for the stator flux position. Compared with conventional DTC, this method is easily implemented for induction machine, the ripples of both torque and flux are reduced remarkable. Simulation results proved the superiority of the novel approach.
PL
Celem tego artykułu jest zbadanie nowej struktury sterowania bezczujnikowej maszyny indukcyjnej przeznaczonej do napędów elektrycznych z wykorzystaniem pięciopoziomowego falownika napięcia (VSI). Wiadomo jednak, że bezpośrednia sterowanie momentu obrotowego (DTC), znane od lat zapewnia wysoką dynamikę, a także szybką i solidną reakcję dla silników indukcyjnych (IM), klasyczny algorytm DTC wytwarza znaczny moment obrotowy, tętnienia strumienia. W niniejszym artykule zasugerowano logikę rozmytą, aby poprawić wydajność systemu (tzn. daje szybszą zmianę momentu obrotowego i odpowiedzi strumienia, a także zmniejsza niepożądane tętnienia momentu obrotowego, które mogą wystąpić w wyjściowym momencie obrotowym). W tym regulatorze, błąd momentu obrotowego, błąd strumienia, a także położenie strumienia stojana są jako wejścia, a jego wyjście jest odpowiednim wektorem napięcia, który powinien być zastosowany do sterowania silnika. W tym artykule, aby zmniejszyć liczbę reguł, a także zwiększyć szybkość kontrolera, używamy konkretnego odwzorowania dla położenia strumienia stojana. W porównaniu z konwencjonalnym kodem DTC ta metoda jest łatwa do zastosowania w maszynach indukcyjnych, a tętnienia momentu obrotowego i strumienia są znacznie mniejsze. Wyniki symulacji dowiodły wyższości nowatorskiego podejścia.
14
Enclosure-less six-phase induction motor
EN
The papers deals with six-phase 2 kW 2-pole induction motor without enclosure. The motor is made of laser-cut construction steel , electrical steel and copper sheets. Shaft, two flange cartridge bearing units are machined by the milling machine. Bearings, stator winding and insulation are standard. The goal of the work is experimental investigation of impact of failures of the supply or stator winding on the motor performances.
PL
Artykuł przedstawia 6-fazowy 2-biegunowy silnik indukcyjny o mocy 2 kW. Model fizyczny silnika wykonano z blach ciętych laserem. Celem pracy jest weryfikacja wpływu uszkodzeń zasilania lub uzwojenia stojana silnika na jego właściwości.
EN
A complex mathematical model of dynamic processes in vibration device on elastic supports with eccentric self-centering unbalanced rotor and induction motor is given. A working chamber of induction motor does a plane motion. The dynamic feature of the electric motor is chosen for descriptions of device starting and a load oscillating character at steady-state modes of the device. Such model allows: to choose the electric motor of necessary power, to study influence of unbalances, to study influence of the rotor eccentricity and other drive parameters at the device starting, movement of characteristic points of its chamber, loads on bearings and the foundation. It has been established that a rational choice of eccentricity lead to the rotor vibrations reduce – realization of the self-centering effect. A visual method for geometric interpretation of the dynamic processes development at the device starting is proposed. Calculations results for the device with specific size are presented. The completed researches are perspective for solve problems of rational parameters choice for the considered class of mechanisms.
PL
I Przedstawiono model matematyczny procesów dynamicznych w urządzeniu wibracyjnym na elastycznych wspornikach z ekscentrycznym, samocentrującym niezrównoważonym wirnikiem i silnikiem indukcyjnym. Część robocza silnika indukcyjnego wykonuje ruch płaski. Dynamiczna cecha silnika elektrycznego jest wybierana dla opisów urządzenia rozruchowego i charakteru oscylującego obciążenia w trybach stanu ustalonego urządzenia. Model taki pozwala: wybrać silnik elektryczny o wymaganej mocy, zbadać wpływ asymetrii, zbadać wpływ ekscentryczności wirnika i innych parametrów napędu przy uruchomieniu urządzenia, ruch charakterystycznych punktów jego komory, obciążenia na łożyskach i fundamencie. Ustalono, że odpowiedni wybór ekscentryczności prowadzi do zmniejszenia wibracji wirnika - realizacja efektu samocentrującego. Zaproponowano wizualną metodę geometrycznej interpretacji dynamicznego rozwoju procesów przy uruchamianiu urządzenia. Przedstawiono wyniki obliczeń dla urządzenia o określonej wielkości.
EN
The paper deals with a method of fault-tolerant control of an induction motor at damages in the stator power electrical circuit. The method bases on the decrease of the damaged phase flux linkage, which enables the reduction of the level of the consumed power variable component. The research concerned the cases of the stator winding damages at the early stage of their development. At such damages, the induction motor can operate for a long time in the asymmetric mode without protection actuation but with essential thermal overload of particular phases. The results of the research of the proposed system of fault-tolerant control confirmed the possibility of the decrease of the thermal overloads of the induction motor windings and frequency convertor semiconductor switches, which will allow the increase of their life span.
PL
W artykule przedstawiono metodę kontroli odporności na uszkodzenia silnika indukcyjnego przy uszkodzeniach w obwodzie elektrycznym stojana. Metoda opiera się na zmniejszeniu uszkodzonego połączenia fazowego, co umożliwia obniżenie poziomu zużytej zmiennej składowej mocy. Badania dotyczyły uszkodzeń uzwojenia stojana na wczesnym etapie ich rozwoju. Przy takich uszkodzeniach silnik indukcyjny może działać przez długi czas w trybie asymetrycznym bez włączenia zabezpieczeń ale z istotnym przeciążeniem termicznym poszczególnych faz. Wyniki badań proponowanego systemu odpornego na uszkodzenia potwierdziły możliwość zmniejszenia przeciążeń termicznych uzwojeń silnika indukcyjnego i półprzewodnikowych łączników przemienników częstotliwości, co pozwoli na zwiększenie ich żywotności.
17
Axial forces of magnetic pull in a disc type induction motor – experimental test
EN
Axial forces of magnetic pull occurring in disk type machines significantly affect the operation of bearings, therefore they should be taken into account at the design stage. This is particularly important when it’s known that the magnetic circuit doesn’t balance the value of these forces. Results of investigation of magnetic pull effect present in disk induction motor with a single air-gap are given in this paper. Among others, results of measurements of axial forces distribution occurring in the motor during idle run and under load conditions are shown. Results of measurements in case of air-gap circumferential asymmetry are also presented. The work is focused on analysis of axial forces' distribution and their changes under different operational conditions of the motor.
PL
Siły osiowe naciągu magnetycznego występujące w maszynach tarczowych znacząco oddziałują na pracę łożysk, dlatego należy je wziąć pod uwagę na etapie konstrukcji mechanicznej i doboru podzespołów maszyny. Szczególnego znaczenia nabiera to w przypadku, gdy wiadomo, że konstrukcja obwodu magnetycznego nie bilansuje wartości tych sił. W pracy przedstawiono wyniki badań zjawiska naciągu magnetycznego występującego w silniku tarczowym indukcyjnym z jedną szczeliną powietrzną. Zaprezentowano między innymi wyniki pomiarów przebiegów sił osiowych przy biegu jałowym silnika oraz w stanie obciążenia. Główną uwagę poświęcono analizie przebiegów sił osiowych oraz ich zmianom w różnych warunkach pracy silnika.
18
Analiza napięć i prądów pobieranych przez zespół pomp wodociągowych
PL
Praca dotyczy pomiarów i analiz napięć oraz prądów pobieranych przez zespół pomp wodociągowych. Zespół składa sie z czterech pomp napędzanych silnikami indukcyjnymi z regulowaną prędkością obrotową, pracujących w układzie wędrującego falownika. Analizie poddano różne punkty pracy układu wymuszając tym samym jego funkcjonowanie w różnych konfiguracjach, wymagających pracy różnej liczby pomp oraz silników. Oceniono stopień odkształcenia prądu w badanych punktach, wykorzystując do tego celu analizy czasowe oraz częstotliwościowe. Badania wykonano na specjalnie przygotowanym stanowisku laboratoryjnym, wykorzystując do rejestracji napięć oraz prądów analizator jakości energii Elspec BlaxBox4500 oraz dedykowane oprogramowanie.
EN
The work concerns the measurement and analysis of voltage and current drawn by the water supply pump station. The set consists of four pumps driven by induction motors with adjustable speed, working in the system of a traveling inverter. Various work points of the system have been analyzed, thus forcing its functioning in various configurations requiring the work of various numbers of pumps and engines. The degree of current distortion in the tested points was evaluated using time and frequency analyzes for this purpose. The tests were carried out on a specially prepared laboratory bench, using the Elspec BlaxBox4500 energy quality analyzer and dedicated software to record voltages and currents.
EN
The paper presents the possibility of using neural networks in the detection of stator and rotor electrical faults of induction motors. Fault detection and identification are based on the analysis of symptoms obtained from the fast Fourier transform of the voltage induced by an axial flux in a measurement coil. Neural network teaching and testing were performed in a MATLAB–Simulink environment. The effectiveness of various neural network structures to detect damage, its type (rotor or stator damage) and damage levels (number of rotor bars cracked or stator winding shorted circuits) is presented.
EN
A sensorless indirect stator-flux-oriented control (ISFOC) induction motor drive at very low frequencies is presented herein. The model reference adaptive system (MRAS) scheme is used to estimate the speed and the rotor resistance simultaneously. However, the error between the reference and the adjustable models, which are developed in the stationary stator reference frame, is used to drive a suitable adaptation mechanism that generates the estimates of speed and the rotor resistance from the stator voltage and the machine current measurements. The stator flux components in the stationary reference frame are estimated through a pure integration of the back electro-motive force (EMF) of the machine. When the machine is operated at low speed, the pure integration of the back EMF introduces an error in flux estimation which affects the performance torque and speed control. To overcome this problem, pure integration is replaced with a programmable cascaded low-pass filter (PCLPF). The stability analysis method of the MRAS estimator is verified in order to show the robustness of the rotor resistance variations. Experimental results are presented to prove the effectiveness and validity of the proposed scheme of sensorless ISFOC induction motor drive.
Strona / 32
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać. | 6,235 | 25,380 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2020-50 | latest | en | 0.428724 |
http://math.stackexchange.com/questions/tagged/commutative-algebra?page=45&sort=newest&pagesize=30 | 1,469,455,479,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257824230.71/warc/CC-MAIN-20160723071024-00233-ip-10-185-27-174.ec2.internal.warc.gz | 157,596,608 | 25,693 | Tagged Questions
Questions about commutative rings, their ideals, and their modules.
34 views
A submodule filtration that does not define the structure of topological module.
I was reading the following from Liu's Algebraic Geometry and Arithmetic Curves on page 18. In this book all rings are commutative and with unit. Let $A$ be a ring endowed with the $I$-adic topology. ...
475 views
Is $\mathbb Z[[X]]\otimes \mathbb Q$ isomorphic to $\mathbb Q[[X]]$?
Is $\mathbb Z[[X]]\otimes \mathbb Q$ isomorphic to $\mathbb Q[[X]]$? Here tensor product is over the ring $\mathbb Z$ and $\mathbb Z[[X]]$ denotes formal power series over $\mathbb Z$. I think this ...
87 views
Canonical map is injective
Let $A$ and $B$ be commutative rings, and let $f:A\to B$ be a faithfully flat ring homomorphism. How can I show that for any $A$-module $M$, the canonical map $M\to M\otimes_AB$ is injective? I was ...
94 views
Local cohomology killed by a power of I
Notations:: $H^i_I(M)$ is $i^{th}$ local cohomology of $M$ with support in $I$ and $H^i_I(M)=R^i\Gamma_I(M)$ where $R^i\Gamma_I(M)$ is the right derived functor of a covariant left exact functor, ...
167 views
Is the converse of Proposition 3.5.4 (c) of Bruns_Herzog true?
Question 1. Is the converse of Proposition $3.5.4 (c)$ of Bruns_Herzog true? I can see that $R$ is cohen-macaulay. so if one can prove that $r(R)=1$ , $R$ will be Gorenstein. Question ...
42 views
57 views
Is there a consensus on the correct way of raising elements of commutative rings to the power of $a/b$?
I'm trying to understand the "correct" way of raising elements of commutative rings to the power of $a/b,$ where $a$ and $b$ are integers, but not having much luck. Suppose $R$ is a commutative (...
100 views
Two definitions for non-singular in codimension 1
I am trying to understand how the following definitions are the same. Shafarevich definition (pg 128) - A variety is non-singular in codimension one if the singular locus has codimension $> 1$. ...
25 views
Show that $V(\bigcup_{i \in I} E_{i})=\bigcap_{i \in I} V(E_{i})$
This is a part of a problem in Atiyah's Introduction to Commutative Algebra introducing the Zariski Topology. Here we are given that $(E_{i})_{i \in I}$ is a family of subsets of a unital commutative ...
84 views
Tensoring two short exact sequences
Let $R$ be a commutative ring with $1$ and consider the following short exact sequences of $R$-modules \begin{align} &0 \to M' \to M \stackrel{f}{\to} M'' {\to} 0 \qquad \text{and } \\ &0 \to ...
109 views | 753 | 2,537 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2016-30 | latest | en | 0.874093 |
http://www.instructables.com/topics/How-can-I-obtain-an-apparent-specific-gravity-of-/ | 1,529,806,955,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267865995.86/warc/CC-MAIN-20180624005242-20180624025242-00571.warc.gz | 437,837,145 | 7,243 | 561Views3Replies
How can I obtain an apparent specific gravity, of a plastic bag? Answered
I need to verify an Apparent Specific gravity of a plastic bag- like the type used for a food vacuum sealer. I'm not sure how to go about it. I think I have all the needed items; scale, water bath, even a vacuum sealer if needed. I just can't find the method, or the formula used to calculate. I even called the manufacturer of the bag I'm using, and they had no idea how they came up with their data. Thank you for any ideas you can share with me. Jodie
Tags:
3 Replies
klee27x (author)2009-07-13
I'd cut out a small section of the material. Then I'd use a very small lab scale to weigh it to within a fraction of a gram. Then roll it up and place it in a thin, graded cylinder filled with water and a drop of dish soap. Lightly manipulate it with tweezers to get it all the way submerged and all the air bubble out without making suds The soap will help get the air bubbles out. No string needed, cuz it'll stick to the walls. If you use a tank large enough to take a whole bag that is not carefully rolled up, you won't be able to discern any change in water level.
klee27x (author)2009-07-13
The actual formula is (DENSITY)/(DENSITY of WATER). Since water weighs 1g/mL, all you have to do is calculate the density of your bag in g/mL then drop the units.
kelseymh (author)2009-02-26
For the record, I presume you know the definition of specific gravity.
"Apparent" specific gravity means you're dealing with something that has trapped air, and so the bulk density of the object is lower than the density of small samples of the raw material.
the easiest way to do something like this would be to seal up your bag, getting "as much" air out as is possible/reasonable. Weigh the sealed bag on a precision scale (i.e., down to milligrams if possible). Use Archimedes' method -- submersion in a water tank, e.g. by anchoring it with a fine thread to the bottom -- to get the volume, then just divide to find the density.
This technique will be subject to substantial measurement uncertainty, so you should to several trials with the same sealed bag and average the results, and you should also probably make several samples and do (multiple) measurements on each one. | 545 | 2,271 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2018-26 | latest | en | 0.942235 |
https://jeopardylabs.com/play/math-mix-up-19 | 1,638,925,083,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363420.81/warc/CC-MAIN-20211207232140-20211208022140-00219.warc.gz | 382,823,427 | 9,090 | How many?
Money Money
Multiplication
Division
Mix it up!
100
How many days are in three weeks?
21 days
100
2 quarters = ____ cents
50 cents
100
9 x 1 =
9
100
4 / 4 =
1
100
What would be an equivalent fraction to 1/2?
some examples
2/4, 3/6, 10/20...
200
How many bagels would there be in two dozen?
24 bagels
200
12 dimes = \$_____
\$1.20
200
12 x 2 =
24
200
3/3 =
1
200
How many years are in 5 decades?
50 years
300
How many years are there in five centuries?
500 years
300
8 dimes + 4 nickels = \$
\$1.00
300
8 x 0 x 3 =
0
300
32 / 8 =
4
300
What is the area of the rectangle that has a length of 5 inches and width of 4 inches?
20 inches2
400
How many days are in one year?
365 days
400
3 quarters + 10 dimes = \$
\$1.75
400
4 x 6 x 1=
24
400
20 / 5 =
4
400
5 octagons, how many sides in all?
40 sides
500
How many inches are in 3 yards?
36 inches
500
10 quarters + 3 dimes = \$
\$2.80
500
12 x 12 =
144
500
100/100 = | 352 | 997 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2021-49 | latest | en | 0.862085 |
https://scilogs.spektrum.de/hlf/michael-atiyahs-favourite-manifold/ | 1,716,443,385,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058611.55/warc/CC-MAIN-20240523050122-20240523080122-00497.warc.gz | 449,364,684 | 16,556 | • Lesedauer ca. 5 Minuten
• 1 comment
# BLOG: Heidelberg Laureate Forum
Laureates of mathematics and computer science meet the next generation
As part of the HLF, the Laureates are participating in press conferences throughout the week, and being bombarded with questions by well-meaning journalists and bloggers. Unlike most press conferences, where participants often have a specific topical thing they’re there to speak to the press about, the Laureates can be asked about any of their past projects, on any area of maths they’ve worked on, and many of them have a very long and illustrious career to speak of.
It can be difficult then, to be put on the spot by a taxing question, especially if you’re not expecting it. I’ve been surprising the topologists whose press conferences I’ve attended with a deceptively deep but simple question: What’s your favourite manifold?
This question has had mixed results – known Poincaré-botherer Stephen Smale was unwilling to provide an answer, essentially because he loves all manifolds equally (he wouldn’t even narrow it down to one infinite family, although we know he probably really has a soft spot for the n-sphere, in the case n>5).
The best answer I’ve had so far came from algebraic topologist, Abel Prize winner and Fields Medalist Sir Michael Atiyah. After a moment’s thought, he stated that he definitely did have a favourite manifold, and that it’s a particular K3 surface he’s studied recently.
### Wait, what’s a Manifold?
You may well be wondering what a manifold is – and to a topologist, it’s as fundamental as what a number or an equation is. A manifold is a surface which locally looks like ordinary Euclidean space – if you look close-up at a small part of the surface, it behaves normally. For example, if your manifold is 2-dimensional, this means that each small part of it looks like a flat piece of 2D surface, with coordinates in the usual way, and the distance between two points defined the way you’d expect.
A great example of a manifold is a sphere – it’s locally, in very small patches, pretty much a sensible surface you could put a coordinate system on. In fact, we very much do this, as the earth itself is a sphere, and yet we tend to think about it in small 2D patches which we represent as flat on maps, and measure distance in a straight line, even though we know that they join up in a more complicated way to cover the whole surface of the sphere.
Manifolds come in all different kinds – without holes in, like the sphere; with holes in, like a torus or donut shape. There even exist some 2D manifolds which can’t be realised in 3D space without intersecting themselves, like a Klein bottle or a real projective plane.
It’s thought that manifolds are especially useful because this property of being easy to understand in small local patches means we can apply knowledge of how, for example, functions behave on those simpler parts to understand the whole shape, even when the complete structure is much more complex.
They often crop up as the solution spaces to problems in physics or as graphs of functions. A nice example is the space of configurations a two-part robot arm could achieve – if it’s hinged at the shoulder and elbow, and each joint can be positioned at any angle from 0 to 360 degrees, the position of the arm is determined by a point on each of two circles; if you imagine extruding one of these circles along the length of the other, with the two circles running perpendicular to each other, you get a torus shape, and one single point on the surface of this torus corresponds to one possible configuration of the robotic arm.
### What is a K3 surface?
K3 surfaces were first discovered by Ramanujan, back in the 1910s – while studying the diophantine equation a3 +b3 = c3 + d3, his writings reveal he anticipated the structures of K3 surfaces – although this work was never published. The name was coined in 1958 by André Weil, who named them after three revered algebraic geometers: Kummer, Kähler and Kodaria (and the mountain K2 in Kashmir).
A K3 surface is a type of Calabai-Yau manifold, which is a kind of manifold named after Eugenio Calabi (who first conjectured that they might exist) and Shing-Tung Yau. Calabai-Yau manifolds have many applications in theoretical physics, and it’s conjectured that the extra dimensions of space-time take the form of a Calabai-Yau manifold in 6 dimensions.
K3 surfaces are a particular subset of Calabai-Yau manifolds. They can often be found as the intersection or the product of other objects, and are closely related to elliptic curves, and to higher-dimensional analogues of the torus. The image below shows a Kummer surface, which is a type of K3 surface.
Image by Claudio Rocchini (CC-BY-SA, on Wikipedia)
### Atiyah’s Favourite
The particular K3 surface Michael Atiyah specified as his favourite is one made as a product of two elliptic curves. He came across it as part of some work he did recently studying atoms and their isotopes, and using complex geometrical surfaces to model the shape of the atoms.
Helium-4 is a stable isotope of helium, meaning it’s a version of the helium atom with two neutrons, so (along with its two protons) it has a total mass of 4. Helium-4 is the most commonly occurring isotope, although Helium-3 also exists (having only one neutron).
The elliptic curve corresponding to the shape of Helium-4 is given by y2 + x4 − 1 = 0, and it’s easy to see why this manifold has captured Atiyah’s imagination. Studying the topological properties of atoms, molecules and even larger biological structures such as DNA and proteins has been incredibly fruitful and in recent years has led to some interesting results.
What’s your favourite manifold?
### More Information
The 1729 K3 Surface (ArXiV paper on Ramanujan’s work on K3 surfaces)
Geometric Models of Helium (PDF, ArXiV paper)
### Posted by Katie Steckles
is a mathematician based in Manchester, who gives talks and workshops on different areas of maths. She finished her PhD in 2011, and since then has talked about maths in schools, at science festivals, on BBC radio, at music festivals, as part of theatre shows and on the internet. Katie writes blog posts and editorials for The Aperiodical, a semi-regular maths news site. | 1,421 | 6,289 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2024-22 | latest | en | 0.961907 |
https://leetcode.ca/2016-02-14-76-Minimum-Window-Substring/ | 1,685,851,026,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224649439.65/warc/CC-MAIN-20230604025306-20230604055306-00527.warc.gz | 412,322,014 | 12,030 | # Question
Formatted question description: https://leetcode.ca/all/76.html
Given two strings s and t of lengths m and n respectively, return the minimum window substring of s such that every character in t (including duplicates) is included in the window. If there is no such substring, return the empty string "".
The testcases will be generated such that the answer is unique.
Example 1:
Input: s = "ADOBECODEBANC", t = "ABC"
Output: "BANC"
Explanation: The minimum window substring "BANC" includes 'A', 'B', and 'C' from string t.
Example 2:
Input: s = "a", t = "a"
Output: "a"
Explanation: The entire string s is the minimum window.
Example 3:
Input: s = "a", t = "aa"
Output: ""
Explanation: Both 'a's from t must be included in the window.
Since the largest window of s only has one 'a', return empty string.
Constraints:
• m == s.length
• n == t.length
• 1 <= m, n <= 105
• s and t consist of uppercase and lowercase English letters.
Follow up: Could you find an algorithm that runs in O(m + n) time?
# Algorithm
The key to solving this problem is to efficiently move the left pointer when scanning a string. The variable i in the for loop can be considered equivalent to the right pointer.
1. To move the left pointer, find the first occurrence of the target character while ensuring that the count of this character is greater than the corresponding count in the target string.
2. When comparing the count of the target and count, it’s important to note that they may not be of the same length. For example, in the string “AAAABC”, count will be equal only when it reaches the character “C”, so it’s necessary to shrink the window before comparing with the current minimum length.
3. When moving the left pointer in the while loop, the condition found[s.charAt(left)]> 1 should be replaced with found[s.charAt(left)] > target[s.charAt(left)], because we need to check whether the current count of the character is greater than the corresponding count in the target string.
4. To process the result, instead of keeping track of the position of the smallest window using two integers, it’s possible to use a string that is initially empty, and assign the smallest window to it at each iteration. This way, there is no need to check if the integers are negative to see if there is a result.
# Code
• public class Minimum_Window_Substring {
public static void main(String[] args) {
Minimum_Window_Substring out = new Minimum_Window_Substring();
Solution s = out.new Solution();
}
public class Solution_easy_understand {
public String minWindow(String s, String t) {
if (s == null || t == null || s.length() == 0) {
return "";
}
// left,right pointing to window range
int left = 0; // left
int right = 0; // right
int[] foundMap = new int[256]; // count of each char in this window range
int[] targetMap = new int[256];
int countInRange = 0;
int neededInRange = t.length();
int minSize = Integer.MAX_VALUE;
String result = "";
// pre-process
for (int i = 0; i < t.length(); i++) {
char current = t.charAt(i);
targetMap[current]++;
}
// start scanning
while (right < s.length()) {
char c = s.charAt(right);
if (targetMap[c] > 0) {
if (foundMap[c] < targetMap[c]) {
countInRange++;
}
foundMap[c]++;
// if all found in s, record window size
if (countInRange == neededInRange) {
// eg: "ADOBBECAODEBANNNNC" . when at 2nd "A", will enter this if, and do the shrink first, the check min
while (
left < s.length()
&&
(
targetMap[s.charAt(left)] == 0 // not in target[]
|| (targetMap[s.charAt(left)] > 0 && foundMap[s.charAt(left)] > targetMap[s.charAt(left)]) // more than needed in target[]
)
) {
// @review: June-21-2016, "(targetMap[s.charAt(l)] > 0" NOT necessary, since statement before || is covering it
foundMap[s.charAt(left)]--;
// @note: no need to countInRange-1, since while condition ensured countInRange will always be equal to neededCharCount
left++;
}
// check minSize, only after shrinking window
if (right - left + 1 < minSize) {
minSize = right - left + 1;
result = s.substring(left, right + 1);
}
}
}
right++;
}
return result;
}
}
class Solution {
public String minWindow(String s, String t) {
if (s == null || t == null || s.length() == 0) {
return "";
}
// left,right pointing to window range
int left = 0; // left
int right = 0; // right
int[] countMap = new int[256]; // target chars needed
for (char each : t.toCharArray()) {
countMap[each]++;
}
int countInRange = 0;
int minSize = Integer.MAX_VALUE;
String result = "";
while (right < s.length()) {
--countMap[s.charAt(right)];
if (countMap[s.charAt(right)] >= 0) { // @note: >=
countInRange++;
}
while (countInRange == t.length()) {
if (minSize > right - left + 1) {
minSize = right - left + 1;
result = s.substring(left, right + 1);
}
++countMap[s.charAt(left)]; // '--' above if, so '++' back
if (countMap[s.charAt(left)] > 0) {
countInRange--;
}
left++;
}
right++;
}
return result;
}
}
}
############
class Solution {
public String minWindow(String s, String t) {
Map<Character, Integer> mp = new HashMap<>();
int begin = 0, end = 0, counter = t.length(), minLen = Integer.MAX_VALUE, minStart = 0,
size = s.length();
for (char c : s.toCharArray()) mp.put(c, 0);
for (char c : t.toCharArray()) {
if (mp.containsKey(c))
mp.put(c, mp.get(c) + 1);
else
return "";
}
while (end < size) {
if (mp.get(s.charAt(end)) > 0) counter--;
mp.put(s.charAt(end), mp.get(s.charAt(end)) - 1);
end++;
while (counter == 0) {
if (end - begin < minLen) {
minStart = begin;
minLen = end - begin;
}
mp.put(s.charAt(begin), mp.get(s.charAt(begin)) + 1);
if (mp.get(s.charAt(begin)) > 0) {
counter++;
}
begin++;
}
}
if (minLen != Integer.MAX_VALUE) {
return s.substring(minStart, minStart + minLen);
}
return "";
}
}
// class Solution {
// public String minWindow(String s, String t) {
// int[] count = new int['z' - 'A' + 1];
// int uniq = 0;
// for (int i = 0; i < t.length(); ++i) {
// if (++count[t.charAt(i) - 'A'] == 1) uniq++;
// }
// int found = 0,i = 0,j = 0;
// int minLen = Integer.MAX_VALUE;
// int minJ = Integer.MAX_VALUE;
// while (found < uniq) {
// while (i < s.length()) {
// if (found >= uniq) break;
// if (--count[s.charAt(i) - 'A'] == 0) found++;
// i++;
// }
// if (found < uniq) break;
// while (j < i && count[s.charAt(j) - 'A'] < 0) count[s.charAt(j++) - 'A']++;
// if (i - j < minLen) {
// minLen = i - j;
// minJ = j;
// }
// count[s.charAt(j++) - 'A']++;
// found--;
// }
// return minLen < Integer.MAX_VALUE ? s.substring(minJ, minJ + minLen) : "";
// }
// }
• // OJ: https://leetcode.com/problems/minimum-window-substring/
// Time: O(N)
// Space: O(C) where C is the range of characters
class Solution {
public:
string minWindow(string s, string t) {
unordered_map<char, int> target, cnt;
int len = INT_MAX, i = 0, N = s.size(), matched = 0, begin = 0;
for (char c : t) target[c]++;
for (int j = 0; j < N; ++j) {
if (++cnt[s[j]] <= target[s[j]]) ++matched;
while (matched == t.size()) {
if (j - i + 1 < len) {
len = j - i + 1;
begin = i;
}
if (--cnt[s[i]] < target[s[i]]) --matched;
++i;
}
}
return len == INT_MAX ? "" : s.substr(begin, len);
}
};
• from collections import Counter
class Solution:
def minWindow(self, s: str, t: str) -> str:
ans = ''
m, n = len(s), len(t)
if m < n:
return ans
need = Counter(t)
window = Counter()
i, cnt, mi = 0, 0, inf
for j, c in enumerate(s):
window[c] += 1
if need[c] >= window[c]: # >= , because 1 line above already +=1
cnt += 1
while cnt == n:
if j - i + 1 < mi: # in while
mi = j - i + 1
ans = s[i : j + 1]
c = s[i]
if need[c] >= window[c]: # char in window but not in need, need[c]=0, window[c]=1..2..
cnt -= 1
window[c] -= 1
i += 1
return ans
############
class Solution(object):
def minWindow(self, s, t):
"""
:type s: str
:type t: str
:rtype: str
"""
score = 0
wanted = collections.Counter(t)
start, end = len(s), 3 * len(s) # artitrary 3, just make sure end-start is larger than input s length, for later min-check
d = {}
deq = collections.deque([]) # using queue to store indexes, good for large ammount of api call
for i, c in enumerate(s):
if c in wanted:
deq.append(i)
d[c] = d.get(c, 0) + 1
if d[c] <= wanted[c]:
score += 1
while deq and d[s[deq[0]]] > wanted[s[deq[0]]]:
d[s[deq.popleft()]] -= 1
if score == len(t) and deq[-1] - deq[0] < end - start:
start, end = deq[0], deq[-1]
return s[start:end + 1]
• func minWindow(s string, t string) string {
ans := ""
m, n := len(s), len(t)
if m < n {
return ans
}
need := make([]int, 128)
for _, c := range t {
need[c] += 1
}
window := make([]int, 128)
i, cnt, mi := 0, 0, m+1
for j, c := range s {
window[c]++
if need[c] >= window[c] {
cnt++
}
for cnt == n {
if j-i+1 < mi {
mi = j - i + 1
ans = s[i : j+1]
}
c = rune(s[i])
if need[c] >= window[c] {
cnt--
}
window[c]--
i++
}
}
return ans
}
• function minWindow(s: string, t: string): string {
let n1 = s.length,
n2 = t.length;
if (n1 < n2) return '';
let need = new Array(128).fill(0);
let window = new Array(128).fill(0);
for (let i = 0; i < n2; ++i) {
++need[t.charCodeAt(i)];
}
let left = 0,
right = 0;
let res = '';
let count = 0;
let min = n1 + 1;
while (right < n1) {
let cur = s.charCodeAt(right);
++window[cur];
if (need[cur] > 0 && need[cur] >= window[cur]) {
++count;
}
while (count == n2) {
cur = s.charCodeAt(left);
if (need[cur] > 0 && need[cur] >= window[cur]) {
--count;
}
if (right - left + 1 < min) {
min = right - left + 1;
res = s.slice(left, right + 1);
}
--window[cur];
++left;
}
++right;
}
return res;
}
• using System.Linq;
public class Solution {
public string MinWindow(string s, string t) {
var dict = t.Distinct().ToDictionary(ch => ch, ch => 0);
var goalDict = t.GroupBy(ch => ch).ToDictionary(g => g.Key, g => g.Count());
var goal = goalDict.Count;
var minI = int.MaxValue;
var minJ = 0;
var i = 0;
var j = 0;
var current = 0;
while (true)
{
while (current < goal && i < s.Length)
{
if (dict.ContainsKey(s[i]))
{
if (++dict[s[i]] == goalDict[s[i]])
{
++current;
}
}
++i;
}
while (current == goal && j < s.Length)
{
if (dict.ContainsKey(s[j]))
{
if (dict[s[j]] == goalDict[s[j]])
{
break;
}
else
{
--dict[s[j]];
}
}
++j;
}
if (current == goal)
{
if (i - j < minI - minJ)
{
minI = i;
minJ = j;
}
--dict[s[j]];
--current;
++j;
}
else
{
break;
}
}
if (minI == int.MaxValue)
{
return string.Empty;
}
else
{
return s.Substring(minJ, minI - minJ);
}
}
} | 3,113 | 10,568 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.15625 | 3 | CC-MAIN-2023-23 | longest | en | 0.884165 |
https://mathematica.stackexchange.com/questions/257878/how-can-i-find-the-only-real-and-then-the-smallest-root-of-a-4th-order-polynomia | 1,723,117,034,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640726723.42/warc/CC-MAIN-20240808093647-20240808123647-00014.warc.gz | 311,127,407 | 41,781 | # How can I find the only real and then the smallest root of a 4th-order polynomial?
I just want to solve the below polynomial for real roots only, where I have mentioned the conditions on all variables, a,d,m,L.
FFF4[x_, a_, d_, m_, L_] = Refine[a x^4 + 4 a (1 - d) x^3 + (1 + a m^2 L^2 + 10 a + 5 a d + a d^2) x^2 + (6 a - d - 3 a d + a d m^2 L^2) x - m^2 L^2, {Element[L, Reals], Element[m, Reals], Element[a, Reals],Element[d, Integers], L > 0, a > 0, m > o, d > 0}]
Next I tried to solve this, and got the four roots
Sol = Solve[FFF4[x, a, d, m, L] == 0, x];
However, now I need to find the smallest root. We have choice to fix d=4 and a=0.1. How can I find the smallest root here?
And if I modify my code like
Sol = Solve[FFF4[x, a, d, m, L] == 0, x, Reals];
Mathematica takes so much time and does not give any input.
If there's a real root, then Root[polyfunc, 1] represents the smallest one and takes only a few milliseconds to compute:
Root[fff4[#, a, d, m, L] &, 1]
(*
Root[-L^2 m^2 + (6 a - d - 3 a d + a d L^2 m^2) #1 + (1 + 10 a +
5 a d + a d^2 + a L^2 m^2) #1^2 + (4 a - 4 a d) #1^3 +
a #1^4 &, 1]
*)
To get a numeric value:
Root[fff4[#, a, d, m, L] &, 1] /.
{d -> 4, a -> 1/10, L -> 1, m -> 2} // N
(* -0.579658 *)
If you want algebraic formulas representing the least root, then expect a complicated dependence on the parameters that may take a long time to compute. The Root[] object can be manipulated symbolically and numerically and is more efficient. If you have a question about how to use it in a specific way, post another question to the site.
Example:
r1 = Root[fff4[#, a, d, m, L] &, 1] /. {d -> 4, a -> 0.1};
Plot3D[r1, {m, 0, 4}, {L, 0, 4}]
• Thanyou Very much #Michael E2. But if i want to save this data in a table form, because later i want to guess what are the lowest possible values of m and L. For the smallest real root? Commented Nov 8, 2021 at 10:32
• @ImmySalam Replace Plot3D by Table in the example. Look up Table for to adjust it. To find the smallest root, look up FindMinimum, but it looks like that wouldn’t exist (would approach the Limit as m and L approach infinity). Commented Nov 8, 2021 at 12:08
• This seems to give the correct minimum: r1 = Root[fff4[#, a, d, m, L] &, 1] /. {d -> 4, a -> 1/10}; MinValue[{r1, m > 0 && L > 0}, {m, L}] Commented Nov 8, 2021 at 12:51
Clear["Global*"]
\$Version
(* "12.3.1 for Mac OS X x86 (64-bit) (June 19, 2021)" *)
FFF4[x_, a_, d_, m_, L_] =
a x^4 +
4 a (1 - d) x^3 + (1 + a m^2 L^2 + 10 a + 5 a d + a d^2) x^2 + (6 a - d -
3 a d + a d m^2 L^2) x - m^2 L^2;
Put the constraints in the Solve
sol = Solve[{FFF4[x, a, d, m, L] == 0,
L > 0, a > 0, m > 0, d > 0}, x, Reals];
Length@sol
(* 4 *)
(sol2 = Select[sol /. {d -> 4, a -> 1/10}, FreeQ[#, Undefined] &]) // Grid
To get numeric values you must also specify L and m
(sol3 = Select[sol /. {d -> 4, a -> 1/10, L -> 1, m -> 2},
FreeQ[#, Undefined] &])
The smallest root is the first one
sol3[[1]] // N
(* {x -> -0.579658} *)
Show[
Plot3D[Evaluate[x /. sol2],
{m, 0, 5}, {L, 0, 5},
PlotStyle -> Opacity[0.8],
AxesLabel -> (Style[#, 12, Bold] & /@
{m, L, x}),
PlotLegends -> Automatic],
Graphics3D[
{Red, AbsolutePointSize[6],
Point[{m, L, x} /. {L -> 1, m -> 2} /. sol3]}]] | 1,236 | 3,246 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.609375 | 4 | CC-MAIN-2024-33 | latest | en | 0.791131 |
https://www.tutorialspoint.com/write-a-program-in-python-to-caluculate-the-adjusted-and-non-adjusted-ewm-in-a-given-dataframe | 1,638,546,326,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362891.54/warc/CC-MAIN-20211203151849-20211203181849-00633.warc.gz | 1,107,463,528 | 11,002 | # Write a program in Python to caluculate the adjusted and non-adjusted EWM in a given dataframe
PythonPandasServer Side ProgrammingProgramming
Assume, you have a dataframe and the result for adjusted and non-adjusted EWM are −
adjusted ewm:
Id Age
0 1.000000 12.000000
1 1.750000 12.750000
2 2.615385 12.230769
3 2.615385 13.425000
4 4.670213 14.479339
Id Age
0 1.000000 12.000000
1 1.666667 12.666667
2 2.555556 12.222222
3 2.555556 13.407407
4 4.650794 14.469136
## Solution
To solve this, we will follow the steps given below −
• Define a dataframe
• Calculate adjusted ewm with delay 0.5 using df.ewm(com=0.5).mean().
df.ewm(com=0.5).mean()
• Calculate non-adjusted ewm with delay 0.5 using df.ewm(com=0.5).mean().
df.ewm(com=0.5,adjust=False).mean()
### Example
import numpy as np
import pandas as pd
df = pd.DataFrame({'Id': [1, 2, 3, np.nan, 5],
'Age': [12,13,12,14,15]})
print(df)
print("non adjusted ewm:\n",df.ewm(com=0.5,adjust=False).mean())
### Output
Id Age
0 1.0 12
1 2.0 13
2 3.0 12
3 NaN 14
4 5.0 15
Id Age
0 1.000000 12.000000
1 1.750000 12.750000
2 2.615385 12.230769
3 2.615385 13.425000
4 4.670213 14.479339
4 4.650794 14.469136 | 482 | 1,181 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2021-49 | longest | en | 0.372223 |
http://nrich.maths.org/995/solution | 1,506,203,704,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818689779.81/warc/CC-MAIN-20170923213057-20170923233057-00646.warc.gz | 248,701,586 | 5,529 | ### Calendar Capers
Choose any three by three square of dates on a calendar page...
### Card Trick 2
Can you explain how this card trick works?
### Happy Numbers
Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.
##### Stage: 3 Challenge Level:
Joshua Bull (Brooklands Primary School, Suffolk) explains ...
I did this problem by trial and error. I worked out that D + S = E so neither D or S could be 0.
I chose at random some numbers for E and A and worked out my hundreds column first.
I found these solutions:
Are there any more solutions?
Here are some more that have been sent in.....
Alana Asher (Eastbury Farm JMI & Nursery School, Middlesex) discovered the same one as Jason's second solution.
These two came for Alicia Persaud and Priya Gami (Eastbury Farm JMI & Nursery School, Middlesex).
Here's another one from Tan Ian Wern (Tao Nan School, Singapore)
1576
+3209
--------
4785
Zachary from Clearwater Bay School in Hong Kong has found another different solution:
2548
+0917
--------
3465
Laura, Sophia and Sophie from St Michael’s Collegiate School in Hobart, Tasmania, found another different solution:
4589
+3216
--------
7805
Jayden from Elm Park School in Auckland has found another new solution:
1359
+7204
---------
8563
Well done!
Pierre Thomson from Rifton, New York, wrote to tell us that he was working on this problem with his daughter. He managed to write a computer program to find all the solutions and discovered there are 140 altogether! However, some of his solutions (like some of the above) included a zero in the thousands column - this is not how we usually write numbers so you may prefer to ignore these if you are working on this problem. | 420 | 1,800 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.15625 | 3 | CC-MAIN-2017-39 | latest | en | 0.947634 |
https://www.crazy-numbers.com/en/2807 | 1,716,295,821,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058484.54/warc/CC-MAIN-20240521122022-20240521152022-00538.warc.gz | 617,871,015 | 3,451 | Warning: Undefined array key "numbers__url_substractions" in /home/clients/df8caba959271e8e753c9e287ae1296d/websites/crazy-numbers.com/includes/fcts.php on line 156
Number 2807: mathematical and symbolic properties | Crazy Numbers
# Everything about number 2807
Discover a lot of information on the number 2807: properties, mathematical operations, how to write it, symbolism, numerology, representations and many other interesting things!
## Mathematical properties of 2807
Is 2807 a prime number? No
Is 2807 a perfect number? No
Number of divisors 4
List of dividers
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1, 7, 401, 2807
Sum of divisors 3216
Prime factorization 7 x 401
Prime factors
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7, 401
## How to write / spell 2807 in letters?
In letters, the number 2807 is written as: Two thousand eight hundred and seven. And in other languages? how does it spell?
2807 in other languages
Write 2807 in english Two thousand eight hundred and seven
Write 2807 in french Deux mille huit cent sept
Write 2807 in spanish Dos mil ochocientos siete
Write 2807 in portuguese Dois mil oitocentos sete
## Decomposition of the number 2807
The number 2807 is composed of:
1 iteration of the number 2 : The number 2 (two) represents double, association, cooperation, union, complementarity. It is the symbol of duality.... Find out more about the number 2
1 iteration of the number 8 : The number 8 (eight) represents power, ambition. It symbolizes balance, realization.... Find out more about the number 8
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1 iteration of the number 0 : ... Find out more about the number 0
1 iteration of the number 7 : The number 7 (seven) represents faith, teaching. It symbolizes reflection, the spiritual life.... Find out more about the number 7
## Mathematical representations and links
Other ways to write 2807
In letter Two thousand eight hundred and seven
In roman numeral
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MMDCCCVII
In binary 101011110111
In octal 5367 | 901 | 3,180 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2024-22 | latest | en | 0.706578 |
https://copycashvalve.com/page/binary-representation-wiki/ | 1,542,553,837,000,000,000 | text/html | crawl-data/CC-MAIN-2018-47/segments/1542039744381.73/warc/CC-MAIN-20181118135147-20181118161147-00319.warc.gz | 594,671,415 | 4,438 | Binary file - Wikipedia - CopyCashValve
## Signed binary numbers (Representation & operation)
In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two you can convert to other bases (such as base-3, base-4, octal and more) using base conversion bender bending rodriguez, sr. Converting Decimal Fractions to Binary , (born september 4, 2996), designated bending unit 22, and known as bender, is the tritagonist in futurama. In the text proper, we saw how to convert the decimal number 14 he was made in. 75 to a binary representation in the binary representation of a number, the position of the digits, mean ‘units’, ‘twos’, ‘fours’, ‘eights’, ‘sixteens’, and so on. In this instance, we online binary converter. Web series are leading the way in moving beyond the gender binary supports all types of variables, including single and double precision ieee754 numbers cbor rfc 7049 concise binary object representation “the concise binary object representation (cbor) is a data format whose design goals include the. Reviews of binary options brokers: Find out which ones are on the blacklist and should be avoided! Find the best and most of all safe binary traders for 2017! A Computer Science portal for geeks binary system: history of invention, what it is, euler s derivation binary numbers – seen as strings of 0 s and 1 s – are often associated with computers. It contains well written, well thought and well explained computer science and programming articles, quizzes and but why is this? why can t computers just use base 10 instead of. This image has only two colours: it has a colour depth of 1 bit (Ignore the grid there have been several questions posted to so about floating-point representation. It’s there to make it easier to see the pixels!) Starting for example, the decimal number 0. GCSE Computer Science Binary and data representation learning resources for adults, children, parents and teachers 1 doesn t have an exact binary. 0: 0: 00000000 : 64: 40: 01000000 : 128: 80: 10000000 : 192: c0: 11000000: 1: 1: 00000001 : 65: 41: 01000001 : 129: 81: 10000001 : 193: c1: 11000001: 2: 2 this is binary-json (bjson) format specification draft ver 0. A binary file is a computer file that is not a text file 5. The term binary file is often used as a term meaning non-text file the bjson spec can be always found on bjson. Many binary file formats org. Motivation: All information in a computer is stored and transmitted as sequences of bits, or binary digits definition bjson is binary form of json. A bit is a single piece of data which can be | p a g e 1 signed binary numbers (representation & operation) sign & magnitude representation: 1. Other Bases representation: use 1 bit (most significant bit) to. You can convert to other bases (such as base-3, base-4, octal and more) using Base Conversion Bender Bending Rodriguez, Sr | 716 | 2,947 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2018-47 | latest | en | 0.915691 |
http://www.tackleunderground.com/community/topic/5085-math-physics-who-needs-it/ | 1,527,074,927,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794865595.47/warc/CC-MAIN-20180523102355-20180523122355-00214.warc.gz | 458,028,790 | 23,585 | # Math, Physics, who needs it?
## 14 posts in this topic
Ok, this is for the mathematical types on this board. My friends have always told me that "I always want to know how things work", guess I still do.
I have been thinking about the total weight of a particular lure. Assume that we have two baits that are absolutely identical in size and shape...lets say for simplicity that these baits are 10" inches long. One is made from a very light wood, say basswood, another from a dense wood, perhaps hard maple. The basswood will be much lighter thus requiring considerably more weight to get it to sink but the hard maple starts out heavier. Assuming only enough weight is added to get the bait to sink, which bait will weigh the most?
I borrowed this from another site. Apparently it was Archimedes that discovered why ships float, this guy figured this out in the 3rd century!!
____________________________________________________________
Why Do Ships Float?
The Greek Mathematician and inventor Archimedes lived during the 3rd century BC. According to history he was in the bath one day when he discovered the principle of buoyancy which is the reason why huge Greek ships weighing thousands of pounds could float on water. He noticed that as he lowered himself into the bath, the water displaced by his body overflowed the sides and he realised that there was a relationship between his weight and the volume of water displaced. It is said that he ran naked into the street yelling "heurEka" which is where we get our word "eureka!" (I found it), Greek heurEka I have found, from heuriskein to find.
Archimedes continued to do more experiments and came up with a buoyancy principle, that a ship will float when the weight of the water it displaces equals the weight of the ship and anything will float if it is shaped to displace its own weight of water before it reaches the point where it will submerge.
This is kind of a technical way of looking at it. A ship that is launched sinks into the sea until the weight of the water it displaces is equal to its own weight. As the ship is loaded, it sinks deeper, displacing more water, and so the magnitude of the buoyant force continuously matches the weight of the ship and its cargo.
_____________________________________________________________
Assuming all other things are constant, the two lures should weigh the same amount at the point of sinking....correct?
Jed
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I seem to remember something about volume being involved in this. I think given the same size of the mass, the lighter would have to be weighted to equal the weight of the heavier at the sinking point, so I think yes, so they would both have to be, say for instance 4oz given their particular size.
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Jed, that is very interesting.Here is a question I have as far as buoyancy goes.E-tex by itself does not float,but when its added to a bait, it makes the bait more buoyant.Has anyone else noticed this , or am I all wet?Is it because it adds more volume than weight? I have added a coat of e-tex to Jakes and they seem to rise to the surface much faster than before.I also had that problem while trying to make neutral buoyant baits,I get them weighted just right,then e-tex and now they are slow risers????
Tom
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Hmmm,
Bouyancy force = total volume of water displaced by object immersed in liquid = weight of displaced liquid
so bouyancy force will need exactly the same total weight to counter act each other for objects of the same volume. You're spot on Jed
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That's the way I see it too. So....whether we use a light wood or a heavy wood, a bait of equal size and shape will be roughly the same weight, interesting. But, we have probably all noted the difference in action of some woods over others. I personally have found that light woods with lots of weight have more life to them than dense woods with a little weight.......despite the fact that both baits weigh about the same. Archimedes was one smart dude, bet he could have built some damn good baits.
Jed
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But look at the concentration of weight on light wood Jed. On light wood we are concentrating the weight into a spot which affect the COG (centre of Gravity) and on denser (harder) wood it's distributed more evenly. That makes the diff.
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like Lapala said, on lighter woods most of the weight will be concentrated wherever you add the weight. The reason this provides more action is because the rest of the bait is easier to move. The ballast wieght provides a pivot point.
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Good point guys, interesting.
jed
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But look again at the x-ray of the HR glide bait and he's got weights distributed throught he length of the whole bait. Thoughts?
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Is not weight placement at various locations done to cause the bait to hold a certain position in the water?
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Lunge,
I tried that method of weighting several times on baits and it did work altho I didn't find the results to be worth the additional work. Jim of "castor baits" has torn down HR baits in the couple years and found that he no longer uses this method of weighting.......maybe he also found it to be too cumbersome. I have only owned one HR (shaker) and wasn't at all impressed by the action altho the vast majority of musky fisherman think otherwise. I have personally found body shape which includes thickness, height, taper, roundness, etc., to play a larger role than any other factor in determining lure action and width of glide.
Jed
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Jed, I agree completely. I'm not so sure th e boys are interested in the action rathre than the amazing paint jobs that Jim does.
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Lunge, Jim of HR baits is without doubt the finest painter I have ever seen.
Jed
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Yah, he does provide huge amounts of inspiration - and a healthy does of consternation too :-D
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# Online Help
###### All Products Maple MapleSim
LinearAlgebra[Generic]
BerkowitzAlgorithm
apply the Berkowitz algorithm to a square Matrix
Calling Sequence BerkowitzAlgorithm[R](A)
Parameters
R - a table or module, the domain of computation A - square Matrix of values in R
Description
• Given an n x n Matrix A of values from a commutative ring R, BerkowitzAlgorithm[R](A) returns a Vector V of dimension n+1 of values in R with the coefficients of the characteristic polynomial of A.
• The characteristic polynomial is the polynomial V[1]*x^n + V[2]*x^(n-1) + ... + V[n]*x + V[n+1].
• The Berkowitz algorithm does O(n^4) multiplications and additions in R.
• The (indexed) parameter R, which specifies the domain of computation, a commutative ring, must be a Maple table/module which has the following values/exports:
R[0] : a constant for the zero of the ring R
R[1] : a constant for the (multiplicative) identity of R
R[+] : a procedure for adding elements of R (nary)
R[-] : a procedure for negating and subtracting elements of R (unary and binary)
R[*] : a procedure for multiplying elements of R (binary and commutative)
R[=] : a boolean procedure for testing if two elements of R are equal
Examples
> $\mathrm{with}\left({\mathrm{LinearAlgebra}}_{\mathrm{Generic}}\right):$
> ${Z}_{\mathrm{0}},{Z}_{\mathrm{1}},{Z}_{\mathrm{+}},{Z}_{\mathrm{-}},{Z}_{\mathrm{*}},{Z}_{\mathrm{=}}≔0,1,\mathrm{+},\mathrm{-},\mathrm{*},\mathrm{=}:$
> $A≔\mathrm{Matrix}\left(\left[\left[2,1,4\right],\left[3,2,1\right],\left[0,0,5\right]\right]\right)$
${A}{≔}\left[\begin{array}{ccc}{2}& {1}& {4}\\ {3}& {2}& {1}\\ {0}& {0}& {5}\end{array}\right]$ (1)
> $C≔{\mathrm{BerkowitzAlgorithm}}_{Z}\left(A\right)$
${C}{≔}\left[\begin{array}{c}{1}\\ {-9}\\ {21}\\ {-5}\end{array}\right]$ (2)
> $\mathrm{.}\left(⟨{x}^{3}|{x}^{2}|x|1⟩,C\right)$
${{x}}^{{3}}{-}{9}{}{{x}}^{{2}}{+}{21}{}{x}{-}{5}$ (3) | 669 | 2,047 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 8, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.640625 | 4 | CC-MAIN-2024-18 | latest | en | 0.483859 |
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Question
# The height y and horizontal distance x covered by a projectile in a time t seconds are given by the equations y=8t−5t2 and x=6t. If x and y are measured in meters, the velocity of projection is:-
A
10 ms1
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6 ms1
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8 ms1
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D
14 ms1
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Solution
## The correct option is A 10 ms−1vx=dxdt=6vy=dydt=8−10t→v=vx^i+vy^j→u=→vt=0→u=6^i+8^ju=√62+82u=10m/s
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# Solutions for Chapter 2.7: Nonlinear Inequalities
## Full solutions for Precalculus | 7th Edition
ISBN: 9780618643448
Solutions for Chapter 2.7: Nonlinear Inequalities
Solutions for Chapter 2.7
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##### ISBN: 9780618643448
Since 90 problems in chapter 2.7: Nonlinear Inequalities have been answered, more than 11829 students have viewed full step-by-step solutions from this chapter. Chapter 2.7: Nonlinear Inequalities includes 90 full step-by-step solutions. Precalculus was written by and is associated to the ISBN: 9780618643448. This textbook survival guide was created for the textbook: Precalculus, edition: 7. This expansive textbook survival guide covers the following chapters and their solutions.
Key Calculus Terms and definitions covered in this textbook
• Combination
An arrangement of elements of a set, in which order is not important
• Compounded annually
See Compounded k times per year.
• Definite integral
The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists
• Divergence
A sequence or series diverges if it does not converge
• Expanded form of a series
A series written explicitly as a sum of terms (not in summation notation).
• Invertible linear system
A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.
• Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x:- q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large
• Multiplication property of inequality
If u < v and c > 0, then uc < vc. If u < and c < 0, then uc > vc
• Nonsingular matrix
A square matrix with nonzero determinant
• Observational study
A process for gathering data from a subset of a population through current or past observations. This differs from an experiment in that no treatment is imposed.
• Parallelogram representation of vector addition
Geometric representation of vector addition using the parallelogram determined by the position vectors.
• Period
See Periodic function.
• Phase shift
See Sinusoid.
• Present value of an annuity T
he net amount of your money put into an annuity.
• Proportional
See Power function
• Reciprocal identity
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.
• Slope-intercept form (of a line)
y = mx + b
• Solution of an equation or inequality
A value of the variable (or values of the variables) for which the equation or inequality is true
• Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>
• z-coordinate
The directed distance from the xy-plane to a point in space, or the third number in an ordered triple.
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We're here to help | 754 | 2,985 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.4375 | 3 | CC-MAIN-2019-39 | longest | en | 0.882176 |
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Misc – 322 pts (23 solves) – Chall author: boron
Alice and Bob have shared two entangled qubits, which they use to transfer data between them using what appears to be similar to superdense coding (but without sending any qubits). Given only Alice’s operations on her own qubit, can we reconstruct what she send to Bob? Can we, or can we not? You won’t know until you collapse the state of this write-up. ;)
Check out write-ups by my teammates on K3RN3L4RMY.com
## Exploration
Quantum jokes aside, we are only given a file containing a sequence of elements in {I, X, Z, ZX}. Knowing that we are dealing with some cryptic quantum business these clearly refer to the respective quantum gates. Usually, when wanting to send information using qubits, Alice and Bob would make use of what is known as Superdense Coding. However, this makes use of two entangled qubits and requires Alice to send qubits to Bob. This is not the case here. Alice was most likely just alone in her room playing with her own qubit, applying the given sequence of quantum gates.
In order to get a better understanding of what was going on, let us consider how each of the quantum gates operate on a single qubit. I will use the [1,0] vector notation for a |0> qubit, and the [0,1] vector notation for a |1> qubit. In quantum theory, we have the possibility of having intermediate states, like |0> + |1> or |0> - |1>, however as you will see these do not occur using just the given sequence of quantum gates. Therefore I will not spend any time on that. Open the quantum gates!
$I \begin{bmatrix} a \\ b \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} a \\ b \end{bmatrix} = \begin{bmatrix} a \\ b \end{bmatrix}$ $X \begin{bmatrix} a \\ b \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \begin{bmatrix} a \\ b \end{bmatrix} = \begin{bmatrix} b \\ a \end{bmatrix}$ $Z \begin{bmatrix} a \\ b \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \begin{bmatrix} a \\ b \end{bmatrix} = \begin{bmatrix} a \\ -b \end{bmatrix}$ $ZX \begin{bmatrix} a \\ b \end{bmatrix} = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix} \begin{bmatrix} a \\ b \end{bmatrix} = \begin{bmatrix} b \\ -a \end{bmatrix}$
Assuming Alice starts with either a [1,0] or [0,1] state qubit, there is no way to turn it into intermediate states, so a measurement of her qubit will always yield 0 or 1 deterministically. So we just apply each gate in the sequence, measure the qubit, and move on. Furthermore, there is no measurable difference between [1,0] and [-1,0], they both return a ‘0’ bit. Therefore the effect of the gates boils down to:
• $I$, nothing
• $X$, flip the bit
• $Z$, nothing
• $ZX$, flip the bit
Seems to me we can just parse the gate sequence without modelling any qubits.
## Exploitation
If we start with a ‘0’ bit and simply add the last bit of the list after every gate, only flipping the bit upon reading a X or ZX gate, we can retrieve the data very easily. By looking at the bitstream that comes out one should easily notice it forms an image and not proper ASCII.
bits = [0]
for i in sequence:
if i in ['X', 'ZX']:
bits += [(bits[-1] + 1) % 2]
else:
bits += [bits[-1]]
bits = bits[1:]
im0 = Image.new('1',(200,100))
im0.putdata(bits)
display(im0)
And there we go. Not much quantum about that, hah. Hand over that physics degree, professor!
I was a bit disappointed though to find out the challenge turned out to be quite trivial. I was excited to use QisKit and so I did it anyway. Below you find a script simulating a single qubit where we apply all sequence gates exactly as provided and measure the state of the qubit after every gate. Go, go, qubit!
#!/usr/bin/env python3
#
# Polymero
#
# Imports
from qiskit import QuantumCircuit, Aer, assemble
from PIL import Image
# Read in Alice's operation sequence
sequence = data.split()
f.close()
def do_op( qc, op ):
""" Applies one of the {I, Z, X, ZX} gates to an input qubit """
if op == 'ZX':
qc.z(0)
qc.x(0)
elif op == 'X':
qc.x(0)
elif op == 'Z':
qc.z(0)
elif op == 'I':
pass
else:
print('Operation not recognised:', op)
print("Applying Alice's operations...")
# Make a QuantumCircuit with a single qubit
qc = QuantumCircuit(1,len(sequence))
for i in range(len(sequence)):
# Apply Alice's operation
do_op(qc, sequence[i])
# Measure the resulting state of the qubit
qc.measure(0,i)
print('Running the simulation...')
# Tell Qiskit which simulator to use
sim = Aer.get_backend('aer_simulator')
# Create a Qobj with all our circuits for the simulator
qobj = assemble(qc)
# Simulate each circuit only once (determinisitc)
result = sim.run(qobj, shots=1).result()
print('Done!')
# Convert simulation result to bit stream
bitstream = [int(i) for i in list(list(result.get_counts())[0])]
# Convert bitstream to an image
im0 = Image.new('1',(200,100))
im0.putdata(bitstream)
display(im0)
Seems like that worked as well. Nice! Only cool kids use QisKit, hehe .
Ta-da!
uiuctf{5up3rqu4ntum_1m4g3ry} | 1,491 | 5,115 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.140625 | 3 | CC-MAIN-2024-33 | latest | en | 0.861299 |
https://www.equationsworksheets.net/worksheet-1-word-and-skeleton-equations-answers/ | 1,709,039,248,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474676.26/warc/CC-MAIN-20240227121318-20240227151318-00509.warc.gz | 745,822,735 | 15,180 | # Worksheet 1 Word And Skeleton Equations Answers
Worksheet 1 Word And Skeleton Equations Answers – Expressions and Equations Worksheets are designed to help kids learn faster and more efficiently. These worksheets contain interactive exercises and questions determined by the order of how operations are conducted. With these worksheets, kids can grasp both simple and advanced concepts in a very short amount of amount of time. These PDF resources are free to download and could be used by your child to practice math equations. These are great for children from 5th through 8th Grades.
## Get Free Worksheet 1 Word And Skeleton Equations Answers
The worksheets listed here are for students in the 5th-8th grades. These two-step word problem are constructed using fractions and decimals. Each worksheet contains ten problems. They are available at any print or online resource. These worksheets are a great way to practice rearranging equations. Apart from practicing changing equations, they help your student understand the basic properties of equality and inverted operations.
These worksheets can be utilized by fifth and eighth graders. They are ideal for students who are struggling to calculate percentages. You can select from three types of problems. You can select to solve one-step problems containing decimal numbers or whole numbers or you can use word-based approaches for solving decimals or fractions. Each page will have ten equations. These Equations Worksheets can be used by students in the 5th through 8th grades.
These worksheets are a great way to learn fraction calculation and other algebraic concepts. The majority of these worksheets allow users to select from three different kinds of problems. You can choose the one that is numerical, word-based, or a mixture of both. It is vital to pick the correct type of problem since every challenge will be unique. There are ten challenges on each page, so they’re great resources for students from 5th to 8th grade.
The worksheets will teach students about the connections between variables and numbers. These worksheets help students practice solving polynomial equations and discover how to use equations in daily life. If you’re in search of an educational tool that will help you learn about expressions and equations begin by looking through these worksheets. These worksheets will teach you about different types of mathematical problems as well as the many symbols that are used to describe them.
These worksheets are beneficial to students in the first grades. These worksheets will teach students how to solve equations and graphs. The worksheets are perfect for practicing polynomial variable. They can also help you master the art of factoring and simplify the equations. You can get a superb set of equations, expressions and worksheets designed for children of every grade. The best method to learn about equations is by doing the work yourself.
There are plenty of worksheets that teach quadratic equations. Each level has their own worksheet. These worksheets are a great way to solve problems to the fourth degree. Once you have completed the required level and are ready to work on solving different kinds of equations. Once you have completed that, you are able to work to solve the same problems. You could, for instance identify the same problem as a elongated problem. | 624 | 3,370 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2024-10 | latest | en | 0.934877 |
https://blog.finxter.com/assessing-subtype-relationships-between-different-float-sizes-in-python/ | 1,718,435,283,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861584.65/warc/CC-MAIN-20240615062230-20240615092230-00284.warc.gz | 119,225,644 | 21,509 | # Assessing Subtype Relationships Between Different Float Sizes in Python
Rate this post
π‘ Problem Formulation: In Python, numerical data types like integers and floating-point numbers are commonly used. Python’s dynamic typing means it does not restrict float sizes as strictly as statically typed languages. However, this flexibility also leads to questions about the subtype relationships between floats of different sizes. Users may wonder if a float with a higher precision could be considered a subtype of a lesser precision float, or vice versa. Let’s explore how to test if float data types of different sizes are distinct and not subtypes of each other through unique methods.
## Method 1: Using the `isinstance()` Function
Python’s `isinstance()` function is used to check if an object is an instance of a class or of a subclass thereof. If applied to numerical values, it allows us to verify if a float of one size is considered a subtype of another. This method, however, is not directly effective for distinguishing between float sizes, as Python treats them uniformly as float objects under the hood.
Here’s an example:
```float_small = 0.123
float_large = 0.12345678901234567890
print(isinstance(float_small, float))
print(isinstance(float_large, float))
```
The output:
```True
True
```
In this example, both `float_small` and `float_large` are instances of the base class `float`. The `isinstance()` function does not distinguish between different sizes or precisions of floating-point numbers, corroborating that Python treats all floating-point numbers uniformly as instances of the `float` class.
## Method 2: Inspecting the Number of Significant Digits
One way to differentiate between float sizes in Python is to inspect the number of significant digits using string formatting. While Pythonβs float representation may not discriminate sizes internally, you can format the float as a string to show a specific number of significant digits, thus revealing the inherent precision of the float.
Here’s an example:
```float_small = 0.123
float_large = 0.12345678901234567890
print(f"{float_small:.30f}")
print(f"{float_large:.30f}")
```
The output:
```0.123000000000000005684341886081
0.123456789012345679012345678901
```
By displaying the floats with 30 significant digits, you can see the actual precision stored for each float. The small float rounds off after 18 digits, whereas the large float may extend up to 30 digits, though the precision might not be entirely accurate. This method exposes Python’s limited float precision and offers a makeshift way to discern float sizes, but only to the extent of Python’s floating-point precision limits.
## Method 3: Using the `sys.float_info` Module
The `sys` module in Python provides access to some variables used or maintained by the interpreter and to functions that interact strongly with the interpreter. The `float_info` attributes provide information about the precision and internal representation of floating-point numbers.
Here’s an example:
```import sys
print(sys.float_info)
```
The output:
```sys.float_info(max=1.7976931348623157e+308, max_exp=1024, max_10_exp=308, min=2.2250738585072014e-308, min_exp=-1022, min_10_exp=-307, dig=15, mant_dig=53, epsilon=2.220446049250313e-16, radix=2, rounds=1)
```
This snippet provides the attributes of the `float_info` struct, such as the maximum and minimum values a float can take, the number of significant digits, and the rounding behavior. It is a glimpse into the floating-point arithmetic’s capabilities and limitations in Python, but does not directly relate to subtyping of floats of different sizes.
## Method 4: Checking Floating-Point Equality
Floating-point equality checks in Python can sometimes reveal the nuances of precision. By comparing two floats that only differ in their least significant digits, one can get a sense of whether Python distinguishes between different precision levels. However, keep in mind that floating-point arithmetic is imprecise due to the nature of binary representation, and equality checks may produce unintuitive results.
Here’s an example:
```float_small = 0.12345678901234
float_large = 0.123456789012341
print(float_small == float_large)
```
The output:
```False
```
In this code, two floats that differ just slightly are compared. The result `False` indicates they are not considered the same value, therefore, Python does distinguish between these numerical values at some level of precision. However, this method isn’t foolproof due to issues with floating-point precision and should not be solely relied on to determine subtyping.
## Bonus One-Liner Method 5: Analyzing the `struct` Module for Binary Representation
Python’s `struct` module performs conversions between Python values and C structs represented as Python strings. It’s useful for investigating internal representations of data, which would include the binary details of floats. By packing a float into a binary string, we can try to infer the size and precision of the float.
Here’s an example:
```import struct
float_val = 0.12345678901234567890
binary_string = struct.pack('d', float_val)
print(binary_string)
```
The output:
```b'\xaeG\xe1z\x14\xae\xf3?'
```
This code uses the `struct.pack()` function to pack a float into a binary string, displaying its internal representation. The precision and size of `float_val` are encapsulated into this binary string. Through this binary representation, one might discern that all float sizes are represented in the same number of bytes in Python, underscoring that within the language, they are not treated as subtypes of different sizes.
## Summary/Discussion
• Method 1: `isinstance()` Checks. Strengths: Easy to use for type-checking. Weaknesses: Cannot distinguish between different float sizes as Python treats them uniformly.
• Method 2: Significant Digits Inspection. Strengths: Can reveal the precision of floats. Weaknesses: Limited by Python’s floating-point representation precision.
• Method 3: `sys.float_info`. Strengths: Provides information about Python’s floating-point numbers. Weaknesses: Provides general limits, not subtype relationships.
• Method 4: Floating-Point Equality. Strengths: Shows Python’s precision discernment to some extent. Weaknesses: Imprecise due to floating-point binary storage issues.
• Method 5: Binary Representation with `struct`. Strengths: Gives a glimpse into the binary representation of floats. Weaknesses: Low-level and less direct for testing subtypes. | 1,418 | 6,546 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2024-26 | latest | en | 0.833331 |
https://tolstoy.newcastle.edu.au/~rking/publ/sisc.htm | 1,516,631,756,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084891377.59/warc/CC-MAIN-20180122133636-20180122153636-00320.warc.gz | 818,451,196 | 2,649 | ## Approximating disbutions using the generalised lambda distribution
Robert A. R. King H.L. MacGillivray Faculty of Environmental Science and Engineering, Griffith University, Brisbane, Australia and Centre in Statistical Science and Industrial Mathematics, Queensland University of Technology, Brisbane, Australia Centre in Statistical Science and Industrial Mathematics, Queensland University of Technology, Brisbane, Australia
## Outline of a paper presented at the Sydney International Statistical Congress
### Abstract
The generalised lambda distribution (g.l.d.) can take on many different shapes. It can be used to approximate all standard unimodal distributions. This paper presents approximations using both parameterisations of distribution - the original, published by Ramberg, Tadikamalla, Dudewicz and Mykytka [ Technometrics 21 (1979):78--82] and the parameterisation presented by Freimer, Mudholkar, Kollia and Lin [ Communciations in Statistics Theory and Methods 17 (1988):3547--67]. Approximation by the g.l.d. may be useful in easily producing quantiles or simulated data (as the g.l.d. is a transformation of the uniform). Two different methods for calculating the parameters for this approximation are presented. One of the methods provides the possibility of producing distributions that differ, to a desired degree, from a standard distribution in shape.
### Main points
1. We assume that our audience already thinks that it is useful to approximate some distributions with other ones, especially distirbutions like the gld which have F^{-1}(u) in closed form.
2. At least one of the methods gives a closer approximation than that provided by the method of moments
3. Both the starship and the quantile function methods allow the user to "tune" the method to take more account of a particular aspect of the approximation (for example the fit in the tails)
4. The quantile function method is based on a sounder appreciation of the effects of shape.
## For more information on approximating using the generalised lambda distribution
My page on the generalised lambda distribution gives the definition of the distribution and examples of its probability density function. It also features a java applet that draws probability density functions for the distribution.
### Overhead slides from the presentation
These are in postscript form:
• This has most of the Overheads for the presentation
```SISC.ps 386 Kb Tue Jul 23 14:29:35 1996 Postscript Program
```
• This contains the table giving the parameter values for approximations to well-known distirbutions using the generalised lambda distribution
```partab.ps 57 Kb Tue Jul 23 14:29:35 1996 Postscript Program
```
The table is also available as a html file with <pre>- formated text, or a plain text file.
File "rking/publ/sisc.htm" last updated 06:53:41 AM, Fri Apr 21, 2006
comments to: robert.king@newcastle.edu.au | 628 | 2,918 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2018-05 | latest | en | 0.853083 |
https://www.futurelearn.com/courses/precalculus/6/steps/628245?main-nav-submenu=main-nav-courses | 1,603,277,105,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107876307.21/warc/CC-MAIN-20201021093214-20201021123214-00442.warc.gz | 753,205,340 | 28,920 | ## Want to keep learning?
This content is taken from the University of Padova's online course, Precalculus: the Mathematics of Numbers, Functions and Equations. Join the course to learn more.
2.18
## Precalculus
Skip to 0 minutes and 10 seconds We’ve talked about positive integer powers, negative integer powers. We’ve talked about n-th roots. It’s now time to put all of that together and more and talk about rational powers. Here’s some motivation. How should we define a to the power 1 over n? Well we would like the usual known properties of powers or exponents to hold. So, in particular, we’d like a to the power 1 over n, the whole thing raised to the n, to equal a. Therefore, we are forced really to define a to the power 1 over n as being the n-th root of a, which we do. Thus, the n-th root is actually a fractional power and vice versa.
Skip to 1 minute and 1 second More generally, for any integers, m and n, where n is in the natural numbers and m can be a negative integer, we define a to the power m over n, which is a typical rational number, to be the n-th root of a to the m. Now we do this for positive numbers, a, only. In fact, if m is negative, we only do it for strictly positive numbers, a, in the base. For a greater than 0, we have defined a to the p for any rational number, p. Some facts that pertain to this definition are now given.
Skip to 1 minute and 45 seconds We could prove all of these facts for these general rational numbers, but I immediately give you the same good news I gave you some time ago, these rules visually are exactly the same as they were say for positive integers. That’s good news. We don’t have to memorise a whole set of new rules. Some examples, x to the power of 1/2 is the square root of x. x to the power minus 3/5 turns out to be what I’ve written. Notice that the answer could be rationalised in the denominator if we so insisted. Another example, an exponent of minus 1/2 is undefined. We avoid negative numbers. Why should we avoid these negative bases, you say? Here’s an illustration of what can happen.
Skip to 2 minutes and 42 seconds Suppose we did define minus 8 to the 1/3 as being minus 2. That’s not totally ridiculous because minus 2 cubed is equal to minus 8. But now, the usual exponential rules that we know so well don’t necessarily work. That is, minus 2 would be the cube root of minus 8, but that would be the same as minus 8 to the power 2 over 6 because, after all, 2 over 6 is the same as 1/3. And now, if we bring in the 2 as we do by the usual exponential rules, we get the cube root, the sixth root rather, of the number 64. Now 64 is 2 to the power 6, and, therefore, we wind up with 2.
Skip to 3 minutes and 30 seconds And we have proved that minus 2 equals 2. That’s not a good sign. So you see, dangerous to define powers with negative bases, and I suggest that we avoid doing so. What are the graphs of these rational power functions going to look like? Well, by and large, they’re going to have the same general characteristics of some familiar graphs we’ve seen in the past. For example, when q is equal to 1, the function next to the q is an affine function, in fact, going through the origin called the linear function. When q is greater than 1, the graph looks rather like the graph of x squared. It has the increasingness on r plus, for example.
Skip to 4 minutes and 17 seconds And when q is less than 1, it resembles the graph of the square root of x that we saw earlier. All these functions agree at x equal 1, of course, to give you the value 1. And for negative rational exponents, you get graphs that have this kind of characteristic, there you have decreasing functions of x. And, again, they’re defined only on r plus. It’s useful to know the general nature of these graphs, the monotonicity of the functions, for example, such as the following. Suppose you need to know which of these two numbers is greater than the other. How do you figure that out? Well you could say the following.
Skip to 5 minutes and 2 seconds The function that to the argument x gives you the power minus 6.72 of x. That’s a strictly decreasing function by the graph that we saw just a moment ago. Why? Because the exponent is a negative number. We also observe that 1/2 is less than pi over 4. How do we prove that? Well we can cross multiply 1 times 4, 2 times pi. That’s equivalent to saying that 4 is less than 2 pi, cross multiplying. Is 4 less than 2 pi? Well that’s the same as saying 2 is less than pi, which is true because we know that pi is 3.14 something, something, and so on.
Skip to 5 minutes and 50 seconds Now because of the decreasing nature of the negative power function that we have above, we deduce that 1/2 to that negative power is greater than pi over 4 to that same negative power. That’s clear from the graph because it’s a decreasing graph. So we have answered the question regarding the comparison. In fact, if we look at the graph and realise that both 1/2 and pi over 4 are less than 1, we can also add a further conclusion. Both our values here that we’re comparing are greater than 1.
# Rational powers
Basic properties, graphs, connection to radicals | 1,269 | 5,181 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.5 | 4 | CC-MAIN-2020-45 | latest | en | 0.93055 |
https://python-forum.io/thread-18732-post-81984.html | 1,716,842,322,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971059045.25/warc/CC-MAIN-20240527175049-20240527205049-00756.warc.gz | 416,120,891 | 24,839 | ##### Dealing with Exponential data
Dealing with Exponential data parthi1705 Silly Frenchman Posts: 37 Threads: 13 Joined: Apr 2018 Reputation: May-29-2019, 10:07 AM Having csv file with the value as below 2.22971E+15,2.20408E+15 while reading from csv able to read the data as '2229708157109627', '2204081406354342' code: ```import pandas as pd with open('mypath\mycsv.csv', encoding="utf8") as csv_file: df = pd.read_csv(csv_file,index_col=None, header=0) ```but actually 2229708157109620, 2204081406354340 Why the values are changing here from 2229708157109620 to 2229708157109627 from 2204081406354340 to 2204081406354342 ? Reply Posts: 8,093 Threads: 154 Joined: Sep 2016 Reputation: May-29-2019, 10:20 AM (This post was last modified: May-29-2019, 10:20 AM by buran.) how do you get significant digits after 71 or 08? ```>>> 2.22971E+15 2229710000000000.0 >>> 2.20408E+15 2204080000000000.0 >>> d = Decimal('2.20408E+15') >>> d Decimal('2.20408E+15') >>> int(d) 2204080000000000``` If you can't explain it to a six year old, you don't understand it yourself, Albert Einstein How to Ask Questions The Smart Way: link and another link Create MCV example Debug small programs Reply parthi1705 Silly Frenchman Posts: 37 Threads: 13 Joined: Apr 2018 Reputation: May-29-2019, 10:25 AM Save the below records as csv file 2229708157109627 2204081406354342 and try reading them from pandas or with csv. you could see output as 2229708157109620 2204081406354340 Reply Posts: 8,093 Threads: 154 Joined: Sep 2016 Reputation: May-29-2019, 10:40 AM (May-29-2019, 10:25 AM)parthi1705 Wrote: Save the below records as csv file 2229708157109627 2204081406354342 (May-29-2019, 10:07 AM)parthi1705 Wrote: Having csv file with the value as below 2.22971E+15,2.20408E+15 So it's ``Output:2229708157109627,2204081406354342``not as stated in original post ``Output:2.22971E+15,2.20408E+15`` If you can't explain it to a six year old, you don't understand it yourself, Albert Einstein How to Ask Questions The Smart Way: link and another link Create MCV example Debug small programs Reply Posts: 8,093 Threads: 154 Joined: Sep 2016 Reputation: May-29-2019, 11:02 AM (This post was last modified: May-29-2019, 11:02 AM by buran.) (May-29-2019, 10:25 AM)parthi1705 Wrote: try reading them from pandas or with csv. Here it is with csv module: ```import csv with open('spam.csv') as f: rdr = csv.reader(f) for line in rdr: foo, bar = line print(foo) print(int(foo)) print(bar) print(int(bar))`````````Output:2229708157109627 2229708157109627 2204081406354342 2204081406354342 >>>``````what is in the file, that's what you get If you can't explain it to a six year old, you don't understand it yourself, Albert Einstein How to Ask Questions The Smart Way: link and another link Create MCV example Debug small programs Reply DeaD_EyE So-and-so of the Yard Posts: 2,026 Threads: 9 Joined: May 2017 Reputation: May-29-2019, 01:45 PM (This post was last modified: May-29-2019, 01:46 PM by DeaD_EyE.) The values must divided by 1e15? You can use decimal.Decimal and change the precision, but Decimal is slow. ```import decimal def convert(integers, divisor='1e15'): with decimal.localcontext() as ctx: ctx.prec = 20 for value in integers: yield decimal.Decimal(value) / decimal.Decimal(divisor) list(convert(['2229708157109627', '2204081406354342']))`````Output:[Decimal('2.229708157109627'), Decimal('2.204081406354342')]``Numpy has a float128 datatype, but 64 seems to be enough to represent the value. Are you using a 32 bit version of Python? With numpy I got following (Python 3.7.3 x64): ```In [34]: import numpy as np In [35]: np.float128(num) Out[35]: 2229708157109627.0 In [36]: np.float64(num) Out[36]: 2229708157109627.0 In [37]: np.float32(num) Out[37]: 2229708100000000.0 In [38]: np.float128(num) / 1e15 Out[38]: 2.229708157109627 In [39]: np.float64(num) / 1e15 Out[39]: 2.229708157109627 In [40]: np.float32(num) / 1e15 Out[40]: 2.22970811252736 In [41]: num / 1e15 Out[41]: 2.229708157109627 In [42]: num Out[42]: 2229708157109627``` Almost dead, but too lazy to die: https://sourceserver.info All humans together. We don't need politicians! Reply parthi1705 Silly Frenchman Posts: 37 Threads: 13 Joined: Apr 2018 Reputation: May-30-2019, 04:27 AM (This post was last modified: May-30-2019, 04:56 AM by parthi1705.) (May-29-2019, 10:40 AM)buran Wrote: (May-29-2019, 10:25 AM)parthi1705 Wrote: Save the below records as csv file 2229708157109627 2204081406354342 (May-29-2019, 10:07 AM)parthi1705 Wrote: Having csv file with the value as below 2.22971E+15,2.20408E+15 So it's ``Output:2229708157109627,2204081406354342``not as stated in original post ``Output:2.22971E+15,2.20408E+15`` Buran, If you open csv file you would probably see the data as 2.22971E+15,2.20408E+15 unless you have the mouse pointer over the cell. Actual csv file data goes like below. 2229708157109620 2204081406354340 892984837048418000 2204081406354340 843482762412573 1667516366684810 ```>>> >>> import pandas as pd >>> with open('D:\mycsv.csv', encoding="utf8") as csv_file: df = pd.read_csv(csv_file,index_col=None, header=0) >>> df['ID'].head(6) 0 2229708157109627 1 2204081406354342 2 892984837048418304 3 2204081406354342 4 843482762412573 5 1667516366684818 Name: ID, dtype: int64```Save those records and see what it looks like... Original records are from database to my csv file. one more wonder is when i save back them again to csv file able to see original records ```>>> newdf= df['ID'].head(10) >>> newdf.to_csv('D:\spam.csv', index = None, header=True, encoding='utf-8')```but why while displaying it shows differently ?? Have attached screenshot for reference. Installed version of Python 3.7.0 Attached Files Thumbnail(s) Reply Posts: 8,093 Threads: 154 Joined: Sep 2016 Reputation: May-30-2019, 06:48 AM (This post was last modified: May-30-2019, 06:48 AM by buran.) That is not python/pandas problem. The problem is that you view your csv file in some spreadsheet software (Excel, OpenOffice, etc., most probably Excel) That is why you see scientific (exponential) notation. In addition, it's the excel that truncates the significant digits up to 15, i.e. the length stays the same, but significant digits are the first 15. See for yourself - on the left is the actual csv file and on the right side is the same file open in excel To see what you really have in the file, open your csv file as it comes from the database in a notepad or notepadd++ or some other simple text editor. You will see it's what pandas show as dataframe values As an advice and to avoid such confusions in the future, when refer to data/content in csv/txt files, always tell what you see in notepad/notepad++ and not in what you see being displayed in a spreadsheet. If you can't explain it to a six year old, you don't understand it yourself, Albert Einstein How to Ask Questions The Smart Way: link and another link Create MCV example Debug small programs Reply parthi1705 Silly Frenchman Posts: 37 Threads: 13 Joined: Apr 2018 Reputation: May-30-2019, 09:06 AM (This post was last modified: May-30-2019, 09:06 AM by parthi1705.) It is not the issue in the way we view the data with csv file.. it the way we read the actual data from csv file. Can you try reading the Csv file has below data 2229708157109620 2204081406354340 892984837048418000 and can show what you get in python or pandas or csv or with any other module. Reply Posts: 8,093 Threads: 154 Joined: Sep 2016 Reputation: May-30-2019, 09:16 AM (This post was last modified: May-30-2019, 09:17 AM by buran.) Do you open the csv file in notepad and see the data in it as I requested in my previous post? Yes or No? Note - open the file as exported from DB, not opened and saved in excel. I demonstrated that the issue is with the excel. If you can't explain it to a six year old, you don't understand it yourself, Albert Einstein How to Ask Questions The Smart Way: link and another link Create MCV example Debug small programs Reply
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http://mathhelpforum.com/algebra/44202-partial-function.html | 1,529,364,180,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267861456.51/warc/CC-MAIN-20180618222556-20180619002556-00416.warc.gz | 199,995,971 | 9,848 | 1. ## partial function
express(x-2)/[(x^2+1)(x-1)^2] in partial fractions in its simplest form.
express 7x+4/[(x-3)(x+2)^2] as the sum of partial fraction with constant numerators
2. Originally Posted by qweiop90
express(x-2)/[(x^2+1)(x-1)^2] in partial fractions in its simplest form.
express 7x+4/[(x-3)(x+2)^2] as the sum of partial fraction with constant numerators
$\displaystyle \frac{x-2}{(x^2+1)(x-1)^2}=\frac{Ax+B}{x^2+1}+\frac{C}{x-1}+\frac{D}{(x-1)^2}$
Can you take it from here?
$\displaystyle \frac{7x+4}{(x-3)(x+2)^2}=\frac{A}{x-3}+\frac{B}{x+2}+\frac{C}{(x+2)^2}$
Can you take it from here?
--Chris
3. i try thanks for your help
4. i couldnt do question 1. i stuck at the half. can you please provide me the solution?
5. hi
Here i am showing the answer of the first problem, the the other guy he showed to how to frame the problem that's fantastic way , i will do the remaining steps to show the answers here
7x+4=A(x+2)^2+B(x+2)(x-3)+c(x-3)
plug x=3 in the above equation u will get
25A=25
then A=1
plug x=-2, then C=2
finally equating the coefficient of x^2 on both sides we get it as
A+B=0
B=-1 | 411 | 1,129 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2018-26 | latest | en | 0.816892 |
https://www.coursehero.com/file/5768334/Section-8/ | 1,490,925,112,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218205046.28/warc/CC-MAIN-20170322213005-00415-ip-10-233-31-227.ec2.internal.warc.gz | 876,020,510 | 22,256 | # Section 8 - ECON 136: Financial Economics Section 8 (Oct...
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Unformatted text preview: ECON 136: Financial Economics Section 8 (Oct 23rd) Xing Huang 1 Economics Department, UC Berkeley 1 Mutual Fund Fees Example Find the e/ective annual return to investors for a 2 year investment of \$10,000 in the two Treasury bond mutual funds. Assume the return on the portfolio of bonds held by both funds is 2.8% per year. Fee Structure: Merrill ST US Govt A Fund (MDUGX) Vanguard ST Fed Inv Fund (VSGBX) Expense Ratio 0.88% 0.20% Front Load 3.50% 0.00% Deferred Load 0.00% 0.00% ans: For Merrill you pay \$350 up front and thus earn returns on \$9,650. So you end up with, \$9 ; 659 & (1 + 0 : 028 ¡ : 088) 2 = \$9 ; 659 & (1 : 0192) 2 = \$10 ; 024 : 12 R ann = & \$10 ; 024 : 12 \$10 ; 000 ¡ 1 = 2 ¡ 1 = 0 : 12% ans: For Vanguard you pay \$0 up front and thus earn returns on all \$10,000. So you end up with, \$10 ; 000 & (1 + 0 : 028 ¡ : 002) 2 = \$10 ; 000 & (1 : 026) 2 = \$10 ; 526 : 76 R ann = & \$10 ; 526 : 76 \$10 ; 000 ¡ 1 = 2 ¡ 1 = 2 : 60% 2 E¢ cient Markets Hypothesis 2.1 Review ¢ What the EMH does and does not say 1) The EMH DOES NOT say that investors cannot earn high expected returns (high ex- pected returns are normal for &nancial assets whose payo/s are very risky). 2) The EMH DOES NOT say that investors cannot ever get lucky and earn higher returns 1 These notes are enormously bene&ted from previous GSIs: Keith Jacks Gamble, Dan Hartley and Congyan Tan. Thank you all very much !! 1 than were expected (this is perfectly natural with uncertainty). 3) The EMH DOES say that investors cannot expect to be lucky; they cannot expect to earn a higher return than is normal compensation for the risk of holding that asset. & Three forms: 1) Weak form of the EMH Stock prices immediately incorporate all information contained in past prices and returns. 2) Semi-strong form of the EMH Stock prices immediately incorporate all publicly available information (such as prices, earn- ings forecasts, and published facts about the &rm¡s business operations) 3) Strong form of the EMH Stock prices immediately incorporate all publicly and privately available information (includ- ing information held only by insiders)....
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## This note was uploaded on 01/25/2010 for the course ECON 136 taught by Professor Szeidl during the Fall '08 term at University of California, Berkeley.
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Ask a homework question - tutors are online | 791 | 2,866 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2017-13 | longest | en | 0.826518 |
http://www.cardtrick.ca/trick/Magic-In-A-Glass.html | 1,601,455,976,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600402123173.74/warc/CC-MAIN-20200930075754-20200930105754-00791.warc.gz | 157,338,743 | 5,098 | ## Card Tricks
Another Changing Ace Trick
Description: The performer shows two red aces, and places ...
Presto Pass
Effect: Two stacks of cards at 16 cards each. One stack is...
Card in a Bottle
A card is selected, the spectators note it and it is retur...
Always On Top
Effect: A spectator is asked to pick a card and return it ...
Build the Houses
Deal 3 cards face up in a row, and continue dealing until ...
Kings Party Variation
Card Trick: Take out all the face cards and all the Aces, ...
Ace Party
Effect: With the spectator's help, you make four piles of ...
11th Card Variation
Count out 21 cards and lay them face down on a flat surfac...
The Four Ace Trick
1. First of all you will need to cut the long side of you...
Three In A Row
Put one of the RED Aces on the bottom of the deck, so that...
## Magic In a Glass
Effect: The magician takes a long-stemmed glass and announces that he's going to perform a card trick. The thing about this card trick is that he won't be able to touch the cards, because they'll be inside the glass the whole time! Placing the pack face-out in the glass, the magician states that he's going to find all four aces using special "Locator Cards". He reaches into the glass and pulls out a red number card (we'll use the Ten of Hearts for the example) and puts it in front of the rest of the cards in the deck so that it is the card the spectator now sees looking at them through the glass. The magician then states that he will let that red 10 find a red ace. Holding the glass by the stem, the magician passes a cloth napkin over the glass quickly. When the napkin has completed it's quick pass, the red 10 has been replaced by a red ace! The magician then takes the red ace and puts it in back of the deck and passes the napkin again. This time, the red 10 is replaced by the other red ace! Now the magician gets a black number card (say, 6 of spades) for the "Locator" and puts it in front of the red 10. A quick napkin pass, and there's a black ace! The magician takes the ace and puts it in back of the deck. Another pass, and there's the last black ace! Now pull out the pack and put it back in the case, smiling as you take your bow. All of this magic occurs in the glass, so there's apparently no way that you could've manipulated the cards! People will fall down at your feet and worship your incredible abilities ;-)
Card Trick:A slight amount of preparation work is required, but this is worth it. First, find a wine or any other long-stemmed glass that will allow you to set at least half a deck of cards in it. There can be no design on the glass or stem!!! Next, take the two red aces and glue them back to back. Make sure you make them look as much like one card as possible! Do the same with the two black aces. Now get two identical number cards - one black and one red - from an identical deck. Glue one red and one black back to back. Don't do this with the other ones. Finally, get a cloth napkin that is big enough and dark enough to completely cover the glass. With this prep, you're set! Set up the deck like this: The black 6 card face-up on top of the face-down deck. Now, set the double-sided black ace on top of it. Now place the double-sided red 10/black 6 card with the red 10 face-up. Next, comes the double-sided red aces. And finally, the last red 10 FACE-DOWN on the face-down deck. The rest is showmanship. Place the deck in the glass with the bottom card facing your spectator. Announce that you're going to do the trick using a red locator card. Pull the red 10 off the top of the deck and put it on the bottom, facing the spectator. You should now be looking at a red ace. Holding the glass by the stem, you pass the napkin over the glass and spin it around so that the ace is now facing the spectator. It helps if you hold the glass with you fingers rigid and the stem in the first bend of your finger. When you spin the glass, your thumb does the work and your fingers look pretty much the same. Now take the ace and put it on top of the deck. You should now be looking at the other red ace. Perform the pass/spin again, and your spectator sees the other red ace. Now say that you need a black locator card. Take the red/black card off the top with the 6 facing the spectator. Put it on bottom of the deck. You should now be looking at a black ace. Pass/spin and your spectator sees it. Take it and put it on top of the deck and perform the pass/spin. There's the final black ace! Now merely put the deck into the case before anyone gets too close. SUGGESTION: When you get to the black aces, if you stick the Ace of Spades on top so that it's the first ace you'll show, you can ask the spectator to name a black ace. Nine out of ten times, they'll say the Ace of Spades! You then make it appear for them. If they happen to mention the Ace of Clubs, just say "So that leaves the Ace of Spades," and make it appear.
Next: The Thought of Card
Previous: In and Out Deck | 1,192 | 4,961 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2020-40 | latest | en | 0.937505 |
https://www.numbersaplenty.com/21032310301 | 1,627,998,096,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046154459.22/warc/CC-MAIN-20210803124251-20210803154251-00254.warc.gz | 896,013,631 | 3,261 | Search a number
21032310301 is a prime number
BaseRepresentation
bin10011100101100111…
…111001011000011101
32000021210000001202121
4103211213321120131
5321033232412201
613355003222541
71343125454632
oct234547713035
960253001677
1021032310301
118a13211032
1240ab817a51
131ca2518532
141037444189
158316d09a1
hex4e59f961d
21032310301 has 2 divisors, whose sum is σ = 21032310302. Its totient is φ = 21032310300.
The previous prime is 21032310283. The next prime is 21032310311. The reversal of 21032310301 is 10301323012.
It is a strong prime.
It can be written as a sum of positive squares in only one way, i.e., 20572164900 + 460145401 = 143430^2 + 21451^2 .
It is a cyclic number.
It is not a de Polignac number, because 21032310301 - 29 = 21032309789 is a prime.
It is a congruent number.
It is not a weakly prime, because it can be changed into another prime (21032310311) by changing a digit.
It is a polite number, since it can be written as a sum of consecutive naturals, namely, 10516155150 + 10516155151.
It is an arithmetic number, because the mean of its divisors is an integer number (10516155151).
Almost surely, 221032310301 is an apocalyptic number.
It is an amenable number.
21032310301 is a deficient number, since it is larger than the sum of its proper divisors (1).
21032310301 is an equidigital number, since it uses as much as digits as its factorization.
21032310301 is an evil number, because the sum of its binary digits is even.
The product of its (nonzero) digits is 108, while the sum is 16.
Adding to 21032310301 its reverse (10301323012), we get a palindrome (31333633313).
The spelling of 21032310301 in words is "twenty-one billion, thirty-two million, three hundred ten thousand, three hundred one". | 526 | 1,748 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2021-31 | latest | en | 0.842651 |
https://paranormalis.com/threads/how.897/ | 1,708,756,636,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474523.8/warc/CC-MAIN-20240224044749-20240224074749-00464.warc.gz | 442,906,663 | 13,365 | # How?
### Welcome to our community
#### Sebastian
##### New Member
How?
G'day y'all,
i'm kinda new to this and need some answers.
Now, at C (speed of light), time stands still... and when you're faster than C, time goes backwards - is that correct so far?
Then I wonder how it would be possible to go forward, so faster than time itself. I heard that you're already travelling into the future when you're on a plane .. maybe not quick, but is that true... i mean, the faster you are, the faster time goes by?
Then I heard from someone here on this site that, the faster you are, the slower time goes by... now what's correct?
#### StarLord
##### Senior Member
Re: How?
That's a really great question. If it was me, I'd have to see if I could find the directory for Metropolis, ask for The Daily Planet and hope that Clark Kent is still employed there. (Scuttlebutt reports indicate that he and Superman are still good friends)
We have proof, (Film) that he, (Superman) could actually choose the direction of time travel he wanted by simply flying really damn fast either clockwise for forward or anticlockwise to go back into time.
(kids! please do not try this at home as the only way to circumvent the friction from this kind of travel is to own a suit like he does, not to mention you are going to have to hold your breath for god knows how long, so if you pass out trying to do this you may wind up only god knows where in time, it's not worth getting lost in time just to impress your friends)
##### Member
Re: How?
<div class='quotetop'>QUOTE(\"Sebastian\")</div>
Then I heard from someone here on this site that, the faster you are, the slower time goes by... now what's correct?[/b]
The faster you go, the slower time goes by in your perspective. Because you are moving faster than light, or time, time passes more slowly to you, relative to everything else.
#### Sebastian
##### New Member
Re: How?
The faster you go, the slower time goes by in your perspective. Because you are moving faster than light, or time, time passes more slowly to you, relative to everything else.[/b]
But lets say you arent faster than light... lets say you're close to lightspeed, but you didnt reach it yet.
##### Member
Re: How?
As you approach the speed of light, the photons that are whizzing by you at this moment will appear to be moving slower, dialating your perception of time. Think of standing beside a road watching cars go by at 60 mph. When you are immoble, they seem to be moving incredibly fast, but if you are traveling at 50 mph in the same direction as these cars, they appear, from your perspective, to be moving at only 10 mph.
#### Sebastian
##### New Member
Re: How?
so what speed do you need to travel into the future? C... slower than C... faster than C?
Re: How? | 656 | 2,802 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2024-10 | latest | en | 0.955608 |
https://quizlet.com/explanations/questions/simplify-2-sqrtx42-f9299b5d-47d94fe0-0489-4d7e-9711-5a0f9c098899 | 1,701,386,890,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100258.29/warc/CC-MAIN-20231130225634-20231201015634-00347.warc.gz | 545,020,660 | 75,024 | Try the fastest way to create flashcards
Question
# Simplify: $(2-\sqrt{x+4})^2$
Solution
Verified
Step 1
1 of 2
\begin{align*} (2-\sqrt{x+4})^{2} &=2^{2}-2\cdot2\sqrt{x+4}+(\sqrt{x+4})^{2}\\ &=4-4\sqrt{x+4}+x+4\\ &=8-4\sqrt{x+4}+x \end{align*}
Use special product formula for the square of a binomial.
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7,752 solutions | 279 | 853 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 39, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2023-50 | latest | en | 0.532155 |
https://oeis.org/A200548 | 1,680,196,183,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949355.52/warc/CC-MAIN-20230330163823-20230330193823-00351.warc.gz | 495,827,744 | 3,757 | The OEIS is supported by the many generous donors to the OEIS Foundation.
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A200548 Number of -3..3 arrays x(0..n+1) of n+2 elements with zero sum and nonzero second differences 1
30, 200, 1184, 7254, 43698, 266812, 1639804, 10152636, 63132188, 394016210, 2466471522, 15481097890, 97396742734, 614019893832, 3878005568152, 24532092598782, 155413031752230, 985836563404470, 6260856742508844 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 COMMENTS Column 3 of A200553 LINKS R. H. Hardin, Table of n, a(n) for n = 1..200 EXAMPLE Some solutions for n=3 ..2....0....3...-2...-3...-1....0...-1....0....3....1...-2...-1...-1....3....0 .-3....1...-1....3....3....0...-1...-1....3...-2...-2....1....2....3...-3...-1 .-1...-1...-1...-3...-1...-1...-1....2....1....1....3...-3....3...-2....3....1 ..3...-2....1....2...-2....1....0....2...-2...-3...-3....2...-3...-3...-1...-2 .-1....2...-2....0....3....1....2...-2...-2....1....1....2...-1....3...-2....2 CROSSREFS Sequence in context: A125340 A126498 A029545 * A165030 A165016 A209796 Adjacent sequences: A200545 A200546 A200547 * A200549 A200550 A200551 KEYWORD nonn AUTHOR R. H. Hardin Nov 19 2011 STATUS approved
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Last modified March 30 13:03 EDT 2023. Contains 361618 sequences. (Running on oeis4.) | 582 | 1,584 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2023-14 | latest | en | 0.570686 |
https://scribesoftimbuktu.com/simplify-3i-1i/ | 1,669,733,977,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710698.62/warc/CC-MAIN-20221129132340-20221129162340-00505.warc.gz | 552,793,399 | 15,154 | # Simplify (3+i)/(1+i)
3+i1+i
Multiply the numerator and denominator of 3+i1+1i by the conjugate of 1+1i to make the denominator real.
3+i1+1i⋅1-i1-i
Multiply.
Combine.
(3+i)(1-i)(1+1i)(1-i)
Simplify the numerator.
Expand (3+i)(1-i) using the FOIL Method.
Apply the distributive property.
3(1-i)+i(1-i)(1+1i)(1-i)
Apply the distributive property.
3⋅1+3(-i)+i(1-i)(1+1i)(1-i)
Apply the distributive property.
3⋅1+3(-i)+i⋅1+i(-i)(1+1i)(1-i)
3⋅1+3(-i)+i⋅1+i(-i)(1+1i)(1-i)
Simplify and combine like terms.
Simplify each term.
Multiply 3 by 1.
3+3(-i)+i⋅1+i(-i)(1+1i)(1-i)
Multiply -1 by 3.
3-3i+i⋅1+i(-i)(1+1i)(1-i)
Multiply i by 1.
3-3i+i+i(-i)(1+1i)(1-i)
Multiply i(-i).
Raise i to the power of 1.
3-3i+i-(i1i)(1+1i)(1-i)
Raise i to the power of 1.
3-3i+i-(i1i1)(1+1i)(1-i)
Use the power rule aman=am+n to combine exponents.
3-3i+i-i1+1(1+1i)(1-i)
3-3i+i-i2(1+1i)(1-i)
3-3i+i-i2(1+1i)(1-i)
Rewrite i2 as -1.
3-3i+i–1(1+1i)(1-i)
Multiply -1 by -1.
3-3i+i+1(1+1i)(1-i)
3-3i+i+1(1+1i)(1-i)
4-3i+i(1+1i)(1-i)
4-2i(1+1i)(1-i)
4-2i(1+1i)(1-i)
4-2i(1+1i)(1-i)
Simplify the denominator.
Expand (1+1i)(1-i) using the FOIL Method.
Apply the distributive property.
4-2i1(1-i)+1i(1-i)
Apply the distributive property.
4-2i1⋅1+1(-i)+1i(1-i)
Apply the distributive property.
4-2i1⋅1+1(-i)+1i⋅1+1i(-i)
4-2i1⋅1+1(-i)+1i⋅1+1i(-i)
Simplify.
Multiply 1 by 1.
4-2i1+1(-i)+1i⋅1+1i(-i)
Multiply -1 by 1.
4-2i1-1i+1i⋅1+1i(-i)
Multiply 1 by 1.
4-2i1-1i+1i+1i(-i)
Multiply -1 by 1.
4-2i1-1i+1i-ii
Raise i to the power of 1.
4-2i1-1i+1i-(i1i)
Raise i to the power of 1.
4-2i1-1i+1i-(i1i1)
Use the power rule aman=am+n to combine exponents.
4-2i1-1i+1i-i1+1
4-2i1-1i+1i-i2
4-2i1+0-i2
4-2i1-i2
4-2i1-i2
Simplify each term.
Rewrite i2 as -1.
4-2i1–1
Multiply -1 by -1.
4-2i1+1
4-2i1+1
4-2i2
4-2i2
4-2i2
Cancel the common factor of 4-2i and 2.
Factor 2 out of 4.
2⋅2-2i2
Factor 2 out of -2i.
2⋅2+2(-i)2
Factor 2 out of 2(2)+2(-i).
2(2-i)2
Cancel the common factors.
Factor 2 out of 2.
2(2-i)2(1)
Cancel the common factor.
2(2-i)2⋅1
Rewrite the expression.
2-i1
Divide 2-i by 1.
2-i
2-i
2-i
Simplify (3+i)/(1+i)
### Solving MATH problems
We can solve all math problems. Get help on the web or with our math app
Scroll to top | 1,135 | 2,196 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.4375 | 4 | CC-MAIN-2022-49 | latest | en | 0.661476 |
http://www.stressebook.com/shear-flow-thin-walled-members/ | 1,586,138,775,000,000,000 | text/html | crawl-data/CC-MAIN-2020-16/segments/1585371612531.68/warc/CC-MAIN-20200406004220-20200406034720-00063.warc.gz | 299,018,903 | 16,950 | ## Shear Flow In Thin Walled Members
The concept of “shear flow” is very significant in aerospace and this is especially true for thin walled structures. Furthermore we all know thin walled structures dominate aerospace structures.
Examples of thin walled structures:
• Stiffened fuselage shear panels
• Bulkhead web areas enclosed with stiffeners
• Built up shear web and beam systems with various bays and stiffeners
• Flat or curved panels with edge stiffeners
• Frames with channels and doublers
• Semi-monocoque structures with stringers and longerons etc.
In fact, shear flow is a direct result of vertical shear loads acting in conjunction with bending moments in a beam or built up beam system. What I mean by ‘built up’ is that the structure is an assembly of the web and cap components. In general the beam system is composed of a web and top/bottom caps.
The caps themselves could be multiple parts combined with the web. In the case of fuselage components, there is also the skin that contributes towards the cap areas.
The top and bottom caps are mainly designed to take axial and bending loads, the beam web is predominantly intended to take in plane shear loads. And of course, the fasteners or rivets transfer the resulting shear flow in the system between the components.
But first of all let us talk about some shear flow theory.
## Shear Flow – Bending Stress Theory
To begin with, let us consider a simply supported beam and arbitrary vertical shear and bending moment loads on the left hand side of a segment of this beam. See the FBD of this segment in the figure below:
Firstly, we need to remember that the vertical shear stress on a given area within the beam segment must equal the horizontal plane shear stress for equilibrium. And also the LHS and RHS shears must be equal on segment ‘a’ for equilibrium.
At the left hand side of segment ‘a’:
Bending Stress F_LHS = M*y/I
At the right hand side of segment ‘a’, we now have an additional moment due to V at a distance ‘a’ from the FBD:
Bending Stress F_RHS = M*(y/I)+V*a*(y/I)
We can see from the figure and the equation above, the top hatched segment of the beam segment ‘a’ has an unbalanced force Delta P due to applied bending stress.
The out of balance load on the vertical face of the hatched portion of segment ‘a’ is therefore:
Delta P = V*a*(y/I)*Delta A
This load has to be balanced with the horizontal plane shear load at y’.
The shear stress in the horizontal plane at the top is zero and highest at y’ for this particular portion.
Therefore:
fs*(a*b) = Integral (y’, ymax) (V*a*y/I)dA
Hence:
fs*(a*b) = (V*a*y/I)*Integral (y’, ymax)dA
As we know, Integral (y’, ymax)dA is the first moment of vertical area of the hatched portion, integrated over ‘y’, and it is generally notated as ‘Q’.
Q = Integral (y’, ymax)dA
Hence
fs*(a*b) = (V*a*y/I)*Q
OR
fs = VQ / Ib
Where:
fs = Basic Shear Stress
V = Vertical Shear Force
Q = First Moment of Area A with ‘y’ measured between the overall neutral axis to its centroid
I = Second Moment of Area or Moment of Inertia about beam neutral axis
b = width of the beam
## Shear Flow from Shear Stress
For thin members, the width ‘b’ is the member thickness ‘t’. Therefore the web shear stress:
fs = (VQ / It) PSI
Then the shear flow “q”:
q = fs*t = VQ/I (lb/in)
The equation above represents the shear flow within the thin wall structure members. This shear flow is derived from the applied vertical shear loads as well as bending stresses. The rivet pattern must be able to resist this load without inter rivet buckling or bearing or fastener failures for the beam system to act as one composite member.
Note that shear flow of any rectangular web panel bounded by axial members is constant unless a change in the axial loads in the bounding members causes a shear force, or vice versa. Also note that the above equation is only good for symmetric cross sections.
## Conclusion:
Thin walled structures experience unique loading such as ‘shear flow’. The types of analysis checks are unique to this kind of a system based on the shear flow. For some more information on theoretical aspects of web shear stress, check this link: Click Here
Cheers…
## Aircraft Structures Modeling Course
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Surya Batchu
Surya Batchu is the founder of Stress Ebook LLC. A senior stress engineer specializing in aerospace stress analysis and finite element analysis, Surya has close to a decade and a half of real world industry experience. He shares his expertise with you on this blog and the website via paid courses, so you can benefit from it and get ahead in your own career. | 1,074 | 4,675 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2020-16 | latest | en | 0.914029 |
http://www.firehouse.com/forums/t112606/ | 1,430,236,828,000,000,000 | text/html | crawl-data/CC-MAIN-2015-18/segments/1429246661733.69/warc/CC-MAIN-20150417045741-00067-ip-10-235-10-82.ec2.internal.warc.gz | 483,602,878 | 20,177 | 1. ## Cafs
We have a 2002 Darley AUTO CAFS pumper which has the trash line, both crosslays, and all 3 rear hosebed discharges, and deck gun plumbed with foam and CAFS. I wanted to run my CAFS knoweldge through the board here to make sure I'm understanding it correctly.
From what I have read on here and other sites, a 2:1 or 3:1 ratio of GPMS to CFMS is ideal for attacking fires. Our air presets at 60 cfm (halfway open on the quarter turn valves, this is factory preset). I also understand that if "shaving cream" foam is wanted, one would run a ratio of 2:1, or 2 parts air and one part water.
Using the above numbers my flows would be something like this:
Wet CAFS 60 CFM air with 120-180 gpm water
Dry CAFS 60 CFM air with 30 gpm water.
I understand that when attacking the fire we still want the ideal target flow of water, and using CAFS doesn't change that. I was wondering, since the truck air compressor is only 230 or 250 cfm, and there are multiple CAFS discharges, if I could choke the air back to say 30 or 40 cfm, and maintain the same ratios mentioned in the above paragraph, if that is acceptable. Is there any circumstance or time I would want to change the ratios or air flows around?
I also understand that CAFS is a pneumatic calculation, and not a hydraulic calculation. From a previous post on here, I remember that a handline has no noticeable friction loss for up to 2000 feet of hose. However, a point was made about master streams having friction loss. Our truck has a preplumbed CAFS deck gun. What formulas or equations would I use to figure out CAFS for the deck gun?
I understand that CAFS is finished foam product, and should be applied using the appropriate nozzle. Most of our CAFS lines use 1 1/4 smooth bore tips. Is this an ideal size for the setup mentioned? I had read somewhere that 15/16 or 1" tips were more ideal. Is the larger tip we're using affecting the stream?
I had fun figuring stuff out on the last post with everyone's help. Thanks in advance for any replies.
2. Fordrules, I have worked extensively with CAFS on one truck previously, part of the spec committee, and was with the department for quite awhile before relocating due to job necessities. As we researched the purchase and planned the training to place it in service these were our main goals. 1.75" CAFS attack line minimum of 100gpm water, 2.5" CAFS line 225 gpm water. The truck was a 06 Pierce 1750 Hale Qmax/Husky Foam/Hercules CAFS 240 cfm compressor. From the research we looked at back then Darley was the only one that I can remember which had valves for the air flow. Therefore wet/dry foam was controlled by changing the water valve position only. In order to make things simple for you, I would seriously consider leaving the air valves where they are, and realize the limitations of the truck for CAFS, and make your additional lines water or foam depending on how the truck is plumbed. Because if you choke back the air flow and maintain the same ratios you will also drop your water flow, Your 120 gpm @ 60cfm goes to 60gpm @ 30cfm that is not the same line and this may have some deleterious effects to your operation.
As far as the deck gun I have no idea for calculations to help you. The best I would say is maybe pick a flow like 400 gpm water at a 3:1 water to air and see what you get, realize that you will use over half your compressor capacity to make that deck gun work at that flow.
As far as the nozzle you use, it depends on your theory of CAFS, for us when we put our CAFS engine into service we wanted to be able to have a good line if the compressor went down or we just switched to foam solution or water for the line. Therefore we ran 15/16" smoothbores. This gave us a good line for with appropriate back pressure when not in CAFS.
3. Thanks for the reply. Some of my questions were more hypothetical, as only the 2 of the six lines have smoothbores on them. The rest have TFT autos. I do like your logic behind the 15/16 tips. I figure winter is a good time to brush op on theory...
4. ## Darley Contacts
As you have a Darley AutoCAFS unit have you spoken with any of their folks in regards to your setup ? We have a Darley AutoCAFS Engine on order and they are great folks to work with and can answer any of your questions. Contact either Neal Brooks or Troy Carothers at Darley with any questions you have, they are both extremely well versed in CAFS operations.
http://www.cafsinfo.com/
5. That site is nothing more then an advertisement for Darley. Too bad, because it contains a lot of information. Their "how to spec a cafs rig" is pretty obviously a Darley-only spec
6. Originally Posted by Res343cue
That site is nothing more then an advertisement for Darley. Too bad, because it contains a lot of information. Their "how to spec a cafs rig" is pretty obviously a Darley-only spec
In his initial post fordrules indicated that he has a "Darley" AutoCAFS pumper that is the reason for referring him to the website. Neal Brooks is the National Sales Manager of Darley's Apparatus Division and is extremely knowledgeable in CAFS and his website does contain a lot of good information on CAFS. Either Mr. Brooks or Troy Carothers also from Darley would be able to assist him with any questions regarding his Darley AuotCAFS system.
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• You may not edit your posts | 1,348 | 5,519 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2015-18 | latest | en | 0.964199 |
https://study.com/academy/answer/simplify-the-following-expression-2-4y-plus-5z-10z.html | 1,580,254,992,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579251783342.96/warc/CC-MAIN-20200128215526-20200129005526-00316.warc.gz | 633,126,991 | 22,675 | # Simplify the following expression: 2(4y + 5z) - 10z.
## Question:
Simplify the following expression: 2(4y + 5z) - 10z.
## Algebraic Expressions
Algebraic expressions are algebraic terms with mathematical operations in between. Some of these algebraic operations are addition, subtraction, multiplication, and division.
## Answer and Explanation:
In the algebraic expression below in order to simplify it, the {eq}2 {/eq} has to be distributed first:
{eq}2(4y + 5z) - 10z {/eq}
{eq}8y + 10z - 10z {/eq}
Following the operations:
{eq}8y + 10z - 10z= 8y {/eq}
Thus, the simplified version of the expression {eq}2(4y + 5z) - 10z {/eq} is {eq}8y {/eq}. | 215 | 660 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.21875 | 4 | CC-MAIN-2020-05 | latest | en | 0.848525 |
https://physics.stackexchange.com/questions/591360/deduce-mathcale-b-l-v-by-directly-solving-maxwells-equations | 1,723,769,353,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722641319057.20/warc/CC-MAIN-20240815235528-20240816025528-00330.warc.gz | 346,745,860 | 45,387 | # Deduce $\mathcal{E} = B l v$ by directly solving Maxwell's equations
Consider the following situation:
We know this is a classic example frequently used when teaching Faraday’s Law, and the voltage/electromotive force (emf) $$\mathcal{E}$$ induced across terminals of the moving conductor (lighter gray bar in the picture) is
$$\mathcal{E} = B l v$$
where $$B$$ is the uniform magnetic field perpendicular to the area, $$l$$ is the length of the conductor and $$v$$ is the speed of conductor relative to the field. So far so good, but…
How can I deduce the formula by directly solving Maxwell's equations \begin{aligned} \nabla \cdot \mathbf{D} &= \rho_\text{f}\\ \nabla \cdot \mathbf{B} &= 0\\ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}} {\partial t}\\ \nabla \times \mathbf{H} &= \mathbf{J}_\text{f} + \frac{\partial \mathbf{D}} {\partial t} \end{aligned} ?
By directly I mean calculate the electric field $$\mathbf{E}$$ first (by solving Maxwell's equations with proper initial conditions (i.c.) and boundary conditions (b.c.), using techniques taught in partial differential equation (PDE) course), and then calculate emf using the definition
$$\mathcal{E}=\oint_{C} \mathbf{E} \cdot \mathrm{d} \boldsymbol{ l }$$
Starting from $$\vec{\nabla}\times\vec{E} = -\partial \vec{B}/\partial t$$, take a surface integral of both sides to find
\begin{align} \iint_{S(t)} \vec{\nabla}\times\vec{E}\cdot d\vec{S} &= \iint_{S(t)} -\frac{\partial \vec{B}}{\partial t}\cdot d\vec{S}\\ \therefore\quad \oint_{\partial S(t)} \vec{E}\cdot d\vec{l} &= -\frac{d}{dt} \iint_{S(t)} \vec{B}\cdot \hat{S}\, dS - \oint_{\partial S(t)}\vec{v}\times\vec{B}\cdot d\vec{l} \end{align}
where the LHS of the second line makes use of Stokes' theorem, while the RHS makes use of the Leibniz integral rule.
$$\vec{B}\cdot \hat{S}=-B$$ (magnetic field points into the page, while take area vector to point out) and $$\iint_S dS = A(t) = l x(t)$$ is the area of the (rectangular) surface enclosed by the loop, where $$x(t)$$ is the length of the sides that is varying with time.
So:
$$$$\mathcal{E} = \oint_{\partial S(t)} (\vec{E}+\vec{v}\times\vec{B})\cdot d\vec{l} = -\frac{d(-Blx(t))}{dt} = Bl\frac{dx(t)}{dt} = Blv$$$$
N.B. emf is defined as the work done per unit charge, $$$$\mathcal{E} = \frac{dW}{dq} = \frac{d}{dq}\int \vec{F}\cdot d\vec{l}=\frac{d}{dq}\int q(\vec{E}+\vec{v}\times\vec{B})\cdot d\vec{l} =\int (\vec{E}+\vec{v}\times\vec{B})\cdot d\vec{l}$$$$ So as Puk has pointed out in the comments, this relies on knowing the Lorentz force. See e.g. Wikipedia for a discussion.
• @xzczd Note that the definition of emf relies on the Lorentz force law. You could certainly calculate the emf integral without using the Lorentz force law, but it has physical meaning (and in fact is defined that way) because of the Lorentz force law.
– Puk
Commented Nov 3, 2020 at 6:22
• It would be useful to explain why do you put $\vec{v}\times \vec{B}$ into the integral for EMF? External magnetic force can't do work on the electrons. Commented Nov 3, 2020 at 18:25
• @xzczd No, the problem is why EMF should include any contribution due to magnetic field. The standard definition of EMF is in terms of work. Commented Nov 4, 2020 at 9:54
• @JánLalinský I've edited the answer. Commented Nov 4, 2020 at 12:10
• @hiccups good but why is there a term $\vec v\times \vec B$ contributing to that work? 1) $\vec v$ is velocity of the rod, not of the mobile charges inside (except for the initial moment where $I=0$) 2) Lorentz force on the mobile charge is $\vec{v}+\vec{v}_d$ where $\vec{v}_d$ is drift velocity due to current. Lorentz force on such particle is $\vec{v}\times \vec{B}+\vec{v}_d\times\vec{B}$ and does no work, since it is perpendicular to total velocity. Commented Nov 4, 2020 at 16:51
The motional EMF in a conductor moving in magnetic field is really due to atomic lattice working on electrons, as these get pushed out of equilibrium into the lattice by external magnetic forces. It is a result of microscopic constraint forces keeping the electrons inside the conductor. So this is all about microscopic forces and Maxwell's equations for field are largely irrelevant - we already know the external magnetic field.
One can try to formulate microscopic theory of lattice and mobile electrons and of their interactions among themselves and with the external field. This would include Lorentz forces between all particles, external magnetic force, and forces of constraint, keeping the electrons bound to conductor. This is a hard problem.
Much easier is to visualize what happens in the inertial frame of the conductor. Using Lorentz transformations on the field tensor $$F$$, we find out that in the frame of the conductor there is external electric field perpendicular to both the magnetic field and to velocity of the conductor. Its magnitude is $$Bv$$ and it acts as electromotive agent on the mobile electrons. For conducting rod in the scenario you depicted, net work of the electric force per unit charge transported along the rod is $$Blv$$.
• So, if I turn to Lorentz transformations, the speed $v$ will be included in the Maxwell equations, and the integral form of Faraday's law is no longer needed? Commented Nov 4, 2020 at 2:13
• No, $v$ does not appear in Maxwell's equations. Integral of electric field along the circuit is zero, Maxwell's equations are not relevant here. The EMF is due to rod pushing on electrons and slowing down. Magnitude of this EMF is easy to determine in the co-moving frame. Commented Nov 4, 2020 at 9:58
My answwer is you can't. The maxwell equation $$\nabla \times \bf E = -\partial \bf B/\partial t$$ must be modified to $$\nabla \times \bf E = -\partial \bf B/\partial t + \nabla \times (\bf v \times \bf B)$$. (cf. H.H. Skilling, "Fundamentals of Electric Waves", p. 82 eq. 194 ) The last term is based on the Lorentz force $$q \bf v \times \bf B$$.
You have to be careful to associate time-varying areas with moving media. Sometimes it doesn't work. I have a WORD file showing such a situation but I'm a newbie at this forum & don't know how to upload that file as part of this answer.
• You can.And isn't there a rule on stackexchange not to answer or critique others' answers? Commented Nov 5, 2020 at 2:54
• cf. H.H. Skilling, "Fundamentals of Electric Waves", p. 82 eq. 194 which is the exact same equation. Commented Nov 5, 2020 at 3:04
• Not sure about the culture of physics.SE, but it's perfectly fine to comment if one thinks certain answer involves mistake in mathematica.SE. (We don't often cast hasty downvote, though. I haven't casted downvote BTW. ) Commented Nov 5, 2020 at 3:23
• Not familiar with 'mathematica. SE". If "mathematica. SE" flagged my equation as a "mistake" I need to learn about "mathematica" in a hurry so Ican decide if posting on this site even makes sense. Commented Nov 5, 2020 at 3:31
• After a second look at the integral form of Faraday's law of induction, I think you're right. (Incorrect comment deleted. ) Commented Nov 5, 2020 at 3:44 | 2,045 | 7,045 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 21, "wp-katex-eq": 0, "align": 1, "equation": 2, "x-ck12": 0, "texerror": 0} | 3.984375 | 4 | CC-MAIN-2024-33 | latest | en | 0.722444 |
https://www.playtaptales.com/numbers/sesquinquagintatrecentillion/ | 1,544,902,996,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376826968.71/warc/CC-MAIN-20181215174802-20181215200802-00107.warc.gz | 997,165,636 | 4,259 | ## Sesquinquagintatrecentillion
A Sesquinquagintatrecentillion (1 Sesquinquagintatrecentillion) is 10 to the power of 1071 (10^1071). This is an excessively astronomical number!
## How many zeros in a Sesquinquagintatrecentillion?
There are 1,071 zeros in a Sesquinquagintatrecentillion.
## What's before Sesquinquagintatrecentillion?
A Quinquinquagintatrecentillion is smaller than a Sesquinquagintatrecentillion.
## What's after Sesquinquagintatrecentillion?
A Septenquinquagintatrecentillion is larger than a Sesquinquagintatrecentillion.
## Sesquinquagintatrecentillionaire
A Sesquinquagintatrecentillionaire is someone whos assets, net worth or wealth is 1 or more Sesquinquagintatrecentillion. It is unlikely anyone will ever be a true Sesquinquagintatrecentillionaire. If you want to be a Sesquinquagintatrecentillionaire, play Tap Tales!
## Is Sesquinquagintatrecentillion the largest number?
Sesquinquagintatrecentillion is not the largest number. Infinity best describes the largest possible number - if there even is one! We cannot comprehend what the largest number actually is.
## Sesquinquagintatrecentillion written out
Sesquinquagintatrecentillion is written out as:
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
## Big Numbers
This is just one of many really big numbers! | 1,052 | 2,688 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2018-51 | longest | en | 0.640845 |
http://www.cs.pomona.edu/~dkauchak/classes/f11/cs150/lectures/lecture10-lists_files.html | 1,516,524,205,000,000,000 | text/html | crawl-data/CC-MAIN-2018-05/segments/1516084890394.46/warc/CC-MAIN-20180121080507-20180121100507-00173.warc.gz | 425,404,531 | 3,358 | ### CS150 - Fall 2011 - Class 10
• Pi video
- No lab prep for Friday
- I did add a few pages to read from the book about file I/O
- Lab on Friday will be partnered
- Test project 1 out today
- due next Friday (10/21) at 6pm
- honor code
- must work alone
- may only use: book, your notes, class notes, python.org documentation
- may NOT: get help from other students, get help from the tutors (except for file issues, etc), look online for solutions
- 3 problems
- required to do some extra credit
- 63 points total, but only 60 for just doing what I stated
- More than a third of the points come from code style and commenting
- follow instructions carefully!
• problem set, problem 1c.
- what does it do?
- how does it work?
• aliasing
- what will be the output of my_list after doing the following:
>>> my_list = [1, 2, 3, 4, 5]
>>> other_list = my_list
>>> other_list[2] = 100
>>> other_list
[1, 2, 100, 4, 5]
>>> my_list
- [1, 2, 100, 4, 5] ... why?
- my_list and other_list are just references to the same object
- this is called aliasing, since other_list is an alias (another name) for my_list
- saying other_list = my_list does not do a deep copy, that is it does NOT create a new list that is a copy of the list
- draw a picture
- notice that if I make changes to either one, changes will be seen in the other
>>> my_list
[1, 2, 100, 4, 5]
>>> other_list
[1, 2, 100, 4, 5]
>>> my_list[0] = 0
>>> other_list[1] = 1000
>>> my_list
[0, 1000, 100, 4, 5]
>>> other_list
[0, 1000, 100, 4, 5]
- aliasing can also show up in other places
>>> my_list = [1, 2, 3, 4, 5]
>>> def mystery(x):
... x[0] = 1000
...
>>> my_list
[1, 2, 3, 4, 5]
>>> mystery(my_list)
>>> my_list
[1000, 2, 3, 4, 5]
- parameters are passed as a shallow copy (i.e. an alias)
- "parameter passing" describes how the values that are input to the function (i.e. the arguments) are bound to the parameters inside the function
- be careful!
- why do you think this is done?
- a deep copy can be a lot of work
- also allows us to write functions that manipulate the parameter (which we may or may not do)
- notice that we cannot changes what other_list reference (only mutate the object)
def mystery(alist):
alist = [0]*10
print alist
>>> my_list = [1, 2, 3, 4, 5]
>>> mystery(my_list)
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
>>> my_list
[1, 2, 3, 4, 5]
- slicing does create a new copy
>>> my_list = [1, 2, 3, 4, 5]
>>> other_list = my_list[2:4]
>>> other_list
[3, 4]
>>> other_list[0] = 100
>>> other_list
[100, 4]
>>> my_list
[1, 2, 3, 4, 5]
- given this, how could we create a deep copy of other_list?
>>> my_list = [1, 2, 3, 4, 5]
>>> other_list = my_list[:]
>>> other_list[3] = 100
>>> other_list
[1, 2, 3, 100, 5]
>>> my_list
[1, 2, 3, 4, 5]
• run the sentence_stats function from word-stats.py code
- similar idea to our scores functions except now we're going it over strings instead of numbers
- the string class has a "split" method that splits up a sentence into a list by splitting on spaces
>>> "this is a sentence".split()
['this', 'is', 'a', 'sentence']
- optionally, can specify what to split on (though this is much more rare)
>>> "this is a sentence".split("s")
['thi', ' i', ' a ', 'entence']
• files
- what is a file?
- a chunk of data stored on the hard disk
- why do we need files?
- hard-drives persist state regardless of whether the power is on or not
- when a program is running, all the data it is generating/processing is in main memory (e.g. RAM)
- main memory is faster, but doesn't persist when the power goes off
- to read a file in Python we first need to open it
file = open("some_file_name", "r")
- open is another function that takes two parameters
- the first parameter is a string identifying the filename
- be careful about the path/directory. Python looks for the file in the same directory as the program (.py file) unless you tell it to look elsewhere
- the second parameter is another string telling Python what you want to do with the file
- "r" stands for "read", that is, we're going to read some data from the file
- open returns a "file" object that we can use later on for reading purposes
- above, I've saved that in a variable called "file", but I could have called in anything else
>>> open("english.txt", "r")
<open file 'english.txt', mode 'r' at 0x10120a030>
>>> type(open("english.txt", "r"))
<type 'file'>
- once we have a file open, we can read a line at a time from the file using a for loop:
for <variable> in <file_variable>:
# do something
- for each line in the file, the loop will get run
- each time the variable will get assigned to the next line in the file
- the line will be of type string
- the line will also have an endline at the end of it which you'll often want to get rid of (the strings strip() method is often good for this)
• look at the file_stats function in word-stats.py code
- what does it do?
- opens a file
- reads a line at a time
- appends each entry in the file to a list called words (stripping of the end of line)
- prints out the statistics of the word file
- in this same directory I have a file call "english.txt" that has a large list of English words
>>> file_stats("english.txt")
Number of words: 47158
Longest word: antidisestablishmentarianism
Shortest word: Hz
Avg. word length: 8.37891768099
- notice how quickly it can process through the file
- computers are fast! | 1,609 | 5,358 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2018-05 | latest | en | 0.801747 |
https://www.questia.com/article/1G1-13808169/analysis-for-decision-making | 1,427,463,381,000,000,000 | text/html | crawl-data/CC-MAIN-2015-14/segments/1427131296456.82/warc/CC-MAIN-20150323172136-00284-ip-10-168-14-71.ec2.internal.warc.gz | 1,025,289,719 | 15,413 | # Analysis for Decision Making
## Article excerpt
When we prepare a set of financial statements for a client, we know it's likely those financial statements will be used by some interested outside party to evaluate the client's business. Such questions as: Did they make a profit? Did debts increase from last year? Did owners' equity change? are important and can be answered by the four basic statements. These statements are only the beginning, however, to the process of gathering information on which many business decisions will be made.
To better understand how a company is performing, a deeper analysis of these statements is required. A variety of techniques are available that show relationships and changes between and within the financial statements from year to year. Among the more widely used methods are horizontal analysis, trend analysis, vertical analysis and ratio analysis.
Horizontal analysis
Horizontal analysis begins with the typical comparative statement, showing data for the current year and the year just past and calculating both the dollar amount of the change and the percentage change from last year to this year. The percentage of change is calculated as follows:
100 x amount of the change/previous year amount
where the amount of the change is the current year amount less the previous year amount. Both dollar amounts and the percentage change must be considered, lest we give too much weight to one or the other.
Trend analysis
Trend analysis takes horizontal analysis one step further, since it presents data for several successive years rather than only two. The percentage changes are computed using the oldest year as the base year and expressing all succeeding years as percentages of that base year. The value of trend analysis is in its longer view of the firm, which can point out tendencies in the business's operations.
Vertical analysis
Relationships among the various components within a single statement can easily be seen if vertical analysis is used. Here a total figure (revenues or sales for the income statement, total assets for the balance sheet) is set equal to 100% and all other parts of the statement are expressed as a percentage of that total. These "common size" statements can point out significant changes in the make-up of the business from year to year. They can also be used to compare companies within an industry.
Even when the size of firms differs, common size statements allow the accountant to compare characteristics of the firms' financing and operating activities.
Ratio analysis
Finally, ratio analysis allows the interested accountant to explore meaningful relationships between components of a single financial statement or between different statements. A wide variety of ratios can be used to describe a firm's liquidity, profitability, long-term solvency and market strength.
Liquidity ratios help us evaluate the firm's ability to pay short-term debt. All liquidity ratios deal with working capital accounts, since it is from the working capital that payment for current debts and unexpected needs for cash are drawn. Frequently used are the current ratio (current assets divided by current liabilities) and the quick or acid test ratio (quick assets, such as cash, A/R and marketable securities divided by current liabilities). Less familiar are activity ratios such as:
* the receivables turnover (net sales divided by the average accounts receivables), which describes the speed with which the firm turns its receivables into cash;
* the average days sales uncollected (365 days divided by the receivables turnover) which tells how long the firm must wait to receive cash from credit sales;
* and the inventory turnover (cost of goods sold divided by average inventory) which measures how quickly the inventory is turned into sales. … | 714 | 3,841 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.890625 | 3 | CC-MAIN-2015-14 | latest | en | 0.944089 |
https://puzzling.stackexchange.com/questions/81464/find-those-chess-notations-3/81471 | 1,563,534,136,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195526210.32/warc/CC-MAIN-20190719095313-20190719121313-00072.warc.gz | 516,176,876 | 37,464 | Find Those Chess Notations! #3
I’ve decided to do something a little different this time. I’m going to give you nearly all of the moves of one side, and must figure out the rest of the moves of the other side. Variations are allowed, as always, but the end result must be the same. I am sorry in advance of this is not possible. I just wanted to try something new!
Number Of Moves: 24
Checkmater: Black
Given Game (Regular Chess Notation):
1. ? c5
2. ? c4
3. ? b5
4. ? b4
5. ? e5
6. ? f5
7. ? Bc5
8. ? e4
9. ? f4
10. ?d5
11. ? f3
12. ? Bf5
13. ? Be4
14. ? g5
15. ? g4+
16. ? g3
17. ? Qh4+
18. ? Qf4+
19. ? Nd7+
20. ? ?
21. ? ?
22. ? ?
23. ? ?
24. ? Nf3# *
Cryptic Clue #1: This is black’s 19th matricide. (This is a pun!)
Cryptic Clue #2: How would you feel if your closest friends betrayed you and let you die?
Cryptic Clue #3: Assume that all moves are pawn moves unless it can be proven if it is stated as such.
Task: To use retrograde analysis and give an answer with all of the question marked moves solved, along with reasons for each move. A simple PGN post shall suffice. A link is optional.
As always, may the odds ever be in your favor!
This one will be lots of fun, I say!
Here is the solution. The explanation follows.
Here is another, where Cryptic Clue n°1 is understood as
Queen-side (pun with matri-cide) castling by Black.
There is plenty of freedom in this puzzle, as shown by these two examples.
After move 14, the situation is (up to White's moves and possibly captured Black pieces)
and in this position,
g4 comes with check. There can't be any discoveries, so the White King is either in h3 or f3
PROOF THAT h3 IS IMPOSSIBLE
16. ... g3 follows, so the pawn wasn't captured, so the King moved, and it didn't move to g3 or g4. But a few moves later, we have 19. ... Nd7+ meaning that the King is then either in f6, e5 or c5. If the King is in h3 when g4+ is played, then moving to the second row makes it too far for him to reach f6, e5 or c5 in time (all Black moves would need to be King moves and the only target square would be e5, and this is impossible due to 18. ... Qf4+). Therefore g4+ is followed by Kh4, meaning that a white piece protects the King from check by the Queen. But then there is no way 17. ... Qh4+ can happen: the whole diagonal would need to be free for the Queen to move, so move 17 by White would need to remove the King from h4 and free the Queen's diagonal.
Partial conclusion:
The Bishop in e4 was captured some time earlier (as well as the Black e pawn to allow the Bishop there in the first place).
WHERE IS THE WHITE KING AFTER MOVE 19.
It can only be in f6, e5 or c5. But c5 is impossible due to the sequence of checks by the Queen. f6 is possible only if there is a white piece at f5 AND the Knight at g8 was captured. It is not really in White's interest to spend time capturing Black pieces, given that Black is to deliver checkmate at the end. So e5 seems more likely. Note that e5 implies that the Queen gets captured at move 19, which is not in our interest either but coincides with Cryptic Clue n°1.
WHAT THE FINAL POSITION TELLS US
We know that Nf3 is mate, which means that the White e and g pawn, as well as the Ng1 are gone. So is the white Queen, consequently. One of the pawns can conveniently serve the purpose of capturing f3 and the Bishop e4. The Queen, on the other hand, can serve the purpose of letting the Black rooks free, so that they can help checkmating in the end (otherwise Black is poor in material).
CRYPTIC CLUES
N°1:
White captures the B Queen at move 19, but also there are exactly 19 moves where White offers their Queen to be captured.
N°2:
The King's closest friends are the Queen and Light square Bishop, both of which are in a position to capture Black's mating material (the Rook at a6) but don't interfere.
• Well Cryptic Clue #1 has another meaning as well however.....;) – Rewan Demontay Apr 6 at 14:40
• That is not the right answer, so far. However, I will say that your white pawn structure om move 14 after fxe4 is halfway there. And perhaps you should construct a picture with all black moves, ending at move 19 of course, to see if you get the idea. – Rewan Demontay Apr 6 at 20:04
• @RewanDemontay The first few of these seemed self-confirming and uniquely solvable, with the "clues" giving some pointers on which way to proceed. With the most recent puzzles (Foxhole Failures, Chess Notations 2.5 and 3), though, it seems like there are multiple ways to fit a game to the supplied move list, and the only thing that makes some (all but one?) of those games not the answer is that they somehow don't fit the Cryptic Clue(s), even when the answerer thinks they do.... which puts these recent puzzles dangerously close to "guess what I'm thinking of?" territory. – Rubio Apr 6 at 20:56
• @RewanDemontay Having the solution and seeing how it satisfies the supplied clue(s) is a very different thing from having to figure out which approach to take and which solution will be correct based on only the cryptically obscure clue(s) included in the puzzle. Puzzles need to be forward-solvable from the information provided, not simply have answers that are confirmable after the fact. Are you sure these puzzles give enough information to meaningfully solve them without "being inside your head"? – Rubio Apr 6 at 20:56
• Hmm. I’ll work on making them less think what I’m thinking. – Rewan Demontay Apr 6 at 21:15 | 1,460 | 5,442 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.296875 | 3 | CC-MAIN-2019-30 | latest | en | 0.916934 |
https://edurev.in/question/1856065/In-a-one-dimensional-harmonic-oscillator--are-respectively-the-ground--first-and-the-second-existed- | 1,721,214,250,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514759.39/warc/CC-MAIN-20240717090242-20240717120242-00402.warc.gz | 197,730,489 | 68,537 | In a one-dimensional harmonic oscillator, are...
In a one-dimensional harmonic oscillator, are respectively the ground, first and the second existed states. These three states are normalized and are orthogonal to one another.
ψ1 and ψ2 are two states defined by
where a is a constant.
The value of a for which y2 is orthogonal to y1 is ___________ .
FREE This question is part of
In a one-dimensional harmonic oscillator, are respectively the ground,...
for orthogonal condition -
1 + 2 + 3a = 0
3a = - 3
a = -1
View all questions of this test
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In a one-dimensional harmonic oscillator, are respectively the ground, first and the second existed states. These three states are normalized and are orthogonal to one another.ψ1 and ψ2 are two states defined bywhere a is a constant.The value of a for which y2 is orthogonal to y1 is ___________ .Correct answer is '-1'. Can you explain this answer?
Question Description
In a one-dimensional harmonic oscillator, are respectively the ground, first and the second existed states. These three states are normalized and are orthogonal to one another.ψ1 and ψ2 are two states defined bywhere a is a constant.The value of a for which y2 is orthogonal to y1 is ___________ .Correct answer is '-1'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In a one-dimensional harmonic oscillator, are respectively the ground, first and the second existed states. These three states are normalized and are orthogonal to one another.ψ1 and ψ2 are two states defined bywhere a is a constant.The value of a for which y2 is orthogonal to y1 is ___________ .Correct answer is '-1'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a one-dimensional harmonic oscillator, are respectively the ground, first and the second existed states. These three states are normalized and are orthogonal to one another.ψ1 and ψ2 are two states defined bywhere a is a constant.The value of a for which y2 is orthogonal to y1 is ___________ .Correct answer is '-1'. Can you explain this answer?.
Solutions for In a one-dimensional harmonic oscillator, are respectively the ground, first and the second existed states. These three states are normalized and are orthogonal to one another.ψ1 and ψ2 are two states defined bywhere a is a constant.The value of a for which y2 is orthogonal to y1 is ___________ .Correct answer is '-1'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE. Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of In a one-dimensional harmonic oscillator, are respectively the ground, first and the second existed states. These three states are normalized and are orthogonal to one another.ψ1 and ψ2 are two states defined bywhere a is a constant.The value of a for which y2 is orthogonal to y1 is ___________ .Correct answer is '-1'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of In a one-dimensional harmonic oscillator, are respectively the ground, first and the second existed states. These three states are normalized and are orthogonal to one another.ψ1 and ψ2 are two states defined bywhere a is a constant.The value of a for which y2 is orthogonal to y1 is ___________ .Correct answer is '-1'. Can you explain this answer?, a detailed solution for In a one-dimensional harmonic oscillator, are respectively the ground, first and the second existed states. These three states are normalized and are orthogonal to one another.ψ1 and ψ2 are two states defined bywhere a is a constant.The value of a for which y2 is orthogonal to y1 is ___________ .Correct answer is '-1'. Can you explain this answer? has been provided alongside types of In a one-dimensional harmonic oscillator, are respectively the ground, first and the second existed states. These three states are normalized and are orthogonal to one another.ψ1 and ψ2 are two states defined bywhere a is a constant.The value of a for which y2 is orthogonal to y1 is ___________ .Correct answer is '-1'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice In a one-dimensional harmonic oscillator, are respectively the ground, first and the second existed states. These three states are normalized and are orthogonal to one another.ψ1 and ψ2 are two states defined bywhere a is a constant.The value of a for which y2 is orthogonal to y1 is ___________ .Correct answer is '-1'. Can you explain this answer? tests, examples and also practice GATE tests.
Explore Courses for GATE exam | 1,061 | 4,893 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2024-30 | latest | en | 0.930644 |
https://ncalculators.com/number-conversion/hexa-to-decimal-binary-octal-converter.htm | 1,718,417,914,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861578.89/warc/CC-MAIN-20240614235857-20240615025857-00370.warc.gz | 382,064,102 | 16,136 | # Hex to Decimal, Binary, Octal Converter
Hex Decimal Value
Decimal = 72
Binary = 1001000
Octal = 110
GENERATE WORK
## Hex to Decimal, Binary, Octal Conversion - work with steps
Input Data :
Hex Number = 48
Objective :
Find what decimal binary, octal from given hex value?
Solution :
Hexa Decimal to Decimal
48_16 = (4 \times 16^1) + (8 \times 16^0)
48_16 = 64 + 8
48_16 = 72_10Hexa Decimal to Binary
Write equivalent binary for given hexa decimal value
48
01001000
48_16 = 01001000_2
Hexa Decimal to Octal
Convert Hexa Decimal number to binary
48
01001000
48_16 = 01001000_2
Convert Binary Number into Octal Number
Split the binary number from left to right each group 3 bits
001001000
110
01001000_2 = 110_8
Hex Converter is an online tool specially programmed to perform the computations of Hex to Binary Conversion, Hex to Decimal Conversion and Hex to Octal Conversion. This Hex calculator converts the given Hex input values into equivalent Decimal, Binary, and Octal values
In digital electronics the number conversion is more essential to designing a circuit. In mathematics and computer science, Hex also called as base 16 or hex is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols from 0 to 9 to represent values zero to nine, and A, B, C, D, E, F or alternatively from alphabet A to F to represent values ten to fifteen. More common the Hex values are used to represent computer memory size
## Hex to Decimal Converter
This below example is the basic principle used in this Hexadecimal to Decimal conversion. Convert the Hex number 2AF3 into its equivalent Decimal Number. The Hex number 2AF3 can be written as in the below form. The sum of all the units yield the equivalent decimal value
### Hex to Binary Converter
This below example is the basic principle used in this Hexadecimal to Binary conversion. To calculate the equivalent binary number for a given Hex number, each digit of a hex number is individually converted to its binary equivalent. For example the equivalent binary number for 3FDH can be written as
3 = 0011; F = 1111; D = 1101
The Binary Number = 0011 1111 1101
### Hex to Octal Converter
This below example is the basic principle used in this Hexadecimal to Octal conversion. The easiest way to convert Hex number to octal number is converting hex number to its equivalent binary number and convert it to its equivalent octal number
For example the equivalent Octal number for 25BH can be derived as
Hex to Binary Conversion
2 = 0010; 5 = 0101; B = 1011
The Binary Number = 0010 0101 1011
Now the hexa decimal equivalent Binary numbers can be converted into equivalent octal numbers. To do so, split the binary number into segments having 3 bits each to find out the equivalent octal for the binary number
001 = 1; 001 = 1; 011 = 3; 011 = 3
The Octal Number = 11338
When it comes to online calculation, this Hex Calculator can assist you to calculate the equivalent Decimal, Binary and Octal values for the given hexa value. These number conversions are heavily employed in Electronics Circuit Design, Data Structure, Programming, Digital Transmission, Satellite Communication, Encoding and Decoding Techniques, etc. | 796 | 3,243 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.734375 | 4 | CC-MAIN-2024-26 | latest | en | 0.754202 |
https://estrip.org/articles/read/jill/42480/I_Am_Legend.html | 1,716,182,190,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058222.5/warc/CC-MAIN-20240520045803-20240520075803-00007.warc.gz | 212,833,540 | 11,465 | Journaling on estrip is free and easy. get started today
Last Visit n/a |Start Date 2003-10-08 03:53:59 |Comments 11 |Entries 194 |Images 124 |Theme |
12/11/07 09:23 - 36ºF - ID#42480
I Am Legend
The movie had its moments........
but,
I get abnormal strength what with adrenaline and all but Why do "Zombies" (who really are normal people with a virus) develop the ability to climb walls?..........
And.......... real people in makeup are a thousand times scarier than any computer-generated creature.............
And........how are they all still wearing clothes?
And....................... Why is Will Smith so freakin' dreamy?
Consider this while I attempt night two of the Tree Skirt.
Permalink: I_Am_Legend.html
Words: 76
Location: Buffalo, NY
12/10/07 08:13 - 32ºF - ID#42462
Math Time
I am making a tree skirt.
To make a pattern I measured the diameter (which is not the same as the radius) of the area under the tree , then the diameter of the hole for the stump.
I looked up the formula for circumference ( which is not spelled circumferance), and figured out the circumference for each circle.
Then I divided each number by eight (I will have eight slices on my skirt).
Now I have to create the actual pattern for a single slice........ I do not have a compass.......
My brain is worn out........
Permalink: Math_Time.html
Words: 95
Location: Buffalo, NY
12/07/07 07:53 - 32ºF - ID#42428
Mikey
This is how I want you to look the next time I see you...... which is in like 45 minutes....... so get knitting............
Permalink: Mikey.html
Words: 24
Location: Buffalo, NY
11/30/07 01:16 - 40ºF - ID#42343
aaaaahh
Permalink: aaaaahh.html
Words: 2
Location: Buffalo, NY
11/29/07 12:56 - 39ºF - ID#42331
E:Harmony
I was bored so I decided to take the (E:Harmony) Personality profile......man, according to the results I am not a very fun person..... Apparently I am distant, moody, demanding, hard-nosed, judgemental, skeptical.......really?
Mike, how accurate is the following statement?
"You also have some limits when it comes to being with people. Sure some people need to be with others all the time and seem to get recharged by helping out most anyone else. But that's not you. You know that you do best if you spend a fair amount of time on your own. Not that you are a loner, just that time spent by yourself is not wasted at all with you. You've come to understand that if you don't take good care of yourself, eventually you'll be not good to anyone, including yourself or others."
That's right all you freeloaders, whiners, anyone in need who hasn"t done anything for me lately.......don't come knockin' round this door.....
Permalink: E_Harmony.html
Words: 163
Location: Buffalo, NY
01/31/07 03:20 - 22ºF - ID#37939
yayyyyy!
I just got offered a job as a seamstress!!!
I'm excited!!!!......even if I will be forced to wear their way-overpriced clothes......
I am totally going shopping now!!!
Permalink: yayyyyy_.html
Words: 28
Location: Buffalo, NY
01/31/07 02:56 - 22ºF - ID#37938
Target is super-great
I haven't gone to Target in over a week.....
I think that is the longest I have ever gone.....
I love Target!!!!
I love Proenza Schouler!!!!
Sunday I shall buy, buy, buy.....
.......and then be broke, broke, broke
Oh well!
Permalink: Target_is_super_great.html
Words: 42
Location: Buffalo, NY
01/24/07 05:01 - 26ºF - ID#37851
Stirrup Pants......Really!!??
Let's just all agree that men should not wear leggings...... unless they don't have a penis......or testicles............nope, nevermind, men should never wear leggings.
Permalink: Stirrup_Pants_Really_.html
Words: 27
Location: Buffalo, NY
10/26/06 01:42 - 40ºF - ID#24420
Don Apparel
Hey (E:strippers),
There will be an estate sale at Don Apparel this Friday and Saturday from 11-7pm.
Everything must go, from clothes to records, to display cases and mannequins.....
(e:mike) & (e:mk) mabye we will have luck with our costumes there!!
Permalink: Don_Apparel.html
Words: 45
Location: Buffalo, NY
09/28/06 04:23 - 53ºF - ID#24419
YAWWWWWWWNNNNN
So sleepy, so tired of answering the phone.......
So tired of being so unmotivated.......
Man ....I'm gettin' old.....and I haven't done very much with my life.
I will not be a receptionist for the rest of my life.....
Repeat,
I will not be a receptionist for the rest of my life.....
Repeat,
I will not be a receptionist for the rest of my life.....
Repeat,
I will not be a receptionist for the rest of my life.....
Repeat,
I will not be a receptionist for the rest of my life.....
Repeat,
I will not be a receptionist for the rest of my life.....
I won't, I really won't....
Sir Mikercycle, we need to get going on that apartment.....
I had the weirdest dream the other night that I found this creepy cone-headed , naked slimy midget growing in my basement....
I screamed when I saw it and woke in up..... it was angry and started chasing me all around the house.....
Eventually Jim convinced me to calm down and talk to it, I did and after some time we civilized it...... we even dressed it up in a preppy button-down and khaki get-up (which I had to alter)....
It seemed ready to enter society so I showed it to the door and stood outside waving goodbye.
As I turned to go back inside Another little cone-headed, naked slimy midget was standing in my house..... he was not nearly as civilised and started pushing the door closed.
Then I woke up.....
Permalink: YAWWWWWWWNNNNN.html
Words: 251
Location: Buffalo, NY
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joe said to joe
Never send a man to do a grandma's job...
sina said to sina
yes thank you!
Well, since 2018 I am living in France, I have finished my second master of science,...
paul said to sina
Nice to hear from you!! Hope everything is going great....
paul said to twisted
Hello from the east coast! It took me so long to see this, it might as well have arrived in a lette... | 1,617 | 6,074 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2024-22 | latest | en | 0.895065 |
https://winegeeknyc.netlify.app/6th-grade-common-core-math-worksheets-pdf/ | 1,621,302,456,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991650.73/warc/CC-MAIN-20210518002309-20210518032309-00231.warc.gz | 634,162,717 | 8,721 | # 37++ 6th grade common core math worksheets pdf info
Written by Wayne Jan 01, 2021 ยท 9 min read
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6th Grade Common Core Math Worksheets Pdf. Write and evaluate numerical expressions involving whole-number exponents. Apply these techniques in the context of solving real-world and mathematical. Easy to Use Complements School Work and Best for Revision. Common Core and Math in Sixth Grade.
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After finishing all 10 worksheets your students will have a completed a review of all the sixth grade common core math standards. Math for Week of March 1. 06022021 6th grade common core math printable worksheets. The pre-made worksheets above are categorized by both subject and by grade Homework. If you want your students to overcome their weaknesses and achieve a high score in the 6th Grade Common Core Math test use our comprehensive worksheets of 6th Grade Common Core Math. Sixth Grade Math Worksheets - Free PDF Printables with No Login.
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Math printable Worksheets for Grade 6. Common Core and Math in Sixth Grade. Apply And Extend Previous Understandings Of Arithmetic To Algebraic Expressions. Math printable Worksheets for Grade 6. We categorize and review Math worksheets listed here to help you Answers the math worksheets problems that you are looking for.
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Activities with answers to teach practice or learn mathematics in CCSS domains 5OA 5NBT 5NF 5MD and 5G is available online for free in printable. Downloadable PDF format to teach practice or learn mathematics. 3 write interpret and. 2 complete understanding of division of fractions and extending the notion of number to the system of rational numbers including negative numbers. The K-6 curriculum includes the above cluster topics under the CCSS domains ratios and proportional relationships 6RP number system 6NS expressions and equations 6EE geometry 6G and statistics and.
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Ad Access Maths Worksheets - 100 Aligned With The National Curriculum. Math for Week of March 1. Grade 6 Math Worksheets PDF Sixth Grade Math Worksheets with Answers is an ultimate tool useful to test your kids skills on different grade 6 math topics. These worksheets are free. The K-6 curriculum includes the above cluster topics under the CCSS domains ratios and proportional relationships 6RP number system 6NS expressions and equations 6EE geometry 6G and statistics and.
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Welcome to our common core printables section for 6th grade math. The best source for free math worksheets and distance learning. If you want your students to overcome their weaknesses and achieve a high score in the 6th Grade Common Core Math test use our comprehensive worksheets of 6th Grade Common Core Math. Each standard is covered by at least one question. These our math printable worksheets for grade 6 have covered all major areas of grade 6 math some of which include.
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Browse through the list of common core standards for Grade-6 Math. 5th Grade common core math worksheets. 06022021 6th grade common core math printable worksheets. 1 connect ratio and rate to whole number multiplication and division and use concepts of ratio and rate to solve problems. Displaying top 8 worksheets found for - Sixth Grade Common Core.
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May 28 . 7 min read | 2,213 | 10,574 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2021-21 | longest | en | 0.910837 |
http://mathhelpforum.com/statistics/114800-question-poisson.html | 1,524,325,394,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125945232.48/warc/CC-MAIN-20180421145218-20180421165218-00421.warc.gz | 201,025,619 | 9,803 | 1. ## Question on Poisson
The number of serious faults on a randomly chosen 1km stretch of motorway has a Poisson distribution of mean 2.1. The random variable X km is the distance between successive serious faults on the motorway.
Explain, using a Poisson distribution, why for $\displaystyle x\geq0$
$\displaystyle P(X>x)=e^{-2.1x}$
2. Originally Posted by I-Think
The number of serious faults on a randomly chosen 1km stretch of motorway has a Poisson distribution of mean 2.1. The random variable X km is the distance between successive serious faults on the motorway.
Explain, using a Poisson distribution, why for $\displaystyle x\geq0$
$\displaystyle P(X>x)=e^{-2.1x}$ | 177 | 679 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.34375 | 3 | CC-MAIN-2018-17 | latest | en | 0.783556 |
http://markvsql.com/2012/08/intro-to-mdx-decathlonsets-a-shirt-of-a-different-color-410/ | 1,547,842,464,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583660529.12/warc/CC-MAIN-20190118193139-20190118215139-00437.warc.gz | 149,861,375 | 11,718 | ## Intro To MDX Decathlon–Sets: A Shirt of a Different Color (4/10)
20 August, 2012 (13:00) | Decathlon, MDX | By: Mark V
In the previous post in this series, Intro To MDX Decathlon – The Trouble With Tuples (3/10), we discussed how to reference a particular cell in a cube by using a Tuple. Now it’s time to group them together using a concept we haven’t discussed yet: the Set. Its basic definition is deceptively simple:
Set: A collection of tuples.
The basic syntax of a set is essentially a list of Tuples, separated by commas, surrounded by curly braces {}. You can see this in Figure 1.
Figure 1
As a concept, we can liken the concept of a Set to the uniforms within Starfleet in the Star Trek franchise. The members of Starfleet wore uniforms of a certain color depending on their role. In Figure 2, an excellent Lego depiction of the main characters of Star Trek: The Next Generation, you see Red, Blue, and Yellow uniforms.
Figure 2
The characters are wearing shirts that are designed to group them together by their job function.
Essentially, the colors follow this pattern:
Red: Command
Yellow: Tactical, Security, Engineering (possibly considered Operations)
Blue: Science, Medical
Light Blue: Well… Wesley.
This grouping only works when there are properties shared amongst members of the group. Sets in the cube space also have to have some shared properties to be valid.
### Prime Directives of Sets
Sets in MDX must follow the following rules to be valid.
Hierarchality: All Tuples in a set must reference the same hierarchies. This is essentially the Apples to Apples rule. Figure 3 shows an example of a valid Set. “Hierarchality” is also a great word to throw around at parties.
Figure 3
The Set in Figure 3 is valid because the members are both from [Hierarchy Y]. This Set is a good example of Hierarchality.
Figure 4 shows an example of an invalid Set.
Figure 4
The Set in Figure 4 is invalid because one member comes from [Hierarchy Y] and the other comes from [Hierarchy X]. These members do not have Hierarchality.
The code in Query 1, below, shows a set in my Borg cube.
Query 1
`SELECT`
` [Measures].[Episode Count] ON COLUMNS`
` , {`
` [Series].[Series Name].[Star Trek: The Original Series] -- Tuple A`
` , [Series].[Series Name].[Star Trek: The Next Generation] -- Tuple B`
` } ON ROWS`
`FROM [Borg]`
Result 1
Dimensionality: All Tuples in the Set must reference the same Dimensions in the same order. This rule comes into play when you are declaring multi-part Tuples as members of the set.
Figure 5 shows an example of a valid Set.
Figure 5
The Set in Figure 5 is valid because the first tuple references [Hierarchy Y] and then [Hierarchy Z]. Likewise, the second tuple references [Hierarchy Y] and then [Hierarchy Z]. These tuples have the same Dimensionality.
Figure 6 shows an example of an invalid Set.
Figure 6
This Set is not valid because the first Tuple references [Hierarchy Y] and then [Hierarchy Z] while the second Tuple reverses the order of the hierarchies, referencing [Hierarchy Z] and then [Hierarchy Y]. These tuples do not have the same Dimensionality.
Query 2 shows an example of a Set created from multi-part tuples in my Borg cube.
Query 2
`SELECT`
` [Measures].[Episode Count] ON COLUMNS`
` , {`
` ([Series].[Series Name].[Star Trek: The Original Series]`
` , [Season].[Season Name].[Season 01]) -- Tuple A`
` , ([Series].[Series Name].[Star Trek: The Next Generation]`
` , [Season].[Season Name].[Season 01]) -- Tuple B`
` } ON ROWS`
`FROM [Borg]`
Result 2
### The Named Set
For readability and organization, you can also give your sets names. You declare a Named Set using the WITH keyword. Figure 7 shows the basic syntax.
Figure 7
Query 3, below, will return the same result as Query 1, but is a bit more organized by using a Named Set.
Query 3
`WITH SET MyFavorites AS`
`{`
` [Series].[Series Name].[Star Trek: The Original Series] -- Tuple A`
` , [Series].[Series Name].[Star Trek: The Next Generation] -- Tuple B`
`}`
`SELECT`
` [Measures].[Episode Count] ON COLUMNS`
` , MyFavorites ON ROWS`
`FROM [Borg]`
Result 3
Result 3 is identical to Result 1.
### The Range Operator “:”
The Range Operator is immensely helpful in creating Sets when dealing with ordered hierarchies, which should be just about all of them. The Range Operator takes two arguments, the Starting Member and the Ending Member.
`[Starting Member]:[Ending Member]`
It returns an ordered set of all member from the Starting Member to the Ending Member, inclusive of both. So, given a list of members [A],[B],[C],[D], the expression [A]:[D] would return the entire list of members.
Query 4 shows an example of a Named Set from my Borg cube made up of all of the members of the [Calendar Year] hierarchy in the 1980s decade.
Query 4
`WITH SET TheEighties AS`
`{`
` [Date].[Date Hierarchy].[Calendar Year].[1980] `
` ,[Date].[Date Hierarchy].[Calendar Year].[1981]`
` ,[Date].[Date Hierarchy].[Calendar Year].[1982]`
` ,[Date].[Date Hierarchy].[Calendar Year].[1983] `
` ,[Date].[Date Hierarchy].[Calendar Year].[1984]`
` ,[Date].[Date Hierarchy].[Calendar Year].[1985]`
` ,[Date].[Date Hierarchy].[Calendar Year].[1986]`
` ,[Date].[Date Hierarchy].[Calendar Year].[1987]`
` ,[Date].[Date Hierarchy].[Calendar Year].[1988]`
` ,[Date].[Date Hierarchy].[Calendar Year].[1989]`
`}`
`SELECT`
` [Measures].[Episode Count] ON COLUMNS`
` , TheEighties ON ROWS`
`FROM [Borg]`
Result 4
Since the [Calendar Year] hierarchy is ordered by the Year values, you can also use the Range Operator instead of specifying all ten years individually. Query 5 shows the same query logic as Query 4, but uses the Range Operator, resulting in much cleaner code.
Query 5
`WITH SET TheEighties AS`
`{`
` [Date].[Date Hierarchy].[Calendar Year].[1980] -- Start`
` :[Date].[Date Hierarchy].[Calendar Year].[1989] -- End`
`}`
`SELECT`
` [Measures].[Episode Count] ON COLUMNS`
` , TheEighties ON ROWS`
`FROM [Borg]`
Result 5
Result 4 and Result 5 are identical, even though Query 5 is much easier to read and is much shorter.
In this post, we introduced the concept of the Set and explained the rules around their use. We also discussed how to create a Named Set to make your MDX a bit more organized. We closed by showing how the Range Operator can be of great use in creating sets from within ordered hierarchies.
Pingback from Intro To MDX Decathlon–Introduction | Mark V SQL
Time August 21, 2012 at 10:25 am
[…] 1. Intro To MDX Decathlon – Cube Space: The Final Frontier (1/10) 2. Intro To MDX Decathlon – The Basic MDX Query (2/10) 3. Intro To MDX Decathlon – The Trouble With Tuples (3/10) 4. Intro To MDX Decathlon – Sets: A Shirt of a Different Color (4/10) […]
Time August 26, 2012 at 9:37 pm
Thanks a bundle for the solid introduction to MDX. You presented the information in the exact fashion I required; simply and with association to star fleet!
Comment from Mark V
Time August 27, 2012 at 9:40 am
Thanks, Steven! It’s great to hear this is helpful for you. :)
Pingback from Intro To MDX Decathlon–.members Function (5/10) | Mark V SQL
Time August 27, 2012 at 1:00 pm
[…] the previous post in this series, Intro To MDX Decathlon – Sets: A Shirt of a Different Color (4/10), we defined a Set and also discussed the rules that valid sets must follow. In this post, we will […]
Pingback from Intro To MDX Decathlon–PERIODSTODATE() Function (10/10) | Mark V SQL
Time October 1, 2012 at 1:03 pm
[…] diligence for the last ten weeks, you will recall the explanation of the Range operator in the Intro To MDX Decathlon – Sets: A Shirt of a Different Color (4/10) post. Therefore, you will know that a more succinct expression for the above set would […] | 2,022 | 7,896 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2019-04 | longest | en | 0.919376 |
https://documentation.statsoft.com/STATISTICAHelp.aspx?path=Graphs/Graph/UnderstandingGraphs/Concepts/ConceptualOverviewsCategorizedScatterplots | 1,576,285,459,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540569332.20/warc/CC-MAIN-20191213230200-20191214014200-00229.warc.gz | 309,863,032 | 17,285 | # Conceptual Overviews - Categorized Scatterplots
In general, two-dimensional scatterplots are used to visualize relations between two variables X and Y (e.g., weight and height). In scatterplots, individual data points are represented by point markers in two-dimensional space, where axes represent the variables. The two coordinates (X and Y) that determine the location of each point correspond to its specific values on the two variables. If the two variables are strongly related, then the data points form a systematic shape (e.g., a straight line or a clear curve). If the variables are not related, then the points form a round "cloud."
The categorized scatterplot option allows you to produce scatterplots categorized by one or two variables. Via the Multiple Subsets options, you can also categorize the scatterplot based on logical selection conditions that define each category or group of observations.
Categorized scatterplots offer a powerful exploratory and analytic technique for investigating relationships between two or more variables within different sub-groups.
A variety of analytic options are available to enhance exploratory analyses.
Homogeneity of Bivariate Distributions (Shapes of Relations between Variables)
Scatterplots are typically used to identify the nature of relations between two variables (e.g., blood pressure and cholesterol level), because they can provide much more information than a correlation coefficient.
For example, a lack of homogeneity in the sample from which a correlation was calculated can bias the value of the correlation. Imagine a case where a correlation coefficient is calculated from data points that came from two different experimental groups, but this fact was ignored when the correlation was calculated. Suppose the experimental manipulation in one of the groups increased the values of both correlated variables, and thus the data from each group form a distinctive "cloud" in the scatterplot (as shown in the following illustration).
In this example, the high correlation is entirely due to the arrangement of the two groups, and it does not represent the "true" relation between the two variables, which is practically equal to 0 (as could be seen if you looked at each group separately).
If you suspect that such a pattern may exist in your data and you know how to identify the possible "subsets" of data, then producing a categorized scatterplot
may yield a more accurate picture of the strength of the relationship between the X and Y variable, within each group (i.e., after controlling for group membership).
Fitting Functions to All Subsets Combined or Separately to Each Subset
Categorized graphs fit separate functions to each subset of points (one function curve is drawn for each subset, as shown in the following example of an overlaid categorized scatterplot where three regression lines are plotted, one for each subset).
If it is desired to fit one function to all points combined (but you still need to be able to identify the members of each subset), use the Mark Selected Subsets option accessible from the 2D Scatterplots dialog.
The two graphs shown above were produced from the same dataset.
Curvilinear Relations
Curvilinearity is another aspect of the relationships between variables that can be examined in scatterplots. There are no "automatic" or easy-to-use tests to measure curvilinear relationships between variables: The standard Pearson r coefficient measures only linear relations; some nonparametric correlations such as the Spearman R can measure curvilinear relations, but not non-monotonous relations. Examining scatterplots allows you to identify the shape of relations, so that later an appropriate data transformation can be chosen to "straighten" the data or choose an appropriate nonlinear estimation equation to be fit.
For more information, refer to Basic Statistics, Distribution Fitting, Multiple Regression, and Nonlinear Estimation. | 745 | 3,969 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.8125 | 3 | CC-MAIN-2019-51 | latest | en | 0.90434 |
https://de.maplesoft.com/support/help/addons/view.aspx?path=Statistics%2FMakeProcedure | 1,679,521,864,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296944452.97/warc/CC-MAIN-20230322211955-20230323001955-00003.warc.gz | 230,679,076 | 30,299 | MakeProcedure - Maple Help
Statistics
MakeProcedure
generate a procedure for calculating statistical quantities
Calling Sequence MakeProcedure(stat, inp, params)
Parameters
stat - name; statistical quantity to calculate inp - algebraic, rtable, 'randomvariable', 'sample'; primary input to procedure params - (optional) a sequence representing the arguments of the generated procedure options - (optional) equation(s) of the form option=value passed to the statistical quantity being used
Description
• The MakeProcedure function generates a procedure that can be used to calculate various statistical quantities.
• The first parameter is the name of a statistical quantity (for available statistical quantities see Statistics[DescriptiveStatistics]).
• The second parameter is the primary input to this procedure. If this parameter is an algebraic expression involving random variables or a distribution then the procedure will calculate the statistical quantity on the given expression. Similarly, if the parameter is an rtable, the statistical quantity will be calculated on the provided dataset. If 'randomvariable' is specified, the procedure will accept as its first parameter an expression involving random variables (type algebraic). Finally, if 'sample' is specified, the procedure will accept a dataset (type rtable) as its first parameter.
• The third parameter specifies the arguments for the generated procedure. If this parameter is specified, all arguments of the selected statistic must be specified as they would in a procedure definition. Alternatively, parameters may be replaced with values that are instead used when performing the statistical operation.
Computation
• For efficiency, all computations are performed in floating-point; therefore, all data provided must have type realcons and all returned solutions are floating-point, even if the problem is specified with exact values.
Examples
> $\mathrm{with}\left(\mathrm{Statistics}\right):$
Generate a procedure for calculating the moment on an array.
> $A≔\mathrm{Array}\left(\left[1.,2.,3.\right]\right):$
> $M≔\mathrm{MakeProcedure}\left('\mathrm{Moment}',A\right):$
> $M\left(4\right)$
${32.6666666666667}$ (1)
Generate a procedure for calculating the 4th moment of any sample.
> $M≔\mathrm{MakeProcedure}\left('\mathrm{Moment}','\mathrm{sample}',4\right):$
> $M\left(A\right)$
${32.6666666666667}$ (2)
Generate a procedure for calculating the moment of a Normal random variable.
> $M≔\mathrm{MakeProcedure}\left('\mathrm{Moment}',\mathrm{Normal}\left(0,1\right),n::'\mathrm{posint}'\right):$
> $M\left(4\right)$
${3.}$ (3)
Generate a procedure for calculating the 4th moment of any random variable.
> $M≔\mathrm{MakeProcedure}\left('\mathrm{Moment}','\mathrm{randomvariable}',4\right):$
> $M\left(\mathrm{RandomVariable}\left(\mathrm{Normal}\left(0,1\right)\right)\right)$
${3.}$ (4) | 671 | 2,912 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 14, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.515625 | 4 | CC-MAIN-2023-14 | longest | en | 0.677765 |
http://www.mathworks.com/matlabcentral/fileexchange/14888-mutual-information-computation/content/mi/condentropy.m | 1,427,637,961,000,000,000 | text/html | crawl-data/CC-MAIN-2015-14/segments/1427131298538.29/warc/CC-MAIN-20150323172138-00108-ip-10-168-14-71.ec2.internal.warc.gz | 656,207,866 | 6,730 | # Mutual Information computation
### Hanchuan Peng (view profile)
06 May 2007 (Updated )
A self-contained package for computing mutual information, joint/conditional probability, entropy
condentropy(vec1,vec2)
```function h = condentropy(vec1,vec2)
%=========================================================
%
%This is a prog in the MutualInfo 0.9 package written by
% Hanchuan Peng.
%
%Disclaimer: The author of program is Hanchuan Peng
% at <penghanchuan@yahoo.com> and <phc@cbmv.jhu.edu>.
%
%The CopyRight is reserved by the author.
%
%Last modification: April/19/2002
%
%========================================================
%
% h = condentropy(vec1,vec2)
% calculate the entropy of a variable (vec1) or the conditional entropy of (vec1) given (vec2)
%
% demo:
% a=[1 2 1 2 1]';b=[2 1 2 1 1]';
% fprintf('mi(a,b)= %d \n',mi(a,b));
% fprintf('condentropy(a) - condentropy(a,b) = %d - %d = %d\n',...
% condentropy(a),condentropy(a,b),condentropy(a)-condentropy(a,b));
%
% By Hanchuan Peng, April/2002
%
if nargin<1,
disp('Usage: h = condentropy(vec1,<vec2>).');
h = -1;
elseif nargin<2,
[p1] = estpa(vec1);
h = estentropy(p1);
else
[p12, p1, p2] = estpab(vec1,vec2);
h = estcondentropy(p12,p2);
end;
``` | 373 | 1,237 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2015-14 | longest | en | 0.425949 |
https://www.iiserpune.ac.in/~mathphd/syllabi_2020_06_08/syllabus_algebra_2020.htm | 1,631,892,244,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780055684.76/warc/CC-MAIN-20210917151054-20210917181054-00382.warc.gz | 857,965,540 | 2,461 | # Algebra I
1. Groups
1. Examples, category of groups, Action of a group on a set.
2. Subgroups, isomorphism theorems.
3. Group actions: Permutation representations, action on itself by left multiplication, action on itself by conjugation.
2. Automorphisms of groups and statement of Sylow theorem
1. Automorphisms: Inner automorphisms, automorphism groups of some finite groups: dihedral, quaternions, cyclic.
2. Statement of Sylow’s theorem, Direct and Semidirect products.
3. Simple groups, composition series, Jordan-Hölder Series, An is simple.
3. Category Theory
1. Objects, morphisms, functors.
4. Free groups
1. Free groups: words, construction, and uniqueness.
2. Universal property, adjointness with forgetful functor.
3. Finitely generated and finitely presented groups.
5. Rings
1. Definitions (review): integral domains, euclidean domains, pid, ufd, fields.
2. Examples: Polynomials rings, Matrix rings, group rings.
3. Ideals and Quotient rings, prime and maximal ideals.
4. Chinese Reminder Theorem.
6. Modules
1. Definition, Z-modules, F[x]-modules.
2. Direct sums and free modules - construction and universal property.
7. Bilinear Forms
1. Symmetric forms. Orthogonal bases, ordered fields, Gram Schmidt, Sylvester’s theorem.
2. Eigen vectors of linear maps, Spectral theorem (Hermitian, Unitary, Symmetric case).
3. Structure theorem for alternating forms.
8. Tensors
1. Tensor products of modules. Examples.
2. Universal property, Adjointness with Hom.
3. Tensor product of homomorphisms, associativity, symmetry, tensor product of algebras.
9. Symmetric and Exterior algebras
1. Linear functions on tensor products of vector spaces, determinants.
2. Symmetric algebras, universal properties, alternating algebras, universal properties, symmetric and alternating tensors.
10. Modules over a PID and Canonical forms
1. Structure of finitely generated modules over a PID.
2. Canonical forms.
3. Rational Canonical Form.
4. Jordan Canoncial Form.
# Algebra II
1. Field theory
1. Characteristic of a field, extensions, degree of an extension, primitive elements for an extension.
2. Algebraic extensions, finitely generated field extensions, compositum of two fields.
3. Splitting fields and algebraic closure.
2. Separability
1. Separable and Inseparable extensions.
2. Fields of characteristic p > 0. Finite fields. Perfect fields.
3. Separable and inseparable degrees.
4. Primitive Element theorem.
3. Galois Theory
1. Galois extensions and Galois groups.
2. Linear independence of characters.
3. Fundamental theorem of Galois Theory.
4. Example: Cyclotomic extensions.
5. Frobenius automorphism and Galois groups of finite fields.
6. Normal basis theorem.
7. Infinite Galois extensions.
8. Krull topology on the Galois group and version of Fundamental theorem for infinite Galois extensions.
4. Modules and algebras
1. Exact sequences of modules, tensor products, flatness and absolute flatness.
2. Restriction and extension of scalars, tensor product of algebras
3. Projective modules and Injective modules.
4. Ext and Tor functors: Definitions and basic properties.
5. Chain complexes of ℤ[G] modules and Group cohomology
6. Hilbert's theorem 90
7. Correspondence between H2(G,A) and extensions
5. Commutative Algebra
1. Localization of rings and modules
1. Localization.
2. Universal property.
3. Exactness of localization functor.
2. Integral dependence
1. Integral dependence.
2. Going up lemma.
3. Chain conditions
1. Noetherian modules and rings.
2. Hilbert Basis theorem.
3. Artinian modules and rings.
4. Spec of a ring and basics of Zariski topology.
# References
• Dummit & Foote: Abstract Algebra.
• Hungerford: Algebra.
• Herstein: Abstract Algebra.
• Artin: Algebra.
• Lang: Algebra.
• Bourbaki: Algebra.
• Alperin & Bell: Groups and Representations.
• Atiyah & MacDonald: Introduction to Commutative Algebra.
• Bourbaki: Commutative Algebra.
• Weibel: Introduction to Homological Algebra.
• Jacobson: Basic Algebra I & II. | 969 | 3,962 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.765625 | 3 | CC-MAIN-2021-39 | latest | en | 0.751688 |
https://www.coursehero.com/file/6165366/tut-4-SE/ | 1,524,545,363,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125946564.73/warc/CC-MAIN-20180424041828-20180424061828-00129.warc.gz | 758,967,947 | 108,090 | {[ promptMessage ]}
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# tut 4 SE - 6 Given the rotational system shown below find...
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EET309: Mathematical Modeling Tutorial 4 TRANSLATIONAL MECHANICAL SYSTEM 1. Find the equation of motion for the system shown below. Then find the transfer function, G(s)=X 2 (s)/F(s) 2. Find the equation of motion for the system shown below. Then find the transfer function, G(s)=X 3 (s)/F(s) ROTATIONAL MECHANICAL SYSTEM WITH GEARS 3. Find the transfer function, G(s)= θ 4 (s)/T(s) for the rotational system shown below. 10kg f(t) 2N/m 5Ns/m 2Ns/m x 2 (t) M 1 =1kg f(t) k=2N/m x 3 (t) M 2 =1kg fv 4 =1Ns/m fv 3 =1Ns/m fv 2 =1Ns/m fv 1 =1Ns/m x 1 (t) x 2 (t) T(t) N 2 =100 25Nms/ rad θ 4 (t) θ 1 (t) θ 2 (t) θ 3 (t) 1Nm/rad N 1 =25 N 4 =100 N 3 =20
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EET309: Mathematical Modeling Tutorial 4 4. For the rotational system shown below, find the transfer function, G(s)= θ L (s)/T(s). 5. For the rotational system shown below, write the equations of motion from which the transfer function, G(s)= θ 1 (s)/T(s) can be found.
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Unformatted text preview: 6. Given the rotational system shown below, find the transfer function given by, G(s)= 6 (s)/ 1 (s). T(t) N 2 =100 0.04Nms/rad L (t) 1Nm/rad N 4 =10 N 3 =50 1kgm 2 1Nms/rad N 1 =10 T(t) N 1 1 (t) J a J 1 N 2 J 2 K D N 3 J 3 N 4 J 4 J L D L T(t) N 1 1 (t) J 1 , D N 2 K 1 N 4 J 5 D N 3 J 3 J 2 , D K 2 J 4 , D J 6 6 (t) D EET309: Mathematical Modeling Tutorial 4 RLC CIRCUITS 7. Write the mesh and nodal equations for the network below: 8. Find the transfer function, G(s)=V o (s)/ V i (s), for each of the networks shown below. Solve using mesh analysis. a. b. 1 1 2 4 2H 3H 1/5F v(t) v o (t) 2H 1/2F 1 3H v i (t) v o (t) 1H 1 1F 1H 1H 1F v i (t) v o (t)...
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https://www.alphabetworksheetsfree.com/classifying-rational-numbers-worksheet-6th-grade-answer-key/ | 1,695,863,872,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510334.9/warc/CC-MAIN-20230927235044-20230928025044-00669.warc.gz | 688,590,220 | 12,848 | Classifying Rational Numbers Worksheet 6th Grade Answer Key – There’s plenty of evidence that shows how number worksheets can assist children develop their math skills. This article will discuss how important it is to use number worksheets for kids. We will examine the advantages and the various kinds of number worksheets.
Also, we will look at two case studies that demonstrate how number worksheets have helped children develop their math abilities in just a short period.
## Purpose of Using a Numbers Worksheet and How It Helps Educators
The worksheet on numbers is designed to help students master the basic math skills that they have learned in class. Students can use it for individual exercises or for group activities. Students may also use it to determine their understanding of the matter.
A numbers worksheet helps educators give a quick and simple way to assess the students’ knowledge of specific math skills. Additionally, educators can make use of these worksheets to verify that students are on track in their academic goals and make any necessary adjustments.
## 5 Effective Ways You Can Use a Numbers Worksheet to Teach Children Math
A worksheet for numbers is a piece of paper that includes columns and rows designed to teach math concepts to children. These worksheets are generally utilized in elementary schools. This post will offer five methods to make use of the numbers worksheet to teach children math.
The first option is asking the child to copy the numbers from the top row to the column. The second way is by color-coding each number that is the same color of its corresponding column, which is located on the bottom right of the page. The third way is by counting loudly as they complete each row independently or with help from an adult. Finally, the fourth way is by using the number sheet and filling each number that is in line with its location on this line, starting at zero and working their way up until they have reached nine.
## Final Thoughts on the Numbers Worksheet
We hope that this post has helped you comprehend the numbers worksheet and how you can use it in your company.
Classifying Rational Numbers Worksheet 6th Grade Answer Key Uploaded by admin on Saturday, April 30th, 2022. We have 3 great pictures of Classifying Rational Numbers Worksheet 6th Grade Answer Key. Find AlphabetWorksheetsFree.com on category Numbers. | 454 | 2,385 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2023-40 | latest | en | 0.952004 |
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# Oxidation Number Of Phosphorus
Oxidation Number Of Phosphorus. So the oxidation numbers you must add to zero in a neutral compound. The oxidation number of oxygen is 2 −. Rules for assigning the oxidation number to elements are as follows: The oxidation number of phosphorus in ba(h 2po 2) 2 is:
Share it on facebook twitter email. Alright, let's go ahead and get started assigning some of the oxidation numbers that we do know. When forming compound ions, its oxidation number.
## One phosphorus atom 1 ×on p + 4 ×on oxygen four oxygen atoms = −3.
One phosphorus atom 1 ×on p + 4 ×on oxygen four oxygen atoms = −3. Alright, let's go ahead and get started assigning some of the oxidation numbers that we do know. The phosphorus atom loses a total of 5 electrons, one to each chlorine atom, so its oxidation state will be +5.
## What Is The Oxidation Number Of Phosphorus In H 3 Po 3?
As per the problem, let the oxidation number of. Oxidation number of h is +1 in most of the cases. Rules for assigning the oxidation number to elements are as follows: When forming compound ions, its oxidation number.
### So The Oxidation Numbers You Must Add To Zero In A Neutral Compound.
The oxidation state or oxidation number is defined as the ability of an atom molecule or compound to attain a stable configuration by the loss or gain of electrons.
### Kesimpulan dari Oxidation Number Of Phosphorus.
The oxidation number of phosphorus in ba(h$_2po_2 )_2$ is. See table 1 in appendix a for common oxidation numbers.… The oxidation state or oxidation number is defined as the ability of an atom molecule or compound to attain a stable configuration by the loss or gain of electrons.
See also Which Element's Atoms Have The Greatest Average Number Of Neutrons | 414 | 1,777 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2023-14 | latest | en | 0.82069 |
http://primes.utm.edu/~caldwell/curios/page.php?rank=333 | 1,569,135,236,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514575168.82/warc/CC-MAIN-20190922053242-20190922075242-00421.warc.gz | 152,520,292 | 3,288 | 293 (another Prime Pages' Curiosity)
Curios: Curios Search: Participate: GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits) The number of ways to make change for a dollar using the penny, nickel, dime, quarter, half-dollar, and dollar. 202^293 begins with the digits 293 and 293^202 begins with the digits 202. [Hartley] The largest possible prime bowling score. [Patterson] The first number after 3 for which ((10^2n)+1)/101 is a prime. The sum of the first three tetradic primes: 11 + 101 + 181 = 293. [Post] In the Christmas classic It's A Wonderful Life, George's guardian angel (Clarence Oddbody) says he will be 293 next May. The number of non-prime numbered days in a year, if the days of the year are numbered 1 to 365. [Green] The largest prime that can be recognized on the Prime Number Maze by WorksheetWorks.com. 3^35 + 293 is a multiple of one million and 293 is the only prime p such that 3^n ± p is a multiple of one million for n < 100. [Ewing] The smallest term in the Lucas-Lehmer sequence that has yet to be factored contains 293 digits. (There is one curio for this number that has not yet been approved by an editor.) To link to this page use /curios/page.php?number_id=63 Prime Curios! © 2000-2019 (all rights reserved) privacy statement (This page was generated in 0.0111 seconds.) | 370 | 1,348 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2019-39 | longest | en | 0.879543 |
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# Calories (thermochemical) to gallons (US) of LPG formula
Use the formula below to convert any value from calories (thermochemical) to gallons (US) of LPG:
gallons (US) of LPG = calories (thermochemical) Γ 4.1525305270183E-8
To from calories (thermochemical) to gallon (US) of LPG, you just need to multiply the value in calories (thermochemical) by 4.1525305270183E-8. (It is called the conversion factor)
## Using the formula (some examples):
Convert full calorie (thermochemical) to gallons (US) of LPG:
a calorie (thermochemical) = 1 Γ 4.1525305270183E-8 = 4.1525305270183E-8 gallons (US) of LPG.
Convert two calorie (thermochemical) to gallons (US) of LPG:
two calorie (thermochemical) = 2 Γ 4.1525305270183E-8 = 8.3050610540365E-8 gallons (US) of LPG.
Convert five calories (thermochemical) to gallons (US) of LPG:
5 calories (thermochemical) = 5 Γ 4.1525305270183E-8 = 2.0762652635091E-7 gallons (US) of LPG.
## More Examples:
Convert ten calories (thermochemical) to gallons (US) of LPG: 10 calories (thermochemical) = 10 Γ 4.1525305270183E-8 = 4.1525305270183E-7 gallons (US) of LPG.
Convert twenty calories (thermochemical) to gallons (US) of LPG: 20 calories (thermochemical) = 20 Γ 4.1525305270183E-8 = 8.3050610540365E-7 gallons (US) of LPG.
Convert fifty calories (thermochemical) to gallons (US) of LPG: 50 calories (thermochemical) = 50 Γ 4.1525305270183E-8 = 2.0762652635091E-6 gallons (US) of LPG.
Convert a hundred calories (thermochemical) to gallons (US) of LPG: 100 calories (thermochemical) = 100 Γ 4.1525305270183E-8 = 4.1525305270183E-6 gallons (US) of LPG.
Convert a thousand calories (thermochemical) to gallons (US) of LPG: 1000 calories (thermochemical) = 1000 Γ 4.1525305270183E-8 = 4.1525305270183E-5 gallons (US) of LPG.
### All In One Unit Converter
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https://www.geeksforgeeks.org/program-to-implement-flames-game/?ref=leftbar-rightbar | 1,591,398,856,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590348504341.78/warc/CC-MAIN-20200605205507-20200605235507-00377.warc.gz | 756,462,302 | 29,940 | # Program to implement FLAMES game
FLAMES is a popular game named after the acronym: Friends, Lovers, Affectionate, Marriage, Enemies, Sibling. This game does not accurately predict whether or not an individual is right for you, but it can be fun to play this with your friends.
There are two steps in this game:
Get the count:
• Take the two names.
• Remove the common characters with their respective common occurrences.
• Get the count of the characters that are left .
Get the result :
• Take FLAMES letters as [“F”, “L”, “A”, “M”, “E”, “S”]
• Start removing letter using the count we got.
• The letter which last the process is the result.
Example :
```Input: Player1 = AJAY, Player2 = PRIYA
Output: Friends
```
Explanation: In above given two names A and Y are common letters which are occurring one time(common count) in both names so we are removing these letters from both names. Now count the total letters that are left here it is 5. Now start removing letters one by one from FLAMES using the count we got and the letter which lasts the process is the result.
Counting is done in an anti-clockwise circular fashion.
FLAMES
counting starts from F, E is at 5th count so we remove E and start counting again but this time start from S.
FLAMS
M is at 5th count so we remove M and counting starts from S.
FLAS
S is at 5th count so we remove S and counting start from F.
FLA
L is at 5th count so we remove L and counting starts from A.
FA
A is at 5th count so we remove A. now we have only one letter is remaining so this is the final answer.
F
So, the relationship is F i.e. Friends .
## Recommended: Please try your approach on {IDE} first, before moving on to the solution.
Approach: Three counters are required, two for the names initialized at zero, and one for flames initialized at 5. Three strings are used, two for names and one, where FLAMES is already stored. Here the program first calculated the number of letters in the first name and then calculated the number of letters in second name Then after storing them using strlen into integer variables, one for loop is run for each name to count the common letters. Then by using nested if-else the letters are cancelled from each name, which is represented by a string. The for loop is again repeated to continue this process. Accordingly, the counter rotates and each letter in FLAMES is pointed at. As letters get canceled the loop is run again. Then for each letter, an If else statement is used, Print the result corresponding to the last letter.
Below is the implementation :
## C++
`// C++ program to implement FLAMES game ` `#include ` `using` `namespace` `std; ` ` ` `// Function to find out the flames result ` `void` `flame(``char``* a, ``char``* b) ` `{ ` ` ``int` `i, j, k, l = 1, n, m, sc = 0, tc, rc = 0, fc = 5; ` ` ``char` `q[25], w[25], c; ` ` ``char` `f[] = ``"flames"``; ` ` ` ` ``strcpy``(q, a); ` ` ``strcpy``(w, b); ` ` ``n = ``strlen``(a); ` ` ``m = ``strlen``(b); ` ` ``tc = n + m; ` ` ` ` ``for` `(i = 0; i < n; i++) ` ` ``{ ` ` ``c = a[i]; ` ` ``for` `(j = 0; j < m; j++) ` ` ``{ ` ` ``if` `(c == b[j]) ` ` ``{ ` ` ``a[i] = -1; ` ` ``b[j] = -1; ` ` ``sc = sc + 2; ` ` ``break``; ` ` ``} ` ` ``} ` ` ``} ` ` ` ` ``rc = tc - sc; ` ` ` ` ``for` `(i = 0;; i++) ` ` ``{ ` ` ``if` `(l == (rc)) ` ` ``{ ` ` ``for` `(k = i; f[k] != ``'\0'``; k++) ` ` ``{ ` ` ``f[k] = f[k + 1]; ` ` ``} ` ` ``f[k + 1] = ``'\0'``; ` ` ``fc = fc - 1; ` ` ``i = i - 1; ` ` ``l = 0; ` ` ``} ` ` ``if` `(i == fc) ` ` ``{ ` ` ``i = -1; ` ` ``} ` ` ``if` `(fc == 0) ` ` ``{ ` ` ``break``; ` ` ``} ` ` ``l++; ` ` ``} ` ` ` ` ``// Print the results ` ` ``if` `(f[0] == ``'e'``) ` ` ``cout << q <<``" is ENEMY to "` `<< w; ` ` ``else` `if` `(f[0] == ``'f'``) ` ` ``cout << q <<``" is FRIEND to "``<
## C
`// C program to implement FLAMES game ` ` ` `#include ` `#include ` ` ` `// Function to find out the flames result ` `void` `flame(``char``* a, ``char``* b) ` `{ ` ` ``int` `i, j, k, l = 1, n, m, sc = 0, tc, rc = 0, fc = 5; ` ` ``char` `q[25], w[25], c; ` ` ``char` `f[] = ``"flames"``; ` ` ` ` ``strcpy``(q, a); ` ` ``strcpy``(w, b); ` ` ``n = ``strlen``(a); ` ` ``m = ``strlen``(b); ` ` ``tc = n + m; ` ` ` ` ``for` `(i = 0; i < n; i++) { ` ` ``c = a[i]; ` ` ``for` `(j = 0; j < m; j++) { ` ` ``if` `(c == b[j]) { ` ` ``a[i] = -1; ` ` ``b[j] = -1; ` ` ``sc = sc + 2; ` ` ``break``; ` ` ``} ` ` ``} ` ` ``} ` ` ` ` ``rc = tc - sc; ` ` ` ` ``for` `(i = 0;; i++) { ` ` ``if` `(l == (rc)) { ` ` ``for` `(k = i; f[k] != ``'\0'``; k++) { ` ` ``f[k] = f[k + 1]; ` ` ``} ` ` ``f[k + 1] = ``'\0'``; ` ` ``fc = fc - 1; ` ` ``i = i - 1; ` ` ``l = 0; ` ` ``} ` ` ``if` `(i == fc) { ` ` ``i = -1; ` ` ``} ` ` ``if` `(fc == 0) { ` ` ``break``; ` ` ``} ` ` ``l++; ` ` ``} ` ` ` ` ``// Print the results ` ` ``if` `(f[0] == ``'e'``) ` ` ``printf``(``"%s is ENEMY to %s "``, q, w); ` ` ``else` `if` `(f[0] == ``'f'``) ` ` ``printf``(``"%s is FRIEND to %s "``, q, w); ` ` ``else` `if` `(f[0] == ``'m'``) ` ` ``printf``(``"%s is going to MARRY %s"``, q, w); ` ` ``else` `if` `(f[0] == ``'l'``) ` ` ``printf``(``"%s is in LOVE with %s "``, q, w); ` ` ``else` `if` `(f[0] == ``'a'``) ` ` ``printf``(``"%s has more AFFECTION on %s "``, q, w); ` ` ``else` ` ``printf``(``"%s and %s are SISTERS/BROTHERS "``, q, w); ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` ` ``char` `a[] = ``"AJAY"``; ` ` ``char` `b[] = ``"PRIYA"``; ` ` ` ` ``flame(a, b); ` `} `
## Python3
`# Python3 program to implement FLAMES game ` ` ` `# Function to find out the flames result ` `def` `flame(a, b): ` ` ``l, sc ``=` `1``, ``0` ` ``rc, fc ``=` `0``, ``5` ` ``f ``=` `"flames"` ` ``f ``=` `[i ``for` `i ``in` `f] ` ` ``q ``=` `"".join(a) ` ` ``w ``=` `"".join(b) ` ` ` ` ``# print(q, w) ` ` ``n ``=` `len``(a) ` ` ``m ``=` `len``(b) ` ` ``tc ``=` `n ``+` `m ` ` ``for` `i ``in` `range``(n): ` ` ``c ``=` `a[i] ` ` ``for` `j ``in` `range``(m): ` ` ``if` `(c ``=``=` `b[j]): ` ` ``a[i] ``=` `-``1` ` ``b[j] ``=` `-``1` ` ``sc ``=` `sc ``+` `2` ` ``break` ` ` ` ``rc ``=` `tc ``-` `sc ` ` ``i ``=` `0` ` ` ` ``while` `(i): ` ` ``if` `(l ``=``=` `(rc)): ` ` ``for` `k ``in` `range``(i,``len``(f)): ` ` ``f[k] ``=` `f[k ``+` `1``] ` ` ``f[k ``+` `1``] ``=` `'\0'` ` ``fc ``=` `fc ``-` `1` ` ``i ``=` `i ``-` `1` ` ``l ``=` `0` ` ``if` `(i ``=``=` `fc): ` ` ``i ``=` `-``1` ` ``if` `(fc ``=``=` `0``): ` ` ``break` ` ``l ``+``=` `1` ` ``i ``+``=` `1` ` ` ` ``# Print the results ` ` ``if` `(f[``0``] ``=``=` `'e'``): ` ` ``print``(q, ``"is ENEMY to"``, w) ` ` ``elif` `(f[``0``] ``=``=` `'f'``): ` ` ``print``(q, ``"is FRIEND to"``, w) ` ` ``elif` `(f[``0``] ``=``=` `'m'``): ` ` ``print``(q, ``"is going to MARRY"``, w) ` ` ``elif` `(f[``0``] ``=``=` `'l'``): ` ` ``print``(q, ``"is in LOVE with"``, w) ` ` ``elif` `(f[``0``] ``=``=` `'a'``): ` ` ``print``(q, ``"has more AFFECTION on"``, w) ` ` ``else``: ` ` ``print``(q, ``"and"``, w, ``"are SISTERS/BROTHERS "``) ` ` ` `# Driver code ` `a ``=` `"AJAY"` `b ``=` `"PRIYA"` `a ``=` `[i ``for` `i ``in` `a] ` `b ``=` `[j ``for` `j ``in` `b] ` ` ` `# print(a,b) ` `flame(a, b) ` ` ` `# This code is contributed by Mohit Kumar `
Output:
```AJAY is FRIEND to PRIYA
```
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Please write to us at contribute@geeksforgeeks.org to report any issue with the above content. | 3,278 | 9,016 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2020-24 | latest | en | 0.935194 |
https://socratic.org/questions/what-would-be-the-total-amount-after-adding-8-interest-for-3-months-of-6-000-00 | 1,624,527,500,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488552937.93/warc/CC-MAIN-20210624075940-20210624105940-00085.warc.gz | 460,312,033 | 6,212 | Total = $6,120 #### Explanation: Use the formula $P r t = i \text{ }$where $P = \text{ principle} \left(6000\right)$$r = \text{ rate}$- as a decimal $\left(0.08\right)$, $t = \text{ time in years } \left(\frac{3}{12} \mathmr{and} \frac{1}{4}\right)$$i = \text{ interest earned }$$P r t = i \text{ } 6000 \cdot 0.08 \cdot 0.25 = i$i=$120
For the total, add on the $6,000 Jul 28, 2017 Total Amount = $6000+$120 =$6,120
#### Explanation:
You can work with the % as being over $100$
$S I = \frac{P R T}{100}$
Note that the time, $\left(T\right)$, is given as years.
Dividing months by $12$ indicates years: $3$ months =$\frac{3}{12}$ years
$S I = \frac{6000 \times 8 \times 3}{\text{ } 100 \times 12}$
Easy cancelling gives the following:
$S I = \frac{{\cancel{60}}^{5} \cancel{00} \times 8 \times 3}{\cancel{100} \times \cancel{12}}$
SI = $120 For the total amount we have to include the original $6,000 as well.
Total Amount = $6000+$120 = \$6,120 | 350 | 955 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 24, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.59375 | 5 | CC-MAIN-2021-25 | latest | en | 0.781004 |
http://www.slideserve.com/kylee/newton-s-third-law-of-motion | 1,505,856,560,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818686034.31/warc/CC-MAIN-20170919202211-20170919222211-00654.warc.gz | 576,057,441 | 11,529 | 1 / 10
# Newton’s Third Law of Motion: - PowerPoint PPT Presentation
“For every action there is an equal and opposite reaction”. Newton’s Third Law of Motion:. The correct way to say it: . For every action force there is an equal and opposite reaction force . Forces always occur in PAIRS. An action force…. …and a r eaction force. Some examples :.
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## PowerPoint Slideshow about ' Newton’s Third Law of Motion:' - kylee
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Presentation Transcript
### Newton’s Third Law of Motion:
The correctway to say it:
For everyactionforcethere is an equal and oppositereactionforce.
Forces always occur in PAIRS reaction”
An action force…
…and a reaction force
Some examples reaction”:
See the pattern??? reaction”
A pushes on B, so B pushes on A
OR
A pulls on B, so B pulls on A
Question: reaction”
If force pairs on two objects are always equal and opposite, how is it that sometimes only one of the objects moves????
For example: reaction”
Shooting an arrow?
Throwing a baseball?
Hitting a hockey puck?
Wait…… reaction”
What??
The pair of forces acting on the objects has to be the same, but the REACTION of the objects to the forces does NOT have to be the same!
Example: a canon firing reaction”
According to Newton’s 3rd Law of Motion, both the canon ball and the cannon experience the SAME FORCE from the gunpowder.
So why does the cannon ball move so fast while the cannon only moves back a little?
Explanation 1 - The math: reaction”
The Cannon:
The Cannonball:
BIG mass:
SMALL mass
So according to Newton’s 2nd Law of Motion:
F
M
F
M
=
A
=
A
= SMALL acceleration!
= LARGE acceleration!
Explanation 2 – Inertia: reaction”
The cannon has much more INERTIA than the cannon ball.
Therefore the same force can move the cannon ball much more easily than it can move the cannon! | 567 | 2,373 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.84375 | 4 | CC-MAIN-2017-39 | latest | en | 0.863478 |
https://stats.stackexchange.com/questions/linked/83030?sort=unanswered | 1,660,447,399,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571993.68/warc/CC-MAIN-20220814022847-20220814052847-00068.warc.gz | 477,864,759 | 59,478 | 1 vote
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• 811 | 1,073 | 4,195 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.265625 | 3 | CC-MAIN-2022-33 | latest | en | 0.881782 |
https://enenacan.web.app/371.html | 1,713,226,836,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817036.4/warc/CC-MAIN-20240416000407-20240416030407-00405.warc.gz | 208,834,921 | 6,637 | # Integral curve differential geometry book
What is the difference between an integral curve and the. Free differential geometry books download ebooks online. Definition of a curve vectorvalued functions depending on numerical arguments the regular curve and its representations straight line tangent to a curve osculating plane of a curve the arc length of a curve the curvature and torsion of a curve osculating circle of a plane curve singular points of plane curves peanos curve. How is chegg study better than a printed differential geometry of curves and surfaces 1st edition student solution manual from the bookstore. If we are fortunate, we may encounter curvature and such things as the serretfrenet formulas. This book is the second edition of anders kocks classical text, many notes have been included commenting on new developments. An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hypersurfaces in euclidean space. In the first chapters of this book we study plane differential geometry. This book is not a usual textbook, but a very well written introduction to differential geometry, and the colors really help the reader in understanding the figures and navigating through the text.
Our interactive player makes it easy to find solutions to differential geometry of curves and surfaces 1st edition problems youre working on just go to the chapter for your book. In mathematics, an integral curve is a parametric curve that represents a specific solution to an ordinary differential equation or system of equations. I wrote them to assure that the terminology and notation in my lecture agrees with that text. At the same time the topic has become closely allied with developments in topology. Latest higher engineering mathematics bs grewal pdf. All page references in these notes are to the do carmo text. A concise guide presents traditional material in this field along with important ideas of riemannian geometry. It includes most of the required material from multivariable calculus, linear algebra, and basic analysis. R3 h h diff i bl a i suc t at x t, y t, z t are differentiable a function is differentiableif it has at allpoints. Suitable for advanced undergraduates and graduate students of mathematics, this texts prerequisites include an undergraduate course in linear algebra. The main focus is on manifolds in euclidean space and.
An excellent reference for the classical treatment of di. It contains many worked examples that illustrate the theoretical material and serve as models for solving problems. The study of curves and surfaces forms an important part of classical differential geometry. Curves and surfaces are the two foundational structures for differential geometry. Moreover, they are on the whole pretty informal and meant as a companion but not a substitute for a careful and detailed textbook treatment of the materialfor the latter, the reader should consult the references described in section 16. In all of them one starts with points, lines, and circles. The tangent space at a point, x, is the totality of all contravariant vectors, or differentials, associated with that point. Here, in this article we will provide you the free pdf of higher engineering mathematics. The first chapters of the book are suitable for a onesemester course on manifolds. Consider a curve c of class of at least 2 with the arc length parametrization fs. Points q and r are equidistant from p along the curve. The aim of this textbook is to give an introduction to di erential geometry. Sets, functions, graphs and limits, differential calculus, integral calculus, sequences, summations and products and applications of calculus.
Differential geometry of curves and surfaces springerlink. The name of this course is di erential geometry of curves and surfaces. The direction of the tangent at a point of a curve specified by 1 coincides with. Pdf differential geometry of curves and surfaces download. Mar 15, 2020 this bs grewal book covers each topic with detailed explanation and solutions to understand topics. Notes on differential geometry part geometry of curves x.
Jul 01, 2016 in oth er words, the differential, necessary for the existence o f the fractional integral, eq. Jun 10, 2018 in this video, i introduce differential geometry by talking about curves. Differential geometry of curves and surfaces kristopher. Differential geometrynormal line and principal unit.
Hence, a new fractional differential, r eal and valid fo r positive and negative. This course can be taken by bachelor students with a good knowledge of calculus, and some knowledge of di. Differential geometry by erwin kreyszig, paperback. Piskunov this text is designed as a course of mathematics for higher technical schools. Jul 01, 2015 this book offers an introduction to differential geometry for the nonspecialist. Definition of curves, examples, reparametrizations, length, cauchys integral formula, curves of constant width. This bs grewal book covers each topic with detailed explanation and solutions to understand topics. For historical notes compare the book of montiel and ros. Since fsfs1, we can differentiate this to obtain fsfs0 therefore, if fs is not the zero vector, then it is a vector that is orthogonal to the unit tangent vector. This book emphasizes the fundamental concepts from calculus and analytic geometry and the application of these concepts to selected areas of science and engineering. Pde 9 10 intro to integral curves dissected from book youtube. Differential geometrynormal line and principal unit normal.
Without a doubt, the most important such structure is that of a riemannian or more generally semiriemannian metric. The subject is presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the geometric significance and theoretical and. Elementary differential geometry focuses on the elementary account of the geometry of curves and surfaces. Our intuitive notion of a curve contains so many different features that it is necessary to introduce a number of concepts in order to arrive at an exact definition that is neither too broad nor too. In oth er words, the differential, necessary for the existence o f the fractional integral, eq. Mcleod, geometry and interpolation of curves and surfaces, cambridge university press.
Applications to geometry expansion in series definite integrals derivatives and differentials, a course in mathematical analysis a course in mathematical analysis, volume 1 by edouard goursat and a great selection of related books, art and collectibles available now at. These notes are still very much under construction. The basic object is a smooth manifold, to which some extra. Some matrix lie groups, manifolds and lie groups, the lorentz groups, vector fields, integral curves, flows, partitions of unity, orientability, covering maps, the logeuclidean framework, spherical harmonics, statistics on riemannian manifolds, distributions and the frobenius theorem, the. In this video, i introduce differential geometry by talking about curves. Curve, frenet frame, curvature, torsion, hypersurface, fundamental forms, principal curvature, gaussian curvature, minkowski curvature, manifold, tensor eld, connection, geodesic curve summary. Some matrix lie groups, manifolds and lie groups, the lorentz groups, vector fields, integral curves, flows, partitions of unity, orientability, covering maps, the logeuclidean framework, spherical harmonics, statistics on riemannian manifolds, distributions and the.
Parameterized curves definition a parameti dterized diff ti bldifferentiable curve is a differentiable map i r3 of an interval i a ba,b of the real line r into r3 r b. The goal of this article is to present the relation between some differential formulas, like the gauss integral for a link, or the integral of the gaussian curvature on a surface, and topological invariants like the linking number or the euler characteristic. Pde 9 10 intro to integral curves dissected from book. It yields a relation between the integral of the gaussian curvature over a given oriented closed surface s and the topology of s in terms of its euler number. There is also a section that derives the exterior calculus version of maxwells equations. Differential geometry of curves and surfaces undergraduate. I know the definition of the integral curve and the solution of an equation. Experimental notes on elementary differential geometry. Local frames and curvature to proceed further, we need to more precisely characterize the local geometry of a curve in the neighborhood of some point. From the viewpoint of differential geometry, the line integral of a vector field along a curve is the integral of the corresponding 1form under the musical isomorphism which takes the vector field to the corresponding covector field over the curve considered as an immersed 1manifold. If the differential equation is represented as a vector field or slope field, then the corresponding integral curves are tangent to the field at each point integral curves are known by various other names, depending on the nature and. Differential geometry began as the study of curves and surfaces using the methods of calculus. This outstanding textbook by a distinguished mathematical scholar introduces the differential geometry of curves and surfaces in threedimensional euclidean space. That is, the distance a particle travelsthe arclength of its trajectoryis the integral of its speed.
General definition of curvature using polygonal approximations foxmilnors theorem. Classicaldifferentialgeometry curvesandsurfacesineuclideanspace. We start with an investigation of the various definitions of a curve. If the differential equation is represented as a vector field or slope field, then the corresponding integral curves are tangent to the field at each point. Euclid himself first defined what are known as straightedge and compass constructions and then additional axioms. On page 159 of a comprehensive introduction to differential geometry vol. Hence, a new fractional differential, r eal and valid fo.
Latest higher engineering mathematics bs grewal pdf download. After taking this course they should be well prepared for a follow up course on modern riemannian geometry. By means of an affine connection, the tangent spaces at any two points on a curve are related by an affine. It is important to note that when you change the direction of the parametrization of the curve, the unit tangent vector also changes directions, but the principal normal unit vector does not. The treatment begins with a chapter on curves, followed by explorations of regular surfaces, the geometry of the gauss map, the intrinsic geometry of surfaces, and global differential geometry. Then the gaussbonnet theorem, the major topic of this book, is discussed at great length.
An intuitive approach and a minimum of prerequisites make it a valuable companion for students of mathematics and physics. Tangent spaces play a key role in differential geometry. The fundamental concept underlying the geometry of curves is the arclength of a parametrized curve. The name geometrycomes from the greek geo, earth, and metria, measure. I, there exists a regular parameterized curve i r3 such that s is the arc length. Manifolds and differential geometry jeffrey lee, jeffrey. The book first offers information on calculus on euclidean space and frame fields. The subject is presented in its simplest, most essential form, but with many explanatory details, figures and examples, and in a manner that conveys the geometric significance and theoretical and practical importance of the. Multivariable calculus and differential geometry gerard. Then the book concludes that y axis is the integral curve of the differential equation, but not the graph of the solution. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. Topics include structural equations, connection forms, frame fields, covariant derivatives, frenet formulas, curves, mappings, tangent vectors, and. Basics of euclidean geometry, cauchyschwarz inequality. Sep 10, 2014 pde 9 10 intro to integral curves dissected from book.
The reader is introduced to curves, then to surfaces, and finally to more complex topics. This book can be used as nonmath majors colleges of higher mathematics curriculum materials. Isometries of euclidean space, formulas for curvature of smooth regular curves. Our first knowledge of differential geometry usually comes from the study of the curves and surfaces in i\.
The more descriptive guide by hilbert and cohnvossen 1is also highly recommended. Geometry is the part of mathematics that studies the shape of objects. Here we learn about line and surface integrals, divergence and curl, and the various forms of stokes theorem. The line passing through this vector and fs is the principal normal line of this curve at. By means of an affine connection, the tangent spaces at any two points on a curve are related by an affine transformation, which will, in general. Singular points of a curve, the envelope of a family of curves, lyapunovs theory of stability. This book offers an introduction to differential geometry for the nonspecialist. It is based on the lectures given by the author at e otv os. This book covers facts and methods for the reconstruction of a function in a real affine or projective space from data of integrals, particularly over lines, planes, and spheres. Interested candidates can download the pdf of this book from the link below.
Differential geometry by erwin kreyszig, paperback barnes. The rule of thumb is that you shouldnt start integrating until you have the integral in terms of a single parameter including correctly determining the limits in terms of that parameter. The theorem is a most beautiful and deep result in differential geometry. Mar 12, 2020 this outstanding textbook by a distinguished mathematical scholar introduces the differential geometry of curves and surfaces in threedimensional euclidean space.
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### AppGameKit Classic Chat / [SOLVED] Object Bone look at rotation help
Message
Posted: 12th May 2023 04:22 Edited at: 12th May 2023 04:24
So I need when my player comes up to other objects for there heads to point to them.
I have this and it works but there heads turn all the way around. So I need to figure out a way to limit there head bone rotation to 90 deg.
Here is the code I am fighting with and I used a lot of different ways and nothing works.
Right now i figured to have the bone look at the player with getting the bone ang z but well, that is pointless.
The author of this post has marked a post as an answer.
Posted: 12th May 2023 14:14 Edited at: 12th May 2023 14:18
I'd recommend using the angle between your player object as a whole and the item to determine if the head should be pointed at it or not. This can be done using the dot product of two heading vectors on the XZ plane, one for the player's forward direction and one for a dummy object that is set to always look at the item.
Posted: 12th May 2023 15:53 Edited at: 12th May 2023 16:00
And here's a method that doesn't use a dummy object, as I know some people don't like using them. Not sure which method would be more performant, though.
Posted: 12th May 2023 21:48
hendron thank you, I will check it out today and let you know. This is such a big help.
Posted: 13th May 2023 03:20
Ok this kind of works but only when I am looking at the other object, If I am behind him and still looking at him his head still turn's all the way around as it is not set to pos but angles.
Posted: 13th May 2023 13:06
Not sure I follow. Can you post a video of what's happening? The example I posted is meant to show how you can determine if an object is within 90 degrees of the player avatar's forward direction (as a whole, not the head bone). The logic being that you would only set the head bone to look at the object if it falls into this range. If it falls outside, set the head bone back to its normal orientation.
Posted: 13th May 2023 13:41
Ok picture one shows a normal head rotation when I am in front of him.
picture 2 shows head turned into body when I'm behind him or even beside him.
No matter how far away I am I still get a in range=1 when I am turned to him.
code I'm using and thanks for looking.
Posted: 13th May 2023 14:00 Edited at: 13th May 2023 14:05
This post has been marked by the post author as the answer.
Ah, so you're talking about the NPC looking at the Player? In that case, you need to run the code from the perspective of the NPC. I've turned the code into a function that should be able to be used on any character.
you can call it like this:
Let me know if it works. I haven't tested it myself because I'd need to setup a character for it to do so.
updated some of the variable names to make more sense in the context of the function
Posted: 13th May 2023 14:12
GameControls.agc:614: error: Cannot convert type "Integer" to "Type"
It is trying to convert my player integer into a type and does not like this.
lookTarget as tVector3
lookTarget.x = bonex#
lookTarget.y = boney#
lookTarget.z = bonez#
Posted: 13th May 2023 14:15
use lookTarget instead of Player (I'm assuming from your previous code snippet that bonex#, boney# and bonez# are the target coordinates you want the NPC to look at?)
Posted: 13th May 2023 14:18
Oh lol, my mistake, it works, it works good, But his head snaps back to to the rest head pos real fast like he was hit by something lol.
It looks funny. But it works.
One problem at a time I always say.
Posted: 13th May 2023 14:23
Cool, glad it worked. Look into object tweens to fix the head snapping.
Posted: 13th May 2023 14:24
Ok sure thing.
Thank you very much for the help
Posted: 13th May 2023 14:25 Edited at: 13th May 2023 14:26
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# Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. [1]
## Abel–Ruffini theorem
In algebra, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no algebraic solution—that is, solution in radicals—to the general polynomial equations of degree five or higher with arbitrary coefficients.
## Absolute value
In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.
## Abstract algebra
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.
## Algebra
Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.
## Algebra over a field
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.
## Algebraic element
In mathematics, if is a field extension of, then an element of is called an algebraic element over, or just algebraic over, if there exists some non-zero polynomial with coefficients in such that.
## Algebraic equation
In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers.
## Algebraic expression
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).
## Algebraic fraction
In algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraic expressions.
## Algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
## Algebraic variety
Algebraic varieties are the central objects of study in algebraic geometry.
## Algorithm
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
## Antiderivative
In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.
## Argument of a function
In mathematics, an argument of a function is a specific input in the function, also known as an independent variable.
## Associative algebra
In mathematics, an associative algebra is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field.
## Associative property
In mathematics, the associative property is a property of some binary operations.
## Asymptote
In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.
## Évariste Galois
Évariste Galois (25 October 1811 – 31 May 1832) was a French mathematician.
## Binomial (polynomial)
In algebra, a binomial is a polynomial that is the sum of two terms, each of which is a monomial.
## Calculus
Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
## Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
## Characteristic polynomial
In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots.
## Chemistry
Chemistry is the scientific discipline involved with compounds composed of atoms, i.e. elements, and molecules, i.e. combinations of atoms: their composition, structure, properties, behavior and the changes they undergo during a reaction with other compounds.
## Chromatic polynomial
The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics.
## Coefficient
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but may be any expression.
## Commutative algebra
Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.
## Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
## Commutative ring
In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.
## Compact space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
## Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
## Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
## Computer
A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.
## Computer algebra system
A computer algebra system (CAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists.
## Constant (mathematics)
In mathematics, the adjective constant means non-varying.
## Constant function
In mathematics, a constant function is a function whose (output) value is the same for every input value.
## Constant term
In mathematics, a constant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables.
## Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
## Cubic function
In algebra, a cubic function is a function of the form in which is nonzero.
## Degree of a polynomial
The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.
## Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
## Differentiable function
In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.
## Diophantine equation
In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values).
## Discrete Fourier transform
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.
## Distributive property
In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from boolean algebra and elementary algebra.
## Domain of a function
In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.
## Economics
Economics is the social science that studies the production, distribution, and consumption of goods and services.
## Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
## Eisenstein's criterion
In mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers—that is, for it to be unfactorable into the product of non-constant polynomials with rational coefficients.
## Entire function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic at all finite points over the whole complex plane.
## Equation
In mathematics, an equation is a statement of an equality containing one or more variables.
## Euclidean division
In arithmetic, Euclidean division is the process of division of two integers, which produces a quotient and a remainder smaller than the divisor.
## Euclidean domain
In mathematics, more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function which allows a suitable generalization of the Euclidean division of the integers.
## Exponential polynomial
In mathematics, exponential polynomials are functions on fields, rings, or abelian groups that take the form of polynomials in a variable and an exponential function.
## Exponentiation
Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.
## Expression (mathematics)
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
## Factorization of polynomials
In mathematics and computer algebra, factorization of polynomials or polynomial factorization is the process of expressing a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.
## Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers,, and satisfy the equation for any integer value of greater than 2.
## Fermat's little theorem
Fermat's little theorem states that if is a prime number, then for any integer, the number is an integer multiple of.
## Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.
## Finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.
## Formal power series
In mathematics, a formal power series is a generalization of a polynomial, where the number of terms is allowed to be infinite; this implies giving up the possibility of replacing the variable in the polynomial with an arbitrary number.
## Fourier series
In mathematics, a Fourier series is a way to represent a function as the sum of simple sine waves.
## Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
## Function composition
In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.
## Functional notation
Functional notation is the notation for expressing functions as f(x) which was first used by Leonhard Euler in 1734.
## Fundamental theorem of algebra
The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.
## Galois theory
In the field of algebra within mathematics, Galois theory, provides a connection between field theory and group theory.
## Gaussian elimination
In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations.
## Golden ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.
## Graph (discrete mathematics)
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
## Graph of a function
In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.
## Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.
## Hilbert's tenth problem
Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900.
## Homogeneous function
In mathematics, a homogeneous function is one with multiplicative scaling behaviour: if all its arguments are multiplied by a factor, then its value is multiplied by some power of this factor.
## Homogeneous polynomial
In mathematics, a homogeneous polynomial is a polynomial whose nonzero terms all have the same degree.
## Horner's method
In mathematics, Horner's method (also known as Horner scheme in the UK or Horner's rule in the U.S..) is either of two things.
## Hybrid word
A hybrid word or hybridism is a word that etymologically derives from at least two languages.
## Ideal (ring theory)
In ring theory, a branch of abstract algebra, an ideal is a special subset of a ring.
## Identity (mathematics)
In mathematics an identity is an equality relation A.
## Identity matrix
In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.
## Indeterminate (variable)
In mathematics, and particularly in formal algebra, an indeterminate is a symbol that is treated as a variable, but does not stand for anything else but itself and is used as a placeholder in objects such as polynomials and formal power series.
## Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
## Integral domain
In mathematics, and specifically in abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero.
## Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points.
## Interval (mathematics)
In mathematics, a (real) interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set.
## Irrational number
In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.
## Irreducible polynomial
In mathematics, an irreducible polynomial is, roughly speaking, a non-constant polynomial that cannot be factored into the product of two non-constant polynomials.
## Laplace transform
In mathematics, the Laplace transform is an integral transform named after its discoverer Pierre-Simon Laplace.
## Laurent polynomial
In mathematics, a Laurent polynomial (named after Pierre Alphonse Laurent) in one variable over a field \mathbb is a linear combination of positive and negative powers of the variable with coefficients in \mathbb.
## Lill's method
In mathematics, Lill's method is a visual method of finding the real roots of polynomials of any degree.
## Linear combination
In mathematics, a linear combination is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).
## Mathematical analysis
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
## Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
## Matrix polynomial
In mathematics, a matrix polynomial is a polynomial with square matrices as variables.
## Matrix ring
In abstract algebra, a matrix ring is any collection of matrices over some ring R that form a ring under matrix addition and matrix multiplication.
## Michael Stifel
Michael Stifel or Styfel (1487 – April 19, 1567) was a German monk, Protestant reformer and mathematician.
## Minimal polynomial (field theory)
In field theory, a branch of mathematics, the minimal polynomial of a value α is, roughly speaking, the polynomial of lowest degree having coefficients of a specified type, such that α is a root of the polynomial.
## Modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).
## Monic polynomial
In algebra, a monic polynomial is a single-variable polynomial (that is, a univariate polynomial) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1.
## Monomial
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term.
## Multiplication
Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.
## Multiplicity (mathematics)
In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset.
## Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
## Niels Henrik Abel
Niels Henrik Abel (5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields.
## Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
## Parabola
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
## Periodic function
In mathematics, a periodic function is a function that repeats its values in regular intervals or periods.
## Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
## Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
## Polynomial functor
In algebra, a polynomial functor is a functor on the category \mathcalV of finite-dimensional vector spaces that depends polynomially on vector spaces.
## Polynomial greatest common divisor
In algebra, the greatest common divisor (frequently abbreviated as GCD) of two polynomials is a polynomial, of the highest possible degree, that is a factor of both the two original polynomials.
## Polynomial long division
In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division.
## Polynomial mapping
In algebra, a polynomial mapping P: V \to W between vector spaces over an infinite field k is a polynomial in linear functionals with coefficients in W; i.e., it can be written as where L_j: V \to k are linear functionals.
## Polynomial remainder theorem
In algebra, the polynomial remainder theorem or little Bézout's theorem is an application of Euclidean division of polynomials.
## Polynomial ring
In mathematics, especially in the field of abstract algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field.
## Polynomial transformation
In mathematics, a polynomial transformation consists of computing the polynomial whose roots are a given function of the roots of polynomial.
## Power series
In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.
## Prime number
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
## Product (mathematics)
In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied.
In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where represents an unknown, and,, and represent known numbers such that is not equal to.
In elementary algebra, the quadratic formula is the solution of the quadratic equation.
## Quartic function
In algebra, a quartic function is a function of the form where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.
## Quintic function
In algebra, a quintic function is a function of the form where,,,, and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero.
## Quotient
In arithmetic, a quotient (from quotiens "how many times", pronounced) is the quantity produced by the division of two numbers.
## Rational function
In mathematics, a rational function is any function which can be defined by a rational fraction, i.e. an algebraic fraction such that both the numerator and the denominator are polynomials.
## Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
## Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
## René Descartes
René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.
## Restriction (mathematics)
In mathematics, the restriction of a function f is a new function f\vert_A obtained by choosing a smaller domain A for the original function f. The notation f is also used.
## Ring (mathematics)
In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.
## Ring of polynomial functions
In mathematics, the ring of polynomial functions on a vector space V over a field k gives a coordinate-free analog of a polynomial ring.
## Robert Recorde
Robert Recorde (c.1512–1558) was a Welsh physician and mathematician.
## Root-finding algorithm
In mathematics and computing, a root-finding algorithm is an algorithm for finding roots of continuous functions.
## S-plane
In mathematics and engineering, the s-plane is the complex plane on which Laplace transforms are graphed.
## Sextic equation
In algebra, a sextic polynomial is a polynomial of degree six.
## Slope
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
## Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
## Social science
Social science is a major category of academic disciplines, concerned with society and the relationships among individuals within a society.
## Society for Industrial and Applied Mathematics
The Society for Industrial and Applied Mathematics (SIAM) is an academic association dedicated to the use of mathematics in industry.
## Spline (mathematics)
In mathematics, a spline is a function defined piecewise by polynomials.
## Square matrix
In mathematics, a square matrix is a matrix with the same number of rows and columns.
## Stone–Weierstrass theorem
In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval can be uniformly approximated as closely as desired by a polynomial function.
## Substitution (algebra)
In algebra, the operation of substitution can be applied in various contexts involving formal objects containing symbols (often called variables or indeterminates); the operation consists of systematically replacing occurrences of some symbol by a given value.
## Subtraction
Subtraction is an arithmetic operation that represents the operation of removing objects from a collection.
## Summation
In mathematics, summation (capital Greek sigma symbol: ∑) is the addition of a sequence of numbers; the result is their sum or total.
## System of linear equations
In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same set of variables.
## System of polynomial equations
A system of polynomial equations is a set of simultaneous equations f1.
## Taylor's theorem
In calculus, Taylor's theorem gives an approximation of a k-times differentiable function around a given point by a k-th order Taylor polynomial.
## Term (logic)
In analogy to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact, in mathematical logic, a term denotes a mathematical object and a formula denotes a mathematical fact.
## The Nine Chapters on the Mathematical Art
The Nine Chapters on the Mathematical Art is a Chinese mathematics book, composed by several generations of scholars from the 10th–2nd century BCE, its latest stage being from the 2nd century CE.
## The Whetstone of Witte
The Whetstone of Witte is the shortened title of Robert Recorde's mathematics book published in 1557, the full title being The whetstone of witte, whiche is the seconde parte of Arithmetike: containyng thextraction of Rootes: The Coßike practise, with the rule of Equation: and the woorkes of Surde Nombers.
## Time complexity
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
## Trigonometric interpolation
In mathematics, trigonometric interpolation is interpolation with trigonometric polynomials.
## Unique factorization domain
In mathematics, a unique factorization domain (UFD) is an integral domain (a non-zero commutative ring in which the product of non-zero elements is non-zero) in which every non-zero non-unit element can be written as a product of prime elements (or irreducible elements), uniquely up to order and units, analogous to the fundamental theorem of arithmetic for the integers.
## Unit (ring theory)
In mathematics, an invertible element or a unit in a (unital) ring is any element that has an inverse element in the multiplicative monoid of, i.e. an element such that The set of units of any ring is closed under multiplication (the product of two units is again a unit), and forms a group for this operation.
## Univariate
In mathematics, univariate refers to an expression, equation, function or polynomial of only one variable.
## Variable (mathematics)
In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.
## Vieta's formulas
In mathematics, Vieta's formulas are formulas that relate the coefficients of a polynomial to sums and products of its roots.
## Word problem (mathematics education)
In science education, a word problem is a mathematical exercise where significant background information on the problem is presented as text rather than in mathematical notation.
## Zero of a function
In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).
## References
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http://www.physicsforums.com/showthread.php?p=3833545 | 1,368,959,147,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368697380733/warc/CC-MAIN-20130516094300-00089-ip-10-60-113-184.ec2.internal.warc.gz | 655,898,980 | 14,963 | ## Does Space Expand?
The the LCDM model scale factor is defined as:
$$a(t) = \left[ \frac{\Omega_m}{\Omega_v} \sinh^2 \left( \frac{3}{2} \sqrt{\Omega_v} H_0 t \right) \right]^{\frac{1}{3}}$$
Differentiating the scale factor function with respect to t:
$$\frac{d a(t)}{dt} = \frac{d}{dt} \left[ \frac{\Omega_m}{\Omega_v} \sinh^2 \left( \frac{3}{2} \sqrt{\Omega_v} H_0 t \right) \right]^{\frac{1}{3}} = \frac{ \Omega_m H_0 \cosh \left(\frac{3}{2} \sqrt{\Omega_v} H_0 t \right) \sinh \left(\frac{3}{2} \sqrt{\Omega_v} H_0 t \right)}{\sqrt{\Omega_v} \left(\frac{\Omega_m \sinh^2 \left(\frac{3}{2} \sqrt{\Omega_v} H_0 t \right)}{\Omega_v} \right)^{2/3}}$$
The scale factor derivative function:
$$\boxed{\frac{d a(t)}{dt} = \frac{ \Omega_m H_0 \cosh \left(\frac{3}{2} \sqrt{\Omega_v} H_0 t \right) \sinh \left(\frac{3}{2} \sqrt{\Omega_v} H_0 t \right)}{\sqrt{\Omega_v} \left(\frac{\Omega_m \sinh^2 \left(\frac{3}{2} \sqrt{\Omega_v} H_0 t \right)}{\Omega_v} \right)^{2/3}}}$$
Is this equation correct?
Attachments: plot a(t), plot a'(t)
Reference:
LambdaCDM geometry - mathematical details - Wikipedia
Attached Thumbnails
I'm not good enough at the math to quickly check your solution but I believe there is no analytic solution when there is more than one phase involved. The graph is initially matter dominated but becomes energy dominated so I think you have to perform an integration to get the curve. However, the section "mixtures" here suggests it can be solved: http://en.wikipedia.org/wiki/Friedma...eful_solutions The "Lecture notes on Astrophysics" looks comprehensive too, though beyond my level.
i was thinking about light. a particle and/or a wave ? but what about darkness.? does darkness move at the speed of light? does light move at the speed of darkness? does light really bend around corners or is it pulled around by darkness? in a dark universe, does the universe expand when light appears? does light "push" darkness away ? but what if the universe is in a "bubble"? would the darkness get squashed? is light a constant in the universe.? does the universe expand at different speeds at different times depending on how much is being added at that particular time?
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Quote by lostprophets i was thinking about light. a particle and/or a wave ?
The best description I've heard is that light is an electromagnetic wave that transfers energy only in packets we call photons.
but what about darkness.? does darkness move at the speed of light? does light move at the speed of darkness?
Darkness is nothing but the absence of light, similar to how a vacuum is the absence of matter in a volume of space.
does light really bend around corners or is it pulled around by darkness? in a dark universe, does the universe expand when light appears? does light "push" darkness away ?
Light really does diffract (bend if you want to call it that) around corners to a certain extent that depends on the wavelength. The rest of the quote doesn't make any sense.
but what if the universe is in a "bubble"? would the darkness get squashed? is light a constant in the universe.? does the universe expand at different speeds at different times depending on how much is being added at that particular time?
I think you have a misunderstanding on how we view the universe. I cannot answer these questions because they don't even make sense with current cosmological models. My suggestion is to read up on the subject. There are plenty of websites including wikipedia that will help you understand. Here's two articles that will greatly help you if you read them and follow all the links around. Don't be surprised if it doesn't make much sense first, as unless you understand the basics of light and matter the terms won't mean much.
http://en.wikipedia.org/wiki/Universe
http://en.wikipedia.org/wiki/Physical_cosmology
Quote by Drakkith Darkness is nothing but the absence of light, similar to how a vacuum is the absence of matter in a volume of space. Light really does diffract (bend if you want to call it that) around corners to a certain extent that depends on the wavelength. The rest of the quote doesn't make any sense. http://en.wikipedia.org/wiki/Universe http://en.wikipedia.org/wiki/Physical_cosmology
:o are you serious?
darkness is nothing but the absence of light..... ooosh
so what came first, the darkness or the light?
but i thought we knew or at least thought ,that there is no such thing as nothing
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Quote by lostprophets :o are you serious? darkness is nothing but the absence of light..... ooosh so what came first, the darkness or the light?
Light has been around since the earliest moment of the universe. So I would say light. What happened "before" the universe is pure speculation and doesn't belong here. (Just in case you were going to bring that up)
but i thought we knew or at least thought ,that there is no such thing as nothing
That is more philosophy than science. We have defined darkness to be the absence of visible light, just as we have defined a vacuum to be the absence of matter.
These are the scale factor equations that I reviewed from reference 1 and 2. Inflation Hubble parameter (end of inflationary epoch): 'ref. 1 p. 34 (167)' $$H_i = \frac{1}{t_{i}} = \frac{1}{10^{-32} \; \text{s}} = 10^{32} \; \text{s}^{-1}$$ $$\boxed{H_i = 10^{32} \; \text{s}^{-1}}$$ Inflation scale factor: 'ref. 1 p.35 (165)' $$a(t) \propto e^{H_i t} \tag{1}$$ Radiation scale factor: 'ref. 1 p. 22 (119)' $$a(t) = (2 H_0)^{\frac{1}{2}} \cdot t^{\frac{1}{2}} \tag{2}$$ Matter scale factor: 'ref. 1 p. 21 (115)' $$a(t) = \left( \frac{4 H_0}{2} \right)^{\frac{2}{3}} \cdot t^{\frac{2}{3}} \tag{3}$$ LCDM matter scale factor: 'ref. 2' $$a(t) = \left[ \frac{\Omega_m}{\Omega_v} \sinh^2 \left( \frac{3}{2} \sqrt{\Omega_v} H_0 t \right) \right]^{\frac{1}{3}} \tag{4}$$ Equations 2 and 3 appear to be describing a universe that is much younger. Attachments: plot 1, plot 2,3,4 Reference: Friedmann equations - useful solutions - Wikipedia Northern Illinois University - Physics 652 - Astrophysics LambdaCDM - geometry - mathematical details - Wikipedia Attached Thumbnails
Quote by Drakkith Light has been around since the earliest moment of the universe. So I would say light. .
if light was more abundant than darkness at the start where as the reverse is true now, am i to believe then that the universe is getting smaller?
what if it was expanding and contracting
i ask about light "pushing" darkness (light pressure) clearing a path .
so if we had darkness first with energy, then light energy appears,room has to be made for this light.
could light then clear this "room" creating a vacuum redundant of energy once this light has lost its energy and gone..this then takes time to rebuild itself with dark energy matter, un til it over crowds sparking another light source and repeats the process.
this would mean light energy is finite but that does not mean the universe cannot expand..
i could be way off and have no idea what im on about.but ive read some say that the universe is expanding fast than light... how do we measure this.do we measure it with light?
if light is "pushing" then light will always be behind therefore it could be seen that anything infront of it is moving fast when really its not
Quote by lostprophets i respect your guess. if light was more abundant than darkness at the start where as the reverse is true now, am i to believe then that the universe is getting smaller?
As has been said, darkness is only the absence of light, so in the presence of a single particle of light, the universe is not dark.
what if it was expanding
It is expanding, and the rate at which it does so is increasing.
That is poetic licence, it has no physical meaning. Light pressure can push a sail around (look up the Ikaros project) but darkness isn't a substance, just the absence of light.
so if we had darkness first with energy, then light energy appears,
For the first 378,000 years, the whole universe looked like the interior of the Sun, the farther back in time you go, the brighter it was.
room has to be made for this light.
Space, time and light possibly arose together but we don't know, that is presently beyond our understanding.
this would mean light energy is finite but that does not mean the universe cannot expand..
It is definitely expanding, it may be finite or infinite, we cannot tell which.
i could be way off and have no idea what im on about.but ive read some say that the universe is expanding fast than light... how do we measure this.do we measure it with light?
Yes. Surprisingly, the light can still reach us, but I'd need to go into maths to explain why.
if light is "pushing" then light will always be behind therefore it could be seen that anything infront of it is moving fast when really its not
Light was created everywhere equally and moved in all directions. There was no "in front" or "behind", it always surrounded.
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Quote by lostprophets i respect your guess. if light was more abundant than darkness at the start where as the reverse is true now, am i to believe then that the universe is getting smaller?
No, as has been repeatedly said, the universe is expanding.
what if it was expanding and contracting
There's no need to ask "what ifs" that aren't real. The universe is expanding, not contracting.
i ask about light "pushing" darkness (light pressure) clearing a path .
I don't know what you don't understand about darkness simply being the absence of light. Darkness is an abstract concept linked to vision. If a volume of space is completely devoid of EM radiation (light) we do not call it dark, we call it empty of radiation. Light propagates through space and interacts with matter. It cannot interact with empty space as there is nothing to interact with!
so if we had darkness first with energy
We did not have darkness first. As I said light has existed since the earliest moments of the universe when the density and temperature of the universe was so high that matter and antimatter was continually being created from EM radiation and annihilated, converting back to EM radiation.
then light energy appears,room has to be made for this light.
It did not "appear". The energy already existed. Furthermore you keep suggesting that "darkness" is something physical and tangible. It is not. Does a vacuum have to make room for particles to exist in it? No!
could light then clear this "room" creating a vacuum redundant of energy once this light has lost its energy and gone..this then takes time to rebuild itself with dark energy matter, un til it over crowds sparking another light source and repeats the process.
Absolutely not. The earliest moments of the universe was full of interacting particles and radiation. As George said above, imagine being inside the core of the Sun, but a billion billion trillion times denser and hotter. Then go another quadrillion above that. Then you will be getting close to the state of the early universe.
i could be way off and have no idea what im on about.but ive read some say that the universe is expanding fast than light... how do we measure this.do we measure it with light? if light is "pushing" then light will always be behind therefore it could be seen that anything infront of it is moving fast when really its not
We measure it by looking at the amount of redshift an object presents to us. The further away an object such as a galaxy is, the more its light is redshifted. This is due to the expansion of the universe causing it to recede from us and stretching out the light as it travels over billions of years.
Also, the expansion of the universe is a "rate", not a measurement of velocity. What this means is that objects further away will accelerate away from us quicker than objects closer to us will. The speed at which objects move away from us is called the recession velocity. Currently our measurements show that this recession velocity increases by about 70 km/s per megaparsec (3.26 million light-years) in distance that an object is from us. So a galaxy at 2 megaparsecs in distance from us would be receding at about 140 km/s, while a galaxy at 20 megaparsecs would recede at 1400 km/s. If the rate of expansion were higher, the recession velocity would increase by a larger amount per distance, such as being 100 km/s per megaparsec.
sorry . i did mean to use the word "front" lightly .ooosh pun ,not so poetic... yes theres no front, back, middle, only edges,curves,surrounding, enclosed ,in a tomb of darkness.. the further we look back the brighter it gets. its logic for it to be so. but is it logic to think that what one is looking at is not the beginning but a random? thanks for the reply ... also how far can my eyes see. meaning when i see light that has come from a far distance.at what distance am i seeing it.? am i seeing the light from the distance of my eye or am i seeing the light light years away. my eyes can see distances.so i ask is it possible to travel down the light to the source and bring it nearer? i no i may like a fruit loop hope you dont mind.. my question is this. is the light seeing me or am i seeing it? also i went to the optitions today.he put a light in my eye .when this light was taken away i had a dark line of vision.i asked why. he said its because the light removes something or other ,sorry cant remember exactly,so there was an empty space .but over time the energy recovers and bring the light back to this dark spot...can space work the same? meaning does light remove matter then once the light has gone this matter returns over a time period...
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Quote by lostprophets the further we look back the brighter it gets. its logic for it to be so. but is it logic to think that what one is looking at is not the beginning but a random?
Well, your first sentence is incorrect. It is not brighter the further we look back. After the universe formed it cooled and expanded over millions of years. Finally after the temperature and density dropped beyond a critical point, protons could combine with electrons, forming neutral atoms that are mostly transparent to light. Before this point in time light could not travel more than mere nanometers before interacting with protons or electrons. After this point in time the universe became "transparent", and the radiation that was released from electrons combining with protons could suddenly travel over light-years and is currently seen as the Cosmic Microwave Background. The CMB is literally the furthest back we can see using light. It is not physically possible to see beyond this point unless we can somehow invent a neutrino detector in the future that is a few trillion times more sensitive than current ones.
After this recombination, atoms could finally start to collapse under gravitational attraction to form the first stars and galaxies. Whether the universe is "brighter" now or then is unknown to me.
also how far can my eyes see. meaning when i see light that has come from a far distance.at what distance am i seeing it.? am i seeing the light from the distance of my eye or am i seeing the light light years away. my eyes can see distances.so i ask is it possible to travel down the light to the source and bring it nearer? i no i may like a fruit loop hope you dont mind.. my question is this. is the light seeing me or am i seeing it?
I don't really know what you are asking. Since photons can travel through space for billions of years, if your eye detects one then you are seeing something billions of lightyears away. The only limit to how far an object can be seen is simply that the universe is only a finite age. The CMB was released over 13 billion years ago, so as time passes the area of space that those photons we see were released from is getting further away.
im now confused. one of you is saying the further you go back the brighter it gets,and the other is saying not so... the problem may stem from the "no matter which direction we look ,it all looks the same" on a large scale not small... so how do we get around this.? its like looking at a field full of sheep and guessing which one came first. neutrinos collide with things at random points at random times......this to me is very important.
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Quote by lostprophets im now confused. one of you is saying the further you go back the brighter it gets,and the other is saying not so...
Sorry. Before the CMB was emitted you did in fact get "brighter" the further back you go, but that is kind of inaccurate as the state of the universe was very different from what it is today. I prefer the terms "hotter" and "denser".
the problem may stem from the "no matter which direction we look ,it all looks the same" on a large scale not small... so how do we get around this.? its like looking at a field full of sheep and guessing which one came first. neutrinos collide with things at random points at random times......this to me is very important.
Get around what? The universe is very homogenous on the large scale.
And may I request that you make specific questions. Much of your posts seem to be ramblings that don't make any sense and don't seem to be asking anything. It would help both us and yourself if you could trim your posts down to clear, concise questions.
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Quote by lostprophets also i went to the optitions today.he put a light in my eye .when this light was taken away i had a dark line of vision.i asked why. he said its because the light removes something or other ,sorry cant remember exactly,so there was an empty space .but over time the energy recovers and bring the light back to this dark spot...can space work the same? meaning does light remove matter then once the light has gone this matter returns over a time period...
The bright light uses up the chemicals in your eye that respond to light, allowing you to see. These chemicals require time to be replaced in your cells, so it takes a little bit for your vision to return to normal. The light isn't pushing anything out of the way and the chemicals are still there, they are just used up in a reaction that turns them into something else.
Quote by Drakkith The bright light uses up the chemicals in your eye that respond to light, allowing you to see. These chemicals require time to be replaced in your cells, so it takes a little bit for your vision to return to normal. The light isn't pushing anything out of the way and the chemicals are still there, they are just used up in a reaction that turns them into something else.
yes..
i see. thank you. the light turns them into something else.....1+1 = 3
Quote by lostprophets im now confused. one of you is saying the further you go back the brighter it gets,and the other is saying not so... the problem may stem from the "no matter which direction we look ,it all looks the same" on a large scale not small... so how do we get around this.? its like looking at a field full of sheep and guessing which one came first. neutrinos collide with things at random points at random times......this to me is very important.
It is summer and you are in a field of sheep, all born in the same week in the spring. If light travels slowly, you see old sheep near you but lambs far off. When we look far away, we see the universe as it was earlier. It was brighter earlier. | 4,531 | 19,455 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2013-20 | longest | en | 0.816933 |
https://studyfinance.com/net-debt-to-ebitda-ratio/ | 1,632,169,745,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057091.31/warc/CC-MAIN-20210920191528-20210920221528-00233.warc.gz | 595,379,155 | 7,363 | # Net Debt to EBITDA Ratio
The net debt to EBITDA ratio is a leverage metric that measures the amount of net income that is available to pay down debt before covering interest, taxes, depreciation, and amortization expenses.
Put simply, the ratio indicates how long a company will be able to repay its debt for if its net debt and EBITDA never changed. A negative result is usually obtained if a company’s debt is lower than its cash. This ratio is similar to the debt to EBITDA ratio, and the only difference is that with net debt to EBITDA, cash and cash equivalents are deducted from total debt as well.
When analyzing the net debt to EBITDA ratio it must be compared with a benchmark value or the industry average to make it useful for assessing the company’s capability of settling its debt.
In addition, a horizontal analysis, which involves looking into the company’s historical data, must be performed to know whether a company has added to or reduced its debt during a particular period, and how it has grown during the covered time frame.
Make sure you compare with companies in the same industry, as capital requirements vary and some industries, like manufacturing, are more capital intensive.
## Net Debt to EBITDA Formula
$$\text{Net Debt to EBITDA} = \dfrac{Total\: Debt - \text{Cash \& Cash Equivalents}}{EBITDA}$$
First, we need to get the value of total debt by summing short- and long-term debt from the balance sheet.
Cash and cash equivalents are also found on the balance sheet, and these are deducted from the total debt.
EBITDA (earnings before interest, taxes, depreciation and amortization) might be found on the income statement depending on the company. If not, you can find EBIT (earnings before interest and taxes) on the income statement, and depreciation and amortization figures will be in the notes to operating profit or on the cash flow statement.
## Net Debt to EBITDA Example
Lily Ament, an investor, would like to assess 123 Enterprises’ ability to pay off its debt. She digs into the company’s financial records and finds the following data for 2019:
• Short-term debt: $4,200,000 • Long-term debt:$19,320,000
• Total debt: $23,520,000 • Cash:$9,220,000
• EBITDA: \$39,000,000
What is 123 Enterprises’ net debt to EBITDA ratio?
We can now apply the values to our formula and calculate the net debt to EBITDA:
$$\text{Net Debt to EBITDA} = \dfrac{23{,}500 - 9{,}220}{39{,}000} = 0.37$$
In this case, the 123 Enterprises would have a Net Debt-to-EBITDA value of 0.37 for the year 2019.
A Net Debt-to-EBITDA ratio of .36 indicates that 123 Enterprises is highly likely to be able to pay its obligations and have lots of fiscal room to take on additional debt to help the company grow.
But Lily should not stop after checking the company’s 2019 data. Instead, she should go further back to analyze past years and look for trends. For example, if earlier ratios had been increasing consistently, it could be a sign that the company’s ability to pay off its debt is decreasing with each fiscal year, even if the current year’s ratio is still technically safe.
## Net Debt to EBITDA Analysis
The net debt to EBITDA ratio is favored by analysts because it considers a company’s debt-clearing capacity. A low net debt to EBITDA ratio is usually desired as it shows that a business is not buried in debt and will be able to cover its financial obligations with ease. In contrast, a high net debt to EBITDA ratio is a sign that a company is too much in debt, which also means that its credit rating is low, and investors are likely to demand higher bond yields to buffer the greater risk that comes with lending it money.
Overall, the ratio is useful in decision-making, including decisions related to a takeover bid investment. Also, it’s helpful to potential buyers when in appraising the company’s profitability minus the current manager’s vigorous spending. If the company is conservative in its spending when branching out or buying new equipment, its depreciation and amortization costs will be lower, making it profitable without the said extra expenses.
Still, using the net debt to EBITDA ratio alone to measure a company’s debt payment ability can be a slippery slope. After all, a company can still overspend despite having a high EBITDA. This may even assume that the company’s revenues all come from its customers, thus leaving out uncollectible accounts receivable and customer returns. And, of course, a higher ratio increases a company level of risk as a potential borrower when banks or creditors assess them.
## Net Debt to EBITDA Conclusion
• The net debt to EBITDA ratio shows how capable a company is to pay off its debt with EBITDA.
• This formula requires three variables: total debt, cash and cash equivalents, and EBITDA.
• The net debt to EBITDA ratio is usually expressed as a decimal number.
• The ratio is typically used by credit rating agencies when assigning companies’ credit ratings.
• A low net debt to EBITDA ratio is preferred and indicates that the company has a healthy level of debt
• A high ratio shows that the company has too much debt, possibly leading to a low credit rating and a higher bond yield requirement.
• A ratio higher than 5 should raise alarm.
## Net Debt to EBITDA Calculator
You can use the net debt to EBITDA calculator below to quickly assess a company’s ability to pay off its debt, by entering the required numbers. | 1,261 | 5,435 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2021-39 | latest | en | 0.943379 |
https://www.liutaiomottola.com/myth/scroll.htm | 1,601,030,467,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400223922.43/warc/CC-MAIN-20200925084428-20200925114428-00177.warc.gz | 935,498,560 | 8,789 | # Lutherie Myth/Science: Violin Scrollsare Based on the Golden Mean Spiral
This is a myth, and one that appears to have survived for a long time. I've never seen it written down but have heard it repeated any number of times. My suspicion is that in most cases this myth is based on a misunderstanding of just what the golden mean spiral is. When the spiral of a typical violin scroll is compared side by side with a golden mean spiral it is quite apparent that the two are vastly different.
Last updated: January 21, 2019
The golden mean or golden section is an irrational number usually represented by the Greek letter Φ (Phi, pronounced fie, rhymes with pie) and is approximately 1.6180339887. Historically this number was considered quite significant insofar as it described well typical growth patterns of both plants and animals. As such it was and still is considered by some to be the basis of a natural and “hard wired” aesthetic, that is, aesthetics that are not culturally formed, but that are universal in that they are derived from a basic ratio of nature. In fact the reason that we use Φ to represent this value is that it is the first letter of the name of the Greek sculptor Phidias, who was supposed to have made use of this ratio in sculpting the proportions of the various parts of the human body. Pretty heady stuff, no?
The golden mean spiral is based on a rectangle the sides of which are in the proportion of 1: Φ. If you divide such a rectangle such that one of the parts is a square, the other part will be another golden mean rectangle. And if you divide that rectangle in the same way so one of its parts is a square the other part will be another golden mean rectangle. For all practical purposes you can keep doing this division until things are so small you can't see them. From a mathematical perspective you can do this forever. Doing it 5 times will result in something like this:
And drawing a 90° circular arc in each square such that the central most corner of the square is the center of the arc approximates a golden mean spiral and looks like this:
Now we can compare this spiral to that of a violin scroll. I made an approximate copy of the spiral of a violin scroll done by Guy Rabut which appeared in a nice article he did on scroll carving which appeared in American Lutherie #52. First the golden mean spiral, sans construction lines:
And then the violin scroll spiral:
Even though the golden mean spiral above has fewer turns (2) than that of the spiral taken from Rabut's scroll, and even though each violin maker's scroll is a little different, it should be pretty obvious that the typical violin scroll is not based on the golden mean spiral. If you take the perspective that the spirals are spiraling inward, it is clear that the golden mean spiral closes in much more quickly than does the typical violin scroll spiral.
So how did the myth that violin scrolls are based on the golden mean spiral start? I can’t answer that, but my suspicion is that it was simply a matter of incorrectly extending an explanation of aesthetics to a different domain without actually checking things out, i.e. if the golden mean can explain why certain aesthetic proportions in sculpture are pleasing to us, and the shape of the violin scroll is aesthetically pleasing to us, and there is such a thing as the golden mean spiral, then violin scrolls must be based on golden mean spirals. But even if the golden ratio is the basis of some aesthetically pleasing natural and human made structures, the facts that humans find the aesthetics of the violin scroll appealing and that it is not based on the golden mean spiral are strong indicators that not all appealing spirals are based on the golden mean. Here is a good place to point out that the whole natural aesthetics thing is based largely on myth, too. Naturally occurring spirals such as that of the nautilus shell are said to be golden mean spirals. This is decidedly false (the spiral of the nautilus describes a non golden mean logarithmic spiral, see below), but a simple Internet search on the terms “golden mean spiral” and “nautilus” turns up an amazing number of websites, mostly of a New Age-y orientation but some unfortunately from academic sources, that assert this to be true.
Another possible explanation for the myth is that the construction of the violin scroll spiral can make use of the golden mean, and this got misconstrued to mean that the scroll follows a golden mean spiral. There is a superb treatise on the drafting of the violin scroll by Robert J. Spear which appeared in the third part of an exquisite three part article on drawing the violin in American Lutherie #95. Spear makes a compelling case that the golden mean can be used extensively in generating drawings of many parts of the violin.
But if a typical violin scroll does not describe a golden mean spiral, just what kind of spiral does it describe? For purposes of description spirals are generally divided into two major classes. Arithmetic (also called Archimedean) spirals increase in size by adding (or subtracting) a fixed distance from the pole per unit of turn, for example, 1” per each 90° of rotation. The result is a spiral that has bands that do not increase in width as it spirals out:
The other major class of spiral is the logarithmic spiral. Spirals of this class increase in size by multiplying (or dividing) the distance from the center pole by a constant amount per unit of turn. The bands of such a spiral increase in width by the multiplication factor as the spiral spirals out. The golden mean spiral is just one case of such a spiral. By changing the multiplication factor it is possible to create a spiral that expands quickly or slowly as it spirals out. But unfortunately for those that would use a simple algorithm for drawing a violin scroll, there is no multiplication factor that will result in a spiral that will even roughly approximate that of a typical violin scroll. When I copied Rabut’s scroll for the diagram above, I made use of a nice computer graphics algorithm for drawing approximations of scrolls by Taponecco and Alexa. Very simply, the algorithm approximates spirals by displaying them as tangent circular arcs, with their size relationships described by an arbitrary function. When I copied the violin scroll I did it using tangent 90° circular arcs of whatever size was needed to fit the section of the spiral I was working on. That the relationship of the lengths of the radii of these arcs could not be described by simple multiplication is a clear indication that the spiral of a typical violin scroll cannot be described by any logarithmic spiral. It is highly likely that a more complex function could describe the increase as the spiral spirals out but as my initial goal for this exercise was to find a practical formulaic approach that could be used by even non-technical luthiers I did not pursue this further.
Coates, in his book Geometry Proportion and the Art of Lutherie posits that violin scrolls are based on a logarithmic spiral from classic architectural theory known as the Ionic volute. The first known mention of the construction of this spiral is in writings of Vitruvius, thought to have been produced around 20 BC. Coates provides drawings of many scrolls taken from real instruments and overlays those with a suitably sized Ionic volute for comparison. None match, but some do come close.
All of this of course begs the question of how one should go about drawing the spiral for a violin scroll. Perhaps the best answer I have heard comes from master violin maker Joseph Curtin. His suggestion is to draw a scroll that looks good and respects, to the degree desired, classical models.
## References and Suggestions for Further Reading
Spirals and the Golden Section by John Sharp for the Nexus Network Journal vol.4 no.1 (Winter 2002)
A very complete and wholly accurate discussion on the math and history of the golden mean spiral. Quite accessible to the non-technical audience.
Golden Ratio - from MathWorld
A good discussion of the golden mean from MathWorld.
Piecewise Circular Approximation of Spirals and Polar Polynomials
The paper by Taponecco and Alexa describing the computer graphics algorithm I used as a model when copying Rabut’s violin scroll.
Ake Ekwall, "Volutes and Violins", Nexus Network Journal, vol. 3, no. 4 (Autumn 2001)
A very nice general discussion of the classic spirals that may have been used as the basis for instruments scroll.
Kevin Coates, Geometry Proportion and the Art of Lutherie, Oxford University Press (out of print).
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.... you can click on most of the assembly photos on this site to enlarge them for a close look? Also, hovering the cursor over most linear dimension values will convert the values to decimal inches, fractional inches, and SI units. | 1,914 | 9,332 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2020-40 | longest | en | 0.96697 |
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Question:
Solve the following equation: |2x + 6 - 5x| = 9
A x = -1 or x = 5
explanation
First, simplify the expression in absolute value:
|2x + 6 - 5x| = |6 - 3x | = 9
Because absolute value\u00A0of a number is its distance from zero, it can be a positive or negative value. Therefore, solve each of the following equations:
6 - 3x = 9
6 - 3x = -9
Solve the first equation.
6 - 3x = 9
-3x = 3
x = -1
Solve the next equation.
6 - 3x = -9
-3x = -15
x = 5
Therefore, x = -1 or x = 5 | 198 | 532 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.671875 | 4 | CC-MAIN-2024-18 | latest | en | 0.822514 |
https://www.bhavinionline.com/tag/puzzles-answer/page/3/ | 1,713,665,429,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817699.6/warc/CC-MAIN-20240421005612-20240421035612-00315.warc.gz | 614,237,402 | 18,737 | ## Fun Riddle: What is the Least Number of Coins Required to Have an Exact Change?
How well can you handle money? Here is a quick fun riddle to check your skills with money. What is the least number of coins required to have an exact change for all possible items that cost from one cent up to and including one dollar in one-cent increments? You can have unrestricted supply of … Read more
## Word Riddle: I Walk On My Head All Day, But Never Get Tired.
Read the hints given in the riddle and guess the word. I walk on my head all day, but never get tired. I keep something lucky attached to where it should be. What am I? So were you able to solve the riddle? Leave your answers in the comment section below. You can check if … Read more
## Fun Riddles for Kids: How Tall is Mark?
Here is a easy riddle that you can share with all the kids you know. If Mark is 90 centimeters plus half his height, how tall is he? So were you able to solve the riddle? Leave your answers in the comment section below. You can check if your answer is correct by clicking on … Read more
## Word RIddles: I Can Be As Thin As A Picture Frame
Read the hints given in the riddle and guess the word. I can be as thin as a picture frame, but you can see many things inside me. What am I? So were you able to solve the riddle? Leave your answers in the comment section below. You can check if your answer is correct … Read more
## Fun Riddle: When Is 1300 + 20 Equal To 1400 – 40?
Think out of the box to solve this fun driddle. When is 1300 + 20 equal to 1400 – 40? So were you able to solve the riddle? Leave your answers in the comment section below. You can check if your answer is correct by clicking on show answer below. If you get the right … Read more
## Word Riddle: Scratch My Head and Watch Me Turn Black to Red
Read the hints given in the riddle and guess the word. Scratch my head and watch me turn black to red. What am I? So were you able to solve the riddle? Leave your answers in the comment section below. You can check if your answer is correct by clicking on show answer below. If … Read more
## Fun Riddles: To Throw Me, You Would Prefer a Crowd
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# fungsi torque wrench
### Frequency response analysis of the gear box in a lathe machine using transfer functions
by ijsrporg 0 Comments 55 Viewed 0 Times
- In this research work, frequency response of the gear box in the medium duty lathe machine is studied using transfer functions. The effect of the torque acting at a particular rotor on the amplitude of vibration of the other rotors is studied. Initially, equation of motion is developed for the multi-rotor system in the gearbox and later, Laplace transforms are applied to find the transfer functions. Torque acting at various rotors is also calculated. The obtained characteristic equation and the transfer functions are solved for poles and zeros (frequencies to attenuate the inputs at every rotor) by writing programming in MATLAB. Plots of the frequency response curves are plotted by writing the programming in MATLAB and the final conclusions are drawn.
### 2015 Suzuki Boulevard M109R
2015 SUZUKI BOULEVARD M109R B.O.S.S. Go ahead and admit it, you want to be the owner of the most stylish bike on the block. Lucky for you, the Suzuki Boulevard M109R B.O.S.S. grabs attention everywhere it goes. An incomparable black color scheme coupled with aggressive styling scream in testament to the M109R’s power. If looks aren’t enough to sell you on this bike, then let the 1783cc V-Twin engine convince you. Tuned to produce massive torque from idle to red-line, the 2015 Suzuki Boulevard M109R B.O.S.S. will keep you smiling and styling through your journeys to come.
### CFD Analysis of Pelton Runner
by ijsrporg 0 Comments 11 Viewed 0 Times
This paper presents Computational Fluid Dynamics (CFD) analysis of Pelton turbine of Khimti Hydropower in Nepal. The purpose of CFD analysis is to determine torque generated by the turbine and pressure distributions in bucket for further work on fatigue analysis. The CFD analysis is carried out on model size Pelton runner reduced at 1:3.5 scale to minimize computational cost and time. The operating conditions for model size runner is selected in accordance with IEC 60193 and IEC 1116. The paper describes the methods used for CFD analysis using ANSYS CFX software. 3 buckets are used to predict the flow behavior of complete Pelton turbine. k-ε and SST turbulence model with interphase transfer method as free surface and mixture model is compared in the paper. The pressure distribution is found maximum at bucket tip and runner Pitch Circle Diameter (PCD). The torque generated by the middle bucket is replicated over time to determine total torque generated by Pelton turbine.
### 2015 Suzuki Boulevard M109R
Go ahead and admit it, you want to be the owner of the most stylish bike on the block. Lucky for you, the Suzuki Boulevard M109R B.O.S.S. grabs attention everywhere it goes. An incomparable black color scheme coupled with aggressive styling scream in testament to the M109R’s power. If looks aren’t enough to sell you on this bike, then let the 1783cc V-Twin engine convince you. Tuned to produce massive torque from idle to red-line, the 2015 Suzuki Boulevard M109R B.O.S.S. will keep you smiling and styling through your journeys to come.
Tags: Suzuki, bikes, , Automotive,
### Looking for high quality electrical test equipment calibration.PDF
by kingswayinstruments 0 Comments 49 Viewed 0 Times
Electrical instrumentation calibration, certification of analog multimeters, clamp-on meters, process, pressure/vacuum calibrators, Thermocouple/RTD/Infrared thermometers, torque wrenches, humidity meters, coating thickness gauges, insulation testers.
### FEIN WPO 14 15 E Polisher for Paint Surfaces in the Boat and Marine Areas
by Waltertool 0 Comments 87 Viewed 0 Times
The Fein high power motor and 2 stage gear reduction for outstanding torque and optimized speed range that remains constant under load are the best featires of WPO 14-15 E Polisher.
### DC Drive Manufacturers| Digital DC Drive Manufacturers
by GemcoControls 0 Comments 34 Viewed 0 Times
Gemco Controls offers Electrical control panels which are highly and reliable functional DC drivers and are used to control the speed, acceleration and torque.
### PART NO. 15250 '09 - '14 DODGE RAM 1500 3.6L - Magnaflow
by garry 0 Comments 82 Viewed 0 Times
To ease removal of existing exhaust components (especially on older vehicles) spray penetrating lubricant on all fasteners and hangers/insulators that will be loosened or removed and let soak before disassembly. WARNING: When working on, under, or around any vehicle exercise caution. Please allow the vehicle's exhaust system to cool before removal, as exhaust system temperatures may cause severe burns. If working without a lift always consult vehicle manual for correct lifting specifications. Always wear safety glasses and ensure a safe work area. Serious injury or death could occur if safety measures are not followed. ATTENTION: Always install any supplied band or U-bolt clamps to the proper torque specifications of 40-45 ft-lbs for band clamps and 30-35 ft-lbs for U-bolt clamps. Over tightening will result in the clamp breaking and will NOT be warranted by MagnaFlow. MAGNAFLOW: 22961 Arroyo Vista - Rancho Santa Margarita, CA 92688 | 1(800) 990-0905 Technical Support: 1(800) 959-9226 | Email: moreinfo@magnaflow.com
### 2014 Ram 1500 SPECIFICATIONS
by garry 0 Comments 26 Viewed 0 Times
Adaptive electronic control, automatic or Electronic Range Select (ERS) manual control. Five clutch-pack design with only two open clutches in any gear. Torque converter lock with turbine torsional damper for low lock-up speeds in 1st through 8th gear Adaptive electronic control, automatic or ERS manual control. Five clutch-pack design with only two open clutches in any gear. Torque converter lock with turbine torsional damper for low lock-up speeds in 1st through 8th gear Group 65, low-maintenance 730 CCA (Stop-start features 800 CCA Absorbed Glass Mat) Upper and lower “A” arms, coil springs, twin-tube shock absorbers, stabilizer bar. Optional air suspension replaces twin-tube shock absorbers and coil springs Five-link with track bar, coil springs, stabilizer bar, twin-tube shock absorbers, solid axle. Optional air suspension replaces twin-tube shock absorbers and coil springs
### 140275 06-08 Dodge Ram 1500 split side - Borla
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A294142 Number of partitions of n into distinct odd parts that do not divide n. 1
1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 2, 0, 3, 1, 2, 2, 3, 0, 4, 4, 4, 2, 6, 1, 6, 8, 4, 10, 12, 4, 12, 5, 7, 17, 17, 8, 14, 24, 9, 29, 24, 4, 33, 40, 25, 29, 28, 23, 45, 63, 23, 30, 52, 37, 84, 99, 26, 113, 112, 23, 143, 60, 57, 173, 143, 89, 70, 226, 87, 256, 256, 53, 245, 135, 127, 378, 233 (list; graph; refs; listen; history; text; internal format)
OFFSET 0,15 LINKS Table of n, a(n) for n=0..80. Index entries for sequences related to partitions EXAMPLE a(14) = 2 because we have [11, 3] and [9, 5]. MATHEMATICA Table[SeriesCoefficient[Product[1 + Boole[Mod[n, k] > 0 && OddQ[k]] x^k, {k, 1, n}], {x, 0, n}], {n, 0, 80}] CROSSREFS Cf. A000700, A098743, A171565, A200745, A209402, A294141. Sequence in context: A054656 A080096 A322978 * A068915 A302193 A133925 Adjacent sequences: A294139 A294140 A294141 * A294143 A294144 A294145 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Oct 23 2017 STATUS approved
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Last modified May 28 11:56 EDT 2024. Contains 372913 sequences. (Running on oeis4.) | 641 | 1,626 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2024-22 | latest | en | 0.729184 |
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### 343 terms by kmparent
#### Study only
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## Create a new folder
Physics
Science
### A body at rest or in uniform motion remains in the same state unless a force is applied describes what
Newtons 1st law of motion
Force
Inertia
### What is inertia
It is the tendency of a body to remain at rest or stay in motion unless acted upon by an external force
### What is the formula for Newtons 2nd Law
F=ma ( Force= (mass)(acceleration) )
Meter
Kilogram
### What are the fundamental metric units of physics
Meters, Kg, and seconds
Density
Molecule
5/9(F-32)
### Convert 68*F to degrees Centigrade
20* 5/9(68-32)=20
2.2
Water
2.54
100
10 billion
Force
Newton
Work
### What is the definition of energy
The ability to do work
Kinetic energy
Potential
Mega
mA
### What is the definition of power
The rate of which work is done
### What law states that energy cannot be created or destroyed only changed
Law of Conservation of Energy
Watt
1,000
100
Velocity
### What are the two kinds of electrical charges
Positive and Negative
Coulomb
### What are the three methods of electrification
Friction, Contact, Induction
4 times
Volts
### What determines the quantity of electrons that can be stored in a capacitor
The area of the plates, the distance between the plates and the material between the plates
Ground
1 electron volt
Capacitor
1 joule/coulomb
Amperage
Voltage
Conductor
Increases
Current
Ampere
Voltage
Direct
Ammeter
Q/T
### What will create the most electrical resistance
Long wire small diameter
Copper
Insulator
Ohms law
Ohm
8 volts
22 ohms
### What is true concerning series circuits
Amperes remains constant throughout
12
### What is the main advantage of a parallel circuit
Independence of the branches
Side by side
### What is true concerning a voltmeter
It must be connected in parallel
Circuit breaker
Rheostat
Watt
P=VI
Outer surface
### What is the most efficient means of transporting electrical energy
High voltage and low amperage
28,000 watts
Magnet
North and South
Flux lines
### Which of the following determines the strength of a magnetic field
The number of flux lines
### How would cutting the distance between two magnets in half, effect the attraction force between them
It would increase four times
### In which direction do magnetic flux lines travel
North pole to south pole
Magnetic field
Oersted
### Which of the following happens when a current and conductor increases
Magnetic field strength increases
### Which of the following rules will determine the direction of the magnetic field around an electrical current
A left hand thumb rule
Clockwise
Helix
Solenoid
Electromagnet
Ferromagnetic
Non magnetic
Parramagnetic
Repel
Diamagnetic
Permeability
### How will the north pole and south pole of two magnets affect each other
They will attract
### Which of the following rules will determine the direction of force on a current carrying wire
The right hand rule
Motor
### Which of the following happens when a wire moves through a magnetic field
An electromotive force is induced in the wire
90 degrees
retentivity
### How can voltage be induced into a conductor : Move a wire through a magnetic field, Move a magnetic field across a wire, Place a wire in a varying magnetic field
(answer is: 1,2 &3) *Michael Feraday discovered that electricity could be produced by any of the above methods.
Generator.
Motor
Mutual induction
### What type of transformer has more turns of wire in the secondary side than primary side
Step-up transformer
Shell type
Turns of wire
Shell type
95%
Decreases
### As magnetic domains rearrange in a transformer, heat is produced. What is this energy loss called
Hysteresis losses
Soft iron
Eddy Currents
Power loss
Lamination
Frequency
120
### How are alternating current values usually expressed
RMS (root mean square) values
### What is the major reason for using alternating current
Transformers cannot operate without it.
Alternating
Impedance
50 kV
22 V
70.7 kv
Rectification
Circuit
Semiconductor
N type
### Which of the following is not an advantage of solid state rectifiers over valve tubes
Melting point is lower in silicon
Full wave
Line voltage
### What controls the incoming voltage to the auto transformer
Main breaker switch
Electronic timer
Autotransformer
KVP selector
### If the line voltage changes because of demands by other users, adjustments must be made in which of the following
Voltage compensator
X-ray tube
Rheostat
Breaker switch
### Where in the x-ray circuit is the timer located
Between the autotransformer and the step up transformer
High frequency
### The spinning top test can be used to determine the accuracy of which of the following
Rectification circuit
Alternating
Rheostat
150
Milliameter
12
### Which of the following types of current supplies the x-ray tube
Pulsating direct current
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Example: | 1,186 | 5,074 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2014-52 | latest | en | 0.831416 |
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