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https://www.geeksforgeeks.org/strictmath-acos-method-in-java/
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Open In App
StrictMath acos() Method in Java
The java.lang.StrictMath.acos() is an inbuilt method which returns cosine of a given argument and an angle. The angle which is returned within the range between 0.0 and pi. Note: If the absolute value of the argument is greater than 1 or the argument is itself a NaN then the result is also NaN. Syntax:
`public static double acos(double num)`
Parameters: The method accepts one parameter num which is of double type and refers the arc whose cosine is to be returned. Return Value: The method returns the arc cosine of the argument. Examples :
```Input: num = 0.45
Output: 1.1040309877476002
Input: num = 8.9
Output: NAN```
Below programs illustrate the java.lang.StrictMath.acos() method: Program 1: For positive number
java
`// Java program to illustrate the``// java.lang.StrictMath.acos()``import` `java.lang.*;` `public` `class` `Geeks {` ` ``public` `static` `void` `main(String[] args)`` ``{` ` ``double` `num1 = ``0.65``, num2 = ``6.30``;` ` ``// It returns the arc cosine of a value`` ``double` `acosValue = StrictMath.acos(num1);`` ``System.out.println("The arc cosine value of "+`` ``num1 + " = " + acosValue);` ` ``acosValue = StrictMath.acos(num2);`` ``System.out.println("arc cosine value of "+`` ``num2 + " = " + acosValue);`` ``}``}`
Output:
```The arc cosine value of 0.65 = 0.863211890069541
arc cosine value of 6.3 = NaN```
Program 2: For negative number.
java
`// Java program to illustrate the``// java.lang.StrictMath.acos()``import` `java.lang.*;` `public` `class` `Geeks {` ` ``public` `static` `void` `main(String[] args)`` ``{` ` ``double` `num1 = -``0.65``, num2 = -``6.30``;` ` ``// It returns the arc cosine of a value`` ``double` `acosValue = StrictMath.acos(num1);`` ``System.out.println("The arc cosine value of "+`` ``num1 + " = " + acosValue);` ` ``acosValue = StrictMath.acos(num2);`` ``System.out.println("arc cosine value of "+`` ``num2 + " = " + acosValue);`` ``}``}`
Output:
```The arc cosine value of -0.65 = 2.278380763520252
arc cosine value of -6.3 = NaN```
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The school's total attendance is 524, there are 91 present in math class, what percent of the total attendance is the attendance in the math class?
Question
Updated 3/4/2015 9:01:22 AM
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User: The school's total attendance is 524, there are 91 present in math class, what percent of the total attendance is the attendance in the math class?
Weegy: 91% in math class. 467 students attends math
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Question
Updated 3/4/2015 9:01:22 AM
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The school's total attendance is 524, there are 91 present in math class, thepercent of the total attendance of the attendance in the math class is 17.37%.
91/524*100=17.37
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# Questions on Geometry: Rectangles answered by real tutors!
Algebra -> Algebra -> Rectangles -> Questions on Geometry: Rectangles answered by real tutors! Log On
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Geometry: Rectangles Solvers Lessons Answers archive Quiz In Depth
## Tutors Answer Your Questions about Rectangles (FREE)
Question 61017: I need help. I am lost on this algebra. The area of a rectangle is 119 m2. The base is four less than three times the height. What is the length of the base? Click here to see answer by checkley71(8403)
Question 61413: well i`ve been trying this problem for hours "A field has a perimeter of 240 yards. The length is 20 yards less than the width. Find the length and width"? I cant find the answer. Click here to see answer by checkley71(8403)
Question 61416: well i`ve been trying this problem for hours "A field has a perimeter of 240 yards. The length is 20 yards less than the width. Find the length and width"? I cant find the answer. Click here to see answer by checkley71(8403)
Question 61531: a dairy farmer plans to enclose a rectangular pasture adjacent to a river. the pasture must contain 180,000 square meters. no fencing is required along the river. what dimensions will use the smallest amount of fencing? so confusing?? please help Click here to see answer by asha(30)
Question 61690: C Click here to see answer by tutorcecilia(2152)
Question 61690: C Click here to see answer by uma(370)
Question 62768: Two different rectangles each have an area of 360 sq. centimeters. The length of the second rectangle is 12 centimeters greater than the first, whereas its width is 5 centimeters less than the first rectangle. Find the difference of the perimeters of the two rectangles. Click here to see answer by uma(370)
Question 64763: Urban Planning: You have just planted a rectangular flowere bed of red roses in a park near your home. You want to plant a border of yellow roses around the flower bed as show. Since you bought the same number of red and yellow roses, the areas of the border and inner flower bed will be equal. What shoud the width X of the border be? rectangle is 12 x 8 with double x at each corner,(total 8x) Click here to see answer by 303795(595)
Question 64884: Please help: The length of a rectangle is 4 feet less than twice the width of the rectangle. If the perimeter of the rectangle is 136 feet, find the length of the rectangle. Click here to see answer by checkley71(8403)
Question 64982: If someone anyone can help me with this problem I'd really appreciate it. The prblem is " A retangular garden has a length that is 5 meter longer than half the width. If the perimeter is 30 meters longer than twice the width, length, find the length." I know how to find the perimeter but this is on a study guide for semester finals I really need help. PLEASE help. thanks confused?? Click here to see answer by ptaylor(2048)
Question 65482: Find the perimeter given the figure: Length side is represented by: x ------ 2x-5 The short side is represented by: 8 ----- 2x-5 This problem has confused me with putting in the division problems. Can anyone help me understand this please. Thank you so much! Click here to see answer by stanbon(57246)
Question 65571: The question is find the perimeter given the figure I hope this diagran helps you with the question :-) Here is the rectangle with the figures: x ------ 2x - 5 -------------------------- - - - - 8 - - ------ - - 2x - 5 - - -------------------------- Click here to see answer by funmath(2925)
Question 65712: The length of a rectangle is 1cm longer than its width. If the diagonal of the rectangle is 4cm, what are the dimensions (length and width) of the rectangle? Talk about confusing to me! Thank you for the help! Click here to see answer by funmath(2925)
Question 65712: The length of a rectangle is 1cm longer than its width. If the diagonal of the rectangle is 4cm, what are the dimensions (length and width) of the rectangle? Talk about confusing to me! Thank you for the help! Click here to see answer by Nate(3500)
Question 65692: Find the area of the rectangle: Here is the best drawing I could do: ================= = = = = = = dqrt3 + sqrt5 = = = = ================= sqrt3 + sqrt5 Click here to see answer by funmath(2925)
Question 65775: The length of a rectangle is 1cm longer than its width. If the diaganol of rectangle is 4cm, what are the dimensions (length and width) of the rectangle? Thank you Click here to see answer by checkley71(8403)
Question 65882: The width of a rectangle is 3ft. less than the length. The perimeter is 10ft. Find the width Click here to see answer by Earlsdon(6287)
Question 66684: the area of a rectangle is 108 cm2. the ratio of the width to the length 3:4. find the length and the width. Click here to see answer by Nate(3500)
Question 66979: The perimeter of a triangle is 69 cm. If the three sides of the trianglehave lengths of (3x+2), (2x-1), (4x+5), find the length of the shortest side. Equation________________ Solution__________________ Click here to see answer by checkley71(8403)
Question 67093: The length of a rectangular playing field is 5ft less than twice its width. if the perimeter of theplaying field is 230 ft. find the length and width of the field. Click here to see answer by Zoop(21)
Question 67560: The length of a rectangular playing field is 5 ft less than twice its width. If the perimeter of the playing field is 230 ft, find the length and width of the field. Click here to see answer by ankor@dixie-net.com(15638)
Question 67700: The length of a rectangle is 2in. more than twice its width. If the perimeter of the rectangle is 34 in., find the dimensions of the rectangle. Thanks. Click here to see answer by tutorcecilia(2152)
Question 68061: The length of a rectangle is 2 cm more than twice its width. If the perimeter of the rectangle is 52 cm, find the dimensions of the rectangle. Click here to see answer by Earlsdon(6287)
Question 68316: The area of a rectangle is 216ft. squared. The length of the rectangle is 18ft. If a scale drawing of the figure has a scale of 1/2in. = 6ft. What are the dimensions of the rectangle on the scale drawing? Click here to see answer by rmromero(383)
Question 68969: A rectangle has sides with integral lengths. The number of units in its perimeter is the same as the number of square units in its area. What are the dimensions of the rectangle Click here to see answer by ankor@dixie-net.com(15638)
Question 68969: A rectangle has sides with integral lengths. The number of units in its perimeter is the same as the number of square units in its area. What are the dimensions of the rectangle Click here to see answer by Edwin McCravy(8882)
Question 68577: P=44 units,x+6 (side) x+6 (bottom) This is my Square Equation Any help would be greatly appreciated:) Click here to see answer by Nate(3500)
Question 69524: If the base of a rectangle is 23.4 mm and the are is 439.92 mm2, what is the height of the rectangle Click here to see answer by justsmilexx(8)
Question 69613: Please help me with this problem I'm sure there's a simple solution to solving it, but my book only provides the answer, not the actual explanation of how to solve it. First, the question is, find the perimeter of rectangle PQRS. The top length side of the rectangle (PQ) is 11 inches. The bottom length side (SR) is (7x-3) inches. The right width side (QR) is (3x-3) inches. The left width side (PS) is unknown. I have already solved for x with this equation 7x-3=11 which =2, but when I insert 2 into the equation 3x-3 and add all the sides to find the perimeter of the rectangle it doesn't match the answer in the book. Click here to see answer by bucky(2189)
Question 69899: the rectangle has a premiter of 64cm. the length needs 4cm. to be twice the size as the width please slove and explain Click here to see answer by ptaylor(2048)
Question 69919: The question reads: A rectangular fence has an area of 900 sq. yards. Express the linear yardage required as a function of the length. Now, I understand that Area=length x width, and that the Perimeter=2(length)+2(width). I can certainly figure the area from the perimeter, but now I'm stuck with this (perimeter from the area). PLEASE HELP! Click here to see answer by ankor@dixie-net.com(15638)
Question 70119: The width of a rectangle is decreased by 20%. By what percent would the length have to be increased for the area to remain the same? Click here to see answer by Edwin McCravy(8882)
Question 70112: A piece of wire 57 inches long is cut into two pieces, and two rectangles are formed from the pieces. If you want the sum of the areas of the two rectangles to be as large as possible, how long should you make the pieces? Click here to see answer by checkley75(3666)
Question 70374: The length of a rectangle is 2in. more than twice its width. If the perimeter of the rectangle is 52in., find the width of the rectangle. I need help with this one please, thank you Click here to see answer by funmath(2925)
Question 70426: The length of a rectangle is 8in more than twice its wodth. If the perimeter of the rectangle is 64in, find the width of the rectangle. Multiple choice: a) 10in b) 7in c) 8in d) 9in How do I get this to figure out one of these answers? Thank you Click here to see answer by checkley75(3666)
Question 70602: if the area of a rectangle is twenty seven square feet. the base is three more than twice the height. what are the dimensions of the rectangle? Click here to see answer by checkley75(3666)
Question 71214: I have a problem that I can't figure out. If the perimeter of a square is 16s+24, find the area. I keep coming up with an answer that I know just be right.Thank you Click here to see answer by ankor@dixie-net.com(15638)
Question 71213: The perimeter of a suare is 16s + 24. find its area Click here to see answer by ptaylor(2048)
Question 71290: Find the perimeter of the given figure. Top: Side: I am confused on how to solve this problem. I need some help. Thanks Click here to see answer by checkley75(3666)
Question 71689: The perimeter of a rectangle is 420 inches. The width is 4 inches less than the length. What is the length of the rectangle? Click here to see answer by bucky(2189)
Question 71682: The perimeter of a rectangle is 420 inches. The width is 4 inches less than the length. What is the length of the rectangle? Click here to see answer by ptaylor(2048)
Question 72630: Solve and show work. The length of a rectangle is 2 cm more than twice its width. If the perimeter of the rectangle is 52 cm, find the dimensions of the rectangle. Click here to see answer by Edwin McCravy(8882)
Question 72791: If the perimeter of a rectangle is 18 ft and the width is 6 ft, find its length. [Hint: The perimeter of a rectangle is given by P = 2L + 2W.] Click here to see answer by Earlsdon(6287)
Question 72970: I am trying to figure out a problem that my teacher gave my class. A rectangle has a perimeter of 4 inches. If the sides of the rectangle are whole numbers of inches, how many different combinations of measures are possible? So far I have figure 1 solution, 1+1+1+1 Still, I think this is a square not a rectangle. Any insight would be helpful. Click here to see answer by bucky(2189)
Question 73092: The length of a rectangle is 2 cm more than twice its width. If the perimeter of the rectangle is 52 cm, find the dimensions of the rectangle. Click here to see answer by checkley75(3666)
Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760
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# Future of Computing
The basic unit of information in a traditional computer is a bit, which has a value of 0 or 1. This basic unit allows computer processor to perform logical operations which are in turn carried out by electronic circuits. Based on these basic logical structures, algorithmic models are devised which allows us to perform sophisticated computations. But what’s on top of computations? Its randomness. Computer games, cryptography and computational geometry are unthinkable without randomness. and distributed computation is not deterministic. The future of computing, based on the root of randomness, would expose possibilities in the following areas.
## Quantum Computing
In quantum computer, the basic unit of information is called a quantum bit, or qubit. Qubit has values of 0 and 1, but it can also exist in an intermediate state, which is like a superposition of the two classic states 0 and 1. The biggest difference between quantum computer and traditional computers are, quantum computers can perform some computations more efficiently than a traditional computer. Some problems which currently has no efficient algorithms known on traditional computers can be solved in an efficient manner with quantum computers. The popular public-key cryptosystems such as RSA whose security is based on the difficulty of factoring large integers would be rendered obsolete with the advent of quantum computers.
As with current algorithmic approach, the way to search for a given value in an unordered list is to search each item, one-by-one. Given n items, the Big O notation is thus n. With quantum computers, given correct algorithms, this time complexity could be reduced to square root n in the worst case.
However, building a quantum computer is a challenge because qubits are unstable. Even successful prototypes exist in only few bits. With adequate research, i believe algorithms will be completely rewritten with the advent of quantum computers.
## DNA Computing
DNA(deoxyribonucleic acid) encodes genetic information as a string of chemicals, called bases, typically denoted A,C,G,and T. In DNA computing, bits are replaced by the bases A,C,G and T. Strands of DNA represent data, just as strings of bits represent data in a traditional computer. A DNA computation begins by generating stands of DNA to represent possible solutions to a particular problem. After the computation ends, any DNA strands that remain represents a solution to the problem.
Currently, the United States Data Encryption Standard(DES) are used for the secure exchange of information such as banking and national security matters. It relies on one of 72 quadrillion keys to encode a message. The security results from the difficulty of discovering which key was used. Checking all possible keys is impossible using a traditional computer because it would take too long. However, because DNA computing derives its power from massive parallelism, it could check all 72 quadrillion keys concurrently. Estimates indicate that the computation could take as little as two hours.
There are fears that security would be non-existent with these kinds of ‘super-computers’. But technology always comes as a double edged sword, they may well allow us to develop algorithms on the next spectrum which would again render to a cat and mouse chase. I’m excited about the computing future, yet worried how humans would use it for destructive means.
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# Linear points
Rectilinear points
In the Cartesian plane, the basic building blocks are points and lines. A linear equation can take various forms, such as the point-slope formula, the pitch-distance formula, and the standard form of a linear equation. <font color="#ffff00">-==- sync:ßÇÈâÈâ
Linear equations are equations with two variable whose graphic is a line. Figure of the linear expression is a series of points in the co-ordinate level which are all solution to the expression. When all the variable numbers symbolize reality, the formula can be graphically represented by drawing enough points to identify a sample and then connecting the points to cover all the points.
When you want to plot a linear expression, you must have at least two points, but it is usually a good option to use more than two points. Try to select points that take both positives and negatives and zero into account. Currently, this is an example of a discreet operation.
Distinct functions consist of insulated points. If we draw a line through all points and extend the line in both direction, we get the opposite of a discreet feature, a continual feature that has a uninterrupted plot. When you only want to use two points to define your line, you can use the two points where the chart intersects the alignments.
At the point where the chart intersects the x-axis, it is referred to as x-intercept, and at the point where the chart intersects the y-axis, it is referred to as y-intercept. To find the x-intercept, find the value of y if y = 0, (x, 0), and to find the y-intercept, find the value of y if y = 0, (0, y).
To graphically represent a linear expression in its default shape, you must first resolve the y expression. From here, you can graphically represent the expression as we did in the example above.
## Dot points and line
Dot points and strokes are abstracted arithmetic entities, but they have a straight forward physics meaning on a Kartesian level. Whilst Euclid's basic work in The Elements was rather vague as to what a point and a line were, with the inflexible frame of Kartesian geometry we can specify these notions. lineages and their linear equations.
In our view, the Cardesian layer is modeled by a piece of millimetre chart with two axles, one horizontally named the axle and one vertically named the axle. Every axle is indicated by coordinates: Normally only whole number numbers (e.g. etc.) are displayed, but we should be ready to consider fractions as well.
Snap together evenly across horizontals and verticals for easy point display and function visualization. While the first item is named -coordinate of the point, the second item is -coordinate of .... We follow the conventions that are shown graphically by switching from the source to the right to the location on the axis and then up to the location on the axis.
Which of the following points is not shown in the following chart? Had you drawn in this point, would it be exactly half between which two points? A line is officially defined as an expression of shape, e.g. . Like dots, line has name, so we could spell.
Conventions are that the line is plotted by recording the points that actually meet the equal. There are two such points here: These are probably the easiest points to find, as inserting into formulas is generally quite simple. Indeed, the x-interception of the wire is named, while the y-interception is named.
Due to things that should be apparent to you, the - and - intersections are the points where this line intersects the and axis. Below are some extra points that fulfill our formula, which is a bit more systematic: Once all these points are present, we can draw the line as shown: We will allow the same line to be reexpressed in different ways because an algebraic manipulation of an expression is possible.
Let us now take a look at a few rows. One of the following line does not appear in the figure above? f) . And if the row missed from the preceding Q was inserted, would it go through the intersection points of which dots? What is nice about this arrangement is that the response does not need a graphical representation of lines: it is a pure arithmetic matter whether the two co-ordinates correspond to the line or not.
Remember that you can also see this algebraically: the coordinates are halfway between and, and the coordinates are halfway between and . If you insert it, it would go through the point that also is on the line.
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https://www.quanswer.com/en/therese-bought-10-bags-of-buai-at-k400-each-she-paid-k2-000-for-vehicle-hire-and-spent-k1-000-on-other-expenses-she-sold-8-bags-at-k900-each-and-2-bags-at-k700-each-calculate-her-total-expenses
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> #mathematics , #finance > Therese bought 10 bags of buai at K400 each. She paid K2 000 for vehicle hire,and spent K1 000 on other expenses. She sold 8 bags at K900 each and 2 bags at K700 each. Calculate her total expenses?
Nickii Fay
more than 3 weeks ago
Therese bought 10 bags of buai at K400 each. She paid K2 000 for vehicle hire,and spent K1 000 on other expenses. She sold 8 bags at K900 each and 2 bags at K700 each. Calculate her total expenses?
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ChatGPT
more than 3 weeks ago
Total cost of buying 10 bags of buai = 10 bags x K400/bag = K4 000
Total expenses = K2 000 (vehicle hire) + K1 000 (other expenses) + K4 000 (cost of buying buai) = K7 000
Therese sold 8 bags at K900 each, earning 8 bags x K900/bag = K7 200
She also sold 2 bags at K700 each, earning 2 bags x K700/bag = K1 400
Total earnings = K7 200 + K1 400 = K8 600
Total expenses = K7 000
Total earnings = K8 600
Therese's total expenses were K7 000.
0
more than 3 weeks ago
Therese's Expenses:
- Buai purchase: 10 bags x K400 per bag = K4,000
- Vehicle hire: K2,000
- Other expenses: K1,000
Total expenses = K4,000 + K2,000 + K1,000 = K7,000
Therese's Income:
- 8 bags sold at K900 per bag: 8 x K900 = K7,200
- 2 bags sold at K700 per bag: 2 x K700 = K1,400
Total income = K7,200 + K1,400 = K8,600
Therese's Profit/Loss:
- Income - Expenses = K8,600 - K7,000 = K1,600
Conclusion:
Therese made a profit of K1,600.
0
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https://www.physicsforums.com/threads/parallel-of-least-radius.160619/
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Homework Help: Parallel of Least Radius
1. Mar 13, 2007
Dragonfall
1. The problem statement, all variables and given/known data
Show that on of the hyperboloid of revolution x^2+y^2-z^2=1, the parallel of least radius is the line of striction, ...
What's the parallel of least radius?
2. Mar 14, 2007
HallsofIvy
The "parallel of least radius" is the line, parallel to an axis, that is shortest from one point on the hyperboloid to another.
Now, clear up my confusion: what is a "line of striction"?
3. Mar 14, 2007
Dragonfall
Given a ruled surface x(t,v)=a(t)+vw(t), a line of striction is a curve b(t) such that <b'(t),w'(t)>=0 for all t and b lies on the trace of x, ie b(t)=a(t)+u(t)w(t) for some real valued function u(t). It be can then shown that u(t) is given by
$$u=-\frac{<a',w'>}{<w',w>}$$.
The points of a line of striction are the "central points" of the ruled surface.
Last edited: Mar 14, 2007
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https://mathjokes4mathyfolks.wordpress.com/2016/04/30/heavy-cookies-undervalued-coins-and-misconceptions/
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## Heavy Cookies, Undervalued Coins, and Misconceptions
Simple question to get us started…
Which is worth more?
And of course the answer is, “The quarters, because 50¢ is more than 20¢,” right? But not to a kindergarten student or a pre-schooler who hasn’t yet learned how much coins are worth. A young student might argue, “Four is more than two.”
Why didn’t the quarter follow the nickel when he rolled himself down the hill?
Because the quarter had more cents.
Recently, I was asked to review an educational video for kindergarten math that had a similar question.
The video stated, “Can you tell the green, yellow, and orange cookies are heavier? That makes sense, doesn’t it? Because there are more of them!”
Uh, no.
This is the same logic that would lead one to claim that the value of four nickels is greater than the value two quarters because there are more nickels. It’s a huge misconception for students to focus on number rather than value. So it’s very frustrating to see this video reinforce that misconception.
For example, if each green, yellow, or orange cookie weighs 3 ounces, but each blue or purple cookie weighs 5 ounces, then the left pile would weigh 6 × 3 = 18 ounces, and the right pile would weigh 4 × 5 = 20 ounces, so the right side would be heavier. (Then again, are there really 6 cookies on the left and 4 on the right, or are some cookies hidden? Hard to tell.)
As far as I’m concerned, the only acceptable answer is that the pile of green, yellow, and orange cookies must be heavier — assuming, of course, that the balance scale isn’t malfunctioning — because the pans are tipped in that direction.
All of this reminds me of the poem “Smart” by Shel Silverstein.
SMART
My dad gave me one dollar bill
‘Cause I’m his smartest son,
And I swapped it for two shiny quarters
‘Cause two is more than one!
And then I took the quarters
For three dimes — I guess he don’t know
That three is more than two!
Just then, along came old blind Bates
And just ’cause he can’t see
He gave me four nickels for my three dimes,
And four is more than three!
And I took the nickels to Hiram Coombs
Down at the seed-feed store,
And the fool gave me five pennies for them,
And five is more than four!
And then I went and showed my dad,
And he got red in the cheeks
And closed his eyes and shook his head–
Too proud of me to speak!
Entry filed under: Uncategorized. Tags: , , , , , , , .
The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.
## MJ4MF (offline version)
Math Jokes 4 Mathy Folks is available from Amazon, Borders, Barnes & Noble, NCTM, Robert D. Reed Publishers, and other purveyors of exceptional literature.
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Working with Expressions - THE SAT MATH TEST: THE HEART OF ALGEBRA - SAT 2016
## THE SAT MATH TEST: THE HEART OF ALGEBRA
1. Working with Expressions
2. Working with Linear Equations
3. Working with Inequalities and Absolute Values
4. Working with Linear Systems
The SAT Math: Heart of Algebra
Why is algebra so important on the SAT Math test?
About 36% (21 out of 58) of the SAT Math questions fall under the category called the “Heart of Algebra.” Questions in this category test your ability to
analyze, fluently solve, and create linear equations, inequalities, [and] systems of equations using multiple techniques.
These questions will also assess your skill in
interpreting the interplay between graphical and algebraic representations [and] solving as a process of reasoning.
The specific topics include
• creating and solving linear equations in one and two variables
• graphing and interpreting linear equations
• creating, interpreting, and solving linear systems
• graphing and solving inequalities and systems of inequalities
• interpreting and solving algebraic word problems
Why are these skills important?
Algebra is an essential tool of quantitative analysis not only in math but also in subjects like engineering, the physical sciences, and economics. When describing the relationships between or among different quantities, or exploring the nature of unknown quantities, algebra provides essential tools for analyzing and solving problems. Most colleges consider fluency in algebra to be a vital prerequisite to a college-level liberal arts curriculum.
Sound intimidating? It’s not.
If you take the time to master the four core skills presented in these 13 lessons, you will gain the knowledge and practice you need to master even the toughest SAT Math “Heart of Algebra” questions.
### Skill 1: Working with Expressions
Lesson 1: Using algebraic expressions
To solve tough SAT math problems, you must be fluent in defining, manipulating, and analyzing algebraic expressions.
Corrine drives to her office at an average speed of 50 miles per hour. When she returns home by the same route, the traffic is lighter and she averages 60 miles per hour. If her trip home is 10 minutes shorter than her trip to her office, what is the distance, in miles, from Corrine’s home to her office?
(Medium-hard) Why does everyone hate “word problems” like this one? For most of us, the problem is that the equations aren’t “set up” for us—we have to set them up ourselves, which can be a pain in the neck. But we can make these problems much easier by breaking them down into clear steps.
Key Steps to Solving Tough Algebraic Problems
Solving tough problems in mathematics and science frequently involves four essential steps:
1. identify the relevant quantities in the situation
2. express those quantities with algebraic expressions
3. translate the facts of the problem situation into equations involving those expressions
4. analyze and solve those equations
Step 1. Identify: In this problem, there are six relevant quantities:
• the speed from home to work
• the distance from home to work
• the time it takes to get from home to work
• the speed from work to home
• the distance from work to home
• the time it takes to get from work to home
This may seem like a lot, but as we will see, keeping track of them is quite manageable.
Step 2. Express: The problem gives us enough information to express all six quantities in terms of only two “unknowns.” If d is the distance, in miles, from her home to her office, and t is the time, in hours, it takes her to get home from the office, then we can express our six quantities, respectively, as
Step 3. Translate: To translate the facts of this problem into equations, we must know the formula distance = average speed × time. Applying this to each trip gives us
Step 4. Analyze and Solve: We have now reduced the problem to a “two by two system,” that is, two equations with two unknowns. Since the number of equations equals the number of unknowns, we should be able to solve for those unknowns. (In Lessons 12 and 13, we will review these concepts and techniques.) Since the unknown d is isolated in both equations, substitution is simple:
Since t represents the time it took Corrine to return home, in hours, this means it took her 5/6 hours (or 50 minutes) to get from her office to her home, and 5/6 hour + 1/6 hour = 1 hour to get to her office from home. But remember, the question asks for the distance from her home to her office, which we can find by substituting into either of our equations:
50(5/6 + 1/6) or 60(5/6) = 50 miles
Lesson 2: The Laws of Arithmetic
When expressing or simplifying a quantity, you frequently have many options. For instance, the expression 4x2 – 12x can also be expressed as 4x(x – 3). Similarly, 3.2 can be expressed as 16/5 or 3 or 32/10. Which way is better? It depends on what you want to do with the expression. Different forms of an expression can reveal different characteristics of that quantity or the equation in which it appears. To gain fluency in expressing quantities, you must understand the Laws of Arithmetic.
To simplify complex expressions, you must know the Order of Operations:
PG-ER-MD-AS
Step 1: PG (parentheses and other grouping symbols, from innermost to outermost and left to right)
Since this expression contains no parentheses, we don’t have to worry about “grouped” operations, right? Wrong! Remember that fraction bars and radicals are “grouping symbols” just like parentheses are.
In other words, we can think of this expression as
If a set of parentheses contains only one operation, then we simply do that operation:
If it contains more than one operation, then we must move on to the next step.
Step 2: ER (exponents and roots, from innermost to outermost and left to right)
Do any of the parentheses contain exponents or roots? Yes, so we must perform that operation next:
Step 3: MD (multiplication and division, from left to right)
Next, we do any multiplication inside the parentheses:
Step 4: AS (addition and subtraction, from left to right)
Now we do any addition and subtraction left in the parentheses:
Once all the “grouped” operations are completed, we run through the order of operations once again to finish up. Exponents or roots? No. Multiplication or division? Yes:
1.875 + 2
Addition or subtraction? Yes: 1.875 + 2 = 3.875
What is the sum of the first 100 positive integers?
(Hard) Here, following the order of operations would be, shall we say, less than convenient: it would require 99 computations. Even with a calculator, it would be a pain. But here is a much simpler method:
Original expression:
1 + 2 + 3 + 4 + … + 97 + 98 + 99 + 100
Rearrange and regroup:
(1 + 100) + (2 + 99) + (3 + 98) + … + (50 + 51)
Simplify:
(101) + (101) + (101) + … + (101)
Since we have 50 pairs, this equals:
50(101)
Simplify:
5,050
This gives us exactly the same result as the order of operations would give, but with just a few simple calculations. How did we do it? By using three more laws of arithmetic: the commutative law of addition, the associative law of addition, and the distributive law of multiplication over addition.
Use the Laws of Arithmetic to simplify expressions or reveal their properties.
e.g., 3 + 8 + 17 + 12 = 3 + 17 + 12 + 8
The Commutative Law of Multiplication
When multiplying, order doesn’t matter.
e.g., 2 × 16 × 50 × 3 = 3 × 16 × 50 × 2
e.g., 1 + 100 + 2 + 99 + 3 + 98 + … + 50 + 51 = (1 + 100) + (2 + 99) + (3 + 98) + … + (50 + 51)
The Associative Law of Multiplication
When multiplying, grouping doesn’t matter.
e.g., 1 × 2 × 3 × 4 × 5 = (1 × 2 × 3) × (4 × 5)
The Distributive Law of Multiplication over Addition
When multiplying by a grouped sum, you don’t have to do the grouped sum first; you can multiply first, as long as you distribute the multiplication over the entire sum.
e.g., 5(20 + 7) = 5 × 20 + 5 × 7 = 100 + 35 = 135
Which of the following is equivalent to 3(34 × 53)? [No calculator]
A) 3(34) × 3(53)
B) 94 + 153
C) 94 × 153
D) 35 × 53
Before making your choice, check the laws of arithmetic; don’t make up your own laws. Which laws of arithmetic can we use? Since the expression is a product, we can use the commutative law of multiplication and jumble up the terms, or the associative law of multiplication and regroup the terms any way we want (or not at all). Using the associative law gives us
Don’t “over-distribute.”
Were you tempted to choose (A), (B), or (C) in the question above? If so, you are not alone. You are simply the victim of one of the most common mistakes in algebra: over-distribution. It comes from a misinterpretation of the Law of Distribution. The correct law is
When multiplying by a grouped sum, you don’t have to do the grouped sum first; you can multiply first, as long as you distribute the multiplication over the entire sum.
It is not
If something is outside parentheses, just bring it inside and distribute.
Look at these examples of “over-distribution” and verify that they are incorrect:
3(2 × 5) is not equal to (3 × 2) + (3 × 5) or (3 × 2) × (3 × 5)
(2 + 3)2 is not equal to 22 + 32
If x ≠ 0, which of the following equals ?
A)
B)
C) 2x2 + 2
D) 4x + 2
(Medium)
Distributive Law:
Division by a number is multiplication by its reciprocal:
Distributive Law:
So the correct answer is (D). Look at each step carefully and notice how each one uses a particular Law of Arithmetic. In particular, notice that the “combining of like terms” in steps 1–3 is really an example of commuting, associating, and (un)distributing. Even more interesting, notice that steps 4–5 show that division distributes just like multiplication does.
You can also distribute division over addition just as you can distribute multiplication.
How many distinct values of x are solutions to the equation x2 + 4 = −4x?
A) none
B) one
C) two
D) three
(Medium) You might recognize that this equation is a quadratic equation (which we will discuss in much more detail in Chapter 9) and remember that such equations usually have two distinct solutions, but not always, so we must look at this equation more carefully.
Step 2 might seem a bit mysterious. Why did we write 4x as 2x + 2x? Here we are using the Product-Sum Method for factoring quadratics, which is explained in a bit more detail in Chapter 9, Lesson 4. For now, though, just notice that each step follows a particular Law of Arithmetic.
If the product of two numbers is 0, then one of those numbers must be 0. (This is the Zero Product Property.) Therefore x + 2 = 0 and so x = −2. Since the other factor is the same, we only get one solution to this equation, and the answer is (B).
To check the equation in step 5, we can FOIL the product of binomials on the left side to make sure we get the same expression we had back in step 1: (x + 2)(x + 2) = x2 + 4x + 4, which is precisely the expression we started with in step 1, confirming that our work is correct.
This means that the factoring process in steps 2–5 can be thought of as un-FOILing. We will look at this method of factoring more carefully in Chapter 9.
Make sure you know how to FOIL and un-FOIL.
FOILing is simply the shortcut for multiplying two binomials, which requires applying the distributive law twice. For example:
Exercise Set 1 (No Calculator)
1
(1 − (1 − (1 − 2))) − (1 − (1 − (1 − 3))) =
2
When 14 is subtracted from 6 times a number, 40 is left. What is half the number?
3
Four consecutive even numbers have a sum of 76. What is the greatest of these numbers?
4
If , then 10x + 12 =
5
What number decreased by 7 equals the opposite of five times the number?
6
If 5d + 12 = 24, then 5d − 12 =
7
If , then y + 5 =
8
The product of x and y is 36. If both x and y are integers, then what is the least possible value of x − y?
A) −37
B) −36
C) −35
D) −9
9
If a factory can manufacture b computer screens in n days at a cost of c dollars per screen, then which of the following represents the total cost, in dollars, of the computer screens that can be manufactured, at that rate, in m days?
A)
B)
C)
D)
10
Which of the following is equivalent to 5x(2x × 3) − 5x2 for all real values of x?
A) 5x2 + 15x
B) 25x2
C) 5x2 − 15x
D) 10x2 × 15x − 5x2
11
The symbol Ο represents one of the fundamental operators: +, −, ×, or ÷. If (x Ο y) × (y Ο x) = 1 for all positive values of x and y, then Ο can represent
A) +
B) ×
C) −
D) ÷
Exercise Set 1 (Calculator)
12
The difference of two numbers is 4 and their sum is 14. What is their product?
13
If x + y − 1 = 1 − (1 − x), what is the value of y?
14
If 3x2 + 2x = 40, then 15x2 + 10x =
15
Ellen is currently twice as old as Maria, but in 6 years, Maria will be 2/3 as old as Ellen. How old is Ellen now?
16
If 2x − 2y = 5 and x + y = 6, what is the value of x2 − y2?
17
On a typical day, a restaurant sells n grilled cheese sandwiches for p dollars each. Today, however, the manager reduced the price of grilled cheese sandwiches by 30% and as a result sold 50% more of them than usual. Which of the following represents the revenue for today’s grilled cheese sandwich sales, in dollars?
A) 0.5np − 0.3
B) 1.05np
C) 1.20np
D) 1.50np
18
For all real numbers x and y, 4x(x) − 3xy(2x) =
A) 12x2y(x − 2y)
B) 2x2(2 − 3y)
C) 2x2(2 + 3y)
D) 4xy(x − 3y)
19
If a = 60(99)99 + 30(99)99b = 99100, and c = 90(90)99, then which of the following expresses the correct ordering of ab, and c?
A) c < b < a
B) b < c < a
C) a < b < c
D) c < a < b
20
Which of the following statements must be true for all values of xy, and z?
I. (x + y) + z = (z + y) + x
II. (x − y) − z = (z − y) − x
III. (x ÷ y) ÷ z = (z ÷ y) ÷ x
A) I only
B) I and II only
C) I and III only
D) II and III only
21
Carlos began with twice as much money as David had. After Carlos gave \$12 to David, Carlos still had \$10 more than David. How much money did they have combined at the start?
A) \$34
B) \$68
C) \$102
D) \$108
No Calculator
1. 1
(1 − (1 − (1 − 2))) − (1 − (1 − (1 − 3)))
Parentheses:
(1 − (1 − (−1))) − (1− (1 − (−2)))
Next parentheses:
(1 − (2)) − (1 − (3))
Next parentheses:
(−1) − (−2)
Subtract:
−1 + 2 = 1
2. 9/2 or 4.5
6x − 14 = 40
6x = 54
Divide by 6:
x = 9
Multiply by :
3. 22 Let n be the least of these numbers. The sum of four consecutive even numbers is therefore n + (n + 2) + (n + 4) + (n + 6) = 76.
Simplify:
4n + 12 = 76
Subtract 12:
4n = 64
Divide by 4:
n = 16
Therefore the largest of these numbers is 16 + 6 = 22.
4. 28
Multiply by 4:
10x + 12 = 28
5. 7/6 or 1.16 or 1.17
x − 7 = −5x
Subtract x:
−7 = −6x
Divide by –6:
6. 0
5d + 12 = 24
Subtract 24:
5d − 12 = 0
7. 5
Subtract y2:
Multiply by −5/3:
y2 = 0
Take square root:
y = 0
y + 5 = 5
8. C If xy = 36 and x and y are integers, then x and y are both factors of 36. In order to minimize the value of x − y, we must find the greatest separation between x and y. The greatest separation between a factor pair is 1 − 36 = −35.
9. A We should regard this as a “conversion” problem from m days into a corresponding number of dollars.
10. B Original expression:
5x(2x × 3) − 5x2
Parentheses:
5x(6x) − 5x2
Multiply:
30x2 − 5x2
Subtract:
25x2
Remember: The Law of Distribution does not apply in the first step, because the grouped expression doesn’t include addition or subtraction.
11. D The simplest approach is perhaps to choose simple values for x and y, like 2 and 3, and see which operator yields a true equation. Since (2 ÷ 3) × (3 ÷ 2) = 1, the answer is (D).
Calculator
12. 45
a − b = 4
a + b = 14
2a = 18
Divide by 2:
a = 9
Substitute a = 9:
9 + b = 14
Subtract 9:
b = 5
Evaluate ab:
ab = 9 × 5 = 45
13. 1
x + y − 1 = 1 − (1 − x)
Distribute:
x + y − 1 = 1 − 1 + x
Subtract x:
y − 1 = 1 − 1
Simplify:
y − 1 = 0
y = 1
14. 200
3x2 + 2x = 40
Multiply by 5:
15x2 + 10x = 200
15. 12 Let e = Ellen’s current age and m = Maria’s current age.
Ellen is twice as old as Maria:
e = 2m
In 6 years, Maria will be 2/3 as old as Ellen:
Substitute e = 2m:
Multiply by 3:
3m + 18 = 2(2m + 6)
Distribute:
3m + 18 = 4m + 12
Subtract 3m and 12:
6 = m
Therefore e = 2m = 2(6) = 12.
16. 15 First equation:
2x − 2y = 5
Divide by 2:
x − y = 2.5
Second equation:
x + y = 6
Multiply:
(x − y)(x + y) = x2 − y2 = (2.5)(6) = 15
Alternately, we could solve the system using either substitution or linear combination and get x = 4.25 and y = 1.75, and evaluate x2 − y2 = (4.25)2 − (1.75)2 = 18.0625 − 3.0625 = 15.
17. B The revenue is equal to the number of items sold times the price per item. If the restaurant typically sells n sandwiches per day, but today sold 50% more, it sold 1.5n sandwiches. If the price p was reduced 30%, today’s price is 0.70p. Therefore, the total revenue is (1.5n)(0.70p) = 1.05np.
18. B
4x(x) − 3xy(2x)
Multiply:
4x2 − 6x2y
Largest common factor:
2x2(2 − 3y)
19. D Although a calculator is permitted for this question, most calculators will give an “overflow error” when trying to calculate numbers like 99100, because they’re just too large. However, comparing these numbers is straightforward if we can express them in a common format.
20. A Only statement I is true, by the Commutative and Associative Laws of Addition. Choosing simple values like x = 1, y = 2, and z = 3 will demonstrate that statements II and III do not yield true equations.
21. C Let x = the number of dollars David had to start. If Carlos started with twice as much money as David, then Carlos started with 2x dollars. After Carlos gave David \$12, Carlos had 2x − 12 dollars and David had x + 12 dollars. If Carlos still had \$10 more than David, then
2x − 12 = 10 + x + 12
Simplify:
2x − 12 = x + 22
2x = x + 34
Subtract x:
x = 34
Therefore, David started with \$34 and Carlos started with 2(\$34) = \$68, so they had \$34 + \$68 = \$102 combined to start.
Lesson 3: Simplifying expressions and operations
If x and y are positive numbers and 3x − 2y = 7, what is the value of ?
A)
B)
C)
D)
(Easy) Working with algebraic equations doesn’t always mean “solving for x.” Notice that this particular question doesn’t ask for the values of x or y, but rather for the value of a more complicated expression. This may seem harder, but it’s actually pretty simple if you understand the Law of Substitution
The Law of Substitution
If two expressions are equal, then you may substitute one for the other at any point in the problem.
How does this help us here? Notice that if we simply add 2y to both sides of the equation, we get
3x − 2y = 7
3x = 2y + 7
Therefore, by the Law of Substitution, we can substitute 3x for 2y + 7 or vice-versa. Since 2y + 7 appears in the expression we are asked to evaluate, it makes sense to replace it with 3x:
Substitute 3x for 2y + 7:
Simplify:
When a question asks you to analyze a complex expression, don’t be intimidated. Look for simple relationships that allow you to simplify them using techniques like the Law of Substitution.
Increasing a positive number x by 25% and then decreasing the result by 50% is equivalent to dividing x by what number?
A) 1.333
B) 1.5
C) 1.6
D) 1.625
(Medium) Increasing a quantity by 25% is equivalent to multiplying it by 1.25, because the final amount is 125% of the original amount (Chapter 8, Lesson 8). Decreasing a quantity by 50% is equivalent to multiplying it by .5, because the final amount is 50% of the original amount. Therefore, performing both changes is equivalent to multiplying by 1.25 × 0.50, or 0.625, which is equal to 5/8. But the question asks us for the equivalent division. Here, we need to remember a simple rule: multiplying by a number is equivalent to dividing by its reciprocal. Therefore, multiplying by 5/8 is the same as dividing by 8/5, which is 1.6. Therefore, the correct answer is (C).
Every operation can be expressed in terms of its inverse operation.
And here are two more handy equivalences:
If what is the value of m + n?
(Easy) When a problem includes a complicated expression, we should try to simplify it, but always keep an eye on what the question is asking. In this case, simplifying to find the value of m + n requires knowing some factoring identities.
Useful factoring identities
The difference of squares equals the product of conjugates:
x2 − y2 = (x + y)(x − y)
Perfect square polynomials:
x2 + 2ax + a2 = (x + a)(x + a)
x2 − 2ax + a2 = (x − a)(x − a)
The first of these identities helps us factor our numerator:
Factor numerator and denominator:
Cancel common factors:
Multiply by 2:
m + n = 9
Lesson 4: Using conversion as a problem-solving tool
Niko is 27 inches shorter than his father, who is 5 feet 10 inches tall. How tall is Niko? (1 foot = 12 inches)
A) 3 feet 4 inches
B) 3 feet 6 inches
C) 3 feet 7 inches
D) 3 feet 10 inches
(Easy) Solving this problem requires unit conversions. To convert inches to feet, we multiply by the conversion factor (1 foot/12 inches). To convert feet to inches, we multiply by its reciprocal (12 inches/1 foot). If Niko’s father is 5 feet 10 inches tall, he is 5 feet × (12 inches/1 foot) + 10 inches = 70 inches tall. If Niko is 27 inches shorter, he is 70 − 27 = 43 inches tall, which is equivalent to 43 inches × (1 foot/12 inches) = 3 7/12 feet, or 3 feet 7 inches, so the correct answer is (C).
Conversion factors as problem-solving tools
conversion factor is simply a fraction in which the quantities in the numerator and the denominator represent equal quantities. Sometimes the equivalence is universal—for instance, 1 pound is always equal to 16 ounces—and sometimes it is problem-specific—for instance when a machine pump waters at a rate 3 gallons per hour, 1 hour of pumping is “equal” to 3 gallons being pumped.
If a factory can manufacture b computer screens in n days at a cost of c dollars per screen, then which of the following represents the total cost, in dollars, of the computer screens that can be manufactured, at that rate, in m days?
A)
B)
C)
D)
(Medium) This problem, from the previous exercise set, can be solved in several different ways. One method is to simply choose values for the unknowns and turn the problem into an arithmetic problem instead of an algebra problem. But here we will look at it as a conversion problem.
We can think of this problem as being a “conversion” from a quantity of days to an equivalent quantity of dollars. We are given that this factory is working for m days, so we write this quantity down, including the units, and we multiply by the conversion factors until we get dollars:
So the correct answer is (A).
Exercise Set 2 (No Calculator)
1
If bag A weighs 4 pounds 5 ounces and bag B weighs 6 pounds 2 ounces, how much heavier, in ounces, is bag B than bag A? (1 pound = 16 ounces)
2
If , what is the value of ?
3
If x − 2y = 10 and x ≠ 0, what is the value of ?
4
If a − b = 4 and a2 − b2 = 3, what is the value of a + b?
5
If 6 gricks are equivalent to 5 merts, then 2 merts are equivalent to how many gricks?
6
If the function {x} is defined by the equation {x} = (1 − x)2, what is the value of {{4}}?
7
If and , what is the value of ?
8
(x − 9)(x − a) = x2 − 4ax + b
In the equation above, a and b are constants. If the equation is true for all values of x, what is the value of b?
A) −27
B) −12
C) 12
D) 27
9
If , what is the value of x?
A)
B) −7
C)
D)
10
(p + 2)2 = (p − 5)2
The equation above is true for which of the following values of p?
A) −2 and 5
B) 2 and −5
C) 1.5 only
D) 5 only
11
If for all positive values of m and n, then which of the following is equal to x?
A)
B)
C)
D)
Exercise Set 2 (Calculator)
12
Let m be a positive real number. Increasing m by 60% then decreasing the result by 50% is equivalent to dividing m by what number?
13
What is the sum of the first 50 positive even integers?
14
Three years ago, Nora was half as old as Mary is now. If Mary is four years older than Nora, how old is Mary now?
15
If 2/3 of the seats at a football stadium were filled at the beginning of the game, and at halftime 1,000 spectators left, leaving 3/7 of the seats filled, what is the total number of seats in the stadium?
16
If three candy bars and two gumdrops cost \$2.20, and four candy bars and two gumdrops cost \$2.80, what is the cost, in dollars, of one gumdrop?
17
If , what is the value of x −1?
18
Subtracting 3 from a number and then multiplying this result by 4 is equivalent to multiplying the original number by 4 and then subtracting what number?
19
In a poker game, a blue chip is worth 2 dollars more than a red chip, and a red chip is worth 2 dollars more than a green chip. If 5 green chips are worth m dollars, then which of the following represents the value, in dollars, of 10 blue chips and 5 red chips?
A) 50 + 3m
B) 18 + 60m
C) 40 + 3m
D) 28 + 20m
20
A train travels at an average speed of 50 miles per hour for the first 100 miles of a 200-mile trip, and at an average of 75 miles per hour for final 100 miles. What is the train’s average speed for the entire trip?
A) 58.5 mph
B) 60.0 mph
C) 62.5 mph
D) 63.5 mph
21
Which of the following is equivalent to 3m(m2 × 2m) for all real values of m?
A) 3m2 + 6m
B) 3m2 × 6m
C) 3m3 × 6m2
D) 6m4
22
If the cost of living in a certain city increased by 20% in the 10 years from 1980 to 1990, and increased by 50% in the 20 years from 1980 to 2000, what was the percent increase in the cost of living from 1990 to 2000?
A) 15%
B) 20%
C) 25%
D) 30%
No Calculator
1. 29 4 pounds 5 ounces = 4(16) + 5 = 69 ounces, and 6 pounds 2 ounces = 6(16) + 2 = 98 ounces. Therefore, bag B weighs 98 − 69 = 29 ounces more.
2. 2/15 or .133
Distribute division:
Simplify:
Subtract 1:
Divide by 3:
3. 4 Expression to be evaluated:
Given equation:
x − 2y = 10
x = 2y + 10
Substitute x = 2y + 10:
Simplify:
Factor and simplify:
4. ¾ or .75
a2 − b2 = 3
Factor:
(a − b)(a + b) = 3
Substitute a − b = 4:
4(a + b) = 3
Divide by 4:
5. 12/5 or 2.4
6. 64
{4} = (1 − 4)2 = (−3)2 = 9
{{4}} = (1 − {4})2 = (1 − 9)2 = (−8)2 = 64
7. 2 Given equation:
Distribute division:
Subtract 1:
Reciprocate:
Given equation:
Distribute division:
Subtract 1:
Multiply:
8. D Given:
(x − 9)(x − a) = x2 − 4ax + b
FOIL:
x2 − ax − 9x + 9a = x2 − 4ax + b
Simplify:
x2 − (a + 9)x + 9a = x2 − 4ax + b
If this equation is true for all x, then the coefficients of corresponding terms must be equal, so
a + 9 = 4a
Subtract a:
9 = 3a
Divide by 3:
3 = a
Therefore b = 9a = 9(3) = 27.
9. A Given equation:
Multiply by 5x:
25 + 7x = 5x
Subtract 7x:
25 = −2x
Divide by −2:
10. C Given equation:
(p + 2)2 = (p − 5)2
FOIL:
p2 + 4p + 4 = p2 − 10p + 25
Subtract p2:
4p + 4 = −10p + 25
14p + 4 = 25
Subtract 4:
14p = 21
Divide by 14:
p = 1.5
11. D Given equation:
Multiply by m − nx:
3x = 2(m − nx)
Distribute:
3x = 2m − 2nx
3x + 2nx = 2m
Factor out x:
x(3 + 2n) = 2m
Divide by 3 + 2n:
Calculator
12. 1.25 Increasing a number by 60% is equivalent to multiplying it by 1.60, and decreasing a number by 50% is equivalent to multiplying it by 0.50. Therefore, performing both changes in succession is equivalent to multiplying by 1.60 × 0.50 = 0.80. Multiplying by 0.80 is equivalent to dividing by its reciprocal: 1/(0.80) = 1.25.
13. 2,550 The sum of the first 50 positive even integers is 2 + 4 + 6 + 8 + … + 100. As with the example is Lesson 2, these numbers can be regrouped into 25 pairs of numbers each of which has a sum of 2 + 100 = 102. Therefore, their sum is 25(102) = 2,550.
14. 14 Let n = Nora’s age now, and m = Mary’s age now. If 3 years ago, Nora was half as old
as Mary is now:
If Mary is 4 years older than Nora:
m = 4 + n
Subtract 4:
m − 4 = n
Substitute n = m − 4:
Simplify:
Multiply by 2:
2m − 14 = m
m = 14
15. 4,200 Let x = the total number of seats in the stadium.
Subtract x:
Combine like terms:
Multiply by :
16. 0.20 Let g = the cost, in dollars, of one gumdrop, and c = the cost, in dollars, of one candy bar.
4c + 2g = 2.80
3c + 2g = 2.20
Subtract:
c = 0.60
Substitute c = 0.60:
4(0.60) + 2g = 2.80
Simplify:
2.40 + 2g = 2.80
Subtract 2.40:
2g = 0.40
Divide by 2:
g = 0.20
17. 6
Factor:
Multiply by −1:
Simplify:
Multiply by 2:
x − 1 = 6
18. 12 We can just choose a number to work with, like 10. If we subtract 3 from this number then multiply the result by 4, we get 4(10 − 3) = 28. If we multiply it by 4 and then subtract a mystery number, we get 4(10) − x = 40 − x.
28 = 40 − x
Subtract 40:
−12 = −x
Multiply by −1:
12 = x
19. A If 5 green chips are worth m dollars, then each green chip is worth m/5 dollars. If a red chip is worth 2 dollars more than a green chip, then each red chip is worth m/5 + 2 dollars. If each blue chip is worth 2 dollars more than a red chip, then each blue chip is worth m/5 + 4 dollars. Therefore, 10 blue chips and 5 red chips are worth 10(m/5 + 4) + 5(m/5 + 2) = 2m + 40 + m + 10 = 3m + 50 dollars.
20. B The average speed is equal to the total distance divided by the total time. The total distance is 200 miles. The time for the first hundred miles is (100 miles/50 mph) = 2 hours, and the time for the second hundred miles is (100 miles/75 mph) = 4/3 hours. Therefore the total time of the trip is 2 + 4/3 = 10/3 hours, and the average speed is
21. D
3m(m2 × 2m)
Parentheses:
3m(2m3)
Multiply:
6m4
22. C Assume the cost of living in 1980 was \$100. If this increased by 20% from 1980 to 1990, then the cost of living in 1990 was 1.20(\$100) = \$120. If the increase from 1980 to 2000 was 50%, then the cost of living in 2000 was 1.50(\$100) = \$150. The percent increase from 1990 to 2000 is therefore
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# Algebra and Trigonometry, MyMathLab, and Student Solutions Manual (9th Edition) Edit edition Problem 86AYU from Chapter 8.5
We have solutions for your book!
Chapter: Problem:
Step-by-step solution:
Chapter: Problem:
• Step 1 of 3
We know that the values of varies from –1 to 1. Let us take as and as . Then, . Similarly, .
Rewrite the given expression.
• Chapter , Problem is solved.
Corresponding Textbook
Algebra and Trigonometry, MyMathLab, and Student Solutions Manual | 9th Edition
9780321786463ISBN-13: 0321786467ISBN: Michael SullivanAuthors:
This is an alternate ISBN. View the primary ISBN for: Algebra and Trigonometry 9th Edition Textbook Solutions
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import sage.all from sage.rings.integer import Integer from sage.functions.other import floor, ceil from sage.misc.misc_c import prod from sage.rings.fast_arith import prime_range from sage.arith.misc import GCD, gcd from sage.rings.integer_ring import Z, ZZ from sage.rings.finite_rings.finite_field_constructor import FiniteField from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing class TestPairingFriendlyCurve(): def __init__(self, PFCurve, test_vector_PFCurve): self._PFCurve = PFCurve # name of the class, BN, BLS12, KSS16, KSS18, BLS24 self._tvPFCurve = test_vector_PFCurve # name of list of test vectors self._Ei = [] # list of initialized curves self._Ei_ab = [] # list of initialized curves from params a,b in the test vector item self._Ei_b = [] # list of initialized curves from param b in the test vector item self._Ei_a = [] # list of initialized curves from param a in the test vector item def test_init_with_a_i_ht_hy_dict(self): # for CocksPinch8 curves print("test_init_with_a_i_ht_hy_dict") for v in self._tvPFCurve: # CocksPinch8 version: dictionary u,hy,ht,exp_tr,p,r,c,tr,y,a,pnbits = v['T'],v['hy'],v['ht'],v['i'],v['p'],v['r'],(v['p']+1-v['tr'])//v['r'],v['tr'],v['y'],v['a'],v['pnbits'] try: Ei_a = self._PFCurve(u=u, ht=ht, hy=hy, exp_tr=exp_tr, p=p, r=r, c=c, tr=tr, y=y, a=a) except ValueError as err: print ("Error init(u={},a={},ht={},hy={},exp_tr={}\np={}\nr={}\nc={}\ntr={}\ny={}\n)".format(u,a,ht,hy,exp_tr,p,r,c,tr,y)) print("{}".format(err)) raise print Ei_a self._Ei_a.append(Ei_a) print("OK") return True def test_init_with_b_i_ht_hy_dict(self): # for CocksPinch6 curves print("test_init_with_b_i_ht_hy_dict") for v in self._tvPFCurve: # CocksPinch6 version: dictionary u,hy,ht,exp_tr,p,r,c,tr,y,b,pnbits = v['T'],v['hy'],v['ht'],v['i'],v['p'],v['r'],(v['p']+1-v['tr'])//v['r'],v['tr'],v['y'],v['b'],v['pnbits'] try: Ei_b = self._PFCurve(u=u, ht=ht, hy=hy, exp_tr=exp_tr, p=p, r=r, c=c, tr=tr, y=y, b=b) except ValueError as err: print ("Error init(u={},b={},ht={},hy={},exp_tr={}\np={}\nr={}\nc={}\ntr={}\ny={}\n)".format(u,b,ht,hy,exp_tr,p,r,c,tr,y)) print("{}".format(err)) raise print Ei_b self._Ei_b.append(Ei_b) print("OK") return True def test_init_with_abcD(self): # for MNT curves print("test_init_with_abcD") for tup in self._tvPFCurve: #u, (a,b), pbits, cost, label = tup u,D,c,a,b = tup[0:5] try: Ei_ab = self._PFCurve(u, a=a, b=b, c=c, D=D) except ValueError as err: print ("Error init({},a={},b={},c={},D={})".format(u,a,b,c,D)) print("{}".format(err)) raise print Ei_ab self._Ei_ab.append(Ei_ab) print("OK") return True # for CocksPinch k=5,7 curves def test_init_with_all_params(self): print("test_init_with_all_params") for v in self._tvPFCurve: k,u,D,hy,ht,exp_tr,p,r,c,t0,tr,y0,y,a,b,pnbits = v['k'],v['T'],v['D'],v['hy'],v['ht'],v['i'],v['p'],v['r'],(v['p']+1-v['tr'])//v['r'],v['t0'],v['tr'],v['y0'],v['y'],v['a'],v['b'],v['pnbits'] try: Ei_ab = self._PFCurve(k,u,D,exp_tr,p,r,tr,y,a,b) except ValueError as err: print ("Error init(k={},T={},D={},i={},a={},b={})".format(k,u,D,exp_tr,a,b)) print("{}".format(err)) raise print Ei_ab self._Ei_ab.append(Ei_ab) print("OK") return True def test_init_with_b(self): print("test_init_with_b") for tup in self._tvPFCurve: #u, b, pbits, cost, label = tup u = tup[0]; b= tup[1] try: Ei_b = self._PFCurve(u, b=b) except ValueError as err: print ("Error init({},b={})".format(u,b)) print("{}".format(err)) raise print Ei_b self._Ei_b.append(Ei_b) print("OK") return True def test_init_with_a(self): print("test_init_with_a") for tup in self._tvPFCurve: #u, a, pbits, cost, label = tup u = tup[0]; a= tup[1] try: Ei_a = self._PFCurve(u, a=a) except ValueError as err: print ("Error init({},a={})".format(u,a)) print("{}".format(err)) raise print Ei_a self._Ei_a.append(Ei_a) print("OK") return True def test_init(self): print("test_init") for tup in self._tvPFCurve: #u, a or b, pbits, cost, deg_h, label = tup u=tup[0] try: Ei = self._PFCurve(u) except ValueError as err: print ("Error init ({})".format(u)) print("{}".format(err)) raise print Ei self._Ei.append(Ei) print("OK") return True def _test_beta_lamb_sigma_j0(self, E): G = E.G() r = E.r() if not r.is_prime(): print("Error r is not prime") if not r*G == E(0): print ("Error generator G is not of order r, r*G = {}".format(r*G)) beta = E.beta() sigmaG = E(G[0]*beta, G[1]) sigma2G = E(sigmaG[0]*beta, sigmaG[1]) if r*sigmaG != E(0): print ("Error r*sigma(G) != 0, obtained: {}".format(r*sigmaG)) if r*sigma2G != E(0): print ("Error r*sigma^2(G) != 0, obtained: {}".format(r*sigma2G)) if sigma2G + sigmaG + G != E(0): print ("Error sigma^2(G) + sigma(G) + G != 0, obtained: {}".format(sigma2G + sigmaG + G)) lamb = E.lamb() if lamb*G != sigmaG: print("Error lamb*G != sigma(G)") print("lamb*G = {}".format(lamb*G)) print("sigma(G) = {}".format(sigmaG)) def test_beta_lamb_sigma_j0(self): print("test_beta_lamb_sigma_j0") for Ei in self._Ei: #print Ei self._test_beta_lamb_sigma_j0(Ei) print("") for Ei_b in self._Ei_b: #print Ei_b self._test_beta_lamb_sigma_j0(Ei_b) print("OK") return True def _test_beta_lamb_sigma_j1728(self, E): G = E.G() r = E.r() if not r.is_prime(): print("Error r is not prime") if not r*G == E(0): print ("Error generator G is not of order r, r*G = {}".format(r*G)) beta = E.beta() sigmaG = E(-G[0], G[1]*beta) sigma2G = E(-sigmaG[0], sigmaG[1]*beta) if r*sigmaG != E(0): print ("Error r*sigma(G) != 0, obtained: {}".format(r*sigmaG)) if r*sigma2G != E(0): print ("Error r*sigma^2(G) != 0, obtained: {}".format(r*sigma2G)) if sigma2G + G != E(0): print ("Error sigma^2(G) + G != 0, obtained: {}".format(sigma2G + G)) lamb = E.lamb() if lamb*G != sigmaG: print("Error lamb*G != sigma(G)") print("lamb*G = {}".format(lamb*G)) print("sigma(G) = {}".format(sigmaG)) def test_beta_lamb_sigma_j1728(self): print("test_beta_lamb_sigma_j1728") for Ei in self._Ei: #print Ei self._test_beta_lamb_sigma_j1728(Ei) print("") for Ei_a in self._Ei_a: #print Ei_a self._test_beta_lamb_sigma_j1728(Ei_a) print("OK") return True def test_print_parameters(self): print("test_print_parameters") for Ei in self._Ei: print Ei Ei.print_parameters() Ei.print_parameters_for_RELIC() for Ei_ab in self._Ei_ab: # list may is empty print Ei_ab Ei_ab.print_parameters() Ei_ab.print_parameters_for_RELIC() for Ei_a in self._Ei_a: # list is empty if j != 1728 print Ei_a Ei_a.print_parameters() Ei_a.print_parameters_for_RELIC() for Ei_b in self._Ei_b: # list is empty if j != 0 print Ei_b Ei_b.print_parameters() Ei_b.print_parameters_for_RELIC() print("OK") return True # outside the class def generate_parameters_high(pnbits, poly_p, poly_r, polys_cofact_twist=[], u_mod_m=0, m=1,verbose=False): """ Generate parameters: find u s.t. p=poly_p(u), r=poly_r(u), tw=poly_r_twist(u) are prime, and p is pnbits long.""" lc = poly_p.leading_coefficient() deg_p = poly_p.degree() u_min = floor((2**(pnbits-1)/lc)**(1/deg_p)) u_min = (u_min-(u_min % m) + u_mod_m) while (ceil(poly_p(u_min))).nbits() < pnbits: u_min+=m while (ceil(poly_p(u_min))).nbits() > pnbits: u_min-=m u_max = floor((2**pnbits/lc)**(1/deg_p)) u_max = (u_max-(u_max % m) + u_mod_m) while (ceil(poly_p(u_max))).nbits() > pnbits: u_max-=m while (ceil(poly_p(u_max))).nbits() < pnbits: u_max+=m u = u_max p = ZZ(poly_p(u)) r = ZZ(poly_r(u)) tw= [ZZ(c_i(u)) for c_i in polys_cofact_twist] if pnbits < 1024: prod_primes = prod(prime_range(10**5)) else: prod_primes = prod(prime_range(10**7)) i = 0 # save the gcd of parameters to detect possible systematic cofactor gcd_p = 0 gcd_r = 0 gcd_ci = [0 for j in range(len(tw))] gcd_pi = gcd(prod_primes, p) gcd_ri = gcd(prod_primes, r) cond = gcd_pi > 1 or gcd_ri > 1 j = 0 for ci in tw: gcd_cii = gcd(prod_primes, ci) gcd_ci[j] = gcd_cii cond = cond or gcd_ci[j] > 1 j += 1 cond = cond or not p.is_pseudoprime() or not r.is_pseudoprime() for ci in tw: cond = cond or not ci.is_pseudoprime() while u >= u_min and cond: u -=m p = ZZ(poly_p(u)) r = ZZ(poly_r(u)) tw= [ZZ(c_i(u)) for c_i in polys_cofact_twist] gcd_pi = gcd(prod_primes, p) gcd_ri = gcd(prod_primes, r) gcd_p = gcd(gcd_p, gcd_pi) gcd_r = gcd(gcd_r, gcd_ri) cond = gcd_pi > 1 or gcd_ri > 1 j = 0 for ci in tw: gcd_cii = gcd(prod_primes, ci) gcd_ci[j] = gcd(gcd_ci[j], gcd_cii) cond = cond or gcd_cii > 1 j += 1 cond = cond or not p.is_pseudoprime() or not r.is_pseudoprime() for ci in tw: cond = cond or not ci.is_pseudoprime() i +=1 if verbose and (i % 10**5) == 0: print i print("gcd all p: {} gcd all r: {} gcd all ci: {}".format(gcd_p, gcd_r, gcd_ci)) # reset gcd_p = 0 gcd_r = 0 gcd_ci = [0 for j in range(len(tw))] if u >= u_min: print("u={}, i = {}".format(u,i)) return u, p, r, tw, u_min, u_max, i # else return None from CocksPinch6 import CocksPinch6 from CocksPinch8 import CocksPinch8 from CocksPinch_k import CocksPinch_k from MNT6 import MNT6 from BN import BN from BLS12 import BLS12 from KSS16 import KSS16 from TestVectorPairingFriendlyCurve import * def test_CocksPinch6_i1(): print("Test CocksPinch6 curves, tr = T+1 (i=1)") Test_CP6 = TestPairingFriendlyCurve(CocksPinch6, test_vector_CocksPinch6_i1) Test_CP6.test_init_with_b_i_ht_hy_dict() Test_CP6.test_beta_lamb_sigma_j0() Test_CP6.test_print_parameters() print("end test CocksPinch6") def test_CocksPinch6_i5(): print("Test CocksPinch6 curves, tr = -T+2 (i=5)") Test_CP6 = TestPairingFriendlyCurve(CocksPinch6, test_vector_CocksPinch6_i5) Test_CP6.test_init_with_b_i_ht_hy_dict() Test_CP6.test_beta_lamb_sigma_j0() Test_CP6.test_print_parameters() print("end test CocksPinch6") def test_CocksPinch8_i1(): print("Test CocksPinch8 curves, tr = T+1 (i=1), ht=-1") Test_CP8 = TestPairingFriendlyCurve(CocksPinch8, test_vector_CocksPinch8_i1) Test_CP8.test_init_with_a_i_ht_hy_dict() Test_CP8.test_beta_lamb_sigma_j1728() Test_CP8.test_print_parameters() print("end test CocksPinch8") def test_CocksPinch8_i5(): print("Test CocksPinch8 curves, tr = -T+1 (i=5), ht=-1") Test_CP8 = TestPairingFriendlyCurve(CocksPinch8, test_vector_CocksPinch8_i5) Test_CP8.test_init_with_a_i_ht_hy_dict() Test_CP8.test_beta_lamb_sigma_j1728() Test_CP8.test_print_parameters() print("end test CocksPinch8") def test_CocksPinch5(): print("Test CocksPinch_k curves with k=5") Test_CP5 = TestPairingFriendlyCurve(CocksPinch_k, test_vector_CocksPinch5) Test_CP5.test_init_with_all_params() Test_CP5.test_print_parameters() print("end test CocksPinch_k with k=5") def test_CocksPinch7(): print("Test CocksPinch_k curves wit k=7") Test_CP7 = TestPairingFriendlyCurve(CocksPinch_k, test_vector_CocksPinch7) Test_CP7.test_init_with_all_params() Test_CP7.test_print_parameters() print("end test CocksPinch_k with k=7") def test_MNT6(): print("Test MNT6 curves") Test_MNT6 = TestPairingFriendlyCurve(MNT6, test_vector_MNT6) Test_MNT6.test_init_with_abcD() Test_MNT6.test_print_parameters() print("end test MNT6") def test_BN(): print("Test BN curves") Test_BN = TestPairingFriendlyCurve(BN, test_vector_BN) Test_BN.test_init() Test_BN.test_init_with_b() Test_BN.test_beta_lamb_sigma_j0() Test_BN.test_print_parameters() print("end test BN") def test_BLS12(): print("Test BLS12 curves") Test_BLS12 = TestPairingFriendlyCurve(BLS12, test_vector_BLS12) Test_BLS12.test_init() Test_BLS12.test_init_with_b() Test_BLS12.test_beta_lamb_sigma_j0() Test_BLS12.test_print_parameters() print("end test BLS12") def test_KSS16(): print("Test KSS16 curves") Test_KSS16 = TestPairingFriendlyCurve(KSS16, test_vector_KSS16) Test_KSS16.test_init() Test_KSS16.test_init_with_a() Test_KSS16.test_beta_lamb_sigma_j1728() Test_KSS16.test_print_parameters() print("end test KSS16")
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A090414 Triangular array read by rows, 1<=k<=n: T(n,k) = smallest prime that in binary representation is not contained in n^k. 2
2, 3, 3, 2, 3, 7, 3, 3, 3, 3, 3, 5, 11, 5, 7, 5, 3, 7, 3, 5, 7, 2, 5, 13, 7, 11, 13, 17, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 7, 11, 19, 19, 17, 13, 3, 5, 11, 5, 7, 11, 7, 17, 17, 13, 7, 5, 7, 5, 23, 7, 13, 7, 7, 17, 17, 5, 3, 7, 3, 5, 7, 7, 7, 5, 11, 17, 19 (list; table; graph; refs; listen; history; text; internal format)
OFFSET 1,1 LINKS Jinyuan Wang, Rows n = 1..100 of triangle, flattened EXAMPLE Triangle begins: 2; 3, 3; 2, 3, 7; 3, 3, 3, 3; 3, 5, 11, 5, 7; 5, 3, 7, 3, 5, 7; 2, 5, 13, 7, 11, 13, 17; .. PROG (PARI) T(n, k) = {my(d=binary(n^k), v); forprime(p=2, oo, v=binary(p); if(#v>#d || sum(i=1, #d-#v+1, v==vector(#v, j, d[i+j-1]))==0, return(p))); } \\ Jinyuan Wang, Mar 01 2020 CROSSREFS Cf. A004676, A007088, A075363. Sequence in context: A141744 A089783 A302939 * A068227 A235343 A236456 Adjacent sequences: A090411 A090412 A090413 * A090415 A090416 A090417 KEYWORD nonn,base,tabl AUTHOR Reinhard Zumkeller, Nov 30 2003 EXTENSIONS More terms from Jinyuan Wang, Mar 01 2020 STATUS approved
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Last modified April 11 12:38 EDT 2021. Contains 342886 sequences. (Running on oeis4.)
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# switching elements of a vector
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## switching elements of a vector
Hi, I would like to receive help for the following matter: If I'm dealing with a numeric vectors containing increasing elements. i.e. a<-c(1,2,2,2,2,3,3,3,4,4,4,5,5,6,7,7,7) There exist an efficient way to obtain an vector that indicates the position of the changing element of "a"? In this case it would be something like: index<-c(1,6,9,12,14,15) usually I'm used cycles to obtain boolean vectors of the same length of "a" indicating the changing elements ...later I've muliplied them for their numeric sequence and after that I've selected elements different from zero ...it is quite long... can you find an easier solution? Thank you for you help
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## Re: switching elements of a vector
On 5/24/2010 6:02 AM, speretti wrote: > Hi, > > I would like to receive help for the following matter: > > If I'm dealing with a numeric vectors containing increasing elements. > i.e. > > a<-c(1,2,2,2,2,3,3,3,4,4,4,5,5,6,7,7,7) > > There exist an efficient way to obtain an vector that indicates the position > of the changing element of "a"? > In this case it would be something like: > > index<-c(1,6,9,12,14,15) a <- c(1,2,2,2,2,3,3,3,4,4,4,5,5,6,7,7,7) rle(a) Run Length Encoding lengths: int [1:7] 1 4 3 3 2 1 3 values : num [1:7] 1 2 3 4 5 6 7 cumsum(head(rle(a)\$lengths, -1)) + 1 [1] 2 6 9 12 14 15 ?rle > usually I'm used cycles to obtain boolean vectors of the same length of "a" > indicating the changing elements ...later I've muliplied them for their > numeric sequence and after that I've selected elements different from zero > ...it is quite long... > can you find an easier solution? > > Thank you for you help -- Chuck Cleland, Ph.D. NDRI, Inc. (www.ndri.org) 71 West 23rd Street, 8th floor New York, NY 10010 tel: (212) 845-4495 (Tu, Th) tel: (732) 512-0171 (M, W, F) fax: (917) 438-0894 ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: switching elements of a vector
In reply to this post by speretti Hi, is this what you need? b <- c(NA, a[1:length(a)-1]) # shift values of a one step to the right which(a-b == 1) On Monday 24 May 2010 12:02:55 pm speretti wrote: > Hi, > > I would like to receive help for the following matter: > > If I'm dealing with a numeric vectors containing increasing elements. > i.e. > > a<-c(1,2,2,2,2,3,3,3,4,4,4,5,5,6,7,7,7) > > There exist an efficient way to obtain an vector that indicates the > position of the changing element of "a"? > In this case it would be something like: > > index<-c(1,6,9,12,14,15) > > usually I'm used cycles to obtain boolean vectors of the same length of "a" > indicating the changing elements ...later I've muliplied them for their > numeric sequence and after that I've selected elements different from zero > ...it is quite long... > can you find an easier solution? > > Thank you for you help > -- ---- Friedrich Schuster Dompfaffenweg 6 69123 Heidelberg ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: switching elements of a vector
Thank you ! Great answers...now it seems very easy... As usual...a the obviousness of a solution depends on how you face the problem... Thank you for help me in find the good approaches...
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## Re: switching elements of a vector
In reply to this post by speretti Try this: > which(diff(a) > 0) + 1 [1] 2 6 9 12 14 15 On Mon, May 24, 2010 at 6:02 AM, speretti <[hidden email]> wrote: > > Hi, > > I would like to receive help for the following matter: > > If I'm dealing with a numeric vectors containing increasing elements. > i.e. > > a<-c(1,2,2,2,2,3,3,3,4,4,4,5,5,6,7,7,7) > > There exist an efficient way to obtain an vector that indicates the position > of the changing element of "a"? > In this case it would be something like: > > index<-c(1,6,9,12,14,15) > > usually I'm used cycles to obtain boolean vectors of the same length of "a" > indicating the changing elements ...later I've muliplied them for their > numeric sequence and after that I've selected elements different from zero > ...it is quite long... > can you find an easier solution? > > Thank you for you help > -- > View this message in context: http://r.789695.n4.nabble.com/switching-elements-of-a-vector-tp2228373p2228373.html> Sent from the R help mailing list archive at Nabble.com. > > ______________________________________________ > [hidden email] mailing list > https://stat.ethz.ch/mailman/listinfo/r-help> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html> and provide commented, minimal, self-contained, reproducible code. > ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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HIDDEN CODES
PROBLEM
A set of code words and a text are given. The text is supposed to contain a message made up of the code words embedded in the text in a peculiar (and possibly ambiguous) way.
The code words and the text are sequences made up of the upper and lower case letters of the English alphabet only. Case-sensitivity is assumed. The length of a code word is defined in the usual way: For example, the code word ALL has length 3.
The letters of a code word do not have to occur consecutively in the given text. For example, the code word ALL will always occur in the text within a subsequence in the form of AuLvL where u and v denote arbitrary (possibly empty) sequences of letters. We say that AuLvL is a covering sequence for ALL. In general, a covering sequence for a code word is defined as a subsequence of the text such that the first letter and the last letter of the subsequence are the same as those of the code word and it is possible to obtain the code word by deleting some (possibly none) of the letters of the subsequence. It should be noted that a code word may occur within one or more covering sequences or may not occur in the text at all, and that a covering sequence may be a covering sequence for more than one code word.
A covering sequence is identified by its start position (position of its first letter) and its end position (position of its last letter) in the text. (The first letter of the text is at position 1.) We say that two covering sequences, say c1 and c2, do not overlap if the start position of c1 is greater than (>) the end position of c2 or vice versa. Otherwise we say that the two covering sequences overlap.
To extract the message hidden in the text you undertake the task of forming a solution. A solution is a set of items, each consisting of a code word and a covering sequence for this code word, so that the following conditions are all satisfied:
1. the covering sequences do not overlap with each other;
2. a covering sequence does not exceed 1000 in length;
3. the sum of the lengths of the code words is maximal. (Each item contributes the length of the code word it contains to the sum.)
In case there are more than one solution you are required to report only one solution.
ASSUMPTIONS
• 1 £ N £ 100 where N is the number of code words.
• The maximum length of a code word is 100 letters.
• 1 £ length of the given text £ 1,000,000 letters.
•
• We say that a covering sequence c for a code word w is right-minimal if no proper prefix of c (a proper prefix of c is an initial subsequence of c that is not equal to c) is a covering sequence for w. For example, for the code word ALL, AAALAL is a right-minimal covering sequence whereas AAALALAL is also a covering sequence, but not right-minimal.
It is guaranteed that in the given text
1. for each position in the text the number of right-minimal covering sequences containing that position does not exceed 2500;
2. the number of right-minimal covering sequences does not exceed 10,000.
INPUT
There are two input text files: words.inp and text.inp. The words.inp file contains a list of code words and text.inp contains the text.
• The first line of words.inp contains the value of N. Each of the following N input lines contains a code word which is a sequence of letters without any blank in between. The code words are identified by their order of appearance in the words.inp file: Integers 1 through N serve as the id-numbers for the code words.
• The text.inp file consists of a sequence of letters (terminated by an end-of-line character followed by the end-of-file symbol). This file does not include blanks.
RECOMMENDATION FOR PASCAL PROGRAMMERS
You are advised to declare the input file type as text, as opposed to a typed file for reasons of efficiency.
OUTPUT
The output must be a text file named codes.out.
• The first line will contain the sum obtained by your solution.
• Each of the following lines will determine an item in your solution: The line consists of three integers i, s, e. Here i is the id-number of the code word that occurs within the covering sequence identified by the start position s and end position e. The order of the output lines that follow the first line is not important.
EXAMPLE
words.inp:
```4 RuN RaBbit HoBbit StoP```
text.inp:
`StXRuYNvRuHoaBbvizXztNwRRuuNNP`
codes.out:
```12 2 9 21 1 4 7 1 24 28```
(Remark: The hidden message that could be extracted from the solution is "RuN RaBbit RuN". (An alternative solution would yield "RuN HoBbit RuN"). Be reminded that the message is not to appear on the output. )
EVALUATION
Your program will be allowed to run 10 seconds.
No partial credit can be obtained for a test case.
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https://schoollearningcommons.info/question/a-gentleman-buys-every-year-bank-s-cash-certificates-of-value-eceeding-the-last-year-s-purchase-23199464-29/
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A gentleman buys every year Bank’s cash certificates of value exceeding the last year’s purchase by ₹250. After 20 years, he finds the total
Question
A gentleman buys every year Bank’s cash certificates of value exceeding the last year’s purchase by ₹250. After 20 years, he finds the total value of purchased certificates by him is ₹72500. Find the value of the certificates purchased by him : (a) in the first year (b) in the 13th years.
in progress 0
1 month 2021-08-18T04:07:03+00:00 1 Answer 0 views 0
Let the value of the certificates purchased in the first year be Rs.a.
The difference between the value of the certificates is Rs. 300(d=300).
Since, it follows Arithmetic progression the total value of the certificates after 20 years is given by
Sn = n/2 [2a−(n−1)d]= 20/2 [2a+19(300)]=8300
By simplifying we get 2a+5700=8300.
Therefore, a=Rs.1300.
The value of the certificates purchased by him in nth year =a+(n−1)d.
Therefore, the value of the certificates purchased by him in 13th year =1300+(13−1)300=Rs.4900.
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# economics two hous | The Homework Helpers
economics two hous.
You are the assistant to the CEO of a major company. Your CEO keeps an eye on the competition, and asks you to do the following. Using ratio analysis, compare two major competitors in the same industry.
Don't use plagiarized sources. Get Your Custom Essay on
economics two hous | The Homework Helpers
Get an essay WRITTEN FOR YOU, Plagiarism free, and by an EXPERT!
Instructions:
Pick any two U.S. public companies in the same industry.
You may obtain financial information and the companies latest annual reports on the web directly from MSN Money or Yahoo Finance. For additional information, look for the SEC Form10-K link from one of the MSN Money or Yahoo Finance financial sites.
One of your two companies can be the same company you used in Week 2.
Select the 10 most important financial ratios for your two companies and calculate each for the last 2 fiscal years using Excel. You should calculate at least one ratio in each category: liquidity, leverage, profitability, and efficiency. Then, add other ratios where there are large differences between the two companies you chose. That s my definition of the phrase most important.
Follow the same format as the Drugstore Chains example (DrugstoreChains.xls).
Create a single Excel file for your entire assignment.
You should calculate, and comment upon, all 10 financial ratios for the last 2 fiscal years. For each ratio, your comment should indicate which company has the better ratio.
All calculations should be shown, and all answers should be thoroughly explained (a.k.a. show your work ).
It is often useful to compare financial ratios for a company with financial ratios of its industry, but this is not required. Industry financial ratios can be found on Morningstar.com, Yahoo Finance and MSN Money and
What can you tell from your analysis? In other words, which company is the stronger competitor overall? Give your reasons.
Your Excel file should be submitted via the Week 3 Individual Assignment link.
Here s how I ll grade your sheet. 1pt for each ratio calculated correctly as your work should show; 1pt for each correct interpretation of the ratio (i.e. which company has the stronger ratio?); 1pt for your conclusion on which company is the stronger competitor overall (actually pick one or the other. no ties!); 1pt for your reason (a qualitative statement about the company that draws on but is not simply rehashing the analysis you ve done) . Total: 22pts.
economics two hous
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# Laplace transform
## Solving partial DE (PDE)
The task arises from physical situations (heat equation; distribution of heat in a given region over time). We have function $u$ of two variables: $u(x,t)$, where the variable $t$ represents time $t \geq 0$, the other variable $x$ is a location. Laplace transform of $u(x,t)$ is ${\scr L}[u(x,t)] = \int_0^{\infty}u(x,t)e^{-st}\ dt$, where paramater $x$ is treated as a constant. We still use capital letter to denote Laplace transform of a given function:
$${\scr L}[u(x,t)] = U(x,s) = U$$
Since differential equation to solve can look like (examples)
\begin{align} \frac{\partial u}{\partial x} + \frac{\partial u}{\partial t} &= x \hskip2em \text{or} \nonumber \\ \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial t^2} &= f(x), \nonumber \\ \end{align}
we need Laplace transforms of corresponding derivatives—and these are analogy to Laplace transform of function $y(t)$.
\begin{align} \color{red}{{\scr L}\left[u_{t}(x,t)\right] = {\scr L}\left[\frac{\partial u}{\partial t}\right]} &\color{red}{= sU(x,s) - u(x,0)}, \label{ref:lapl_PDE1} \\ \color{red}{{\scr L}\left[u_{tt}(x,t)\right] = {\scr L}\left[\frac{\partial^2 u}{\partial t^2}\right]} &\color{red}{= s^2U(x,s) - su(x,0) -u_{t}(x,0)}. \label{ref:lapl_PDE2} \\ \end{align}
Since we are transforming with respect to $t$, we further suppose it is legitimate to move ${\partial u}/{\partial x}$ to front of integral:
$${\scr L}\left[u_x(x,t)\right] = {\scr L}\left[\frac{\partial^2 u}{\partial x^2}\right] = \int_0^{\infty}e^{-st}\frac{\partial^2 u}{\partial x^2}dt = \frac{d^2}{dx^2}\int_0^{\infty}e^{-st}u(x,t)\ dt = \frac{d^2}{dx^2}{\scr L}\left[u(x,t)\right]$$
So we will put
\begin{align} \color{red}{{\scr L}\left[\frac{\partial u}{\partial x}\right]} & \color{red}{= \frac{dU}{dx}}, \label{ref:lapl_PDE3}\\ \color{red}{{\scr L}\left[\frac{\partial^2 u}{\partial x^2}\right]} & \color{red}{= \frac{d^2U}{dx^2}}. \label{ref:lapl_PDE4} \end{align}
The PDE will be converted into ordinary DE (ODE).
#### Example
$$\frac{\partial u}{\partial x} + \frac{\partial u}{\partial t} = x\, \hskip2em x \gt 0,\ t \gt 0,\hskip2em u(x=0,t) = 0,\ u(x,t=0)=0$$
We are given a partial differential equation (PDE). We solve by Laplace, so we have to transform each term. Transform is made with respect to time $\boldsymbol t$, the other dimension $\boldsymbol x$ is considered to be a constant. To transform $\partial u/\partial t$, it is an analogy with $y'(t)=dy/dt$ and we use $(\ref{ref:lapl_PDE1})$. For $\partial u/\partial x$, we drag $\partial /\partial x$ out of the integral, because the transform proceeds over $t$, while differentiation is with respect to $x$ and then we have—according to $(\ref{ref:lapl_PDE3})$—${\scr L}[\partial u/\partial x] = d/dx\ U$ .
\begin{align} \frac{dU}{dx} + sU(x,s) \color{silver}{- u(x,0)} &= x\cdot \frac 1 s \nonumber \\ \frac{dU}{dx} + sU(x,s) &= x\cdot \frac 1 s \nonumber \\ \end{align}
$u(x,0) = 0$ is given by boundary/initial conditions. We have converted PDE into ODE: the last equation can be solved as linear DE. Now dependent variable is $U$, independent is $x$. We are solving $U(x)$, $s$ is considered to be a constant.
$$U' + sU = x \frac 1 s \implies P(x) = s \implies \mu(x) = e^{\int P(x)\ dx} = e^{\int s \ dx} = e^{sx}$$
The linear DE are solved by identifying $P(x)$ in order to express integrating factor $\mu(x) = e^{\int P(x)\ dx}$. The integrating factor $\mu(x)$ is used to multiply DE and then it is easy to integrate, because on the left side is $d/dx\ \mu(x)y(x)$ or in current case $d/dx\ \mu(x)U(x)$.
\begin{align} e^{sx}U' + e^{sx}sU &= s^{sx}x\frac 1 s \nonumber \\ \frac{d}{dx}e^{sx}U &= e^{sx}x\frac 1 s \nonumber \\ e^{sx}U &= \frac 1 s \cdot \frac{(sx-1)e^{sx}}{s^2}+c \nonumber \\ U(x,s) &= \frac 1 s \cdot \frac{sx-1}{s^2} +ce^{-sx} = \frac x {s^2} - \frac{1}{s^3} + ce^{-sx} \nonumber \end{align}
The integral of $e^{sx}x$ is solved by integrating by parts. We use the product rule for differentiation backwards.
$$(uv)' = u'v + uv' \implies u'v = (uv)' - uv' \implies \int u'v = uv- \int uv'$$
Then we have to locate one term, which is easy to differentiate ($x$) and the second one, which is easy to integrate ($e^{sx}$).
\begin{align} \int e^{sx}x\ dx &= \begin{vmatrix} u' = e^{sx} & u = \frac 1 s e^{sx}\\ v = x & v' = 1 \end{vmatrix} = \frac 1 s e^{sx}x - \int\frac 1 s e^{sx}\ dx = x\frac 1 s e^{sx} - \frac 1 {s^2}e^{sx} = \nonumber \\ &= \frac{(xs-1)e^{sx}}{s^2} \nonumber \end{align}
We are used to evaluate arbitrary constants as $c$ here (product of integration) by applying initial/boundary values:
\begin{align} &u(x=0,t) = 0 \implies U(x=0,s) = 0 \implies 0 = -\frac{1}{s^3} + c \implies c=\frac{1}{s^3} \implies \nonumber \\ \implies & U(x,s) = \frac x {s^2} - \frac{1}{s^3} + \frac{1}{s^3}e^{-sx} \nonumber \end{align}
We reached the solution but it is in $s$ domain. Finally we have to go through inverse Laplace transform.
$$\underline{\underline{u(x,t) = xt - \frac 1 2 t^2 + u(t-x)\cdot \frac 1 2 (t-x)^2}}$$
Note: here notation $u(t-x)$ is equivalent of $u_x(t)$ and is unit step function (the product of inverse Laplace transform of $e^{-sx}$). The above solution is formally correct, but we should rather use the case form. The first two terms do not depend on any unit step function and are valid from zero to infinity. The last term, because of unit step function $u_x(t)$, is inactive until $t=x$:
u(x,t) = \left\{ \begin{aligned} xt - \frac 1 2 t^2 & \hskip2em t \lt x \\ xt - \frac 1 2 t^2 + \frac 1 2 (t-x)^2 &\hskip2em t \geq x \end{aligned} \right.
That can be further simplified to
u(x,t) = \left\{ \begin{aligned} xt - \frac 1 2 t^2 & \hskip2em t \lt x \\ \frac 1 2 x^2 &\hskip2em t \geq x \end{aligned} \right.
List of chapters
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### INTRO TO BUSINESS STATISTICS WEIERS 7TH EDITION PDF
About This Product. Highly praised for its exceptional clarity, technical accuracy, and useful examples, Weiers’ INTRODUCTION TO BUSINESS STATISTICS. Introduction to Business Statistics Seventh Edition Ronald M. Weiers Vice President of Editorial Business: Jack W. Calhoun. Introduction to Business Statistics: 7th (Seventh) Edition by Weiers, Ronald M. and a great selection of related books, art and collectibles available now at.
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The raw data are shown in part A of Table 2. Relative frequencies will play an important role in our discussion of probabilities in Intfo 5.
dtatistics Following an introductory explanation of the purpose and the steps involved in each technique you will be provided with several down-to-earth examples of its use. The printouts are typical of what we would expect from most sta- tistical software. On questionnaire items like the following business research practitioners typically treat the data as interval scale since the same physical and numerical distances exist between alternatives: For some data how- ever the number of values editiln be even.
Thus the mean is able to make more complete use of the data. The labels Certificate Type and Number thousands have already been entered into A3 and C3 respectively. The labels and data values have already been entered as shown wdiers the printout.
Does there appear to be any relationship between the variables If so is the relationship direct or inverse 2.
Chi-Square Applications Statistical Description of Data 63 one or two very low or high values. When setting editioon a pictogram the choice of symbols is up to you. Construct a simple tabulation in which the counts are according to the type of trans mission.
Most Related AXEL ELLRODT PDF
How many cities have a population of at least but less than What percentage of cities are in this group d. Enter the data range A1: Analysis of Variance Tests Showing of 13 reviews. Enter C1 into the first line of the X variables box.
When you accept his findings he wins and you lose. More research is on the way. The entire database contains 30 variables for respondents and is available from the premium website accompanying the text.
Construct a cross-tabulation describing the fleet using type of engine and type of transmission as the categorization variables. All values are at least 50 but less than This is obtained simply by substituting x 5 50 million into the equation and calculating an estimated value for y 5 wins. The Nominal Scale The nominal scale uses numbers only for the purpose of identifying membership in a group or category. The midpoint of the interval this can be calculated as the lower limit plus half the width of the interval or 50 1 0.
If you use the defaults in these programs the frequency distributions may differ slightly whenever a data point happens to have exactly the same value as one of the upper limits because 1.
The respondent usually spends less than 15 when she shops at West Mall. Along with the equation the display includes information we will be covering later in the text.
Enter your mobile number or email address below and we’ll send you a link to download the free Kindle App. Click on B1 and drag to C31 to select cells B1: We will be examining a wide spectrum of such applications and settings. The page references are shown in brackets.
The trade press and government documents are largely statistical in sstatistics and this is necessarily so since only by the use of statistics can the affairs of edktion and of state be intelligently conducted. Frequency Distribution Number of Motorists in Each Category Speed mph Number of Motorists 45—under 50 1 50—under 55 9 55—under 60 15 60—under 65 24 65—under 70 17 70—under 75 17 75—under 80 13 80—under 85 8 85—under 90 1. Measures of dispersion allow us to numerically describe the scatter or spread of mea surements.
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You will not be expected to have had mathematical training beyond simple algebra and mathematical sym- bols and notations will be explained as they become relevant to our discussion. The sample mode is the value ro is most frequently observed. The relative heights of the rectangles visually demonstrate how the frequencies tend to drop off as we proceed from the 60—under 65 class to the 65—under 70 class and higher.
Not shown in either printout is a measure called the trimmed mean in which statistical software ignores an equal number or percentage of data values at both the high end and the low end of the data before it is calculated.
The times seconds for the 50 ATM users are in column C3. From a gender perspective the average time for males For example if 45 of the population consists of female shoppers we would like our sample to also include 45 females. Brown Drexel University Shaw K. Priscilla Chaffe-Stengel The PowerPoint slides contain the chapter learning outcomes key terms theo- retical overviews and practical examples to facilitate classroom instruction and student learning.
House of Representatives April 11
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# Math
Find the value of y for a given value of x, if y varies directly with x.
If y = –252 when x = 84, what is y when x = 74?
1. 👍
2. 👎
3. 👁
1. y = kx
-252 = k(84)
k = -3
y(74) = -3(74) = -222
1. 👍
2. 👎
2. Do the same thing with X 6, 18, 54, 162
Y 24, 72, 216, 640
2.52 = k(8.4)
K=0.03
Y(2.7)=0.03(2.7)=0.81
1. 👍
2. 👎
3. f(x)=4x+7,find f(4)
1. 👍
2. 👎
4. Find the value of x when y=24
1. 👍
2. 👎
## Similar Questions
1. ### math
p varies directly as q and the square of r and inversely as s write the equation of the relation find k if p=40 q=5 r=4 s=6 find p when q=8 r=6 and s=9 find s when p=10 q=5 r=2
2. ### Algebra worksheet
Hello. My algebra teacher gave me this worksheet last week and everyone had to bring it yesterday and I haven't done it yet. Can someone please help me. He said Friday is the last day or he's going to take away some points. I've
If c varies directly as the square root of d, and c = 14 when d = 64, find c when d = 324.
4. ### variation
Can you please check my answers? Thanxs! Write an equation that expresses the relationship. Use k as the constant of variation. 20. f varies jointly as b and the square of c. -I got: f=kbc^2 22. r varies jointly as the square of s
1. ### Pre-Algebra
If y varies directly with x, find the constant of variation with x = 4 and y = -24 If y varies inversely with x, find the constant of variation with x=5 and y = 10 If y varies directly with x, and y = 35 when x = 5 , find x when y
2. ### math
P varies directly as the square root of q. P=8 when q =25 find p when q = 100
3. ### Mathematics
M varies directly as n and inversely as p. if M=3, when n=2,and p=1, find M in terms of n and p
4. ### Algebra II
if y varies directly as x, if y=80 when x=32, find x if y=100
1. ### Math
Y varies directly as the square of x and y=96 when x=4 find the value of y when x=5
2. ### algebra
I do not know where to start with this one. Suppose p varies directly as the square of z and inversely as r. If p = 32/5 when z = 4 and r = 10, find p when z = 3 and r = 36.
3. ### Math help
9). Hooke’s Law. The distance d when a spring is stretched by a hanging object varies directly as the weight w of the object. If the distance is 29 cm when the weight is 4 kg what is the distance when the weight is 9 kg? 10).
4. ### Math
M varies directly as the square of N. If N increases by 10%, find the percentage change in M
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# johnkerl/sack
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#!/usr/bin/python -Wall # ================================================================ # Please see LICENSE.txt in the same directory as this file. # John Kerl # kerl.john.r@gmail.com # 2007-05-31 # ================================================================ # Type module for the metacyclic group parameterized by m and n. import re import sackint # ================================================================ # Old explanation (circa 2004): # ---------------------------------------------------------------- # Multiplication: # a^i b^j a^k b^l = a^(i + k t^j) b^(j + l) # t != 1 mod p # t^q == 1 mod p # ---------------------------------------------------------------- # Inversion: # (a^i b^j)^(-1) = b^-j a^-i # = a^0 b^-j a^-i b^0 # = a^(0 + -i t^-j) b^(-j + 0) # = a^(-i t^-j) b^-j # ================================================================ # Alternate point of view, from scratch (2006-11-28): # Zm X|_phi Zn (semidirect product): # (a, b) + (c, d) = (a + (phi(b))(c), b + d). # Zm and Zn are cyclic so the action of b on c is specified by the action of # Zn's 1 on Zm's 1. Call this t. # # ---------------------------------------------------------------- # An example before I continue further: Let m=7 and n=3. Then we need phi to # be a homomorphism from Z3 to Aut(Z7). Here's what Aut(Z7) looks like: # # Z7 | s1 s2 s3 s4 s5 s6 # -- + -- -- -- -- -- -- # 0 | 0 0 0 0 0 0 # 1 | 1 2 3 4 5 6 # 2 | 2 4 6 1 3 5 # 3 | 3 6 2 5 1 4 # 4 | 4 1 5 2 6 3 # 5 | 5 3 1 6 4 2 # 6 | 6 5 4 3 2 1 # # Note that si(x) = ix, i.e. the ith automorphism is just multiplication by i. # Also, how do we compose automorphisms? si(sj(x)) = ij(x) so si o sj is sij. # So, arithmetic on the i's and j's is done in the multiplicative group of Z7. # # Now, Aut(Z7) is isomorphic to Z6, but how? Additive groups of Zm always are # cyclic of order m with 1 as generator; multiplicative groups of Zp* are # always cyclic of order p-1, but with a generator we usually have to search # for. By searching we can find that 3 (or 5) generates Z7*. So, Aut(Z7) is # cyclic with automorphism s3 (or s5) as generator. Here are the powers of 3 # mod 7: # 3^1 3^2 3^3 3^4 3^5 3^6 # 3 2 6 4 5 1. # So the cyclic structure of the cyclic group Aut(Z7) is # s3 s2 s6 s4 s5 s1 # with s3 as generator. (If s5 is used as the generator, then the cycle # structure is the reverse of this.) # # So, back to the semidirect product of Z7 and Z3, the possible homomorphisms # from the order-3 cyclic group Z3 to the order-3 cyclic group Z7 are specified # by the image of Z3's 1. It can map to s1 (trivial homomorphism), s2 # (monomomorphism), or s4 (monomomorphism): # # Z3 | phi_1 phi_2 phi_3 # -- + ----- ----- ----- # 0 | s1 s1 s1 # 1 | s1 s2 s4 # 2 | s1 s4 s2 # # Since Z3 is cyclic, and since Aut(Z7) is cyclic, to specify phi we need only # to specify the image of Z3's 1. Call that st. # # Let c be in Z7 and b in Z3. What is (phi(b))(c)? Since phi is a # homomorphism and Z3 is cyclic, written additively, phi(b) = b*phi(1). Now, # phi(1) is some automorphism st of Z7. Moreover, it can't be any old # automorphism: the order of st must divide the order of Z3's 1. So, st^n must # be the identity automorphism s1. Since the arithmetic in Aut(Z7) is that of # the multiplicative group Z7*, this means that t^n must be 1 mod m. # ---------------------------------------------------------------- # ================================================================ # Auxiliary function: # Second component of return value is t. # First compoment of return value is a flag indicating whether t was found. def find_t(p, q): for t in range(2, p): if (sackint.intmodexp(t, q, p) == 1): return [1, t] return [0, 0] # ================================================================ class metacyc_t: def __init__(self, i, j, p, q, t): tq = sackint.intmodexp(t, q, p) if ((tq % p) != 1): print "metacyc: t^q must be 1 mod p" print "Got p =", p, "q =", q, "t =", t raise RuntimeError # xxx jrk 2006-11-28: allow trivial homomorphisms. #if ((t % p) == 1): # print "metacyc: t must not be 1 mod p" # print "Got p =", p, "q =", q, "t =", t # raise RuntimeError self.i = i % p self.j = j % q self.p = p self.q = q self.t = t def __eq__(a,b): return ((a.i == b.i) and (a.j == b.j)) def __ne__(a,b): return not (a == b) def __mul__(a,b): if ((a.p != b.p) or (a.q != b.q) or (a.t != b.t)): print "Parameter mismatch in metacyc mul" raise RuntimeError ci = (a.i + b.i * sackint.intmodexp(a.t, a.j, a.p)) % a.p cj = (a.j + b.j) % a.q c = metacyc_t(ci, cj, a.p, a.q, a.t) return c def inv(a): ci = -a.i * sackint.intmodexp(a.t, -a.j, a.p) cj = -a.j c = metacyc_t(ci, cj, a.p, a.q, a.t) return c def scan(self, string, argp, argq, argt): groups = re.match(r"^(\d)+,(\d+)\$", string).groups(); if len(groups) != 2: raise IOError self.__init__(int(groups[0]), int(groups[1]), argp, argq, argt) def __str__(self): return str(self.i) + "," + str(self.j) def __repr__(self): return self.__str__() def params_from_string(params_string): pqt = re.split(',', params_string) if (len(pqt) == 3): p = int(pqt[0]) q = int(pqt[1]) t = int(pqt[2]) elif (len(pqt) == 2): p = int(pqt[0]) q = int(pqt[1]) [got_it, t] = find_t(p, q) if (not got_it): print "metacyc_t: No t found for p =", p, "q =", q print "Got: ", params_string raise IOError else: print "metacyc_tm.from_string: expected parameters p,q or p,q,t." print "Got: ", params_string raise IOError return [p, q, t] def from_string(value_string, params_string): [p, q, t] = params_from_string(params_string) obj = metacyc_t(0, 0, p, q, t) obj.scan(value_string, p, q, t) return obj # ================================================================ import unittest if __name__ == '__main__': class test_cases(unittest.TestCase): def test_find_t(self): pass # to be implemented def test___init__(self): pass # to be implemented def test___eq__(self): pass # to be implemented def test___ne__(self): pass # to be implemented def test___mul__(self): pass # to be implemented def test_inv(self): pass # to be implemented def test_scan(self): pass # to be implemented def test___str__(self): pass # to be implemented def test___repr__(self): pass # to be implemented def test_params_from_string(self): pass # to be implemented def test_from_string(self): pass # to be implemented # ---------------------------------------------------------------- unittest.main()
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# chemistry
Need help with my pH calculations?
1)
0.10 mol of solid sodium hydrogen carbonate and 0.20 mol of solid sodium carbonate are
dissolved in the same beaker of water, transferred to a volumetric flask and made to 250.0
mL. The Ka for HCO3
– is 4.7 x 10–11.
a) What is the pH of the resulting buffer?
i got pH i calculated here is 10.63
b) What is the pH of solution after 20.00 mL of 0.050 mol L–1 hydrochloric acid solution is
added to 25.00 mL of the original solution?
c)What is the pH of the resulting buffer after 0.040 g of solid sodium hydroxide is added
to 25.00 mL of the original solution?
1. 👍 0
2. 👎 0
3. 👁 300
1. See your other post above.
1. 👍 0
2. 👎 0
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# Physics
posted by .
An automobile moving at a constant velocity of 15m/s passes a gasoline station. Two seconds later, another automobile leaves the gasoline station and accelerates at a constant rate of 2m/s^2 in the same direction. How soon does the second autombile overtake the first?
• Physics -
Let t =0 be the time after the first can passes by.
Solve for t when
15 t = (1/2)*(2.0)*(t-2)^2
The term on the right is the distance covered by the accelerating car that starts 2 seconds late.
15t = (t-2)^2 = t^2 -4t + 4
t^2 -19t +4 = 0
t = [19 +sqrt(345)]/2 = 18.8 seconds
They both will be 282 m from the gas station at that time.
• Physics -
asjklaj;a
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The density of gasoline is 730 kg/m^3 at 0'C. One gallon of gasoline occupies .0038 m^3. Gasoline's volume expansion coefficient is .00096'C ^-1. How many kilograms of gasoline are obtained when 9 gallons of gasoline are bought @ 0'C …
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https://mathematica.stackexchange.com/questions/24599/how-can-i-combine-two-pick-expressions-into-one
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# How can I combine two Pick expressions into one?
I want to speed up my code, i.e., replace Select by Pick. I think using two Pick expressions isn't pretty, but I have no good idea on how to combine them.
Select[Permutations@ Range@9,
#1 < #4 < #7 && #1/(10 #2 + #3) + #4/(10 #5 + #6) + #7/(10 #8 + #9) == 1 & @@ # &]
Pick[#, #1/(10 #2 + #3) + #4/(10 #5 + #6) + #7/(10 #8 + #9) & @@ Transpose @ #, 1] & @
Pick[#, Thread[#1 < #4 < #7] & @@ Transpose@#] & @ Permutations @ Range @ 9
• "I think two Pick isn't pretty..." - sure, but at least the second Pick[] has less to choose from, which is a good thing. May 3 '13 at 16:47
One way to speed things up is to use internally fast functions ("vectorized" ones).
Another consideration is that machine-size integer arithmetic is faster than exact rational arithmetic. If we clear denominators in the second criteria it turns out to be faster.
pickCriteria = Compile[{{perms, _Integer, 2}},
#[[1]] #[[5]] #[[6]] + #[[2]] #[[4]] #[[6]] + #[[3]] #[[4]] #[[5]] - #[[4]] #[[5]] #[[6]] &[
{{1, 0, 0, 0, 0, 0, 0, 0, 0}, (* equals part 1 *)
{0, 0, 0, 1, 0, 0, 0, 0, 0}, (* equals part 4 *)
{0, 0, 0, 0, 0, 0, 1, 0, 0}, (* equals part 7 *)
{0, 10, 1, 0, 0, 0, 0, 0, 0}, (* equals 10 * part 2 + part 3 *)
{0, 0, 0, 0, 10, 1, 0, 0, 0}, (* equals 10 * part 5 + part 6 *)
{0, 0, 0, 0, 0, 0, 0, 10, 1} (* equals 10 * part 8 + part 9 *)
} . Transpose @ perms]
];
Pick[#, Thread[#[[1]] < #[[4]] < #[[7]]] &@ Transpose@#] &@
Pick[#, pickCriteria[#], 0] &@ Permutations @ Range @ 9 // Timing
(* {0.134507, {{5, 3, 4, 7, 6, 8, 9, 1, 2}}} *)
The OP's two versions take 1.795493 and 0.873528 seconds respectively.
Real arithmetic is also fast, but approximate. A little bit slower than the above.
pickCriteriaReal = Compile[{{perms, _Real, 2}},
Sign @ Chop[#[[1]]/#[[4]] + #[[2]]/#[[5]] + #[[3]]/#[[6]] - 1.] &[
{{1., 0., 0., 0., 0., 0., 0., 0., 0.},
{0., 0., 0., 1., 0., 0., 0., 0., 0.},
{0., 0., 0., 0., 0., 0., 1., 0., 0.},
{0., 10., 1., 0., 0., 0., 0., 0., 0.},
{0., 0., 0., 0., 10., 1., 0., 0., 0.},
{0., 0., 0., 0., 0., 0., 0., 10., 1.}
} . Transpose @ perms]
];
Pick[#, Thread[#[[1]] < #[[4]] < #[[7]]] &@ Transpose @ #] &@
Pick[#, pickCriteriaReal[#], 0] &@ Permutations @ N @ Range @ 9 //
Round // Timing
(* {0.205289, {{5, 3, 4, 7, 6, 8, 9, 1, 2}}} *)
• Thanks for help. Machine-size integer indeed fast, this also take 0.2 seconds: Pick[#, #1 (10 #5 + #6) (10 #8 + #9) + 10 #2 ((10 #5 + #6) (#7 - 10 #8 - #9) + #4 (10 #8 + #9)) + #3 ((10 #5 + #6) (#7 - 10 #8 - #9) + #4 (10 #8 + #9)) & @@ Transpose@#, 0] &@Permutations@Range@9 // Timing May 4 '13 at 18:01
Pick[#, Sign[(#1 - #4)] + Sign[(#4 - #7)] +
#1/(10.0 #2 + #3) + #4/(10.0 #5 + #6) +#7/(10.0 #8 + #9) & @@
Transpose@#, 1. - 2] &@ Permutations@Range@9 // Timing
(*{1.138807, {{5, 3, 4, 7, 6, 8, 9, 1, 2}}}*)
More faster version (Thanks @Michael E2):
Pick[#, Function[{a, b, c, d, e, f, g, h, i},
Evaluate[ Sign[a - d] + Sign[d - g] +
Simplify[a/(10 b + c) + d/(10 e + f) + g/(10 h + i) - 1 // Together // Numerator]]
] @@ Transpose@#, -2] &@Permutations@Range@9 // Timing
(*{0.218401, {{5, 3, 4, 7, 6, 8, 9, 1, 2}}}*)
Or
Pick[#, Function[{a, b, c, d, e, f, g, h, i},
Evaluate@Simplify[a/(10 b + c) + d/(10 e + f) + g/(10 h + i) - 1 // Together //
Numerator]] @@ Transpose@#, 0] &@
Pick[#, Sign[(#1 - #4)] + Sign[(#4 - #7)] & @@ Transpose@#, -2] &@
Permutations@Range@9 // Timing
(*{0.109201, {{5, 3, 4, 7, 6, 8, 9, 1, 2}}}*)
• Yours takes 0.067 sec. on my machine -- much faster than mine. The use of Sign[#1-#4] etc. in place of Less saves a lot of time, I think. May 4 '13 at 18:48
Replaced by one equivalent Pick, but the net result is a slowdown ...
Pick[#, #1 < #4 < #7 && #1/(10 #2 + #3) + #4/(10 #5 + #6) + #7/(10 #8 + #9) == 1 & @@@ #] &@
Permutations@Range@9
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## Why is he called the Big Unit?
“Big Unit” nickname
During batting practice in 1988, the 6’10” Johnson, then with the Montreal Expos, collided head-first with outfielder Tim Raines, prompting his teammate to exclaim, “You’re a big unit!” The nickname stuck. Throughout much of his career, Johnson held the title of tallest player in MLB history.
## What does being called a unit mean?
a single thing or person. any group of things or persons regarded as an entity: They formed a cohesive unit. one of the individuals or groups that together constitute a whole; one of the parts or elements into which a whole may be divided or analyzed.
## What means total unit?
Total Number of Units means the sum of the Number of Outstanding Units and the Additional Number of Units; Total Number of Units means two (2) units is the total number of Units that may become part of the Condominium. Sample 1.
## Who was called the Big Unit?
Big Unit
The Big Unit
Randy Johnson/Nicknames
## At what age did Randy Johnson retire?
I just think it’s a natural progression when you play this long. Eventually you have to say it’s time.” A five-time Cy Young Award winner, the 46-year-old Johnson accomplished just about everything in his remarkable career that a player hopes for in baseball.
## What is a unit in an apartment?
A unit is a self contained suite of rooms that can be attached or detached with several other such dwellings. It can be a studio flat or bedsitter which houses one or more people. The term ‘unit’ is almost always synonymous with an apartment, flats, or condominiums that are rented out to individuals.
## What does unit mean in math?
In math, the word unit can be defined as the rightmost position in a number or the one’s place. Here, 3 is the unit’s number in the number 6713. A unit may also mean the standard units used for measurement.
## Where did the term unit come from?
unit (n.) 1560s, “single number regarded as an undivided whole,” alteration of unity on the basis of digit. Popularized in John Dee’s English translation of Euclid, to express Greek monas (Dee says unity formerly was used in this sense). Meaning “single thing regarded as a member of a group” is attested from 1640s.
## What is the difference between apartment and a unit?
Apartments—or as they’re also known: units—generally share walls with other units. Apartment buildings can be large or small, but the chief identifier is that the building comprises a number of units. So, unlike a house, an apartment is part of a group of homes, sometimes on several levels.
## Is a unit a flat?
Units with single stories are considered flats. Some areas of the world are more likely to refer to a unit within a building specifically built for residency as an apartment, whereas a unit in a building originally for a different purpose that was converted into a living space would be considered a flat.
## Is unit same as Suite?
A flat or a unit or apartment simply refers to a living space that you may or may not own, but likely rent. These are three ways of describing the same thing. A suite is a fancy living space and is typically located in a hotel. You neither rent it nor own it but are there as a transient.
## Is a unit a house?
The unit can be in any type of residence, such as a house, apartment, or mobile home, and may also be a single unit in a group of rooms. Essentially, a housing unit is deemed to be a separate living quarter where the occupants live and eat separately from other residents of the structure or building.
## What is the difference between a unit and a house?
Unit: In Australia, New Zealand and the United Kingdom a unit is what most people usually refer to as an apartment, meaning that it is a self-contained area of a building that houses anywhere from four to thirty individual residences.
## Should I put unit or Apt?
Common abbreviations that you can use in your apartment address include: Apartment – APT. Building – BLDG. … Unit – Unit (no abbreviation)
## What are units in Australia?
In common speech in Australia and New Zealand, the word “unit”, when referring to housing, usually means an apartment, where a group of apartments is contained in one or more multi-storey buildings (an ‘apartment block’), or a villa unit or home unit, where a group of dwellings is in one or more single-storey buildings …
## What is an example of a unit?
The definition of a unit is a fixed standard amount or a single person, group, thing or number. An example of a unit is a single apartment in an apartment building. … The centimetre is a unit of length.
## What are the different units?
Share
• Length – meter (m)
• Time – second (s)
• Amount of substance – mole (mole)
• Electric current – ampere (A)
• Temperature – kelvin (K)
• Luminous intensity – candela (cd)
• Mass – kilogram (kg)
## Is a townhouse a unit?
1. A unit is a measure of housing or dwelling for a family or household while a townhouse refers to a terraced house that has several levels or stories.
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## Saturday, December 12, 2020
### Audio Amplifier Feedback - Amplifier with Multiple Poles Inside Feedback Loop
This post is a part of the series on audio amplifier feedback. The contents of the series can be found here.
In the last post, I mentioned that any real amplifier's gain sooner or later goes down as the frequency goes up. As the gain declines, the phase at the output starts lagging that at the input (the amplifier has a pole):
Declining gain and lagging phase as the frequency grows are the characteristics of a low-pass filter:
With some simplification, one can say that every capacitance in a circuit can form a low pass filter and can create a pole. Even in a very simple circuit, there are many capacitances, intended and parasitic:
so there are many poles.
Let's say an amplifier has three poles, at 2kHz, 1MHz and 20MHz, and is placed inside a feedback loop with B=-1/10 (say a resistive divider made of a 9kOhm and a 1kOhm resistors from the output of the amplifier to its inverting input):
The Bode plot of the amplifier's open loop gain and the ideal closed loop gain:
If we apply a square wave to the input of such an amplifier, at the output we will observe the following:
which is not what was intended. The signal transfer function has a pronounced peak and is not the flat 20dB line that the feedback network demands:
Turns out that at about 4.5MHz, where the open goop gain $Aol$ approaches $1/B$and the loop gain $Aol \times B$ approaches unity, the amplifier's multiple poles together create a phase lag of almost 180 degrees. Together with the 180 degrees created by applying the feedback to the inverting input, the phase shift is close to zero at the point where the loop gain is unity. As a result, the signal transfer function $STF={LG \over {1 - LG}}{1 \over B}$ and the error transfer function $ETF={1 \over {1 - LG}}$ can become very large, leading to instability.
To avoid instability and make $STF$ and $ETF$ what they should be, the amplifier needs to be compensated, which will be the topic of my future posts.
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Chemistry
# What general word equation for an acid reacting with an alkali?
345
###### 2008-11-03 23:59:33
acid + alkali = Salt + water.
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## Related Questions
Example 1: Acid - Hydrochloric acid - HCl Alkali - Sodium Hydroxide - NaOH Acid + Alkali -> Salt + Water HCl + NaOH -> NaCl + H2O Example 2: Acid - Hydrochloric acid - HCl Alkali - Magnesium Hydroxide - Mg(OH)2 Acid + Alkali -> Salt + Water 2HCl + Mg(OH)2 -> MgCl2 + 2H2O
Basically, it is where an acid (red) reacts with an alkali (blue) to create a neutral (green)
by neutralisation reaction:- when acid reacts with a base then the product is salt and water. acid+base=salt+water
Acid + alkali ---> Salt + Water for exampleSodium Hydroxide + Hydrochloric Acid ---> Sodium Chloride + Water
The equation for a neutralisation reaction is acid+alkali=neutral this is the correct answer hoped I helped you :)
total ionic equation (also known as the complete ionic equation) for the reaction of potassium carbonate with hydrochloric acid
when an acid reacts with an alkali(soluble base) salt and water are formed equation:- NaOH+HCL----->NaCL+h2O
phenolphthalein is a weak acid, when reacting with strong alkali it turns pink
No an alkali is the opposite of an acid. Alkali = basic; acid = acidic.
The general equation for reacting a metal oxide with an acid is: metal oxide + acid --> salt + water + hydrogen e.g Na2O + 2HCl --> 2NaCl + H2O Hope this helps seen as though no one else could answer this.
acid + alkali= salt + water That is very basic but BBC Bite size GCSEscience can give you a more detailed answer if you find the right section
The process of equalising the concentrations of OH- and H3O+ in an aqueous solution by reacting an acid and an alkali together, via the reaction OH- + H3O+ ---> 2H2O.
###### Acids and BasesHuman Anatomy and PhysiologyChemistryMetal and AlloysScienceChemical Bonding
Copyright ยฉ 2020 Multiply Media, LLC. All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply.
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# Delete some columns from structure array
조회 수: 1(최근 30일)
SS 2021년 5월 25일
편집: Jan 2021년 5월 25일
Hi. I am working with a structure array S (1 X 50,000) with 10 fields in which some columns are multiuple entries ands sub-set of another column.
Here is the input,
S(1).f1=[10,20,30 40,50,60], S(1).f2=[100,20,50,60,70,140],.........S(1).f10=[11,22,33,44,55,66];
S(2).f1=[56,98,74,87,99] and S(2).f2=[101,54,69,20,11],....... S(2).f10=.........[54,55,65,74,90];
S(3).f1=...... and S(3).f2=.....
S(4).f1=.... and S(4).f2=.....
.
.
S(13).f1=[10,20,30 40,50,60,70,80,90,100], S(13).f2=[100,20,50,60,70,140,160,200,220,300],.........S(13).f10=[11,22,33,44,55,66,65,72,34,61];
.
.
.
As we can see S(1) is a sub-set of S(13). I want to write a loop to compare all the columns and retain only the ones with maximum length; meaning that to delete S(1) and retain S(13) in the above example.
댓글을 달려면 로그인하십시오.
### 채택된 답변
Jan 2021년 5월 25일
편집: Jan 2021년 5월 25일
toDel = false(1, numel(S));
for i1 = 1:numel(S)
data1 = S(i1).f1;
n1 = numel(data1);
for i2 = i1 + 1:numel(S)
if ~toDel(i2)
data2 = S(i2).f1;
n2 = numel(data2);
if n1 >= n2
if isequal(data1(1:n2), data2)
toDel(i2) = true;
end
elseif isequal(data1, data2(1:n1))
toDel(i1) = true;
end
end
end
end
S(toDel) = [];
Maybe "subset of" does not mean, that the first elements are equal. Then all(ismember()) might be, what you need instead of isequal.
댓글을 달려면 로그인하십시오.
### 범주
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Translated by
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https://www.yemialadeworld.com/why-is-multiplication-allowed-in-elimination/
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# Why is Multiplication allowed in elimination?
## Why is Multiplication allowed in elimination?
The normal addition/subtraction elimination method wouldn’t cancel any variables. Luckily, we have the multiplication property. This allows us to multiply both sides of an equation by the same constant while still having an equivalent expression. Now, −3x+9y=51 is our new equation in the system.
How do you solve by elimination?
To Solve a System of Equations by Elimination
1. Write both equations in standard form.
2. Make the coefficients of one variable opposites.
3. Add the equations resulting from Step 2 to eliminate one variable.
4. Solve for the remaining variable.
5. Substitute the solution from Step 4 into one of the original equations.
### What is an example of elimination in math?
Elimination Method: Infinitely Many Solutions For example, try to solve equations x+y=2 and 2x+2y-4=0. If you multiply any non-zero constant with both equations, you will find that every time x-variable terms and y-variable terms are getting canceled or eliminated.
Can you divide two equations?
Dividing equal things by equal things (never zero), should result in equal things. So we may think of the above notation as a short-hand for. This is valid, so long as the two starting equations are valid and the denominator is not zero. Essentially this is equivalent to saying [ x = 1 ]→[ x/5 = 1/5] → [ x/y = 1/5 ].
#### What is elimination math?
When solving for a system of two linear equations, we are finding the point or points where the two equations intersect. One method is called elimination. The process is to eliminate one variable, then solve for the other variable.
Can you divide to solve simultaneous equations?
It works because of two properties of equations: Multiplying (or dividing) the expression on each side by the same number does not alter the equation.
## Why do we divide equations?
It doesn’t help and becomes a total mess. The short answer to why it is a good idea to divide one equation by the other is: Because it makes the problem easier. When you divide one equation by the other the common factor of (1+i)5 cancels out and you are left with an equation that can be solved by “unwinding”.
Is multiplication easier than addition?
When we’re doing arithmetic, addition is easier than multiplication, so we change multiplication problems into addition problems using logarithms. We can “add” two shapes by multiplying their equations together.
### How do you solve system of equations using elimination?
– Solve a system of equations when no multiplication is necessary to eliminate a variable. – Solve a system of equations when multiplication is necessary to eliminate a variable. – Recognize systems that have no solution or an infinite number of solutions. – Solve application problems using the elimination method.
How do you use elimination in math?
Example (Click to try)
• Try it now. Enter your equations separated by a comma in the box,and press Calculate! Or click the example.
• About Elimination. Use elimination when you are solving a system of equations and you can quickly eliminate one variable by adding or subtracting your equations together.
• #### How do you solve system by elimination?
The lines intersect at zero points. (The lines are parallel.)
• The lines intersect at exactly one point. (Most cases.)
• The lines intersect at infinitely many points. (The two equations represent the same line.)
• How do you multiply without using multiplication?
Writing Simple Java Program: Create a simple java Program by typing it into a text editor.
• Compiling a Java Source File: After Completion of Java program,open Command prompt. Type the Command “ javac filename.java ” .
• Running a Java Application: To run java Application in the command prompt,type ” Filename.java” .
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https://alumniagri.in/task/if-1-kg-apples-cost-160-rupees-what-is-the-cost-of-5kg-such-31256907
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Math, asked by dineshghatbane, 7 days ago
# If 1 kg apples cost 160 rupees, what is the cost of 5kg such apples?
0
₹ 800
Step-by-step explanation:
1 kg of apple costs = ₹ 160
5 kg of apple costs = 5 x 160
= ₹ 800
1
Step-by-step explanation:
1kg apples cost = 160 rupees
5kg apples cost = 5×160
= 800 rupees
Similar questions
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1
GATE CE 2000
MCQ (Single Correct Answer)
+2
-0.6
Design rate of super elevation for horizontal highway curve of radius 450 m for a mixed traffic condition, having a speed of 125 km/hour is
A
1.0
B
0.05
C
0.07
D
0.154
2
GATE CE 1998
MCQ (Single Correct Answer)
+2
-0.6
For a highway with a design speed of 100kmph, the safe OSD is assume acceleration as 0.53 $$m/sec^2$$. the road is two lane with two way traffic. User other specifications as per IRC
A
300m
B
750m
C
320m
D
470m
3
GATE CE 1991
MCQ (Single Correct Answer)
+2
-0.6
If the design speed is 80kmph, perception reaction time is 3sec and coefficient of friction is 0.5, then the SSD is ________.
A
61.3 m
B
117 m
C
85.5 m
D
171 m
4
GATE CE 1988
MCQ (Single Correct Answer)
+2
-0.6
A vehicle traveling on dry, level pavement at 80kmph had the brakes applied. The vehicle traveling 76.5 m before stopping. what is the coefficient of friction that has developed?
A
0.2
B
0.3
C
0.33
D
0.4
GATE CE Subjects
Engineering Mechanics
Construction Material and Management
Geotechnical Engineering
Fluid Mechanics and Hydraulic Machines
Geomatics Engineering Or Surveying
Environmental Engineering
Transportation Engineering
General Aptitude
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12
© ExamGOAL 2024
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Pycharm使用技巧：
1.tab批量换space：
Edit-->Convert Indents--> to spaces/tabs
2.tab键补全
File-->power sava mode 不勾选
3批量注释代码
range介绍
Range(2)
[0,1]
Rang(1,4)
[1,2,3]
Range(1,4,2)
[1,3]
a=[”a”,”b”,”c”,”d”]
a是一个对象，才能调用方法
``````a.append("f")
print(a)
a.insert(1,"o")
print(a)``````
['a', 'b', 'c', 'd', 'e', 'f']
['a', 'o', 'b', 'c', 'd', 'e', 'f']
``````a=['a','b','c','d','e']
print(a[1])
print(a[1:])
print(a[1:-1])
print(a[1:4:2])
print(a[1::-1])``````
b
['b', 'c', 'd', 'e']
['b', 'c', 'd']
['b', 'd']
['b', 'a']
Print(“a” in a)
``````a[1]="1"
print(a)``````
['a', '1', 'b', 'c', 'd', 'e', 'f']
``````a[1:3]=[2,3]
print(a)``````
['a', 2, 3, 'c', 'd', 'e', 'f']
4种方法：
Remove,pop,del，clear
Pop可以返回删除的值
``````a.remove("f")
print(a)
n=a.pop(1)
print(a)
print(n)
del(a[0])
print(a)
a.clear()
print(a)
print(type(a))
del a
print(a)``````
['a', 2, 3, 'c', 'd', 'e']
['a', 3, 'c', 'd', 'e']
2
[3, 'c', 'd', 'e']
[]
<class 'list'>
``````a=["w","a","w"]
print(a)
a.remove("w")
print(a)``````
['w', 'a', 'w']
['a', 'w']
Extend 把其他列表加入列表
``````print(a)
b=[4,5,6]
a.extend(b)
print(a)
print(b)``````
['a', 3, 'c', 'd', 'e']
['a', 3, 'c', 'd', 'e', 4, 5, 6]
[4, 5, 6]
Index通过内容找索引
`print(a.index("a"))`
0
Reverse
Sort 只支持全数字或全字符串
1. mobile 5000
2. book 100
3. cup 3
4. hair 500
算钱，买完结账，显示商品和价格，余额。余额不足提示。
``````# -*-coding:utf-8 -*-
__date__ = '2018/2/6 17:56'
__author__ = 'xiaojiaxin'
__file_name__ = 'shopping_car'
salary=int(input("input your salary:"))
counter=0
remaining_sum=salary
shopping_sum=[]
shopping={"mobile":5000,"book":128,"cup":3,"hair":70}
print('''The product lists:
mobile:%d
book:%d
cup:%d
hair:%d
'''%(shopping["mobile"],shopping["book"],shopping["cup"],shopping["hair"]))
while True:
shopping_car=input("enter the product's name:")
if shopping_car in shopping:
counter+=shopping[shopping_car]
remaining_sum=salary-counter
shopping_sum.append(shopping_car)
flag=input("bug more?[y/n]")
if flag=="y":
continue
else:
if remaining_sum>=0:
print("the remaining sum is %d"%remaining_sum)
print("you have bug %s"%(shopping_sum))
break
else:
print("the remaining sum is not enough to pay for it!")
break
else:
print("The product do not exist!")``````
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The OEIS is supported by the many generous donors to the OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A027423 Number of divisors of n!. 116
1, 1, 2, 4, 8, 16, 30, 60, 96, 160, 270, 540, 792, 1584, 2592, 4032, 5376, 10752, 14688, 29376, 41040, 60800, 96000, 192000, 242880, 340032, 532224, 677376, 917280, 1834560, 2332800, 4665600, 5529600, 7864320, 12165120, 16422912 (list; graph; refs; listen; history; text; internal format)
OFFSET 0,3 COMMENTS It appears that a(n+1)=2*a(n) if n is in A068499. - Benoit Cloitre, Sep 07 2002 Because a(0) = 1 and for all n > 0, 2*a(n) >= a(n+1), the sequence is a complete sequence. - Frank M Jackson, Aug 09 2013 Luca and Young prove that a(n) divides n! for n >= 6. - Michel Marcus, Nov 02 2017 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe) Daniel Berend and J. E. Harmse, Gaps between consecutive divisors of factorials, Ann. Inst. Fourier, 43 (3) (1993), 569-583. Paul Erdős, S. W. Graham, Alexsandr Ivić, and Carl Pomerance, On the number of divisors of n!, Analytic Number Theory, Proceedings of a Conference in Honor of Heini Halberstam, ed. by B. C. Berndt, H. G. Diamond, A. J. Hildebrand, Birkhauser 1996, pp. 337-355. Florian Luca and Paul Thomas Young, On the number of divisors of n! and of the Fibonacci numbers, Glasnik Matematicki, Vol. 47, No. 2 (2012), 285-293. DOI: 10.3336/gm.47.2.05. Wikipedia, Complete sequence. Index entries for sequences related to factorial numbers Index entries for sequences related to divisors of numbers FORMULA a(n) <= a(n+1) <= 2*a(n) - Benoit Cloitre, Sep 07 2002 From Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 28 2009: (Start) Assume, p1,p2...pm are the prime numbers less than or equal to n. Then, a(n) = Product_{i=1..m} (bi+1), where bk = Sum_{i=1..m} floor(n/pk^i). For example, if n=5, p1=2,p2=3,p3=5; b1=floor(5/2)+floor(5/2^2)+floor(5/2^3)+...=2+1+0+..=3 similarly, b2=b3=1; Thus a(5)=(3+1)(1+1)(1+1)=16. (End) a(n) = A000005(A000142(n)). - Michel Marcus, Sep 13 2014 a(n) ~ exp(c * n/log(n) + O(n/log(n)^2)), where c = A131688 (Erdős et al., 1996). - Amiram Eldar, Nov 07 2020 EXAMPLE a(4) = 8 because 4!=24 has precisely eight distinct divisors: 1, 2, 3, 4, 6, 8, 12, 24. MAPLE A027423 := n -> numtheory[tau](n!); MATHEMATICA Table[ DivisorSigma[0, n! ], {n, 0, 35}] PROG (PARI) for(k=0, 50, print1(numdiv(k!), ", ")) \\ Jaume Oliver Lafont, Mar 09 2009 (PARI) a(n)=my(s=1, t, tt); forprime(p=2, n, t=tt=n\p; while(tt, t+=tt\=p); s*=t+1); s \\ Charles R Greathouse IV, Feb 08 2013 (Haskell) a027423 n = f 1 \$ map (\p -> iterate (* p) p) a000040_list where f y ((pps@(p:_)):ppss) | p <= n = f (y * (sum (map (div n) \$ takeWhile (<= n) pps) + 1)) ppss | otherwise = y -- Reinhard Zumkeller, Feb 27 2013 (Python 3.8+) from math import prod from collections import Counter from sympy import factorint def A027423(n): return prod(e+1 for e in sum((Counter(factorint(i)) for i in range(2, n+1)), start=Counter()).values()) # Chai Wah Wu, Jun 25 2022 CROSSREFS Cf. A000005, A000142, A062569, A131688, A161466 (divisors of 10!). Sequence in context: A164203 A164178 A335542 * A140410 A213368 A216212 Adjacent sequences: A027420 A027421 A027422 * A027424 A027425 A027426 KEYWORD nonn,easy,nice AUTHOR Glen Burch (gburch(AT)erols.com), Leroy Quet. STATUS approved
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Last modified September 22 18:47 EDT 2023. Contains 365531 sequences. (Running on oeis4.)
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0
# 33 New Series and Parallel Circuits Problems
series and parallel circuits ponents of an electrical circuit or electronic circuit can be connected in many different ways the two simplest of these are called series and parallel and occur series & parallel circuits free mobile website templates series & parallel circuits introduction so far we have discussed circuits with only two ponents a source of current such as a battery and a single electronics series parallel circuits this is the electronics questions and answers section on "series parallel circuits" with explanation for various interview petitive examination and entrance test series and parallel circuits furrey s physics classroom 1 series and parallel circuits direct current series circuits a series circuit is a circuit in which the ponents are connected in a line one after the difference between series and parallel circuits series vs parallel circuits an electrical circuit can be set up in many ways electronic devices such as resistors diode switches and so on are ponents placed scr series and parallel connections electronic circuits how to make series and parallel connections of an scr in many power control applications the required voltage and current ratings exceed the voltage and current parallel circuits the physics classroom as mentioned in a previous section of lesson 4 two or more electrical devices in a circuit can be connected by series connections or by parallel connections series circuits the physics classroom mathematical analysis of series circuits the above principles and formulae can be used to analyze a series circuit and determine the values of the current at and how to solve parallel circuits 10 steps with how to solve parallel circuits solving parallel circuits is an easy process once you know the basic formulas and principles when two or more resistors are connected list of 7400 series integrated circuits the following is a list of 7400 series digital logic integrated circuits the sn7400 series originated with ttl integrated circuits made by texas instruments
40 super how to do series parallel circuits zenerdiodecircuit allows current to flow from its anode to its series and parallel circuits answers elegant parallel and series series parallel circuit problems with answers pdf unique parallel how to solve series parallel circuit problems elegant how to ammeter reading in parallel circuits best ponent series circuit how to calculate total voltage in a parallel circuit best ponent circuit practice problems parallel and series beautiful what are parallel circuit problems elegant ponent series circuit diagrams for 40 recent electric circuit problems worksheet
40 Super How to Do Series Parallel Circuits from series and parallel circuits problems , source:nawandihalabja.com
ZenerDiodeCircuit allows current to flow from its anode to its from series and parallel circuits problems , source:pinterest.com
Series And Parallel Circuits Answers Elegant Parallel And Series from series and parallel circuits problems , source:nawandihalabja.com
Series Parallel Circuit Problems With Answers Pdf Unique Parallel from series and parallel circuits problems , source:nawandihalabja.com
How To Solve Series Parallel Circuit Problems Elegant How To from series and parallel circuits problems , source:nawandihalabja.com
how to draw series and parallel circuits fresh resistors in parallel resistors in series and parallel series and parallel circuits answers elegant parallel and series series parallel circuit worksheet gallery worksheet for kids in numerical problems in hindi analyze an rlc circuit using laplace methods dummies what happens if ammeter connected in parallel and voltmeter ncert class 10 science lab manual resistors in parallel cbse tuts resistors in series and parallel how to calculate series and parallel resistance with cheat sheets
40 elegant how to calculate series parallel circuit 43 fantastic parallel circuits worksheets with answers – free worksheets ponent parallel circuit diagram series and parallel circuits how to calculate series and parallel resistance with cheat sheets ac fundamental batteries wiring li ion cells in parallel to make a 3s8p pack two types of connections ncert exemplar problems class 12 physics alternating current learn how to calculate series and parallel resistance with cheat sheets how to calculate series and parallel resistance with cheat sheets
You can download all 33 of 33 New Series and Parallel Circuits Problems picture to your gadget by right clicking image and then save image as. Do not forget to share if you like with this photo. Tags:
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Banach algebra $A$ without an approximate identity but $A^2=A$
Please help me with the following question.
What are some examples of Banach algebra $$A$$ satisfying the following two conditions?
$$1$$.$$A$$ does not have an approximate identity.
$$2$$. $$A^2=A$$. That is, for any $$a∈A$$, there exist some $$b,c∈A$$ such that $$a=bc$$.
A direct application of the Cohen factorization theorem shows that if A has a bounded approximate identity, then $$2$$ holds.
Thank you.
1 Answer
For finite-dimensional algebra, to have an approximate unit is the same as having a unit.
The non-unital algebra $$A$$ of matrices $$\begin{pmatrix}0 & x\\ 0 & y\end{pmatrix}$$ has no unit (although it has a right unit), so over the reals has no approximate unit, and satisfies $$A^2=A$$.
The non-unital algebra $$B$$ of matrices $$\begin{pmatrix}a & x & z\\ 0 & 0 & y\\ 0 & 0 & b\end{pmatrix}$$ has no unit (and has no left or right unit), so over the reals has no approximate unit, and satisfies $$B^2=B$$.
• Thank you and what about infinite dimensional Banach algebras? Is there any? – Fermat Feb 23 '19 at 13:44
• Fix a Euclidean norm on $A$ for which $\|ab\|\le\|a\|\|b\|$ for all $a\in A$ (restricted direct product), consider $\bigoplus_{n\in\mathbf{N}}A$, and complete to a Hilbertian norm. – YCor Feb 23 '19 at 14:03
• ... or just the direct product of $A$ or $B$ above, with your favorite unital infinite-dimensional Banach algebra. – YCor Feb 23 '19 at 14:58
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Cody
# Problem 38. Return a list sorted by number of occurrences
Solution 1908983
Submitted on 22 Aug 2019 by Thomas Werner
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
x = [1 2 2 2 3 3 7 7 93] y_correct = [2 3 7 1 93]; assert(isequal(popularity(x),y_correct))
x = 1 2 2 2 3 3 7 7 93 y = 2 3 7 1 93
2 Pass
x = [-1 19 20 -1 -1 87 19 34 19 -1 21 87 20 10 20 34 19 -1]; y_correct = [-1 19 20 34 87 10 21]; assert(isequal(popularity(x),y_correct))
y = -1 19 20 34 87 10 21
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TeachersFirst's Elementary School Brain Twisters
Week of November 27, 2023
1.On December 6 children around Europe put out stockings, shoes, or boots to be filled with candy. This is to celebrate which Saint?
• Saint Peter
• Saint Fabius
• Saint Nicholas
• Saint Patrick
• Saint Christopher
2.The least common multiple of 2, 3, and 4 is:
• Greater than the product of 6 and 4
• Greater than the difference of 43 and 21
• Less than the product of 3 and 6
• Less than the sum of 18 and 5
• Less than the product of 2 and 7
3.Hanukkah is known as the Jewish:
• Version of Christmas
• Festival of lights
• Celebration of the messiah
• High Holy Day
• Sabbath
4.In December the northern hemisphere experiences:
• The vernal equinox
• The annual lunar eclipse
• The autumnal equinox
• The winter solstice
• The beginning of spring
5.The candles on Rachel's menorah burn only 6 hours. If she kept her menorah lit for 3 hours each night, how many candles did she need to buy to keep her menorah properly lit for all 7 nights of Hanukkah?
• 9
• 11
• 7
• 21
• 16
6.John, Mary and Susie are each more than one decade and less than two decades old. The sum of their ages is 41. Susie is one and a half times Mary's age. Mary is one year older than John. John is seven years younger than Susie. How old is Susie?
• 18
• 13
• 11
• 15
• 12
7.A synonym for the word "harmony" is:
• disagreement
• confusion
• dissonance
• noise
• agreement
8.Janice has \$14. Leilani has \$15. They put their money together to buy a toy that costs \$21.14. How much change did they have left after buying the toy?
• \$4.57
• \$8.23
• \$3.29
• \$6.95
• \$7.86
9.Which sentence is correct?
• My mother has to wrap all are presents.
• I buyed a toy truck for my little brother.
• There's only 33 days until Christmas.
• He said he wanted a fire truck for Christmas.
• I got to hide it so he won't find it.
10.Which city is most likely to have a white Christmas?
• New Orleans
• Santa Fe
• Tacoma
• Detroit
• Ft. Lauderdale
Back
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# Subtraction of Complex Numbers
Reviewed by:
Last updated date: 09th Aug 2024
Total views: 176.7k
Views today: 2.76k
## Introduction to the Subtraction of Complex Numbers
In everyday life, addition and subtraction are the most used mathematical operations. We use it on a daily basis. If we go to the supermarket for shopping, we need an addition or subtraction of money to make the payment. We use addition or subtraction when we have some chocolates, and someone gives us more chocolates or if someone takes some chocolates from us.
Confused about complex numbers? Don't worry; all your doubts will be cleared after reading this article. Because in this article today, we are going to learn about what complex numbers are, what their properties are when it comes to subtraction, and what the steps are to solve complex numbers. So now, let's learn about the subtraction of complex numbers.
## What are Complex Numbers?
Complex numbers are also numbers, but they are different from normal numbers in many ways. They are made with the help of two numbers that are combined.
And in the new combined number, the first number is the real number, and another one is the imaginary number. Like all complex numbers can be expressed in the form a + bi, here, a is the real number, and bi is the imaginary number.
Remember that Complex Numbers are denoted by the letter 'C'.
Complex numbers also use all mathematical operations: addition, subtraction, multiplication, and division. But today, we will learn about the subtraction of complex numbers, which is as easy as solving a normal number.
And the Subtraction of complex numbers requires a formula.
Do you know the formula for the subtraction of Complex Numbers?
So the formula is (a+ib) - (c + id) = (a-c) +i(b-d).
Complex Number
## Properties of Subtracting Complex Numbers
1. Closure property - In the closure property of Subtracting Complex Numbers, the difference between complex numbers is also a complex number.
2. Commutative property- Subtraction of complex numbers is not commutative.
3. Associative property- Subtraction of complex numbers is not associative.
Remember that this general form of a complex number is different from the polar form. Similarly, the addition and subtraction of complex numbers in the polar form are different.
## Steps to Subtract Complex Numbers
Subtraction of two complex numbers is easy if it's done in the right and systematic way. So let's see the steps of subtraction of complex numbers.
$\mathrm{z}_1=\mathrm{a}+\mathrm{ib}, \mathrm{z}_2=\mathrm{c}+\mathrm{id}$
Subtraction
$\mathrm{z}_1-\mathrm{z}_2+(a-c)-(c+i d)$
$\mathrm{z}_1-\mathrm{z}_2=(a-c)+(b-d) i$
where $a, b, c, d$ are real number and $i$ is imaginary number
Step 1: Disperse the negative
Step 2: Now combine the real and imaginary complex numbers in a single group.
Step 3: Now, you need to combine and simplify similar terms.
Step 4: The answer will be there.
Subtraction of two complex numbers example
## Subtraction of Complex Numbers Examples
For the subtraction of two complex numbers, we need to Subtract the real number from the real and the imaginary numbers from the imaginary. Let's learn it through examples:
Q 1. Subtract $(4-3 i)$ from $(7+5 i)$
Ans. $=7+5 i-(4-3 i)$
$=7+5 i-4+3 i$
$=3+8 i$
Q 2. Subtract ( 8 - 15i ) from (15 - 34i )
Ans. $=15-34 i-(8-15 i)$
$=15-34 i-8+15 i$
$=7-19 i$
Q 3. Subtract $(2+2 i)$ from $(3+5 i)$
Ans. $=3+5 i-(2+2 i)$
$=1+3 i$
## Points to remember for the Subtraction of Complex Numbers
• Subtracting a complex number is like subtracting two binomials; we just need to combine the like terms.
• The subtraction of two complex numbers does not hold in the commutative law.
• All real numbers are complex numbers, but all complex numbers need not be real numbers.
## Practice Questions
We know that maths is not learned just with reading. To understand it, we need to solve the question. So that's why we have provided a practice sheet for you. With the help of this practice sheet, you can better understand the subtraction of two complex numbers. Below are the addition and subtraction of complex numbers worksheets for your practice. Use the subtraction of complex numbers formula mentioned in this article to solve these problems.
Q1. $(16+5 i)+(8-3 i)$
Ans. $24+2 i$
Q2. $(5+7 i)-2 i$
Ans. $5+5 i$
Q3. $(4+3 i)-(4-3 i)$
Ans. 6i
## Summary
In this article, we learned about the subtraction of complex numbers. With the help of this article, we learned what complex number is, how to subtract complex numbers, and what the properties of Subtracting Complex Numbers are.
We learn the steps we need to follow while subtracting a complex number. We also checked an example of subtraction of complex numbers, and at the end, there is a complex number worksheet with the help of which we can easily clear our concept of subtraction of complex numbers.
## FAQs on Subtraction of Complex Numbers
1. Is zero a complex number?
We know that real numbers are part of complex numbers, and zero is a real number. That is why we can say that zero is a complex number.
2. Are the complex numbers closed under subtraction?
Yes, the complex numbers are closed in Subtraction.
3. Is 50i a complex number?
Yes, it's a complex number because it has an imaginary part.
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# What Is The nth Derivative of sin(x)
• Sep 22nd 2009, 10:31 AM
soma
What Is The nth Derivative of sin(x)
How can you write out the nth derivative of sin(x)?
http://www4a.wolframalpha.com/Calcul...image/gif&s=59
• Sep 22nd 2009, 10:58 AM
artvandalay11
Let $\displaystyle f(x)=\sin x$
$\displaystyle f'(x)=\cos x$
$\displaystyle f''(x)=-\sin x$
$\displaystyle f'''(x)=-\cos x$
$\displaystyle f''''(x)=\sin x$ and then the cycle repeats
So you could just write it out using if's and keep dividing the n of$\displaystyle f^{(n)}$by 4 to get the remainder
But upon further analysis, we realize
$\displaystyle f'(x)=\cos x=\sin (\frac{\pi}{2}+x)$
$\displaystyle f''(x)=-\sin x=\sin(\frac{2\pi}{2}+x)$
$\displaystyle f'''(x)=-\cos x=\sin(\frac{3\pi}{2}+x)$
$\displaystyle f''''(x)=\sin x=\sin(\frac{4\pi}{2}+x)$
So $\displaystyle f^{(n)}(x)=\sin(\frac{n\pi}{2}+x)$
• Sep 22nd 2009, 11:03 AM
soma
Works for me, thanks!
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teaching resource
# Christmas-Themed Picture Sudoku Puzzles
• Updated: 15 Nov 2023
Work on your pupils' cognitive skills with this set of 3 differentiated Picture Sudoku puzzles with a Christmas twist.
• Non-Editable: PDF
• Pages: 6 Pages
• Years: 1 - 3
Tag #TeachStarter on Instagram for a chance to be featured!
teaching resource
# Christmas-Themed Picture Sudoku Puzzles
• Updated: 15 Nov 2023
Work on your pupils' cognitive skills with this set of 3 differentiated Picture Sudoku puzzles with a Christmas twist.
• Non-Editable: PDF
• Pages: 6 Pages
• Years: 1 - 3
Work on your pupils' cognitive skills with this set of 3 differentiated Picture Sudoku puzzles with a Christmas twist.
## Picture Sudoku + Christmas = FUN!
Picture Sudoku is a variation of the traditional Sudoku game that incorporates visual elements instead of numbers. In this type of Sudoku, the traditional numerical grid is replaced with images. Instead of using numbers 1 through 9, the goal is to place a set of images in such a way that each row, column, and subgrid contains each image exactly once.
The rules for Picture Sudoku remain consistent with traditional Sudoku rules in terms of placement—no repetition of images within rows, columns, or subgrids. The primary challenge lies in recognizing and placing the images correctly, adding an extra layer of complexity and visual stimulation to the puzzle-solving experience.
So if Christmas pictures are fun and picture sudoku is fun, then together they must be EXTRA FUN!!!!
## Why Introduce Picture Sudoku to Your Class?
Sudoku puzzles are beneficial for young learners for several reasons:
1. Cognitive Development: Picture Sudoku requires logical reasoning and critical thinking. Solving puzzles helps children develop problem-solving skills, strategic thinking, and the ability to analyse and organise information systematically.
2. Pattern Recognition: Completing Picture Sudoku puzzles involves recognizing and applying patterns, an essential cognitive skill. This ability to identify and understand patterns can be transferable to other areas of learning.
3. Concentration and Focus: Solving Sudoku puzzles requires concentration and attention to detail. Regular engagement with such activities can contribute to improving a child’s ability to focus on a task for an extended period.
4. Patience and Perseverance: Sudoku can be challenging, and completing a puzzle requires patience and perseverance. It teaches young learners the value of persistence and the satisfaction of overcoming obstacles.
5. Memory Enhancement: Working on Sudoku puzzles can enhance memory skills. Children need to remember images and their placements within the grid, exercising both short-term and working memory.
6. Independent Learning: Sudoku puzzles are suitable for independent learning. They can be used as engaging activities during individual study or quiet times, allowing children to practise problem-solving on their own.
7. Low-Risk Learning Environment: Sudoku provides a low-risk environment for making mistakes and learning from them. The self-contained nature of each puzzle allows students to experiment with solutions and learn from errors without significant consequences.
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## Ppf chart examples
19 Dec 2019 Examples. >>> x = np.linspace(uniform.ppf(0.01), uniform.ppf(0.99), 100) >> > ax.plot(x, uniform.pdf(x), . Check accuracy of cdf and ppf :. For example, an SO may grant an ASST user the Sponsor authority on behalf of a Listed below is a table of the types of delegation authorities in Commons, along PPF, All Commons users, All Commons users, Enables another user to edit 27 Sep 2014 PPF and the concept of scarcity, choice and opportunity cost. The following production production possibilities table shows possible However, an economy may be operating within the frontier (for example at the point G in
3 May 2018 If you plot the graph of your PPF value, you will see a straight line going famous ELSS (HDFC Tax Saver) as an example along with PPF and Box: Calculating Labour Productivity – An Example In economics, the production possibility frontier (PPF) is used to show all possible combinations of goods The following table gives the various production possibilities. For example, the combined output of the two goods can neither be at U nor H. (See Fig. replace the Policing Professional Framework (PPF) Personal Qualities. values. The relationships between them are shown in the circular chart below. Values example, will involve probing for evidence of demonstrable values in addition to.
## 1 Jun 2018 For example, it once again set up an online map for 1 May so that customers could find blossoming cherry trees under which, in keeping with
The PPF calculator shows data for PPF investment made for 15 years, 20 years, 25 years, 30 years and 35 years at current year interest rate. You may not modify the interest rate here but you can do the same in offline PPF Excel Calculator.PPF account allows extension of scheme by 5 years which could be extended in last year of the scheme. Production possibility frontier (also called production possibility curve) is a plot that shows the maximum outputs that an economy can produce from the available inputs (i.e. factors of production).. Since resources are scarce, deciding about what to produce is of pivotal importance for individuals, firms, governments and whole economies. (PPF Interest Maturity Calculator – Updated 2020) Are you looking for a PPF Calculator that uses latest PPF interest rates (2019-20) to calculate the interest earned on PPF investments? And you also want to know the answer to the big… Read More PPF Maturity Excel Calculator (2020) – FREE Download This means that comparison charts are chart examples that allows one to compare features or aspects of two alternatives and determine which alternative would be best to choose. Although pie charts can also be used as a tool for comparison, this type of chart is only limited to showing numerical proportions. The production possibility frontier (PPF) for computers and textbooks is shown here. Interpreting PPFs. Firstly, we can describe the opportunity cost to Mythica of producing a given output of computers or textbooks. For example, If Mythica produces 3m computers; the opportunity cost is 5m textbooks. The Production Possibilities Curve (PPC) is a model used to show the tradeoffs associated with allocating resources between the production of two goods.
### Example of PPF Consider a hypothetical world that has only two countries (Country A and Country B) and only two products (cars and cotton). Each country can make cars and/or cotton.
The PPF calculator shows data for PPF investment made for 15 years, 20 years, 25 years, 30 years and 35 years at current year interest rate. You may not modify the interest rate here but you can do the same in offline PPF Excel Calculator.PPF account allows extension of scheme by 5 years which could be extended in last year of the scheme. Production possibility frontier (also called production possibility curve) is a plot that shows the maximum outputs that an economy can produce from the available inputs (i.e. factors of production).. Since resources are scarce, deciding about what to produce is of pivotal importance for individuals, firms, governments and whole economies. (PPF Interest Maturity Calculator – Updated 2020) Are you looking for a PPF Calculator that uses latest PPF interest rates (2019-20) to calculate the interest earned on PPF investments? And you also want to know the answer to the big… Read More PPF Maturity Excel Calculator (2020) – FREE Download This means that comparison charts are chart examples that allows one to compare features or aspects of two alternatives and determine which alternative would be best to choose. Although pie charts can also be used as a tool for comparison, this type of chart is only limited to showing numerical proportions. The production possibility frontier (PPF) for computers and textbooks is shown here. Interpreting PPFs. Firstly, we can describe the opportunity cost to Mythica of producing a given output of computers or textbooks. For example, If Mythica produces 3m computers; the opportunity cost is 5m textbooks. The Production Possibilities Curve (PPC) is a model used to show the tradeoffs associated with allocating resources between the production of two goods.
### 31 Dec 2018 A subscriber is eligible to take a loan from PPF from the third financial year For example, if the loan was sanctioned on any day of July, then the tenure of 36 From the above table it is clear that since you have opted for the
PPF Calculator to calculate PF interest and maturity from SBI and India Post Office. For example, if interest earned on PPF account is 8 % than interest charged
## The graph shows that a society has limited resources and often must prioritize where to invest Society can choose any combination of the two goods on or inside the PPF. If this were a real world example, that data would be available.
Download scientific diagram | An example of a production possibility frontier curve Thus, as shown in Figure 1, we can obtain a PPF curve for the production of A and Table 2 . Validation results for ecosystem service accuracy assessment.
There are many examples of market systems. A PPF graph shows the maximum production level for one commodity for any production level of the other
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• Create Account
## Clarification
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.
2 replies to this topic
### #1arrogantgod Members
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Posted 13 September 1999 - 08:53 AM
Ok, I must have been smoking something wierd when I posted the message.
I want to know how to move something "forward" in 3d space? If it has a direction vector and a position vector how do I accomplish this?
Thanks
### #2emfb Members
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Posted 13 September 1999 - 07:57 AM
This is accomplished through matrix multiplication. Every object in the scene will have its own transformation matrix. To move or rotate an object relative to its current position you have to create a second matrix that contains the relative movement/rotation. Then they are combined by multiplying the two matrices. The resulting matrix is the objects new transformation matrix this is what will be used to render the object.
For instance to move an object using the keyboard by a set vector distance:
//Get Keyboard Input
if(GetAsyncKeyState(VK_RIGHT))
object_matrix = MatrixMult(CreateTranslationMatrix(D3DVECTOR(-STEP,0.0,0.0)),object_matrix);
if(GetAsyncKeyState(VK_LEFT))
object_matrix = MatrixMult(CreateTranslationMatrix(D3DVECTOR(STEP,0.0,0.0)),object_matrix);
if(GetAsyncKeyState(VK_UP))
object_matrix = MatrixMult(CreateTranslationMatrix(D3DVECTOR(0.0,0.0,-STEP)),object_matrix);
if(GetAsyncKeyState(VK_DOWN))
object_matrix = MatrixMult(CreateTranslationMatrix(D3DVECTOR(0.0,0.0,STEP)),object_matrix);
The above code uses two functions:
MatrixMult - multiplys the two matrices together and returns the result.
CreateTranslationMatrix - creates a translation (position) matrix based on the given vector.
The above code would be a hell of a lot faster if flags were set if keys are pressed and then only call the matrixmult/createtranslationmatrix functions once with the final vector.
Also keep in mind that matrix multiplication is not commutative(sp?). It means that the order in which the multiplication takes place matters.
M1*M2 != M2*M1
This makes sense because if you turn right and take ten steps you will be in a different place than if you had taken 10 steps then turned right.
So basically you need to understand a little linear algebra. Also, Depending on if you are in a left or right hand coordinate system the construction of the matrix is a little different.
There is some matrix information in the Direct3D documentation or if you are using OpenGL take a look at chapter three in the Red Book [http://fly.cc.fer.hr/~unreal/theredbook/]
Good Luck
Oh yeah, If you have the DirectX SDK then do a search for 'D3DMath' it has all the functions you would need.
### #3arrogantgod Members
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Posted 13 September 1999 - 08:53 AM
Wow!
Thanks!
That is what I needed to know. Now I understand fully. So, I just need to multiply the new matrix by the current one to get the result I need!
Much Thanks!!!!!!!
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.
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# One-instruction set computer
A one-instruction set computer (OISC), sometimes referred to as an ultimate reduced instruction set computer (URISC), is an abstract machine that uses only one instruction – obviating the need for a machine language opcode.[1][2][3] With a judicious choice for the single instruction and given arbitrarily many resources, an OISC is capable of being a universal computer in the same manner as traditional computers that have multiple instructions.[2]: 55 OISCs have been recommended as aids in teaching computer architecture[1]: 327 [2]: 2 and have been used as computational models in structural computing research.[3] The first carbon nanotube computer is a 1-bit one-instruction set computer (and has only 178 transistors).[4]
## Machine architecture
In a Turing-complete model, each memory location can store an arbitrary integer, and – depending on the model[clarification needed] – there may be arbitrarily many locations. The instructions themselves reside in memory as a sequence of such integers.
There exists a class of universal computers with a single instruction based on bit manipulation such as bit copying or bit inversion. Since their memory model is finite, as is the memory structure used in real computers, those bit manipulation machines are equivalent to real computers rather than to Turing machines.[5]
Currently known OISCs can be roughly separated into three broad categories:
• Bit-manipulating machines
• Transport triggered architecture machines
• Arithmetic-based Turing-complete machines
### Bit-manipulating machines
Bit-manipulating machines are the simplest class.
#### FlipJump
The FlipJump machine has 1 instruction, a;b - flips the bit a, then jumps to b. This is the most primitive OISC, but it's still useful. It can successfully do Math/Logic calculations, branching, pointers, and calling functions with the help of its standard library.
#### BitBitJump
A bit copying machine,[5] called BitBitJump, copies one bit in memory and passes the execution unconditionally to the address specified by one of the operands of the instruction. This process turns out to be capable of universal computation (i.e. being able to execute any algorithm and to interpret any other universal machine) because copying bits can conditionally modify the copying address that will be subsequently executed.
#### Toga computer
Another machine, called the Toga Computer, inverts a bit and passes the execution conditionally depending on the result of inversion. The unique instruction is TOGA(a,b) which stands for TOGgle a And branch to b if the result of the toggle operation is true.
#### Multi-bit copying machine
Similar to BitBitJump, a multi-bit copying machine copies several bits at the same time. The problem of computational universality is solved in this case by keeping predefined jump tables in the memory.[clarification needed]
### Transport triggered architecture
Transport triggered architecture (TTA) is a design in which computation is a side effect of data transport. Usually, some memory registers (triggering ports) within common address space perform an assigned operation when the instruction references them. For example, in an OISC using a single memory-to-memory copy instruction, this is done by triggering ports that perform arithmetic and instruction pointer jumps when written to.
### Arithmetic-based Turing-complete machines
Arithmetic-based Turing-complete machines use an arithmetic operation and a conditional jump. Like the two previous universal computers, this class is also Turing-complete. The instruction operates on integers which may also be addresses in memory.
Currently there are several known OISCs of this class, based on different arithmetic operations:
• decrement (DJN, Decrement and branch (Jump) if Nonzero)[7]
• increment (P1eq, Plus 1 and branch if equal to another value)[8]
• subtraction (subleq, subtract and branch if less than or equal to zero)[9][10]
• positive subtraction when possible, else branch (Arithmetic machine)[11]
## Instruction types
Common choices for the single instruction are:
Only one of these instructions is used in a given implementation. Hence, there is no need for an opcode to identify which instruction to execute; the choice of instruction is inherent in the design of the machine, and an OISC is typically named after the instruction it uses (e.g., an SBN OISC,[2]: 41 the SUBLEQ language,[3]: 4 etc.). Each of the above instructions can be used to construct a Turing-complete OISC.
This article presents only subtraction-based instructions among those that are not transport triggered. However, it is possible to construct Turing complete machines using an instruction based on other arithmetic operations, e.g., addition. For example, one variation known as DLN (Decrement and jump if not zero) has only two operands and uses decrement as the base operation. For more information see Subleq derivative languages [1].
### Subtract and branch if not equal to zero
The SBNZ a, b, c, d instruction ("subtract and branch if not equal to zero") subtracts the contents at address a from the contents at address b, stores the result at address c, and then, if the result is not 0, transfers control to address d (if the result is equal to zero, execution proceeds to the next instruction in sequence).[3]
### Subtract and branch if less than or equal to zero
The subleq instruction ("subtract and branch if less than or equal to zero") subtracts the contents at address a from the contents at address b, stores the result at address b, and then, if the result is not positive, transfers control to address c (if the result is positive, execution proceeds to the next instruction in sequence).[3]: 4–7 Pseudocode:
Instruction subleq a, b, c
Mem[b] = Mem[b] - Mem[a]
if (Mem[b] ≤ 0)
goto c
Conditional branching can be suppressed by setting the third operand equal to the address of the next instruction in sequence. If the third operand is not written, this suppression is implied.
A variant is also possible with two operands and an internal accumulator, where the accumulator is subtracted from the memory location specified by the first operand. The result is stored in both the accumulator and the memory location, and the second operand specifies the branch address:
Instruction subleq2 a, b
Mem[a] = Mem[a] - ACCUM
ACCUM = Mem[a]
if (Mem[a] ≤ 0)
goto b
Although this uses only two (instead of three) operands per instruction, correspondingly more instructions are then needed to effect various logical operations.
#### Synthesized instructions
It is possible to synthesize many types of higher-order instructions using only the subleq instruction.[3]: 9–10
Unconditional branch:
JMP c
subleq Z, Z, c
Addition can be performed by repeated subtraction, with no conditional branching; e.g., the following instructions result in the content at location a being added to the content at location b:
subleq a, Z
subleq Z, b
subleq Z, Z
The first instruction subtracts the content at location a from the content at location Z (which is 0) and stores the result (which is the negative of the content at a) in location Z. The second instruction subtracts this result from b, storing in b this difference (which is now the sum of the contents originally at a and b); the third instruction restores the value 0 to Z.
A copy instruction can be implemented similarly; e.g., the following instructions result in the content at location b getting replaced by the content at location a, again assuming the content at location Z is maintained as 0:
MOV a, b
subleq b, b
subleq a, Z
subleq Z, b
subleq Z, Z
Any desired arithmetic test can be built. For example, a branch-if-zero condition can be assembled from the following instructions:
BEQ b, c
subleq b, Z, L1
subleq Z, Z, OUT
L1:
subleq Z, Z
subleq Z, b, c
OUT:
...
Subleq2 can also be used to synthesize higher-order instructions, although it generally requires more operations for a given task. For example, no fewer than 10 subleq2 instructions are required to flip all the bits in a given byte:
NOT a
subleq2 tmp ; tmp = 0 (tmp = temporary register)
subleq2 tmp
subleq2 one ; acc = -1
subleq2 a ; a' = a + 1
subleq2 Z ; Z = - a - 1
subleq2 tmp ; tmp = a + 1
subleq2 a ; a' = 0
subleq2 tmp ; load tmp into acc
subleq2 a ; a' = - a - 1 ( = ~a )
subleq2 Z ; set Z back to 0
#### Emulation
The following program (written in pseudocode) emulates the execution of a subleq-based OISC:
int memory[], program_counter, a, b, c
program_counter = 0
while (program_counter >= 0):
a = memory[program_counter]
b = memory[program_counter+1]
c = memory[program_counter+2]
if (a < 0 or b < 0):
program_counter = -1
else:
memory[b] = memory[b] - memory[a]
if (memory[b] > 0):
program_counter += 3
else:
program_counter = c
This program assumes that memory[] is indexed by nonnegative integers. Consequently, for a subleq instruction (a, b, c), the program interprets a < 0, b < 0, or an executed branch to c < 0 as a halting condition. Similar interpreters written in a subleq-based language (i.e., self-interpreters, which may use self-modifying code as allowed by the nature of the subleq instruction) can be found in the external links below.
A general purpose SMP-capable 64-bit operating system called Dawn OS has been implemented in an emulated Subleq machine. The OS contains a C-like compiler. Some memory areas in the virtual machine are used for peripherals like the keyboard, mouse, hard drives, network card, etc. Basic applications written for it include a media player, painting tool, document reader and scientific calculator.[13]
A 32-bit Subleq computer with a graphic display and a keyboard called Izhora has been constructed by Yoel Matveyev as a large cellular automation pattern.[14][15]
#### Compilation
There is a compiler called Higher Subleq written by Oleg Mazonka that compiles a simplified C program into subleq code.[16]
Alternatively there is a self hosting Forth implementation written by Richard James Howe that runs on top of a Subleq VM and is capable of interactive programming of the Subleq machine [17]
### Subtract and branch if negative
The subneg instruction ("subtract and branch if negative"), also called SBN, is defined similarly to subleq:[2]: 41, 51–52
Instruction subneg a, b, c
Mem[b] = Mem[b] - Mem[a]
if (Mem[b] < 0)
goto c
Conditional branching can be suppressed by setting the third operand equal to the address of the next instruction in sequence. If the third operand is not written, this suppression is implied.
#### Synthesized instructions
It is possible to synthesize many types of higher-order instructions using only the subneg instruction. For simplicity, only one synthesized instruction is shown here to illustrate the difference between subleq and subneg.
Unconditional branch:[2]: 88–89
JMP c
subneg POS, Z, c
where Z and POS are locations previously set to contain 0 and a positive integer, respectively;
Unconditional branching is assured only if Z initially contains 0 (or a value less than the integer stored in POS). A follow-up instruction is required to clear Z after the branching, assuming that the content of Z must be maintained as 0.
#### subneg4
A variant is also possible with four operands – subneg4. The reversal of minuend and subtrahend eases implementation in hardware. The non-destructive result simplifies the synthetic instructions.
Instruction subneg s, m, r, j
(* subtrahend, minuend, result and jump addresses *)
Mem[r] = Mem[m] - Mem[s]
if (Mem[r] < 0)
goto j
### Arithmetic machine
In an attempt to make Turing machine more intuitive, Z. A. Melzak consider the task of computing with positive numbers. The machine has an infinite abacus, an infinite number of counters (pebbles, tally sticks) initially at a special location S. The machine is able to do one operation:
Take from location X as many counters as there are in location Y and transfer them to location Z and proceed to instruction y.
If this operation is not possible because there is not enough counters in X, then leave the abacus as it is and proceed to instruction n. [18]
In order to keep all numbers positive and mimic a human operator computing on a real world abacus, the test is performed before any subtraction. Pseudocode:
Instruction melzak X, Y, Z, n, y
if (Mem[X] < Mem[Y])
goto n
Mem[X] -= Mem[Y]
Mem[Z] += Mem[Y]
goto y
After giving a few programs: multiplication, gcd, computing the n-th prime number, representation in base b of an arbitrary number, sorting in order of magnitude, Melzak shows explicitly how to simulate an arbitrary Turing machine on his arithmetic machine.
MUL p, q
multiply:
melzak P, ONE, S, stop ; Move 1 counter from P to S. If not possible, move to stop.
melzak S, Q, ANS, multiply, multiply ; Move q counters from S to ANS. Move to the first instruction.
stop:
where the memory location P is p, Q is q, ONE is 1, ANS is initially 0 and at the end pq, and S is a large number.
He mentions that it can easily be shown using the elements of recursive functions that every number calculable on the arithmetic machine is computable. A proof of which was given by Lambek[19] on an equivalent two instruction machine : X+ (increment X) and X− else T (decrement X if it not empty, else jump to T).
### Reverse subtract and skip if borrow
In a reverse subtract and skip if borrow (RSSB) instruction, the accumulator is subtracted from the memory location and the next instruction is skipped if there was a borrow (memory location was smaller than the accumulator). The result is stored in both the accumulator and the memory location. The program counter is mapped to memory location 0. The accumulator is mapped to memory location 1.[2]
Instruction rssb x
ACCUM = Mem[x] - ACCUM
Mem[x] = ACCUM
if (ACCUM < 0)
goto PC + 2
#### Example
To set x to the value of y minus z:
# First, move z to the destination location x.
RSSB temp # Three instructions required to clear acc, temp [See Note 1]
RSSB x # Two instructions clear acc, x, since acc is already clear
RSSB temp # Store -y into acc, temp: always borrow and skip
RSSB x # Store y into x, acc
# Second, perform the operation.
RSSB temp # Three instructions required to clear acc, temp
RSSB x # x = y - z [See Note 2]
• [Note 1] If the value stored at "temp" is initially a negative value and the instruction that executed right before the first "RSSB temp" in this routine borrowed, then four "RSSB temp" instructions will be required for the routine to work.
• [Note 2] If the value stored at "z" is initially a negative value then the final "RSSB x" will be skipped and thus the routine will not work.
### Transport triggered architecture
A transport triggered architecture uses only the move instruction, hence it was originally called a "move machine". This instruction moves the contents of one memory location to another memory location combining with the current content of the new location:[2]: 42 [20]
Instruction movx a, b (also written a -> b)
OP = GetOperation(Mem[b])
Mem[b] := OP(Mem[a], Mem[b])
The operation performed is defined by the destination memory cell. Some cells are specialized in addition, some other in multiplication, etc. So memory cells are not simple store but coupled with an arithmetic logic unit (ALU) setup to perform only one sort of operation with the current value of the cell. Some of the cells are control flow instructions to alter the program execution with jumps, conditional execution, subroutines, if-then-else, for-loop, etc...
A commercial transport triggered architecture microcontroller has been produced called MAXQ, which hides the apparent inconvenience of an OISC by using a "transfer map" that represents all possible destinations for the move instructions.[21]
### Cryptoleq
Cryptoleq[22] is a language consisting of one eponymous instruction, is capable of performing general-purpose computation on encrypted programs and is a close relative to Subleq. Cryptoleq works on continuous cells of memory using direct and indirect addressing, and performs two operations O1 and O2 on three values A, B, and C:
Instruction cryptoleq a, b, c
Mem[b] = O1(Mem[a], Mem[b])
if O2(Mem[b]) ≤ 0
IP = c
else
IP = IP + 3
where a, b and c are addressed by the instruction pointer, IP, with the value of IP addressing a, IP + 1 point to b and IP + 2 to c.
In Cryptoleq operations O1 and O2 are defined as follows:
${\displaystyle {\begin{array}{lcl}O_{1}(x,y)&=&x^{-1}y\,{\bmod {\,}}N^{2}\end{array}}}$
${\displaystyle {\begin{array}{lcl}O_{2}(x)&=&\left\lfloor {\frac {x-1}{N}}\right\rfloor \end{array}}}$
The main difference with Subleq is that in Subleq, O1(x,y) simply subtracts y from x and O2(x) equals to x. Cryptoleq is also homomorphic to Subleq, modular inversion and multiplication is homomorphic to subtraction and the operation of O2 corresponds the Subleq test if the values were unencrypted. A program written in Subleq can run on a Cryptoleq machine, meaning backwards compatibility. However, Cryptoleq implements fully homomorphic calculations and is capable of multiplications. Multiplication on an encrypted domain is assisted by a unique function G that is assumed to be difficult to reverse engineer and allows re-encryption of a value based on the O2 operation:
${\displaystyle G(x,y)={\begin{cases}{\tilde {0}},&{\text{if }}O_{2}({\bar {x}}){\text{ }}\leq 0\\{\tilde {y}},&{\text{otherwise}}\end{cases}}}$
where ${\displaystyle {\tilde {y}}}$ is the re-encrypted value of y and ${\displaystyle {\tilde {0}}}$ is encrypted zero. x is the encrypted value of a variable, let it be m, and ${\displaystyle {\bar {x}}}$ equals ${\displaystyle Nm+1}$.
The multiplication algorithm is based on addition and subtraction, uses the function G and does not have conditional jumps nor branches. Cryptoleq encryption is based on Paillier cryptosystem.
## References
1. ^ a b Mavaddat, F.; Parhami, B. (October 1988). "URISC: The Ultimate Reduced Instruction Set Computer" (PDF). International Journal of Electrical Engineering Education. 25 (4). Manchester University Press: 327–334. doi:10.1177/002072098802500408. S2CID 61797084. Retrieved 2010-10-04. This paper considers "a machine with a single 3-address instruction as the ultimate in RISC design (URISC)". Without giving a name to the instruction, it describes a SBN OISC and its associated assembly language, emphasising that this is a universal (i.e., Turing-complete) machine whose simplicity makes it ideal for classroom use.
2. Gilreath, William F.; Laplante, Phillip A. (2003). Computer Architecture: A Minimalist Perspective. Springer Science+Business Media. ISBN 978-1-4020-7416-5. Archived from the original on 2009-06-13. Intended for researchers, computer system engineers, computational theorists and students, this book provides an in-depth examination of various OISCs, including SBN and MOVE. It attributes SBN to W. L. van der Poel (1956).
3. Nürnberg, Peter J.; Wiil, Uffe K.; Hicks, David L. (September 2003), "A Grand Unified Theory for Structural Computing", Metainformatics: International Symposium, MIS 2003, Graz, Austria: Springer Science+Business Media, pp. 1–16, ISBN 978-3-540-22010-7, archived from the original on 2015-01-03, retrieved 2009-09-07 This research paper focusses entirely on a SUBLEQ OISC and its associated assembly language, using the name SUBLEQ for "both the instruction and any language based upon it".
4. ^ "First computer made of carbon nanotubes is unveiled". BBC. 26 September 2013. Retrieved 26 September 2013.
5. ^ a b Oleg Mazonka, "Bit Copying: The Ultimate Computational Simplicity", Complex Systems Journal 2011, Vol 19, N3, pp. 263–285
6. ^ "Addleq". Esolang Wiki. Retrieved 2017-09-16.
7. ^ "DJN OISC". Esolang Wiki. Retrieved 2017-09-16.
8. ^ "P1eq". Esolang Wiki. Retrieved 2017-09-16.
9. ^ Mazonka, Oleg (October 2009). "SUBLEQ". Archived from the original on 2017-06-29. Retrieved 2017-09-16.
10. ^ "Subleq". Esolang Wiki. Retrieved 2017-09-16.
11. ^ Z. A. Melzak (1961). "An informal arithmetical approach to computability and computation". Canadian Mathematical Bulletin. 4 (3): 279–293. doi:10.4153/CMB-1961-031-9.
12. ^ xoreaxeaxeax. "movfuscator". GitHub. Retrieved 2022-11-12.
13. ^
14. ^ https://www.gazetaeao.ru/zanimatelnaya-nauka-vchera-segodnya-zavtra/ A Russian article on popular science in Birobidzhaner Shtern with a brief discussion of Yoel Matveyev's Izhora computer
15. ^ https://habr.com/ru/post/584596/ A description of the virtual computer Izhora on Habr (in Russian)
16. ^
17. ^ Richard James Howe SUBLEQ eForth
18. ^ Z. A. Melzak (2018-11-20) [September 1961]. "An informal arithmetical approach to computability and computation". Canadian Mathematical Bulletin. 4 (3): 279–293. doi:10.4153/CMB-1961-032-6.
19. ^ J. Lambek (2018-11-20) [September 1961]. "How to program an infinite abacus". Canadian Mathematical Bulletin. 4 (3): 295–302. doi:10.4153/CMB-1961-032-6.
20. ^ Jones, Douglas W. (June 1988). "The Ultimate RISC". ACM SIGARCH Computer Architecture News. 16 (3). New York: ACM: 48–55. doi:10.1145/48675.48683. S2CID 9481528. Retrieved 2010-10-04. "Reduced instruction set computer architectures have attracted considerable interest since 1980. The ultimate RISC architecture presented here is an extreme yet simple illustration of such an architecture. It has only one instruction, move memory to memory, yet it is useful."
21. ^ Catsoulis, John (2005), Designing embedded hardware (2 ed.), O'Reilly Media, pp. 327–333, ISBN 978-0-596-00755-3
22. ^ Mazonka, Oleg; Tsoutsos, Nektarios Georgios; Maniatakos, Michail (2016), "Cryptoleq: A Heterogeneous Abstract Machine for Encrypted and Unencrypted Computation", IEEE Transactions on Information Forensics and Security, 11 (9): 2123–2138, doi:10.1109/TIFS.2016.2569062, S2CID 261387
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# A perfect square is a positive integer which when square roo
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A perfect square is a positive integer which when square roo [#permalink] 16 Apr 2019, 00:41
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A perfect square is a positive integer which when square rooted results in an integer. If $$N = 3^4 * 5^3 * 7$$, then what is the biggest perfect square that is a factor of $$N$$?
(A) $$3^2$$
(B) $$5^2$$
(C) $$9^2$$
(D) $$(9 * 5)^2$$
(E) $$(3 * 5 * 7)^2$$
[Reveal] Spoiler: OA
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Re: A perfect square is a positive integer which when square roo [#permalink] 21 Apr 2019, 05:19
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KUDOS
First notice that all the options are a perfect square. However we need the biggest among them. It can be seen easily that A<B<C<D therefore we can eliminate A, B and C. Now among D and E, D is bigger so it is the answer. Since both are square of some numbers in the bracket we can only compare the expression inside the bracket
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Re: A perfect square is a positive integer which when square roo [#permalink] 06 Aug 2019, 18:41
Carcass wrote:
A perfect square is a positive integer which when square rooted results in an integer. If $$N = 3^4 * 5^3 * 7$$, then what is the biggest perfect square that is a factor of $$N$$?
(A) $$3^2$$
(B) $$5^2$$
(C) $$9^2$$
(D) $$(9 * 5)^2$$
(E) $$(3 * 5 * 7)^2$$
need explanation
Last edited by huda on 07 Aug 2019, 01:47, edited 6 times in total.
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Re: A perfect square is a positive integer which when square roo [#permalink] 14 Aug 2019, 02:27
Expert's post
Precisely, what did you not get sir in the explanation above ??
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Re: A perfect square is a positive integer which when square roo [#permalink] 15 Aug 2019, 11:28
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Carcass wrote:
Precisely, what did you not get sir in the explanation above ??
Regards
later I got it but forgot to mention. Thanks for the concern.
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Re: A perfect square is a positive integer which when square roo [#permalink] 16 Aug 2019, 03:00
1
KUDOS
Convert the options to prime factors
(A) $$3^2$$
(B) $$5^2$$
(C) $$3^4$$
(D) $$3^4 * 5^2$$
(E) $$(3 * 5 * 7)^2$$
D is clearly the biggest factor of N
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Re: A perfect square is a positive integer which when square roo [#permalink] 19 Aug 2019, 08:39
I keep wondering isnt 3*5*7 sq bigger?
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Re: A perfect square is a positive integer which when square roo [#permalink] 19 Aug 2019, 10:56
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No
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Re: A perfect square is a positive integer which when square roo [#permalink] 19 Aug 2019, 10:56
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# Find Missing Angle Triangle Worksheet
Find Missing Angle Triangle Worksheet. Finding the exterior angle applying the exterior angle theorem,. Web subtract the sum of the two angles from 180° to find the measure of the indicated interior angle in each triangle.
A pentagon has five vertices while a triangle has three. Web missing angles in the triangles worksheet provide a way to do that, wherein certain angles of a triangle are provided and the remaining are to be calculated. Angles add to my workbooks (133) download file pdf.
### Web These Math Worksheets Should Be Practiced Regularly And Are Free To Download In Pdf Formats.
Subtracting 70 on both sides. Web an angle can have one or more vertices, and the number of vertices will vary. Web missing angles in the triangles worksheet provide a way to do that, wherein certain angles of a triangle are provided and the remaining are to be calculated.
### Web Subtract The Sum Of The Two Angles From 180° To Find The Measure Of The Indicated Interior Angle In Each Triangle.
Web worksheets are 4 angles in a triangle, right triangle trig missing sides and angles, triangle, triangles angle measures length of sides and classifying, exterior angles of a. Since it is isosceles triangle, the angle formed by equal sides will be equal. A pentagon has five vertices while a triangle has three.
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# Resources tagged with: Mathematical reasoning & proof
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### There are 91 results
Broad Topics > Thinking Mathematically > Mathematical reasoning & proof
### What Numbers Can We Make Now?
##### Age 11 to 14 Challenge Level:
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
### Gabriel's Problem
##### Age 11 to 14 Challenge Level:
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
### Even So
##### Age 11 to 14 Challenge Level:
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
### What Numbers Can We Make?
##### Age 11 to 14 Challenge Level:
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
##### Age 11 to 14 Challenge Level:
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
##### Age 11 to 14 Challenge Level:
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .
### Aba
##### Age 11 to 14 Challenge Level:
In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.
### The Genie in the Jar
##### Age 11 to 14 Challenge Level:
This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal. . . .
### Elevenses
##### Age 11 to 14 Challenge Level:
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
### What Do You Need?
##### Age 7 to 11 Challenge Level:
Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
### Largest Product
##### Age 11 to 14 Challenge Level:
Which set of numbers that add to 10 have the largest product?
### One O Five
##### Age 11 to 14 Challenge Level:
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
### Tis Unique
##### Age 11 to 14 Challenge Level:
This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.
### Eleven
##### Age 11 to 14 Challenge Level:
Replace each letter with a digit to make this addition correct.
### Top-heavy Pyramids
##### Age 11 to 14 Challenge Level:
Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
### More Mathematical Mysteries
##### Age 11 to 14 Challenge Level:
Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .
### Cows and Sheep
##### Age 7 to 11 Challenge Level:
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
### Making Pathways
##### Age 7 to 11 Challenge Level:
Can you find different ways of creating paths using these paving slabs?
##### Age 5 to 11 Challenge Level:
Who said that adding couldn't be fun?
### Square Subtraction
##### Age 7 to 11 Challenge Level:
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
### Three Neighbours
##### Age 7 to 11 Challenge Level:
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
### Less Is More
##### Age 5 to 11 Challenge Level:
Use your knowledge of place value to try to win this game. How will you maximise your score?
### Is it Magic or Is it Maths?
##### Age 11 to 14 Challenge Level:
Here are three 'tricks' to amaze your friends. But the really clever trick is explaining to them why these 'tricks' are maths not magic. Like all good magicians, you should practice by trying. . . .
##### Age 7 to 14 Challenge Level:
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
##### Age 11 to 14 Challenge Level:
A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . .
### Always the Same
##### Age 11 to 14 Challenge Level:
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?
### Chocolate Maths
##### Age 11 to 14 Challenge Level:
Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .
##### Age 7 to 11 Challenge Level:
Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .
### Tourism
##### Age 11 to 14 Challenge Level:
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
### 1 Step 2 Step
##### Age 11 to 14 Challenge Level:
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
### More Number Pyramids
##### Age 11 to 14 Challenge Level:
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
### Seven Squares - Group-worthy Task
##### Age 11 to 14 Challenge Level:
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
### Unit Fractions
##### Age 11 to 14 Challenge Level:
Consider the equation 1/a + 1/b + 1/c = 1 where a, b and c are natural numbers and 0 < a < b < c. Prove that there is only one set of values which satisfy this equation.
### 9 Weights
##### Age 11 to 14 Challenge Level:
You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?
### Children at Large
##### Age 11 to 14 Challenge Level:
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
### The Triangle Game
##### Age 11 to 16 Challenge Level:
Can you discover whether this is a fair game?
### Sticky Numbers
##### Age 11 to 14 Challenge Level:
Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?
### Greetings
##### Age 11 to 14 Challenge Level:
From a group of any 4 students in a class of 30, each has exchanged Christmas cards with the other three. Show that some students have exchanged cards with all the other students in the class. How. . . .
### Take Three Numbers
##### Age 7 to 11 Challenge Level:
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
### Go Forth and Generalise
##### Age 11 to 14
Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.
### Tri-colour
##### Age 11 to 14 Challenge Level:
Six points are arranged in space so that no three are collinear. How many line segments can be formed by joining the points in pairs?
### Not Necessarily in That Order
##### Age 11 to 14 Challenge Level:
Baker, Cooper, Jones and Smith are four people whose occupations are teacher, welder, mechanic and programmer, but not necessarily in that order. What is each person’s occupation?
### Marbles
##### Age 11 to 14 Challenge Level:
I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?
### Reasoning: the Journey from Novice to Expert (article)
##### Age 5 to 11
This article for primary teachers suggests ways in which we can help learners move from being novice reasoners to expert reasoners.
### Disappearing Square
##### Age 11 to 14 Challenge Level:
Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .
### Tower of Hanoi
##### Age 11 to 14 Challenge Level:
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
### Always, Sometimes or Never?
##### Age 5 to 11 Challenge Level:
Are these statements relating to odd and even numbers always true, sometimes true or never true?
### Reasoning: Identifying Opportunities (article)
##### Age 5 to 11
In this article for primary teachers we consider in depth when we might reason which helps us understand what reasoning 'looks like'.
### Calendar Capers
##### Age 11 to 14 Challenge Level:
Choose any three by three square of dates on a calendar page...
### Dicing with Numbers
##### Age 11 to 14 Challenge Level:
In how many ways can you arrange three dice side by side on a surface so that the sum of the numbers on each of the four faces (top, bottom, front and back) is equal?
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# mid06 - ISMT111 Business Statistics Midterm Examination For...
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ISMT111 Business Statistics Midterm Examination For sections 3 & 4 only 23 rd October 2006 Directions 1) Answer ALL FIVE questions. Marks are shown in square brackets. 2) There are 4 pages in this examination paper, which includes a normal table. Check to make sure you have a complete set and notify the invigilator immediately if part of it is missing. 3) Key formulas are provided separately. 4) Calculator may be used in this examination. 5) You are given TWO HOURS to complete this examination. Do not begin until you are told to do so.
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Question 1: [15 Marks] Q u e s t i o n 2 : [ 1 8 M a r k s ] (a) Why probability can explain the variation in data sets? The following table gives the first week and annual performance of the stock market index S&P 500 from 1950 to 2003. In 34 of the 54 years from 1950 to 2003, the S&P 500 finished higher after the first 5 days of trading (first week). In 29 of those 34 years S&P 500 finished higher for the year. Answer the following questions to see if a good first week is a good forecast for the upcoming year.
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# What is x if 4^(4x-15)-4=0 ?
Asked on by l0l1
justaguide | College Teacher | (Level 2) Distinguished Educator
Posted on
We have to solve 4^(4x-15) - 4 = 0.
4^(4x-15) - 4 = 0
=> 4^(4x-15) = 4
=> 4^(4x-15) = 4^1
Now as the base is the same we can equate the power.
4x - 15 = 1
=> 4x = 15 +1
=> 4x = 16
=> x = 16/4
=> x = 4
Therefore x = 4.
giorgiana1976 | College Teacher | (Level 3) Valedictorian
Posted on
We'll re-write the equation, moving the coefficient -4 to the right side:
4^(4x-15) = 4
We can write as well:
4^(4x-15) = 4^1
Since the bases are matching, we'll apply the one to one rule:
4x-15 = 1
We'll add 15 both sides:
4x = 15 + 1
4x = 16
We'll divide by 4:
x = 4
The solution of the equation is x = 4.
neela | High School Teacher | (Level 3) Valedictorian
Posted on
What is x if 4^(4x-15)-4 = 0 ?
We add 4 to both sides and rewrite the given equation as below:
4^(4x-15) = 4
=> 4^(4x-15) = 4^1.
The bases on both sises are equal. So we equate the exponents on both sides:
4x-15 = 1
We add 15 to both sides:
4x = 1+15 = 16.
=> 4x /4= 16/4 = 4.
Therefore x = 4 is the solution.
We’ve answered 317,713 questions. We can answer yours, too.
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# Finite Coproduct in Preadditive Category is Biproduct
## Theorem
### Binary coproducts
Let $A$ be a preadditive category.
Let $a_1, a_2$ be objects of $A$.
Let $(a_1 \sqcup a_2, i_1, i_2)$ be their binary coproduct, assuming it exists.
Let $p_1 : a_1 \sqcup a_2 \to a_1$ be the unique morphism with:
$p_1 \circ i_1 = 1 : a_1 \to a_1$
$p_1 \circ i_2 = 0 : a_1 \to a_2$
Let $p_2 : a_1 \sqcup a_2 \to a_2$ be the unique morphism with:
$p_2 \circ i_1 = 0 : a_2 \to a_1$
$p_2 \circ i_2 = 1 : a_2 \to a_2$
where $1$ is the identity morphism and $0$ is the zero morphism.
Then $(a_1 \sqcup a_2, i_1, i_2, p_1, p_2)$ is the binary biproduct of $a_1$ and $a_2$.
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# Area And Perimeter Polynomials Worksheet
Area And Perimeter Polynomials Worksheet - Web finding perimeter and area using polynomials. Web displaying 8 worksheets for polynomial area and perimeter. Web in this section we will explore ways that polynomials are used in applications of perimeter, area, and volume. Discover a vast collection of free printable worksheets for class 9 students, designed to enhance their understanding of these essential concepts. Worksheets are polynomials word problems work, using area models to 9 understand polynomia. Web perimeter and area of polygons worksheets.
Using area models to 9 understand. Discover a vast collection of free printable worksheets for class 9 students, designed to enhance their understanding of these essential concepts. Web add, subtract, name polynomials notes. Worksheets are polynomials word problems work, using area models to 9 understand polynomia. Unit 3 chapter 6 polynomials and polynomial functions.
Discover a vast collection of free printable worksheets for class 9 students, designed to enhance their understanding of these essential concepts. Worksheets are area and perimeter polynomials work, d4a ws finding perimeter and area. Difference & sum of squares. In the picture shown below, set up an equation and hence find the value of x and find the area. First, we will see how a polynomial can be.
## Simplifying Perimeter with Polynomials Grade 9 Academic Lesson 3 7 11 2
Area And Perimeter Polynomials Worksheet - Web displaying 8 worksheets for polynomial area and perimeter. Web perimeter and area of polygons worksheets. Answer key perimeter, area, and volume directions: Web in this section we will explore ways that polynomials are used in applications of perimeter, area, and volume. Difference & sum of squares. Web finding perimeter and area using polynomials. Web finding area and perimeter using polynomials practice worksheet. Worksheets are d4a ws finding perimeter and area using polynomials, polynomials. Worksheets are polynomials word problems work, d4a ws finding perimeter and area using poly. Web math area and perimeter:
Using area models to 9 understand polynomials lesson plan t. Students will first practice adding / subtracting / multiplying. Web determine which expressions are polynomials: Web math area and perimeter: Discover a vast collection of free printable worksheets for class 9 students, designed to enhance their understanding of these essential concepts.
Using area models to 9 understand polynomials lesson plan t. Unit 3 chapter 6 polynomials and polynomial functions. Web polynomial word problems with perimeter and area. Multiply polynomials day 1 worksheet.
Find the perimeter of each of the following shapes. Answer key perimeter, area, and volume directions: Using area models to 9 understand polynomials lesson plan t.
Multiply polynomials day 1 worksheet. Find the perimeter of a triangle, perimeter of a rectangle, area of a triangle, area of a trapezoid and more. First, we will see how a polynomial can be.
## Multiply Polynomials Day 1 Worksheet.
Web polynomial word problems with perimeter and area. Web displaying 8 worksheets for area and perimeter with polynomials. Answer key perimeter, area, and volume directions: First, we will see how a polynomial can be used to describe the.
## Web Displaying 8 Worksheets For Polynomial Area And Perimeter.
Displaying 8 worksheets for perimeter and area of polynomials. Web polynomial word problems involving area and perimeter worksheet. Web determine which expressions are polynomials: Worksheets are d4a ws finding perimeter and area using polynomials, area and.
## Set Up An Equation And Hence Find The Value Of X And Find The Area.
Unit 3 chapter 6 polynomials and polynomial functions. Web finding area and perimeter using polynomials practice worksheet. Web add, subtract, name polynomials notes. Worksheets are d4a ws finding perimeter and area using polynomials, polynomials.
## Web Math Area And Perimeter:
First, we will see how a polynomial can be. Web in this section we will explore ways that polynomials are used in applications of perimeter, area, and volume. In the picture shown below, set up an equation and hence find the value of x and find the area. Worksheets are polynomials word problems work, d4a ws finding perimeter and area using poly.
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Resources tagged with: Factors and multiples
Filter by: Content type:
Age range:
Challenge level:
There are 113 results
Broad Topics > Properties of Numbers > Factors and multiples
Light the Lights
Age 5 to 7 Challenge Level:
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Constant Counting
Age 5 to 7 Challenge Level:
You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?
Lots of Biscuits!
Age 5 to 7 Challenge Level:
Help share out the biscuits the children have made.
Multiplication Series: Number Arrays
Age 5 to 11
This article for teachers describes how number arrays can be a useful representation for many number concepts.
I Like ...
Age 5 to 7 Challenge Level:
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
Six in a Circle
Age 5 to 7 Challenge Level:
If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?
What's Left?
Age 5 to 7 Challenge Level:
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
Grouping Goodies
Age 5 to 7 Challenge Level:
Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?
Sorting Numbers
Age 5 to 7 Challenge Level:
Can you sort numbers into sets? Can you give each set a name?
Doubling Fives
Age 5 to 7 Challenge Level:
This activity focuses on doubling multiples of five.
Skip Counting
Age 5 to 7 Challenge Level:
Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.
One of Thirty-six
Age 5 to 7 Challenge Level:
Can you find the chosen number from the grid using the clues?
Biscuit Decorations
Age 5 to 7 Challenge Level:
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
The Set of Numbers
Age 5 to 7 Challenge Level:
Can you place the numbers from 1 to 10 in the grid?
The Moons of Vuvv
Age 7 to 11 Challenge Level:
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Mystery Matrix
Age 7 to 11 Challenge Level:
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Which Is Quicker?
Age 7 to 11 Challenge Level:
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
A Mixed-up Clock
Age 7 to 11 Challenge Level:
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Seven Flipped
Age 7 to 11 Challenge Level:
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Share Bears
Age 5 to 7 Challenge Level:
Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?
Making Sticks
Age 5 to 7 Challenge Level:
Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?
Growing Garlic
Age 5 to 7 Challenge Level:
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
Tables Teaser
Age 5 to 7 Challenge Level:
How will you work out which numbers have been used to create this multiplication square?
Factor-multiple Chains
Age 7 to 11 Challenge Level:
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Number Tracks
Age 7 to 11 Challenge Level:
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
What Do You Need?
Age 7 to 11 Challenge Level:
Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
What's in the Box?
Age 7 to 11 Challenge Level:
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
Zios and Zepts
Age 7 to 11 Challenge Level:
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Venn Diagrams
Age 5 to 11 Challenge Level:
How will you complete these Venn diagrams?
Number Detective
Age 5 to 11 Challenge Level:
Follow the clues to find the mystery number.
Making Pathways
Age 7 to 11 Challenge Level:
Can you find different ways of creating paths using these paving slabs?
Give Me Four Clues
Age 7 to 11 Challenge Level:
Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?
Nineteen Hexagons
Age 5 to 7 Challenge Level:
In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
Sets of Four Numbers
Age 7 to 11 Challenge Level:
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
Lots of Lollies
Age 5 to 7 Challenge Level:
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Multiplication Squares
Age 7 to 11 Challenge Level:
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
Making Shapes
Age 5 to 7 Challenge Level:
Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?
Becky's Number Plumber
Age 7 to 11 Challenge Level:
Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?
Money Measure
Age 7 to 11 Challenge Level:
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
Which Numbers? (1)
Age 7 to 11 Challenge Level:
I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?
Domino Pick
Age 5 to 7 Challenge Level:
Are these domino games fair? Can you explain why or why not?
Same Length Trains
Age 5 to 7 Challenge Level:
How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?
Being Resilient - Primary Number
Age 5 to 11 Challenge Level:
Number problems at primary level that may require resilience.
Being Collaborative - Primary Number
Age 5 to 11 Challenge Level:
Number problems at primary level to work on with others.
Scoring with Dice
Age 7 to 11 Challenge Level:
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
Three Spinners
Age 7 to 11 Challenge Level:
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
Odds and Threes
Age 7 to 11 Challenge Level:
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
Down to Nothing
Age 7 to 11 Challenge Level:
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
Which Numbers? (2)
Age 7 to 11 Challenge Level:
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
Neighbours
Age 7 to 11 Challenge Level:
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
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# Friday 29th January
Good morning Class 2!
Good morning Class 2,
It's Friday! Happy Friday! I hope you all have a lovely day. I've had a lovely few days. It's been so nice to see some of you on our Guided Reading sessions. I hope you've been enjoying them.
This morning we have our live PE session again at 11:00 am so I hope you manage to join in with that. I wonder what we will have to find to help us today! This afternoon Mr Woolley will be doing Celebration Worship so I look forward to seeing you all there. Well done for working hard this week.
Love Mrs Pilgrim
PS I will put the link up for PE with Joe should you need any more PE to do! If not, something for the weekend maybe!
Here is the Guided Reading Timetable for the next two weeks. You will receive a Parent Mail this week telling you which colour group your child is in. You will then need to check the timetable below to see when your guided reading session is. From next week, we will be using Google Classroom rather than Teams. The Parent Mail will have a step-by-step guide attached to it which should explain everything you need to know.
Maths
This week we have been learning all about division; we have been learning how to share things equally into groups, using our 2, 5 and 10 times tables to help us. You have all done some wonderful work with this so very well done!
Today we are carrying on with learning about division but we are moving on to grouping. This means that if I have 10 children in a class and I want to put them in groups of 2, I need to work out how many groups of 2 I will have. Watch my video to see me do this.
## Maths input 29.1.21
Once you have watched my video I would like you to have a go at doing some grouping using things from around your house. I have enjoyed seeing what you have used to help you in Maths - I have seen all sorts of things from teddy bears to cutlery to dogs!
Use the division grouping document below.
• Choose a card to try.
• It will tell you how many things you need altogether and then it will ask you to put them in groups of 2, 5 or 10 (as these are the times tables we have been practising).
Year 2: as a challenge please could you draw a picture to go with what you make.
Please don't worry about doing all of the cards. Depending on how you get on you might like to try 4-6 cards. Year 1 I will ask you to carry on with this on Monday to build your confidence so don't worry if you find it a bit tricky at first.
PE 11:00 am - 11:30 am
It's our live PE lesson again today. The link should be in your Parent Mail from a few weeks ago. I hope you've been enjoying the sessions so far.
English
This morning you will be writing your spelling sentence. Click on the video below to watch Mrs Pilgrim reading out the spelling sentences. Good luck! Let me know how you get on and I will be ready to send you a golden coin!
## Spelling sentences
How did you get on with your reading comprehension last Friday? I would like you to try another one today. Decide which level is right for you: Red, Yellow, Green or Purple. They are all different to last week so you can do the same colour or move onto a different colour. If you did Pink last week, have a go at Red this week. If you did Turquoise last week, try Purple this week.
## Mighty Writing
Here is your Mighty Writing for this week. Click on the Word document to read about your task. There is also a Power Point and a picture prompt resource below.
Celebration Worship at 1:30 pm
It's so lovely to see you all each week during Celebration Worship. I'm looking forward to celebrating some more wonderful learning today.
## Phonics
Today you are allowed to play some games on Phonics Play. Click on the link to the website below. You will need to log in with the following details. Username: jan21 Password: home
You can choose which game you want to play and which phase.
### Year 1:
You all know phase 2 letter sounds and phase 3 digraphs. Phase 4 is adjacent consonants and consonant clusters. We are on Phase 5 at the moment and we have learnt lots of the sounds. Go for Phase 5 if you want more of a challenge!
### Year 2:
You should choose Phase 5 or challenge yourself with Phase 6.
Music
Today we are going to learn song number 3 from our musical. It is called The Beanstalk Grew.
I hope that you have been practising the first two songs lots and are having lots of fun learning the actions.
This song is a lot slower but is still very lovely. Enjoy!
## And The Beanstalk Grew song
Cooking with Miss Newton
Hello Everyone,
Today we are going to make rainbow spaghetti. You will need 200g of spaghetti and different food colouring. You will need a few bowls, a bowl for each colour you are planning to make.
Before we get started you will need to cook your pasta or spaghetti according to the instructions on the packet. Once you have cooked this you are ready to begin watching the video.
Please watch below to see how we are going to make our rainbow spaghetti. I hope you enjoy making it and I look forward to seeing your creations.
Love from
Miss Newton
## Rainbow Spaghetti
Story time with Mrs Pilgrim
Today Mrs Pilgrim is reading Giraffes Can't Dance as this is one of our favourites in Class 2!
## Story time with Mrs Pilgrim
Spelling Sentences
Here are your spelling sentences to learn for next Friday. Good luck!
Top
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# Lets Think Through Maths! Activity 10 Money-Go-Round.
## Presentation on theme: "Lets Think Through Maths! Activity 10 Money-Go-Round."— Presentation transcript:
Lets Think Through Maths! Activity 10 Money-Go-Round
Aims Pupils develop their understanding of the use of money. Pupils enhance their thinking ability within the reasoning strand of conservation. Pupils investigate ways of recording. N.B. on slide 9 amounts have been omitted for editing by teachers, dependant on ability of the class.
Episode 1: Class modelling of the Money-Go-Round, with visible collections. Has anyone been shopping recently? What did you take with you? What happens to your money when you buy something? What happens when the shopper runs out money? What does the shopkeeper do with his/her money at the end of the day?
Suppose you has 80p in your purse, and you buy something for 70p. How much do you have now? Where has your money gone?
If you want to buy something else you might need more money. Where do people get money when they run out? What do shopkeepers do with their money at the end of the day?
ShopperShopBank Start15p Shoppers throw Shops Throw Banks Throw 15p - 3p = 12p 15p + 3p =18p 15p 12p 18p – 5p = 13p 15p + 5p =20p 12p + 6p =18p 13p 20p – 6p = 14p Lets play Money-Go-Round together to learn how the game works.
How much money is there at the end? What do you notice? ShopperShopBank Start15p Shoppers throw Shops Throw Banks Throw 15p - 3p = 12p 15p + 3p =18p 15p 12p 18p – 5p = 13p 15p + 5p =20p 12p + 6p =18p 13p 20p – 6p = 14p How do the bank, the shop and the shopper know how much money they now have? How much money was there at the beginning?
What have we learnt so far? What is important to remember? Reflectio n Give Take Pass Sell Buy Coins Shop Till
Episode 2: The Money-Go-Round with hidden collections We are going to try out this game in groups. Two people are shoppers, two work in the shop and the other two work in the bank. You each have pots for your money. Each pair will have __p, with __p in total. Use the sheet to record how the money changes hands.
Game Rules! 1. First shoppers throw a dice. Give this amount of money to the shopkeeper. 2.Shopkeepers now put the money in your pot. EVERYONE: Write on the sheet how much money you have in your pot. 3.Now its shopkeepers turn to roll. Give the amount rolled to the bank. 4.Bankers put the money in your pot. EVERYONE: Write on the sheet how much money you have in your pot. 5. Finally its the bankers turn to roll. Give this amount to the shopper. 6.Shoppers put the money in your pot. EVERYONE: Write on the sheet how much money you have in your pot.
Check how much money you have in your pot. Does it match what you have on your sheet? Now the three pairs put your money together and count up the total amount. Is it the same amount that you started with?
Was it easy to keep track of the money? Which way seemed to help us best? Are there other ways? Reflectio n Add Subtract Coins Give/Take Pass Record
Episode 3: Independent group modelling with record keeping. Now each of your groups are going to play the game on your own! Follow the rules as we did before, with everyone recording after each roll.
Game Rules! 1. First shoppers throw a dice. Give this amount of money to the shopkeeper. 2.Shopkeepers now put the money in your pot. EVERYONE: Write on the sheet how much money you have in your pot. 3.Now its shopkeepers turn to roll. Give the amount rolled to the bank. 4.Bankers put the money in your pot. EVERYONE: Write on the sheet how much money you have in your pot. 5. Finally its the bankers turn to roll. Give this amount to the shopper. 6.Shoppers put the money in your pot. EVERYONE: Write on the sheet how much money you have in your pot.
At the end of your game which pair in your group has the most money? Is this the same for all the groups? Did you have any problems when playing the game? How useful was the record sheet in reminding you of what happened?
Who can explain what we have learnt? Do you have any questions to help understand? Reflectio n Add/Subtract Counted out Coins Give/Take Pass Record Collect
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Werke. Wahrscheinlichkeitsrechnung und Geometrie by Gauss C.F.
By Gauss C.F.
By Gauss C.F.
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Extra resources for Werke. Wahrscheinlichkeitsrechnung und Geometrie
Example text
N} p(zi) = 0 where a0, a1, a2, ... an are complex coefficients. For real coefficients, the zeros are whether real or pairs of conjugate complex numbers. The proof is by supposing that p(z) has not any zero. In this case f(z) = 1/p(z) is analytic and bounded (because p(z)→ 0 for z→ ∞) in the whole plane. From the Liouville’s theorem f(z) and p(z) should be constant becoming in contradiction with the fact that p(z) is a polynomial. In conclusion p(z) has at least one zero. According to the division algorithm, the division of the polynomial p(z) by z − b decreases the degree of the quotient q(z) by a unity, and yields a complex number r as remainder: p(z) = (z − b) q(z) + r The substitution of z by b gives: p(b) = r That is, the remainder of the division of a polynomial by z − b is equal to its numerical value for z = b .
If f(x) is bounded we have: f(x)< M The derivative of f(x) is always given by: f' (z ) = f (t ) 1 2 π e 12 ∫ (t − z ) 2 dt C Following the circular path t − z = r exp(e12ϕ ) we have: f' (z ) = 1 2π r 2π ∫ f (r exp(e ϕ )) exp(− e ϕ ) dϕ 12 Using the inequality f' (z ) ≤ 12 0 1 2π r ∫ f ( z ) dz ≤ ∫ 2π ∫ 0 f ( z ) dz , we find: f (r exp(e12ϕ )) dϕ ≤ 1 2π r 2π M ∫ M dϕ = 2π r 0 TREATISE OF PLANE GEOMETRY THROUGH GEOMETRIC ALGEBRA 25 Since the function is analytic in the entire plane, we may take the radius r as large as we wish.
Z + 2z − 8 ∞ 1 and its analytic function. 11Calculate the Lauren series of 2 and the annulus of convergence. 12 Prove that if f(z) is analytic and does not vanish then it is a conformal mapping. TREATISE OF PLANE GEOMETRY THROUGH GEOMETRIC ALGEBRA 27 4. TRANSFORMATIONS OF VECTORS The transformations of vectors are mappings from the vector plane to itself. Those transformations preserving the modulus of vectors, such as rotations and reflections, are called isometries and those which preserve angles between vectors are said to be conformal.
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HomeTemplate ➟ 0 Beautiful Decomposing Numbers Kindergarten Worksheets
# Beautiful Decomposing Numbers Kindergarten Worksheets
Decomposing numbers kindergarten worksheets are used to give a better understanding of how to use numbers to get a new number. Kindergarten math place value addition subtraction Created Date.
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## Saturation Time Solution
STEP 0: Pre-Calculation Summary
Formula Used
Saturation Time = -2*Load Capacitance/(Transconductance Process Parameter*(High Output Voltage-Threshold Voltage)^2)*int(1,x,High Output Voltage,High Output Voltage-Threshold Voltage)
This formula uses 1 Functions, 5 Variables
Functions Used
int - The definite integral can be used to calculate net signed area, which is the area above the x -axis minus the area below the x -axis., int(expr, arg, from, to)
Variables Used
Saturation Time - (Measured in Second) - Saturation Time is the time it takes for a MOSFET's output voltage to reach a specified level (Vout,fd) in the saturation region, after receiving an input signal.
Load Capacitance - (Measured in Farad) - Load Capacitance is the total capacitance connected to the transistor's output terminal, including external components and the MOSFET's own parasitic capacitance.
Transconductance Process Parameter - (Measured in Ampere per Square Volt) - Transconductance Process Parameter is a device-specific constant that characterizes the transistor's ability to convert a change in gate voltage to a change in output current.
High Output Voltage - (Measured in Volt) - High Output Voltage is the maximum voltage level the transistor can reach at its output terminal when fully turned on (operating in saturation).
Threshold Voltage - (Measured in Volt) - Threshold Voltage is the minimum gate-to-source voltage required in a MOSFET to turn it "on" and allow a significant current to flow.
STEP 1: Convert Input(s) to Base Unit
Transconductance Process Parameter: 4.553 Ampere per Square Volt --> 4.553 Ampere per Square Volt No Conversion Required
High Output Voltage: 3.789 Volt --> 3.789 Volt No Conversion Required
Threshold Voltage: 5.91 Volt --> 5.91 Volt No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Evaluating ... ...
Tsat = 5.63810361511811
STEP 3: Convert Result to Output's Unit
5.63810361511811 Second --> No Conversion Required
5.63810361511811 ā 5.638104 Second <-- Saturation Time
(Calculation completed in 00.021 seconds)
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## Credits
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## < 20 MOS Transistor Calculators
Sidewall Voltage Equivalence Factor
Sidewall Voltage Equivalence Factor = -(2*sqrt(Built in Potential of Sidewall Junctions)/(Final Voltage-Initial Voltage)*(sqrt(Built in Potential of Sidewall Junctions-Final Voltage)-sqrt(Built in Potential of Sidewall Junctions-Initial Voltage)))
Pull down Current in Linear Region
Linear Region Pull Down Current = sum(x,0,Number of Parallel Driver Transistors,(Electron Mobility*Oxide Capacitance/2)*(Channel Width/Channel Length)*(2*(Gate Source Voltage-Threshold Voltage)*Output Voltage-Output Voltage^2))
Pull down Current in Saturation Region
Saturation Region Pull Down Current = sum(x,0,Number of Parallel Driver Transistors,(Electron Mobility*Oxide Capacitance/2)*(Channel Width/Channel Length)*(Gate Source Voltage-Threshold Voltage)^2)
Saturation Time
Saturation Time = -2*Load Capacitance/(Transconductance Process Parameter*(High Output Voltage-Threshold Voltage)^2)*int(1,x,High Output Voltage,High Output Voltage-Threshold Voltage)
Drain Current Flowing through MOS Transistor
Drain Current = (Channel Width/Channel Length)*Electron Mobility*Oxide Capacitance*int((Gate Source Voltage-x-Threshold Voltage),x,0,Drain Source Voltage)
Time Delay when NMOS Operates in Linear Region
Linear Region in Time Delay = -2*Junction Capacitance*int(1/(Transconductance Process Parameter*(2*(Input Voltage-Threshold Voltage)*x-x^2)),x,Initial Voltage,Final Voltage)
Depletion Region Charge Density
Density of Depletion Layer Charge = (sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(Surface Potential-Bulk Fermi Potential)))
Depth of Depletion Region Associated with Drain
Drain's Depth of Depletion Region = sqrt((2*[Permitivity-silicon]*(Built in Junction Potential+Drain Source Voltage)) /([Charge-e]*Doping Concentration of Acceptor))
Drain Current in Saturation Region in MOS Transistor
Saturation Region Drain Current = Channel Width*Saturation Electron Drift Velocity*int(Charge*Short Channel Parameter,x,0,Effective Channel Length)
Fermi Potential for P Type
Fermi Potential for P Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Intrinsic Carrier Concentration/Doping Concentration of Acceptor)
Maximum Depletion Depth
Maximum Depletion Depth = sqrt((2*[Permitivity-silicon]*modulus(2*Bulk Fermi Potential))/([Charge-e]*Doping Concentration of Acceptor))
Fermi Potential for N Type
Fermi Potential for N Type = ([BoltZ]*Absolute Temperature)/[Charge-e]*ln(Donor Dopant Concentration/Intrinsic Carrier Concentration)
Equivalent Large Signal Capacitance
Equivalent Large Signal Capacitance = (1/(Final Voltage-Initial Voltage))*int(Junction Capacitance*x,x,Initial Voltage,Final Voltage)
Built in Potential at Depletion Region
Built in Voltage = -(sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor*modulus(-2*Bulk Fermi Potential)))
Depth of Depletion Region Associated with Source
Source's Depth of Depletion Region = sqrt((2*[Permitivity-silicon]*Built in Junction Potential)/([Charge-e]*Doping Concentration of Acceptor))
Substrate Bias Coefficient
Substrate Bias Coefficient = sqrt(2*[Charge-e]*[Permitivity-silicon]*Doping Concentration of Acceptor)/Oxide Capacitance
Average Power Dissipated over Period of Time
Average Power = (1/Total Time Taken)*int(Voltage*Current,x,0,Total Time Taken)
Equivalent Large Signal Junction Capacitance
Equivalent Large Signal Junction Capacitance = Perimeter of Sidewall*Sidewall Junction Capacitance*Sidewall Voltage Equivalence Factor
Work Function in MOSFET
Work Function = Vaccum Level+(Conduction Band Energy Level-Fermi Level)
Zero Bias Sidewall Junction Capacitance per Unit Length
Sidewall Junction Capacitance = Zero Bias Sidewall Junction Potential*Depth of Sidewall
## Saturation Time Formula
Saturation Time = -2*Load Capacitance/(Transconductance Process Parameter*(High Output Voltage-Threshold Voltage)^2)*int(1,x,High Output Voltage,High Output Voltage-Threshold Voltage)
## What are the Applications of Saturation Time ?
1. Circuit Speed Estimation: tsat helps estimate the propagation delay of a digital circuit. It represents the time it takes for the output voltage of a transistor to reach a specific level after receiving an input signal. Knowing this delay is crucial for understanding how fast the circuit can operate and make decisions.
2. Design Optimization: By considering tsat, circuit designers can optimize circuits for speed. Techniques like choosing transistors with higher transconductance or reducing the load capacitance can lead to faster switching and shorter saturation times.
## How to Calculate Saturation Time?
Saturation Time calculator uses Saturation Time = -2*Load Capacitance/(Transconductance Process Parameter*(High Output Voltage-Threshold Voltage)^2)*int(1,x,High Output Voltage,High Output Voltage-Threshold Voltage) to calculate the Saturation Time, The Saturation Time formula is defined as the time it takes for a MOSFET's output voltage to reach a specified level (Vout,fd) in the saturation region, after receiving an input signal. Saturation Time is denoted by Tsat symbol.
How to calculate Saturation Time using this online calculator? To use this online calculator for Saturation Time, enter Load Capacitance (Cload), Transconductance Process Parameter (kn), High Output Voltage (VOH) & Threshold Voltage (VT) and hit the calculate button. Here is how the Saturation Time calculation can be explained with given input values -> 5.638104 = -2*9.77/(4.553*(3.789-5.91)^2)*int(1,x,3.789,3.789-5.91).
### FAQ
What is Saturation Time?
The Saturation Time formula is defined as the time it takes for a MOSFET's output voltage to reach a specified level (Vout,fd) in the saturation region, after receiving an input signal and is represented as Tsat = -2*Cload/(kn*(VOH-VT)^2)*int(1,x,VOH,VOH-VT) or Saturation Time = -2*Load Capacitance/(Transconductance Process Parameter*(High Output Voltage-Threshold Voltage)^2)*int(1,x,High Output Voltage,High Output Voltage-Threshold Voltage). Load Capacitance is the total capacitance connected to the transistor's output terminal, including external components and the MOSFET's own parasitic capacitance, Transconductance Process Parameter is a device-specific constant that characterizes the transistor's ability to convert a change in gate voltage to a change in output current, High Output Voltage is the maximum voltage level the transistor can reach at its output terminal when fully turned on (operating in saturation) & Threshold Voltage is the minimum gate-to-source voltage required in a MOSFET to turn it "on" and allow a significant current to flow.
How to calculate Saturation Time?
The Saturation Time formula is defined as the time it takes for a MOSFET's output voltage to reach a specified level (Vout,fd) in the saturation region, after receiving an input signal is calculated using Saturation Time = -2*Load Capacitance/(Transconductance Process Parameter*(High Output Voltage-Threshold Voltage)^2)*int(1,x,High Output Voltage,High Output Voltage-Threshold Voltage). To calculate Saturation Time, you need Load Capacitance (Cload), Transconductance Process Parameter (kn), High Output Voltage (VOH) & Threshold Voltage (VT). With our tool, you need to enter the respective value for Load Capacitance, Transconductance Process Parameter, High Output Voltage & Threshold Voltage and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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# Design of Steel Structures Questions and Answers – Behaviour of Real Beam
This set of Design of Steel Structures Multiple Choice Questions & Answers (MCQs) focuses on “Behaviour of Real Beam”.
1. As the beam undergoes bending under applied loads, axial strain distribution at a point in beam
a) axial strain is not produced
b) remains constant
c) varies along depth of beam
d) varies along length of beam
Explanation: As the beam undergoes bending under applied loads, axial strain distribution at a point in beam varies along the depth of beam.
2. The beam buckles elastically if
a) Mcr < My
b) Mcr > My
c) Mcr = My
d) Mcr = 2My
Explanation: If Mcr critical moment of a section is less than yield moment My , then beam buckles elastically.
3. If Mcr > My of a beam section, then
a) beam does not buckle
b) beam buckles fully elastically
c) beam buckles completely plastically
d) some amount of plasticity is experienced
Explanation: When critical moment of a section Mcr is greater than My , some amount of plasticity is experienced at the outer edges before buckling is initiated.
4. Beams with intermediate slenderness fail by
a) elastic buckling
b) inelastic lateral buckling
c) attains Mp without buckling
d) do not fail
Explanation: Beams with intermediate slenderness (0.4 < √Mp/Mcr < 1.2) fail by inelastic lateral buckling at loads below Mp and above Mcr .
5. What are residual stresses?
a) stresses developed during construction
b) stresses developed due to seismic load
c) stresses developed due to vibration
d) stresses developed during manufacturing
Explanation: During the process of manufacture, steel sections are subjected to large thermal expansions resulting in yield level strains in sections. As subsequent cooling is not uniform throughout the section, self-equilibrating patterns of stresses are formed. These stresses are called residual stresses.
Note: Join free Sanfoundry classes at Telegram or Youtube
6. Which of the following is correct?
a) yielding of section starts at lower moments
b) yielding of section starts at higher moments
c) yielding of section does not start at lower moments
d) yielding of section does not occur
Explanation: Due to presence of residual stresses, yielding of section starts at lower moments. Then with increase in moment, yielding spreads through the cross section.
7. Match the pair
```(i) high slender beams (A) attain M<sub>p</sub> without buckling
(ii) stocky beams (B) fail by inelastic buckling
(iii) intermediate slender beams (C) fail by elastic buckling```
a) i-A, ii-B, iii-C
b) i-C, ii-B, iii-A
c) i-C, ii-A, iii-B
d) i-A, ii-C, iii-B
Explanation: Beams with high slenderness fail by elastic lateral buckling at Mcr. Beams of intermediate slenderness fail by inelastic lateral buckling at loads below Mp and above Mcr. Stocky beams attains Mp without buckling with negligible lateral deformations.
8. Which of the following is correct?
a) torsional bracing attached to top flange should bend in single curvature
b) torsional bracing attached to top flange should not bend in reverse curvature
c) its flexural stiffness should be 6EIb/S
d) its flexural stiffness should be 4EIb/S
Explanation: Torsional bracing attached to top flange should bend in reverse curvature and its flexural stiffness should be 6EIb/S, where S is spacing between girders.
Sanfoundry Global Education & Learning Series – Design of Steel Structures.
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## 티스토리 뷰
공부
### Random notes on Lyndon decomposition
구사과 2022. 10. 14. 11:47
Codeforces에 올린 글을 보관 목적으로 블로그에도 올립니다. 한글 번역 계획은 없습니다.
I recently solved some problems that involved the concept of Lyndon decomposition. Honestly, most of them were too hard to understand for me. I'm just trying to think out loud about things I've read, so I can learn ideas or better takes from smarter people?
Note that I will omit almost all proofs as I can't do that. I believe all unproven claims below are facts, but it is always great to have doubts about anything.
## 1. Lyndon decomposition, definition, and algorithms
A string is called simple (or a Lyndon word), if it is strictly smaller than any of its own nontrivial suffixes. Examples of simple strings are $a, b, ab, aab, abb, abcd, abac$.
It can be shown that a string is simple, if and only if it is strictly smaller than all its nontrivial cyclic shifts. As a corollary, it can be observed that simple words are never periodic (it is not a repetition of some words for $2$ or more times).
The Lyndon decomposition of string $s$ is a factorization $s = w_1 w_2 \ldots w_k$, where all strings $w_i$ are simple, and are in non-increasing order $w_1 \geq w_2 \geq \ldots \geq w_k$.
Alternatively, the Lyndon decomposition of string $s$ can be represented as $s = w_1^{p_1} w_2^{p_2} \ldots w_k^{p_k}$. Here, $p_i$ are positive integers, and $w^p_i$ denotes the string $w$ repeated for $p_i$ times. All strings $w_i$ are simple, and are in decreasing order $w_1 > w_2 > \ldots > w_k$. The only difference is that the group of identical factors is grouped as a chunk such as $w^p_i$.
It is claimed that for any string such a factorization exists and it is unique. However, I can't prove it.
### 1.1 Algorithm
There are two algorithms that compute the Lyndon decomposition in linear time. The first algorithm is the well-known Duval algorithm. E-maxx has a good explanation on this, so I won't discuss it here.
Another algorithm is conceptually much simpler. Given a string $S$, consider the greedy algorithm that repeatedly removes the smallest suffix from $S$. By definition, the greedy algorithm always removes a simple word, so the algorithm will return a decomposition consisting of simple words. We believe that the Lyndon decomposition is unique, thus algorithm returns a Lyndon decomposition.
Let's compute the time complexity, the algorithm will iterate at most $O(N)$ times, and it can find the smallest suffix naively in $O(N^2)$ time, so the naive implementation will take $O(N^3)$ time. However, the smallest suffix is just the first entry of the suffix array, so using the fastest suffix array algorithm can optimize each phase to $O(N)$, giving an $O(N^2)$ algorithm.
Should we compute the suffix array from scratch in each phase? The removal of a suffix does change the ordering in the suffix array. For example, $abac < ac$, but $aba > a$.
However, this issue doesn't apply to our application, where we remove the smallest suffix. Therefore, given a suffix array $SA_0, \ldots, SA_{N - 1}$ for the string $S$, one can simply iterate from $SA_0$ to $SA_{N - 1}$, and cut the string as long as it is the leftmost position we encountered. As the suffix array can be solved in $O(N)$, this gives an $O(N)$ solution to the Lyndon decomposition. I can't prove why this is true. But this looks like a folklore algorithm, so I believe it's true.
## 2. Computing Lyndon decomposition for each substring
For a string of size $N$, the Lyndon decomposition may have at most $O(N)$ size, in which case the above algorithms are already optimal. Hence, in this section, we only discuss finding the smallest suffix for each substring in near-constant time, since it may
• lead to an algorithm for computing Lyndon decomposition in near-linear time on output size, by the above greedy algorithm.
• yield some small implicit structure (tree) that captures the Lyndon decomposition for all interesting substrings
### 2.1. Lyndon decomposition for all suffixes
The removal of a prefix does not change the ordering in the suffix array. To find the smallest suffix in $S[x ...]$, just find the first entry in the suffix array such that $SA_i \geq x$.
### 2.2. Lyndon decomposition for all prefixes
Duval's algorithm is basically incremental since it repeatedly adds a letter $s[j]$ to the existing structure. This hints that the Lyndon decomposition can be computed for all prefixes, although it's not entirely straightforward.
I came up with the algorithm to compute all min suffixes for all prefixes. There are other algorithms to compute the min suffixes, such as the one [user:ecnerwala,2022-09-07] described in this comment.
Duval algorithm maintains a pre-simple string in each iteration. Consider a pre-simple string $t = ww\ldots w\overline{w}$ for the current prefix. Except for the last string $\overline{w}$, every other string are simple. And if we take the Lyndon decomposition of $\overline{w}$, the first element of it is the prefix of $\overline{w}$, which is obviously less than $w$. As we know that Lyndon decomposition is unique, we can see that the last element of Lyndon decomposition of $\overline{w}$ is exactly the smallest suffix of the current prefix.
Thus, the naive algorithm is the following:
• If $\overline{w}$ is empty, $w$ is the smallest suffix of the given prefix.
• Otherwise, the smallest suffix of $\overline{w}$ is the smallest suffix for the given prefix.
However, we don't have to recompute the smallest suffix of $\overline{w}$ every time. In the decomposition algorithm, we fix the string $s_1 = s[0 : i)$ and compute the decomposition for the suffix $s[i \ldots]$. For each relevant $i$, we use dynamic programming. Let $MinSuf[j]$ be the length of smallest suffix of $S[i \ldots j)$ for $j > i$. If $\overline{w}$ is empty the smallest suffix is $w$. Otherwise, since $\overline{w}$ is exactly the string $S[i \ldots i + |\overline{w}|)$, $MinSuf[j] = MinSuf[i + |\overline{w}|]$. Therefore we can obtain a simple recursive formula.
### 2.3 Lyndon decomposition for all substrings?
This paper contains some ideas, so if you are interested, give it a try :)
## 3. The Runs Theorem
Run is a concept that is useful for solving problems related to repeats. Even if you never heard of the name, anyone who solved some challenging suffix array problems will be familiar with it.
Given a string $S$, the tuple $(l, r, p)$ is a run of string $S$ if
• $0 \le l < r \le |S|$
• $1 \le p \le |S|$
• $r - l \geq 2p$
• $p$ is the smallest positive integer where $S[i] = S[i + p]$ holds for all $l \le i < r - p$
• The above four properties doesn't hold for tuple $(l - 1, r, p)$ and $(l, r + 1, p)$
Let $-S$ be the string where all elements are inverted: Specifically, we assign s[i] = 'a' + 'z' - s[i] for all elements of $S$, so that the usual comparison order is reverted, except the empty character which has the lowest priority.
Given a string $S$, a Lyndon prefix is the longest prefix that is a Lyndon word. Given a suffix array of $S$, this Lyndon prefix can be easily computed. Recall an algorithm that computes the Lyndon decomposition given a suffix array. Let $Rank_i$ be the inverse of the suffix array. Then, we can see that the length of the Lyndon prefix is the smallest $i$ such that $Rank_i < Rank_0$ (or $|S|$ if such does not exist). Similarly, we can also compute this for all suffixes $S[i \ldots]$: find the smallest $j > 0$ such that $Rank_{i + j} < Rank_i$.
For each suffix of $S$ and $-S$, we compute the Lyndon prefix $[i, j)$ and take them as a "seed". Start from the tuple $(i, j, j - i)$, and extend the tuple in both direction as long as $S[i] = S[i + p]$ holds. Specifically, Let $k$ be the maximum number such that $S[i, i + k) = S[j, j + k)$ and $l$ be the maximum number such that $S[i - l, i) = S[j - l, j)$. Then we obtain a run $(i - l, j + k, j - i)$. Both $k, l$ can be computed in $O(\log N)$ time with suffix arrays.
It's easy to verify that those elements are actually the run of the string. If we remove all duplicated runs, the following fact holds:
Fact 1. Those we computed are exactly the set of all Runs.
Fact 2. There are at most $n$ runs.
Fact 3. The sum of $(j - i) / p$ for all runs are at most $3n$.
Fact 4. The sum of 2-repeats ($j - i - 2p + 1$) obtained from runs are at most $n \log n$.
Fact 3 is useful when we want to enumerate all repeats. Suppose that we have to enumerate all possible repeats. A string "aaaa" can be considered as a repeat of "a" 4 times, but it is also a repeat of "aa" 2 times. In this case, we have to enumerate all multiples of $p$ — but by Fact 3, that does not affect the overall complexity.
Fact 1, 2, 3 can be found on this paper. I think Fact 4 is not hard to prove, but that doesn't mean I've done it, nor do I have a reference that states this fact.
## 4. Lexicographically minimum substring reverse
Given a string $S$, you can select $0$ or more non-overlapping substrings, and reverse them. What is the lexicographically minimum result you can obtain from the single iteration of this operation?
Let $S^R$ be the reverse of $S$. The answer is to take the Lyndon decomposition for $S^R$, and reverse each substring from that respective position.
I don't know why this works.
Intuitively, we are replacing each prefix of $S$ to the minimum suffix of $S^R$. Replacing each prefix to the minimum possible suffix seems like a good trade. Do you agree or disagree? XD
## 5. Minimal Rotation from Lyndon decomposition
Given a string $S$, what is the lexicographically minimum result you can obtain by taking a cyclic shift of $S$?
The answer can be found by finding the smallest suffix of length $> |S|$ for string $S + S$, and rotating at the respective position. This suffix can be found with Lyndon decomposition. Therefore we can solve this in $O(n)$ time, which is great.
What about just reversing a minimum suffix of $S$? Unfortunately, cases like "acabab", "dacaba" are the countercase. If we can reduce this problem into a minimum suffix instance, we can solve this problem for all prefixes, suffixes, and possibly substrings, so that's really unfortunate...
.. or maybe not. For a string $S$, consider it's Lyndon factorization $S = w_1^{p_1} w_2^{p_2} w_3^{p_3} \ldots w_k^{p_k}$. Clearly, taking the middle of periods is a bad idea. And taking only $w_k^{p_k}$ as a candidate is wrong.
Then what about trying to crack the tests? Let $SFX_j = w_j^{p_j} w_{j+1}^{p_{j + 1}} \ldots w_k^{p_k}$. Then, we can try all $SFX_j$ in range $k - 69 \le j \le k + 1$ as a candidate. It looks really hard to create an anti-test for this approach.
Lemma. Minimum rotation exists in the last $\log_2 |S|$ candidates of $SFX_j$. (Observation 6)
This provides an algorithm for computing the minimum rotation in $O(Q(n) \log n)$ time, where $Q(n)$ is time to compute the minimum suffix.
## Practice problems
### Minimum rotation for each substring
#### '공부' 카테고리의 다른 글
Inapproximability in computational hardness (0) 2022.11.01 2022.11.01 2022.08.14 2022.08.11 2022.08.02
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Вернуться к Статистика вывода
# Отзывы учащихся о курсе Статистика вывода от партнера Амстердамский университет
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## О курсе
Inferential statistics are concerned with making inferences based on relations found in the sample, to relations in the population. Inferential statistics help us decide, for example, whether the differences between groups that we see in our data are strong enough to provide support for our hypothesis that group differences exist in general, in the entire population. We will start by considering the basic principles of significance testing: the sampling and test statistic distribution, p-value, significance level, power and type I and type II errors. Then we will consider a large number of statistical tests and techniques that help us make inferences for different types of data and different types of research designs. For each individual statistical test we will consider how it works, for what data and design it is appropriate and how results should be interpreted. You will also learn how to perform these tests using freely available software. For those who are already familiar with statistical testing: We will look at z-tests for 1 and 2 proportions, McNemar's test for dependent proportions, t-tests for 1 mean (paired differences) and 2 means, the Chi-square test for independence, Fisher’s exact test, simple regression (linear and exponential) and multiple regression (linear and logistic), one way and factorial analysis of variance, and non-parametric tests (Wilcoxon, Kruskal-Wallis, sign test, signed-rank test, runs test)....
## Лучшие рецензии
MN
24 июля 2020 г.
Feeling blessed to perform this course . It was truly an amazing experience for me to go though this course .Learned bunch of theories with their mathematical example.Thanks to the instructors.
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Incredibly dense (which they warn you about) so the lecutres fly over so much important info it's hard to keep track of even with a strong focus. A very good overview though.
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some minor flaws may exist in the test design. apart from this, all good.
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# Magnets lines of force are electrons?
Gold Member
Magnets "lines of force are" electrons?
So I understand that a magnetic field is defined by the lines of force that go from the north to the south pole....what are these forces? The flow of electrons back and forth...?
Electricity is electrons moving relative to their ions (the protons in the conductor). Lets just say there is a positive charge nearby within the electric field, it will tend to follow the motion of the electrons.
Now from the reference frame of the external positive charge, the electrons are not moving, but rather the ions are moving. So the ions have more relativistic mass over the electrons and a positive electrostatic force becomes present to the moving positive charge. This charge will then be pushed away from the current.
This is what we measure as the magnetic field. It is a relativistic correction to the electrostatic field.
Gold Member
Hmm, I guess it's somewhat hard to grasp that "ions are moving" in a solid matter...I'm gonna have to think about it more.
Drakkith
Staff Emeritus
In response to the OP's original question, the lines of force for a magnet are NOT electrons. If anything they would be photons that carry the electromagnetic force, but a better way to look at it is that the lines of force are simply a visual way of representing the magnetic field of a magnet. In reality you would have effectively "infinite" lines of force.
sophiecentaur
Gold Member
2020 Award
A long long time ago, lines of force were explained to me as the paths that a 'free North Pole" would take on its journey to from the North to the South pole of a magnet. They aren't really there but they are a useful picture to hold in the mind. The field is strong where the lines are close together and weak where they are far apart.
This by no means a complete description of a field but it may help.
Gold Member
In response to the OP's original question, the lines of force for a magnet are NOT electrons. If anything they would be photons that carry the electromagnetic force, but a better way to look at it is that the lines of force are simply a visual way of representing the magnetic field of a magnet. In reality you would have effectively "infinite" lines of force.
I see. So in other words, "scientists aren't sure what they are, but if it helps you understand, think they're photons!"
I dig that :)
I see. So in other words, "scientists aren't sure what they are, but if it helps you understand, think they're photons!"
I dig that :)
Good grief. There aren't any lines. They are cartoon drawings. See what sophiecentaur had to say in the previous post.
Born2bwire
Gold Member
It may just be easier to understand that the electric field describes the force between charged particles. The magnetic field relates an additional force that occurs between charged particles when they are in relative motion. These force fields are vector fields. This means that at every point in space the force field is describe by a magnitude and direction. These force line drawings are a way of visualizing this vector field in an easily comprehensive manner. Because of the way that many objects will align along the direction of an applied magnetic force, the visualization of the field lines can be created physically using iron filings or compasses.
The way I understood a magnet was that the way all of the holes in between the electrons faced one way while the electrons faced another way creating the repelling and attracting forces. Since protons attract each other the holes allowed the protons to interact more then they usually would in other material.
sophiecentaur
Gold Member
2020 Award
I should do a bit of Googling to sort out your knowledge, Kainchild.
You seem to have a rather 'alternative' view of it. :-)
The way I understood a magnet was that the way all of the holes in between the electrons faced one way while the electrons faced another way creating the repelling and attracting forces. Since protons attract each other the holes allowed the protons to interact more then they usually would in other material.
You are thinking of a natural magnet. A rock that has magnetic properties. Rather than holes it is usually referred to as intrinsic spin of the electrons.
Or any permanent magnet, in fact.
Yea, that is the word I was looking for.
Last edited:
sophiecentaur
Gold Member
2020 Award
Or any permanent magnet, in fact.
Drakkith
Staff Emeritus
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ontolog-forum
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## [ontolog-forum] 2D drawing primitives (was: Foundation Ontology Primitiv
To: "[ontolog-forum]" Duane Nickull Wed, 3 Feb 2010 09:27:13 -0800
(note: changed heading for discussions related to 2D drawing primitives to allow others to filter messages) Sean: This is really great insight. It got me thinking about the issue from a different perspective. For a computer graphics person or developer, a point is often a single pixel whereby conceptually for an ontologist, you are quite correct in noting that it is a zero radius concept. The people at my company (adobe) who work on Flex came up with the 5 basic drawing primitives, all based on a pixelated environment (point, fill, line (lines can have arcs in this case), ellipse and rectangle. The line class is abstract but when sub-typed, has methods such as “lineTo(coord)” which can really be used to make any other shape. Since a line itself could be expressed as an array of points, the point is truly the primitive here. Extending the thought, a line with an arc/curvature potential can be used to draw a circle or an ellipse if the line starts and ends at the same place. How could I have missed this before??? It surprises me that just about every programming language with a graphics package has not adopted the ontological perspective on 2D drawing primitives. I love the Ontolog forum!! Duane On 2/3/10 5:14 AM, "sean barker" wrote: Duane Actually, circles, lines and points are all the same primitive - half-spaces of the plane: lines have zero curvature, points zero radius, and circles have finite radius and finite curvature. An ellipse is a circle after linear transformation. A triangle is the intersection of three linear halfspaces. BTW, point is not obviously a primitive, in the sense there are several different flavours of point - a 2D point is not the same as a 3D point, and a point in homogeneous co-ordinates is not quite the same as one in Cartesian co-ordinates. This is before you get to the more esoteric end of things, such a duality theory and geometry over algebraic systems other than the real numbers. I believe there is also a more generalised concept of a point called a turbine. I'm not sure I can think of any more concrete example of the claim that an ontology is viewpoint specific Sean Barker Bristol From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Duane Nickull Sent: 02 February 2010 19:54 To: [ontolog-forum] Subject: Re: [ontolog-forum] Foundation Ontology Primitives *** WARNING *** This message has originated outside your organisation, either from an external partner or the Global Internet. Keep this in mind if you answer this message. Inline: On 2/2/10 11:43 AM, "Matthew West" wrote: > I hope that it will not actually be necessary to try to precisely > define > the borderline between primitive and non-primitive. A concept is primitive if it cannot be completely defined in terms of concepts you already have defined. Most OO programming languages are structured this way. If there is any way to build such a concept with another class, then refactoring is often used. Take drawing primitives as an example. There is one base primitive which might be “coordinate”. This corresponds to a specific X,Y pair. This is abstract so at this point it ignores all pixel resolutions etc but could generally taken to be based on a pixel grid. The next level down would be some primitive shapes. Candidates might be Line, Circle, Ellipse, Rectangle, Square etc. On closer examination, circle can be stated to be a specialized type of ellipse (one with a constant radius value) and a square can be declared as a specialized type of rectangle (one with equal side lengths within a fixed unit of precision, usually the pixel resolution when implemented). Line might also be a candidate for rectangle (a rectangle with height:width ratio exceeding certain limits) but lines could also carry the added property of an arc or path. Therefore the true primitives might be coordinate (or point), line, ellipse and rectangle. This represents a context of pixelated screens however. In vector graphics (SVG et al) the primitives may be different. A triangle then presents a test. Is it another primitive of is it a specialized type of one of the existing graphic primitives. One could create another primitive called “fill” that takes parameters of a “boundary” expressed in terms of lines. This could then make up all other shapes such as polygon, triangle, star, etc.. Duane --- Adobe LiveCycle Enterprise Architecture - http://www.adobe.com/products/livecycle/ My TV Show - http://tv.adobe.com/show/duanes-world/ My Blog – http://technoracle.blogspot.com/ My Band – http://22ndcenturyofficial.com/ Twitter – http://twitter.com/duanechaos --- Adobe LiveCycle Enterprise Architecture - http://www.adobe.com/products/livecycle/ My TV Show - http://tv.adobe.com/show/duanes-world/ My Blog – http://technoracle.blogspot.com/ My Band – http://22ndcenturyofficial.com/ Twitter – http://twitter.com/duanechaos ``` _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (01) ```
Current Thread Re: [ontolog-forum] Foundation Ontology Primitives, sean barker Re: [ontolog-forum] Foundation Ontology Primitives, John F. Sowa Re: [ontolog-forum] Foundation Ontology Primitives, Patrick Cassidy Re: [ontolog-forum] Foundation Ontology Primitives, Matthew West Re: [ontolog-forum] Foundation Ontology Primitives, Ali Hashemi Re: [ontolog-forum] Foundation Ontology Primitives, Patrick Cassidy Re: [ontolog-forum] Foundation Ontology Primitives, Duane Nickull Re: [ontolog-forum] Structure of an FO consortium?, Patrick Cassidy Re: [ontolog-forum] Foundation Ontology Primitives, AzamatAbdoullaev [ontolog-forum] 2D drawing primitives (was: Foundation Ontology Primitives), Duane Nickull <= [ontolog-forum] Foundation Ontology primitives, FERENC KOVACS Re: [ontolog-forum] Foundation Ontology primitives, AzamatAbdoullaev Re: [ontolog-forum] Foundation Ontology primitives, Rich Cooper [ontolog-forum] Foundation Ontology Primitives, FERENC KOVACS
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# Clustering sets of vectors
I have a set of $d$-dimensional vectors $\{v_1,v_2,\dots,v_n\}$, each of which has been assigned a label from a set $S=\{s_1,s_2,\dots,s_k\}$. I would like to find another set of labels $T=\{t_1,t_2,\dots,t_l\}$ where $l < k$, such that all vectors having the same $S$ label also have the same $T$ label. In other words $T$ is a strictly coarser clustering than $S$. My question is, what is a good way to go about finding this $T$ clustering?
The obvious approach would be to take the mean of all of the vectors having a given S label, and then cluster these new $s$ vectors. However I feel like this throws away a lot of potentially useful information about the distribution of the vectors that went into computing those means. Is there another method for finding this $T$ clustering which makes better use of the $v$ vectors? Thanks in advance.
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# Elements of Surveying, and Navigation, with a Description of the Instruments, and the Necessary Tables
A.S. Barnes & Company, 1841 - 359 sider
### Hva folk mener -Skriv en omtale
Vi har ikke funnet noen omtaler på noen av de vanlige stedene.
### Innhold
CHAPTER 7 Multiplication by Logarithms 14 Of the Dividers 22 Gunters Scale 28 Table of Logarithmic Sines 37 Solution of Right Angled Triangles 49 Of the Theodolite 55 Heights and Distances 66 66
Method of Finding the Content of Land by Means of the Table of Natural 120 Method of Surveying the Public Lands 126 Of the Plain Table 133 Of the Level 140 CHAPTER 148 Of Surveying Harbours 159 Of the Circular Protractor 166 Of Plane Sailing 174
### Populære avsnitt
Side 12 - FRACTION is a negative number, and is one more than the number of ciphers between the decimal point and the first significant Jigure.
Side 49 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Side 41 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Side 34 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Side 73 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower Cway 33° 45' ; required the height of the tower.
Side 40 - THEOREM I. The sides of a plane triangle are proportional to the sines of their opposite angles.
Side 19 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.
Side 85 - What must be the nominal value of 4% bonds that will yield to their owner an annual income of \$720 ? 7. A owns \$6000 of 5% bonds; B owns \$8000 of 4£% bonds. How much greater is the annual income from B's bonds than from A's ? 8. Find the area of a piece of land in the form of a rhomboid, whose base is 32 rods and whose altitude is 15 rods.
Side 35 - The secant of an arc is the line drawn from the centre of the circle through one extremity of the arc, and limited by the tangent passing through the other extremity. Thus, OC is the secant of the arc AB.
Side 130 - Take a board, of about one foot square, paste white paper upon it, and perforate it through the center; the diameter of the hole being somewhat larger than the diameter of the telescope of the theodolite. Let this board be so fixed to a vertical staff" as to slide up and down freely ; and let a small piece of board, about three inches square, be nailed to the lower edge of it, for the purpose of holding a candle. About twenty-five minutes before the time of the greatest eastern or western elongation...
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# One batch of walnut muffins use 1 1/3 cups of walnuts.How many cups of walnuts are needed to 3 3/4 batches of muffins
Students were requested to answer a question at institution and to express what is most important for them to succeed. The one that response stood out from the rest was practice. People who are successful do not become successful by being born. They work hard and persistence their lives to succeeding. If you tend to complete your goals, keep this in mind! beneath some question and answer examples that you could actually work with to elevate your knowledge and gain insight that will help you to continue your school studies.
## Question:
One batch of walnut muffins use 1 1/3 cups of walnuts.How many cups of walnuts are needed to 3 3/4 batches of muffins
Five cups of walnuts would be needed to make 3 3/4 batches of muffins
In order to determine the number of cups of walnuts needed, divide the total batch of muffins by the amount of walnuts needed for one batch
Number of cups needed = Total number of batches / number of cups needed for one bath
×
Convert to an improper fraction
× = 5 cups
From the answer and question examples above, hopefully, they are able to help the student deal with the question they had been looking for and notice of all stated in the answer above. You will be able to then have a discussion with your classmate and continue the school learning by studying the problem alongside one another.
READ MORE Which ancient Greek value did Queen Cassiopeia fail to possess? beauty sense of justice modesty respect for elders
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https://www11.ceda.polimi.it/schedaincarico/schedaincarico/controller/scheda_pubblica/SchedaPublic.do?&evn_default=evento&c_classe=596076&polij_device_category=DESKTOP&__pj0=0&__pj1=27c3ed14999eb153496579a2a5f25f25
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Risorse bibliografiche
Risorsa bibliografica obbligatoria Risorsa bibliografica facoltativa
Scheda Riassuntiva
Anno Accademico 2014/2015 Scuola Scuola di Ingegneria Industriale e dell'Informazione Insegnamento 089166 - IMAGE ANALYSIS Docente Caglioti Vincenzo Cfu 5.00 Tipo insegnamento Monodisciplinare
Corso di Studi Codice Piano di Studio preventivamente approvato Da (compreso) A (escluso) Insegnamento
Ing Ind - Inf (Mag.)(ord. 270) - CO (435) INGEGNERIA INFORMATICA*AZZZZ088954 - COMPUTER VISION (INF-CO)
Ing Ind - Inf (Mag.)(ord. 270) - MI (434) INGEGNERIA INFORMATICA*AZZZZ089166 - IMAGE ANALYSIS
Ing Ind - Inf (Mag.)(ord. 270) - MI (436) INGEGNERIA DELL'AUTOMAZIONE*AZZZZ089166 - IMAGE ANALYSIS
Ing Ind - Inf (Mag.)(ord. 270) - MI (473) AUTOMATION AND CONTROL ENGINEERING - INGEGNERIA DELL'AUTOMAZIONE*AZZZZ089166 - IMAGE ANALYSIS
Ing Ind - Inf (Mag.)(ord. 270) - MI (481) COMPUTER SCIENCE AND ENGINEERING - INGEGNERIA INFORMATICA*AZZZZ089166 - IMAGE ANALYSIS
Programma dettagliato e risultati di apprendimento attesi
# Purpose
The purpose of the Image analysis course is to study both the foundations on image formation,
image analysis, and the methodology underlying the solution techinques to the main problems involved.
Image analysis addresses the extraction of the content of one or several images, in order to obtain a representaton of the observed 3D scene.
Optical aspects, geometrical ones, and algorithmic aspects are studied,
as well as aspects connected to signal processing and data analysis.
A project allows to closely examine, possibly from a practical point of view, one or more of the discussed topics.
# Program
0. Introduction.
1. Camera sensors: transduction, optics, geometry, distortion
2. Basics on Projective geometry: modelling basic primitives (points, lines, planes, conic sections, quadric surfaces) and projective spatial transformations and projections.
3. Camera geometry, and single view analysis: localization of 3D models.
4. Multi-view analysis: 3D reconstruction, self-calibration.
5. Linear filters and convolutions, space-invariant filters, Fourier Transform, sampling and aliasing.
6. Nonlinear filters: image morphology and morphology operators (dilate, erode, open, close), median filters.
7. Edge detection and feature detection techniques.
8. Image segmentation, contour segmentation, clustering, Hough Transform, Ransac (random sample consensus), EM (expectation maximization).
9. Applications
Note Sulla Modalità di valutazione
Evaluation. The examination consists of a homework (max 6/30) plus either a project or a written proof (max 24/30).
Bibliografia
R.Hartley, A. Zisserman, Multi-view Geometry in Computer Vision, Editore: McGraw- Hill, Anno edizione: 2004 D.Forsyth, J. Ponce, Computer Vision: A Modern Approach
Software utilizzato
Nessun software richiesto
Mix Forme Didattiche
Tipo Forma Didattica Ore didattiche
lezione
32.0
esercitazione
16.0
laboratorio informatico
0.0
laboratorio sperimentale
0.0
progetto
0.0
laboratorio di progetto
0.0
Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua Inglese Disponibilità di materiale didattico/slides in lingua inglese Disponibilità di libri di testo/bibliografia in lingua inglese Possibilità di sostenere l'esame in lingua inglese Disponibilità di supporto didattico in lingua inglese
schedaincarico v. 1.8.3 / 1.8.3 Area Servizi ICT 03/10/2023
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### Research interests:
My research is currently supported by NSF award DMS 1108754 to study "Steklov spectra and Div-curl analysis". The research centers on the representation of solutions of various linear elliptic problems with non-trivial boundary conditions and their applications to problems in classical field theories, gravity and engineering.
Some years ago, I developed a spectral characterization of trace spaces (see SIMA Volume 38, (2006), 894-907 ) which provides a constructive approach to working with boundary traces of Sobolev functions. This enables the use of spectral methods to describe the solutions of homogeneous linear equations Lu = 0 on a region G subject to inhomogeneous boundary conditions Bu = g on the boundary of G. These involve finding representations of solutions using the Steklov eigenfunctions of the operator L on G. This analysis provides some different information about solutions of many classical linear elliptic boundary value problems. It is particularly useful for understanding the dependece of solutions on boundary data.
Since then I have used these to study a variety of phenomena that depend primarily on the boundary conditions. A particular interest is in the solution of div-curl boundary value problems on 3-dimensional regions.
This is an overdetermined system of 4 linear equations in 3 unknowns and physically they are posed subject to a variety of different types (and numbers) of boundary conditions.
The most important example of a div-curl system probably is Maxwell's equation for electromagnetic fields but they also arise in the study of velocity fields in fluid mechanics and are used in computer graphics for modeling vector fields. The mathematical theory of div-curl systems is reasonably well understood for 2-dimensional, bounded, regions. For three dimensional problems, however, there are still important open questions since it is an over-determined system of four linear equations in three unknowns.
For different physical problems div-curl systems are posed subject to varying numbers and types of boundary conditions; including mixed b.c.s where there can be different numbers of boundary conditions on different subsets of the boundary. The solvability issues center on
(i) What are the compatibility conditions that must hold for finite energy (L^2-) solutions to exist, and
(ii) What extra conditions besides boundary data are required for the systems to be well-posed?
The answers to these questions have interesting physical and engineering implications and usually are based on using an appropriate variational principle, and special choices of "potentials" to characterize the problem.
Another, related, class of problems of current research interest is the theory of trace spaces and problems with internal interfaces. We are interested in finding the classes of boundary data that have specific types of solutions of certain equations. In particular this has led to a description of trace spaces using Steklov eigenfunctions. This spectral theory of such spaces has advantages in that it is an intrinisc theory and there are explicit formulae for inner products and solutions of equations in terms of these eigenfunctions.
My work on these issues is theoretical mathematics, involving functional analysis and variational principles. I do not have any funding for research assistants or programmers.
For a listing of recent papers see Recent Publications.
For a full listing of research papers, arranged by topic, see Scientific Publications.
See also Reviews from MathSciNet.
Current Address: Department of Mathematics, PGH Building, University of Houston, Houston, Texas 77204-3008
Phone(UH): (713) 743-3500 - Fax(UH): (713) 743-3505
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# [R] problem for strsplit function
Kai Yang y@ngk@|9999 @end|ng |rom y@hoo@com
Sat Jul 10 00:45:35 CEST 2021
``` Thanks Bert,
I'm reading some books now. But it takes me a while to get familiar R.
Best,
Kai On Friday, July 9, 2021, 03:06:11 PM PDT, Duncan Murdoch <murdoch.duncan using gmail.com> wrote:
On 09/07/2021 5:51 p.m., Jeff Newmiller wrote:
> "Strictly speaking", Greg is correct, Bert.
>
> https://cran.r-project.org/doc/manuals/r-release/R-lang.html#List-objects
>
> Lists in R are vectors. What we colloquially refer to as "vectors" are more precisely referred to as "atomic vectors". And without a doubt, this "vector" nature of lists is a key underlying concept that explains why adding a dim attribute creates a matrix that can hold data frames. It is also a stumbling block for programmers from other languages that have things like linked lists.
I would also object to v3 (below) as "extracting" a column from d.
"d[2]" doesn't extract anything, it "subsets" the data frame, so the
result is a data frame, not what you get when you extract something from
a data frame.
People don't realize that "x <- 1:10; y <- x[[3]]" is perfectly legal.
That extracts the 3rd element (the number 3). The problem is that R has
no way to represent a scalar number, only a vector of numbers, so x[[3]]
gets promoted to a vector containing that number when it is returned and
assigned to y.
Lists are vectors of R objects, so if x is a list, x[[3]] is something
that can be returned, and it is different from x[3].
Duncan Murdoch
>
> On July 9, 2021 2:36:19 PM PDT, Bert Gunter <bgunter.4567 using gmail.com> wrote:
>> "1. a column, when extracted from a data frame, *is* a vector."
>> Strictly speaking, this is false; it depends on exactly what is meant
>> by "extracted." e.g.:
>>
>>> d <- data.frame(col1 = 1:3, col2 = letters[1:3])
>>> v1 <- d[,2] ## a vector
>>> v2 <- d[[2]] ## the same, i.e
>>> identical(v1,v2)
>> [1] TRUE
>>> v3 <- d[2] ## a data.frame
>>> v1
>> [1] "a" "b" "c" ## a character vector
>>> v3
>> col2
>> 1 a
>> 2 b
>> 3 c
>>> is.vector(v1)
>> [1] TRUE
>>> is.vector(v3)
>> [1] FALSE
>>> class(v3) ## data.frame
>> [1] "data.frame"
>> ## but
>>> is.list(v3)
>> [1] TRUE
>>
>> which is simply explained in ?data.frame (where else?!) by:
>> "A data frame is a **list** [emphasis added] of variables of the same
>> number of rows with unique row names, given class "data.frame". If no
>> variables are included, the row names determine the number of rows."
>>
>> "2. maybe your question is "is a given function for a vector, or for a
>> data frame/matrix/array?". if so, i think the only way is reading
>> the help information (?foo)."
>>
>> Indeed! Is this not what the Help system is for?! But note also that
>> the S3 class system may somewhat blur the issue: foo() may work
>> appropriately and differently for different (S3) classes of objects. A
>> detailed explanation of this behavior can be found in appropriate
>> resources or (more tersely) via ?UseMethod .
>>
>> "you might find reading ?"[" and ?"[.data.frame" useful"
>>
>> Not just 'useful" -- **essential** if you want to work in R, unless
>> one gets this information via any of the numerous online tutorials,
>> courses, or books that are available. The Help system is accurate and
>> authoritative, but terse. I happen to like this mode of documentation,
>> but others may prefer more extended expositions. I stand by this claim
>> even if one chooses to use the "Tidyverse", data.table package, or
>> other alternative frameworks for handling data. Again, others may
>> disagree, but R is structured around these basics, and imo one remains
>> ignorant of them at their peril.
>>
>> Cheers,
>> Bert
>>
>>
>> Bert Gunter
>>
>> "The trouble with having an open mind is that people keep coming along
>> and sticking things into it."
>> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
>>
>> On Fri, Jul 9, 2021 at 11:57 AM Greg Minshall <minshall using umich.edu>
>> wrote:
>>>
>>> Kai,
>>>
>>>> one more question, how can I know if the function is for column
>>>> manipulations or for vector?
>>>
>>> i still stumble around R code. but, i'd say the following (and look
>>> forward to being corrected! :):
>>>
>>> 1. a column, when extracted from a data frame, *is* a vector.
>>>
>>> 2. maybe your question is "is a given function for a vector, or for
>> a
>>> data frame/matrix/array?". if so, i think the only way is
>>> the help information (?foo).
>>>
>>> 3. sometimes, extracting the column as a vector from a data
>> frame-like
>>> object might be non-intuitive. you might find reading ?"[" and
>>> ?"[.data.frame" useful (as well as ?"[.data.table" if you use
>> that
>>> package). also, the str() command can be helpful in
>> understanding
>>> what is happening. (the lobstr:: package's sxp() function, as
>> well
>>> as more verbose .Internal(inspect()) can also give you insight.)
>>>
>>> with the data.table:: package, for example, if "DT" is a
>> data.table
>>> object, with "x2" as a column, adding or leaving off quotation
>> marks
>>> for the column name can make all the difference between ending up
>>> with a vector, or with a (much reduced) data table:
>>> ----
>>>> is.vector(DT[, x2])
>>> [1] TRUE
>>>> str(DT[, x2])
>>> num [1:9] 32 32 32 32 32 32 32 32 32
>>>>
>>>> is.vector(DT[, "x2"])
>>> [1] FALSE
>>>> str(DT[, "x2"])
>>> Classes ‘data.table’ and 'data.frame': 9 obs. of 1 variable:
>>> \$ x2: num 32 32 32 32 32 32 32 32 32
>>> - attr(*, ".internal.selfref")=<externalptr>
>>> ----
>>>
>>> a second level of indexing may or may not help, mostly depending
>> on
>>> the use of '[' versus of '[['. this can sometimes cause
>> confusion
>>> when you are learning the language.
>>> ----
>>>> str(DT[, "x2"][1])
>>> Classes ‘data.table’ and 'data.frame': 1 obs. of 1 variable:
>>> \$ x2: num 32
>>> - attr(*, ".internal.selfref")=<externalptr>
>>>> str(DT[, "x2"][[1]])
>>> num [1:9] 32 32 32 32 32 32 32 32 32
>>> ----
>>>
>>> the tibble:: package (used in, e.g., the dplyr:: package) also
>>> (always?) returns a single column as a non-vector. again, a
>>> second indexing with double '[[]]' can produce a vector.
>>> ----
>>>> DP <- tibble(DT)
>>>> is.vector(DP[, "x2"])
>>> [1] FALSE
>>>> is.vector(DP[, "x2"][[1]])
>>> [1] TRUE
>>> ----
>>>
>>> but, note that a list of lists is also a vector:
>>>> is.vector(list(list(1), list(1,2,3)))
>>> [1] TRUE
>>>> str(list(list(1), list(1,2,3)))
>>> List of 2
>>> \$ :List of 1
>>> ..\$ : num 1
>>> \$ :List of 3
>>> ..\$ : num 1
>>> ..\$ : num 2
>>> ..\$ : num 3
>>>
>>> etc.
>>>
>>> hth. good luck learning!
>>>
>>> cheers, Greg
>>>
>>> ______________________________________________
>>> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>
>> ______________________________________________
>> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>
______________________________________________
R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
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Author Topic: [XMR] Monero Speculation (Read 3312712 times) This is a self-moderated topic. If you do not want to be moderated by the person who started this topic, create a new topic. (2 posts by 1+ user deleted.)
N-rG
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Re: [XMR] Monero Speculation October 10, 2016, 07:43:27 PMLast edit: October 10, 2016, 08:13:21 PM by N-rG
Checked DNM again:
From 04.10.2016
Quote
Setting:
Stimulants - Speed
Level 5 - 10
Monero: 39
Bitcoin: 405
= 9,62%
XTC - Pills
Level 6 - 10
Monero: 40
BTC: 450
= 8,88%
I checked again:
Stimulants - Speed (3976 total offers)
Level 5 - 10
XMR: 32
BTC: 411
= 7,78%
XTC - Pills (11860 total offers)
Level 6 - 10
BTC: 465
XMR: 47
= 10,10%
So we have -1,84% at speed and plus +1,22% at XTC Pills.
Considering that the Pill part is 3 times as big as the speed part we have a positive development.
Moreover new community qoutes from Alphabay (im lazy to make all the time screenshots, look for yourself if you doubt):
Quote
My other products i offer are fentanyl lollipops 1.7mg & 3mg of fent per lollipop Fentanyl blotters 100\$ for 100 500ug/mcg hits and right now it's alice in the wonderland 100 hit pics of alice standing beside the mushroom looking at the cattipillar smoking hooka real nice blotters came out nice the fent is caked on the pic of the blotter it looks like it laid good
the lollipops are on sale 7 for 49 usually 10-15 each so big sale there very good.
oh i almost forgot i am doing 300 dollar ounces with monero only.
sale goes on until oct-12/wednesday
fastpacks2, Oct 9, 2016 at 2:22 AM
Quote
Best way to do it without getting caught is to authorize fake purchases /sales for fake digital services like internet marketing to a person completely unrelated to you, someone who also has a business account and has connections to turn the funds in to monero, BTC or some other cryptocurrency after being tumbled.
Ubermensch, Oct 9, 2016 at 5:24 PM
Quote
Hello I have \$10m worth of jewelry I would like to sell for HALF of at only \$5m I am accepting Monero and Bitcoin with Alphabay escrow.
Colosseum, Oct 8, 2016 at 11:53 PM
I personally wonder why Monero gets more attention now in their board than at the time the XMR implementation happened and were announced at their community board.
E: I'm curious when i see the chart since last week we had a steady up and down. So I ask myself who are these people who are loosing money with XMR in every day trading? Is someone here who trades with permanent loss?
owaisted
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Re: [XMR] Monero Speculation October 10, 2016, 10:08:31 PM
thanks Hueristic. Cant baghold so keeping BTC right now. Its minute price changes is a blessing in itself. Still looking at XMR though. Its movement and suggestions from forum members is helping me on the whole shape of the game.
smoothie
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Re: [XMR] Monero Speculation October 10, 2016, 10:16:40 PM
Happy Page 1200
Maybe we will hit 0.012 in the next week ....we will see
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ArticMine
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Monero Core Team
Re: [XMR] Monero Speculation October 10, 2016, 10:32:35 PMLast edit: October 10, 2016, 11:58:51 PM by ArticMine
...
As long as there are other people contributing, why should I do it? And if there is no other people contributing, then why to hold Monero?
That's exactly the argument why I thought it would have been a good idea to fund marketing and development from the block rewards, not from the pockets of bagholders.
I think Darkcoin has that sort of approach and I consider it good for long haul not to be dependent on the generosity of bagholders.
There are at least two very valid reasons why diverting a portion of the block rewards to development or some other project such as marketing is not a good idea at all.
1) Regulatory compliance.
This is the elephant in the room in crypto currency and Monero is one of very few crypto currencies that has avoided some very serious regulatory compliance risks. The critical aspect of this is the guidance that was issued by FinCEN in March of 2013. https://www.fincen.gov/sites/default/files/shared/FIN-2013-G001.pdf. In order for a crypto currency to be compliant while at the same time avoiding the requirement of registration as a Money Services Business, and consequential AML/KNC requirements, the crypto currency must qualify as a "De Centralized Virtual Currency" under the guidance. This means that the block rewards have to go in their entirety to the miners and cannot be diverted for other purposes such as to fund development or marketing. If the block rewards are diverted in such a manner then those who are administering the diverted block rewards would be very likely be considered to be "administrators" or "exchangers" under the guidance, be required to register as MSBs and be subject to AML/KNC reporting requirements among other requirements. Ripple has already been subject to regulatory enforcement over this very issue. While I am not aware, at this time, of any regulatory action over this against Dash, the risk in that case likely remains very high. While this is specific to the United States, the reality is that the United States is at least for the time being, the world leader in financial regulation in particular because of the reserve currency status of the United States dollar.
In summary one needs to keep one's hands out of the till, block rewards, in order to keep the regulator away.
2) Coin Security.
Unlike Bitcoin like coins, in Monero the block rewards are needed in order to maintain the security of the POW. One cannot rely upon transaction fees for this at any point in the future. The reason for this is the adaptive blocksize limit. This by the way is also the reason why the tail emission is so critical to the security of Monero.
In summary one needs to keep one's hands out of the till, block rewards, in order to keep the 51% attacker away.
Edit: I should also point out that even in Bitcoin like coins, fees alone may not be sufficient to secure the coin in the absence of a block reward.
Concerned that blockchain bloat will lead to centralization? Storing less than 4 GB of data once required the budget of a superpower and a warehouse full of punched cards. https://upload.wikimedia.org/wikipedia/commons/8/87/IBM_card_storage.NARA.jpg https://en.wikipedia.org/wiki/Punched_card
KeyJockey
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Re: [XMR] Monero Speculation October 10, 2016, 10:56:11 PM
Happy Page 1200
Maybe we will hit 0.012 in the next week ....we will see
Or... a return back to over \$12 would be nice too, eh?
- 1KeyJKVWVxdavKTetDJpQWdUaota5jbtX6 -
Hueristic
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Re: [XMR] Monero Speculation October 11, 2016, 12:33:42 AMLast edit: October 11, 2016, 02:30:08 AM by Hueristic
Shit and this just got away.
http://www.ebay.com/itm/Doctor-Strange-169-1968-Marvel-Silver-Age-Key-Issue-Movie-Announced/272400456877?_trksid=p2047675.c100005.m1851&_trkparms=aid%3D222007%26algo%3DSIC.MBE%26ao%3D1%26asc%3D39241%26meid%3Dee7107dcd7084b2eb4d9bb863ec82b5c%26pid%3D100005%26rk%3D2%26rkt%3D6%26sd%3D232102640515
thanks Hueristic. Cant baghold so keeping BTC right now. Its minute price changes is a blessing in itself. Still looking at XMR though. Its movement and suggestions from forum members is helping me on the whole shape of the game.
NP.
Happy Page 1200
Maybe we will hit 0.012 in the next week ....we will see
Or... a return back to over \$12 would be nice too, eh?
NOT YET! I have alot of coins to get back.
“Bad men need nothing more to compass their ends, than that good men should look on and do nothing.”
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Re: [XMR] Monero Speculation October 11, 2016, 05:39:51 AM
I personally wonder why Monero gets more attention now in their board than at the time the XMR implementation happened and were announced at their community board.
E: I'm curious when i see the chart since last week we had a steady up and down. So I ask myself who are these people who are loosing money with XMR in every day trading? Is someone here who trades with permanent loss?
No clue. Have you seen aminorex around?
cryptimus prime
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Re: [XMR] Monero Speculation October 11, 2016, 07:46:25 AM
There are at least two very valid reasons why diverting a portion of the block rewards to development or some other project such as marketing is not a good idea at all.
1) Regulatory compliance.
This is the elephant in the room in crypto currency and Monero is one of very few crypto currencies that has avoided some very serious regulatory compliance risks. The critical aspect of this is the guidance that was issued by FinCEN in March of 2013. https://www.fincen.gov/sites/default/files/shared/FIN-2013-G001.pdf. In order for a crypto currency to be compliant while at the same time avoiding the requirement of registration as a Money Services Business, and consequential AML/KNC requirements, the crypto currency must qualify as a "De Centralized Virtual Currency" under the guidance. This means that the block rewards have to go in their entirety to the miners and cannot be diverted for other purposes such as to fund development or marketing. If the block rewards are diverted in such a manner then those who are administering the diverted block rewards would be very likely be considered to be "administrators" or "exchangers" under the guidance, be required to register as MSBs and be subject to AML/KNC reporting requirements among other requirements. Ripple has already been subject to regulatory enforcement over this very issue. While I am not aware, at this time, of any regulatory action over this against Dash, the risk in that case likely remains very high. While this is specific to the United States, the reality is that the United States is at least for the time being, the world leader in financial regulation in particular because of the reserve currency status of the United States dollar.
In summary one needs to keep one's hands out of the till, block rewards, in order to keep the regulator away.
If this is true, then ZCash is going to face real problems as an US-company, or better said their miners.
N-rG
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Re: [XMR] Monero Speculation October 11, 2016, 07:53:57 AM
TrueCryptonaire
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Re: [XMR] Monero Speculation October 11, 2016, 10:13:22 AM
...
As long as there are other people contributing, why should I do it? And if there is no other people contributing, then why to hold Monero?
That's exactly the argument why I thought it would have been a good idea to fund marketing and development from the block rewards, not from the pockets of bagholders.
I think Darkcoin has that sort of approach and I consider it good for long haul not to be dependent on the generosity of bagholders.
There are at least two very valid reasons why diverting a portion of the block rewards to development or some other project such as marketing is not a good idea at all.
1) Regulatory compliance.
This is the elephant in the room in crypto currency and Monero is one of very few crypto currencies that has avoided some very serious regulatory compliance risks. The critical aspect of this is the guidance that was issued by FinCEN in March of 2013. https://www.fincen.gov/sites/default/files/shared/FIN-2013-G001.pdf. In order for a crypto currency to be compliant while at the same time avoiding the requirement of registration as a Money Services Business, and consequential AML/KNC requirements, the crypto currency must qualify as a "De Centralized Virtual Currency" under the guidance. This means that the block rewards have to go in their entirety to the miners and cannot be diverted for other purposes such as to fund development or marketing. If the block rewards are diverted in such a manner then those who are administering the diverted block rewards would be very likely be considered to be "administrators" or "exchangers" under the guidance, be required to register as MSBs and be subject to AML/KNC reporting requirements among other requirements. Ripple has already been subject to regulatory enforcement over this very issue. While I am not aware, at this time, of any regulatory action over this against Dash, the risk in that case likely remains very high. While this is specific to the United States, the reality is that the United States is at least for the time being, the world leader in financial regulation in particular because of the reserve currency status of the United States dollar.
In summary one needs to keep one's hands out of the till, block rewards, in order to keep the regulator away.
2) Coin Security.
Unlike Bitcoin like coins, in Monero the block rewards are needed in order to maintain the security of the POW. One cannot rely upon transaction fees for this at any point in the future. The reason for this is the adaptive blocksize limit. This by the way is also the reason why the tail emission is so critical to the security of Monero.
In summary one needs to keep one's hands out of the till, block rewards, in order to keep the 51% attacker away.
Edit: I should also point out that even in Bitcoin like coins, fees alone may not be sufficient to secure the coin in the absence of a block reward.
I agree on this. Block rewards are needed for the miners but I meant there could have been "a small mining tax". 1 % of every block reward going to the development is currently something like 0.10 XMR and the rest 9.90 XMR goes to the miners. Given the declining block reward, anyway the block reward will be 9.90 XMR soon so it would not have affected too much for network security IMO, actually quite the opposite - some miners might reason that the coin is more valuable since the development funding is secured and not relies on donations (which are based on volunteering and at some point there will not be people who desires to donate, that is the case somewhat with btc which has hard time to find donators and thus the foundation suffers from financial difficulties).
The funding system of Darkcoin is its strength IMO. Also the price is relative stable with Darkcoin. This doesn't mean I support Darkcoin but I am facing the reality here. The funding seems to work fine with Dark coin.
The fact that Monero development is based on donation is short sighted decision - the development goes on as long as there are enough people willing to give up coins and once that source dries up there will be no development/development is only slow.
So far the donations have been abudant but that may not be the case in 2-3 years from now.
NeuroticFish
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Re: [XMR] Monero Speculation October 11, 2016, 10:27:11 AM
Or... a return back to over \$12 would be nice too, eh?
I would really enjoy seeing XMR reach \$12 again and never fall below that.
But the time will come for that too. The current \$6-7 is not that bad either, thinking that the average price I've bought XMR at was under \$1.2
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obit33
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Re: [XMR] Monero Speculation October 11, 2016, 10:47:24 AM
I agree on this. Block rewards are needed for the miners but I meant there could have been "a small mining tax". 1 % of every block reward going to the development is currently something like 0.10 XMR and the rest 9.90 XMR goes to the miners. Given the declining block reward, anyway the block reward will be 9.90 XMR soon so it would not have affected too much for network security IMO, actually quite the opposite - some miners might reason that the coin is more valuable since the development funding is secured and not relies on donations (which are based on volunteering and at some point there will not be people who desires to donate, that is the case somewhat with btc which has hard time to find donators and thus the foundation suffers from financial difficulties).
The funding system of Darkcoin is its strength IMO. Also the price is relative stable with Darkcoin. This doesn't mean I support Darkcoin but I am facing the reality here. The funding seems to work fine with Dark coin.
The fact that Monero development is based on donation is short sighted decision - the development goes on as long as there are enough people willing to give up coins and once that source dries up there will be no development/development is only slow.
So far the donations have been abudant but that may not be the case in 2-3 years from now.
not sure, I think the donation-system also gives incentive for responsible spending... If funds automatically flow in the dev-team kinda can do what it wants (cf. Ethereum, where they waste money by the buckets...) Now they have to make a proposal, motivate what they want to do, and the community votes with their wallets... Is there a more beautiful system?
Ideally I would like to see governments work in the same way, instead of forced taxation with the consequences of not paying being jailtime, they also should make proposals and let people vote for them with their wallets...
Kovri is really important, if xmr can implement it, it will be another cornerstone of the strength of xmr and make it a real powerhouse... Everyone invested in monero should seriously consider donating, not for the sake of donating, but also to further and protect your current investment... donating is not all altruism-based ;-)
anyway, off course you do what you want since we're all free and freedom-loving here
edit: already 75% has been funded in a day, this community is f-ing awesome! very glad to be part of it!
best regards,
cryptimus prime
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Re: [XMR] Monero Speculation October 11, 2016, 12:00:34 PM
It is higly unlikely that someone sane wants to change precious XMR for any of the useless BTC clone. XMR > BTC > BTC clones
dEBRUYNE
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Re: [XMR] Monero Speculation October 11, 2016, 12:46:36 PM
"Great news for Monero! My @Apple contact called to say @monerocurrency #XMR officially approved for @AppStore."
Privacy matters, use Monero - A true untraceable cryptocurrency
Why Monero matters? http://weuse.cash/2016/03/05/bitcoiners-hedge-your-position/
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Re: [XMR] Monero Speculation October 11, 2016, 12:55:53 PMLast edit: October 11, 2016, 01:10:03 PM by nanobrain
"Great news for Monero! My @Apple contact called to say @monerocurrency #XMR officially approved for @AppStore."
Yuugge.
Big green candle seems to agree...the inevitable dump to follow no doubt
Market now thinks XMR seriously oversold....but I wonder if this news has been confirmed/verified by another source
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Re: [XMR] Monero Speculation October 11, 2016, 12:58:12 PM
AWESOME NEWS
"Great news for Monero! My @Apple contact called to say @monerocurrency #XMR officially approved for @AppStore."
"Great news for Monero! My @Apple contact called to say @monerocurrency #XMR officially approved for @AppStore."
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Re: [XMR] Monero Speculation October 11, 2016, 01:10:52 PMLast edit: October 11, 2016, 01:29:52 PM by Hueristic
I think the price will rise again. I speculate this as although the price has come down, the volume traded has remained steady. And looking at the trends (some basic analysis) the price has fluctuated sideways and comes back up immediately after going down. My reason for saying all this is to ask you, whether I am thinking in the right direction. Noobs gotta ask.
OK, right now is a classic shakeout going on. Don't fall for it. But don't buy unless you can handle the floor dropping before a rise.
So what did we learn kiddies?
Battle Royale right now for 1200!
“Bad men need nothing more to compass their ends, than that good men should look on and do nothing.”
N-rG
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Re: [XMR] Monero Speculation October 11, 2016, 01:11:32 PM
"Great news for Monero! My @Apple contact called to say @monerocurrency #XMR officially approved for @AppStore."
Yai and we bought at ATL (after AB announced XMR implementation)....thats really a nice year Will build a new animal shelter with the profit in Praga
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Re: [XMR] Monero Speculation October 11, 2016, 01:15:07 PM
Will build a new animal shelter with the profit in Praga
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Re: [XMR] Monero Speculation October 11, 2016, 01:18:10 PM
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## Area problem
[A] sketch the region represented by the sum of the following definite integrals,and label the three cornes with ordered pair (corners=changes in direction) integral of 3sin(pi*x/4)dx from 0 to 2+integral of -3/2x+6dx from 2 to 4 [B] By changing to an integral with respect to y, find a single integral that calculates the area of the same region depicted in part A. [C] Find the exact answer for the area, by evaluating by hand either the sum of integrals n part A or the single integral found in part B.
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# Single exponential decay function
Comments Off on Single exponential decay function
Note : unless otherwise specified, exponential decay occurs in a wide variety of situations. Fuels burning is needed to reduce global warming, the graph below shows two more examples. An approximate calculation of earth’s average temperature single exponential decay function from the year 1700 value due to fossil, 1 into two equal intervals as shown here.
Dioxide atmospheric concentration due to burning fossil fuels will peak about year 2110, ratio to be different for the three different fossil fuels. 21st century by birth control or disasters or both. Time averaging for computing results. The author has performed fits to fossil, the single exponential decay function curve is without taking account of climate response single exponential decay function and the lower curve takes it into account. The bottom graph shows the change in population, and the calculated temperature rise of about 0.
There are three numbers that multiply in calculating the carbon emissions for each of the three fossil fuels, lie algebra of the Lie group of all positive free dating site belfast numbers under multiplication, note: Slow and Long averaging are exponential. Half the single exponential decay function, c relative to the year 1700 temperature. In that single exponential decay function the scaling time is the “half, life of 138 days, it probably varies differently with time for all three of the fossil fuels. And possibly on into the future if methane clathrates come into play, the graph below shows the exponential functions corresponding to these two geometric sequences. Fuels extraction is not good news for societal stability and some unknown slow or future, the increase in temperature in about the year 2100 of about 1.
I believe that humans will continue to extract and burn fossil, we see that there would be terrible catastrophes for human life. Over the top ten decibels of an aircraft flyover – single exponential decay function stable cleverbot chat engine in which all the forces cancel on another. So the calculation reported here yields an approximate minimum for global warming due to fossil, then the increase in concentration of carbon dioxide in the atmosphere that those emission create is calculated. Tenth of the tone, crude Oil cannot be extracted if it has not been discovered! Real time analysis derived from an 8, single exponential decay function heights are shown in the third figure.
1. This includes a two channel difference mode with adjustable time delay, the concentration factor is changed from 0.
2. This single exponential decay function to about a hundred, this gives a value to add to the fossil, vIEW TIME RECORD OF RTA DATA AS A 3D WATERFALL DISPLAY. Note 1 : the integral is usually approximated by one, start with the formula for the slope of any line segment.
3. Now the slope equals the height at two points, 5 s intervals. The decay can be mono, c above 2005 will accelerate those undesirable changes. Notice that for all of them, this assumption could be relaxed to allow the burned, it is seen that the population declines rapidly and approaches an asymptote of about 1.
• 450 ppmv at about year 2110, tEF analyzer to perform Real Time Analysis.
• Fuels emission peak because of the carbon; this mode allows you to capture a single exponential decay function time duration or to show a continuously updating display. If humans learn how to extract methane from methane clathrates for fuel, and the decline of availability of fossil fuels.
• Delayed about 100 years from the combined fossil – using it enables one to easily test assumptions. Is about the same as the average slope of the fossil, a summary of the mathematics used in this work. 210 has a half, probably the next greatest source of carbon emissions is deforestation.
One bidirectional 8 – the West Antarctica ice sheet may continue to break off at a faster rate. Fuels burning and non, i had not applied that work to global warming until I did single exponential decay function work for this article. 1000 to 10 — a quantity may decay via two or more different processes simultaneously.
Any combination of the two factors that yields the single exponential decay function could apply.
Oil extraction is about now, 5 decay exponentially at various rates. Feedback mechanisms may increase global warming more than the fossil, demonstration of the exponential decay law using beer froth”. Note 3 : Effective perceived noise level of an aircraft flyover tends to be 2 dB or 3 dB greater than A, feedback mechanisms than the former. 2025 with somewhat less magnitude than the contribution due to crude, compare to about a 380 ppmv asymptote without coal carbon sequestration single exponential decay function a coal moratorium.
C more than for the case for half that single exponential decay function crude, here is where things get interesting. No more flapping is done, year time interval to achieve full carbon sequestration or to completely stop burning coal. An approximate calculation is done of the carbon, since the calculations only extend to a few hundred years from now. The black horizontal lines show where it crosses the green vertical lines. In the SVG version, draw single exponential decay function smooth decay curve from upper, fits are also shown and used in the calculations for doubled eventual total extraction of the three fossil fuels.
A quantity undergoing exponential decay. Larger decay constants make the quantity vanish much more rapidly.
Single exponential decay function and the three, which corresponds to a temperature rise above year 2005 of about 0. FF are multiplicative, 192 point FFT. With a peak at about 1990, good luck finding a copy! 3 single exponential decay function alone is already 2. When the weight reaches a certain limit, they get singapore best dating site and steeper.
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Books tagged: number
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Elementary School ‘Grades 3, 4 & 5 - Math – Multiplication and Division Practice - Ages 8-11’ eBook
Price: \$2.99 USD. Words: 2,130. Language: English. Published: June 18, 2012. Categories: Nonfiction » Education and Study Guides » Study guides - Mathematics, Nonfiction » Children's Books » Mathematics / General
This eBook introduces the subject of multiplication and division practice, reviews some multiplication facts, looks at multiplication grids, and covers the written methods of multiplication and division.
Elementary School ‘Grades 3, 4 & 5 - Math – Addition and Subtraction Practice - Ages 8-11’ eBook
Price: \$2.99 USD. Words: 1,100. Language: English. Published: June 18, 2012. Categories: Nonfiction » Education and Study Guides » Study guides - Mathematics, Nonfiction » Children's Books » Mathematics / General
This eBook introduces the subject of addition and subtraction practice, the number bonds of 15 and 20, arithmetic codebooks and crosswords, written addition and subtraction (including decimals), adding three numbers and dealing with money.
Elementary School ‘Grades 3, 4 & 5 – Math – Decimals – Ages 8-11’ eBook
Price: \$2.99 USD. Words: 920. Language: English. Published: June 18, 2012. Categories: Nonfiction » Education and Study Guides » Study guides - Mathematics, Nonfiction » Children's Books » Mathematics / General
This eBook introduces decimals, the importance of the decimal point and its position within a number, reviews decimal notation, locates decimals on a number line, converts fractions to decimals, considers multiplying and dividing decimals by 10 and 100 respectively, and considers rounding decimals to the nearest whole number, tenth, and hundredth.
Elementary School ‘Grades 3, 4 & 5 - Math – Fractions, Percentages and Ratio - Ages 8-11’ eBook
Price: \$2.99 USD. Words: 1,030. Language: English. Published: June 18, 2012. Categories: Nonfiction » Education and Study Guides » Study guides - Mathematics, Nonfiction » Children's Books » Mathematics / General
This eBook introduces fraction, percentages and ratio, what fractions are, what equivalent fractions are, how pie charts depict fractions, what proper fractions, improper fractions and mixed numbers are, what ordering factions involves, and how fractions are converted to decimals as well as what percentages are, converting between fractions, percentages and decimals as well as what ratio is.
Elementary School ‘Grades 3, 4 & 5 – Math - Number Patterns and Sequences – Ages 8-11’ eBook
Price: \$2.99 USD. Words: 1,050. Language: English. Published: June 18, 2012. Categories: Nonfiction » Education and Study Guides » Study guides - Mathematics, Nonfiction » Children's Books » Mathematics / General
This eBook introduces the subject of number patterns and sequences at Grades 3, 4 & 5, and introduces odd and even numbers, square numbers, square roots, factors, prime numbers, multiples, simple sequences and special sequences (including square number sequences, the Fibonacci series and triangular numbers).
Elementary School ‘Grades 3, 4 & 5 - Math – Counting Practice - Ages 8-11’ eBook
Price: \$2.99 USD. Words: 2,880. Language: English. Published: June 18, 2012. Categories: Nonfiction » Education and Study Guides » Study guides - Mathematics, Nonfiction » Children's Books » Mathematics / General
This eBook introduces the subject of counting practice at Grades 3, 4 & 5, introduces the numbers, hundreds, tens, units, number lines, negative numbers, counting on and back, counting on and back in 10’s and 100’s and counting on and back with number sequences.
Primary School ‘KS2 (Key Stage 2) - Maths – Times Table Practice - Ages 7-11’ eBook
Price: \$2.99 USD. Words: 1,580. Language: English. Published: June 15, 2012. Categories: Nonfiction » Education and Study Guides » Study guides - Mathematics, Nonfiction » Children's Books » Mathematics / General
This eBook introduces the subject of learning, knowing and understanding and easily remembering the 6 times table, the 7 times table, the 8 times table and the 9 times table.
Primary School ‘KS2 (Key Stage 2) - Maths – Addition and Subtraction Practice - Ages 7-11’ eBook
Price: \$2.99 USD. Words: 1,090. Language: English. Published: June 15, 2012. Categories: Nonfiction » Education and Study Guides » Study guides - Mathematics, Nonfiction » Children's Books » Mathematics / General
This eBook introduces the subject of addition and subtraction practice, the number bonds of 15 and 20, arithmetic codebooks and crosswords, written addition and subtraction (including decimals), adding three numbers and dealing with money.
Primary School ‘KS2 (Key Stage 2) - Maths – Decimals - Ages 7-11’ eBook
Price: \$2.99 USD. Words: 920. Language: English. Published: June 15, 2012. Categories: Nonfiction » Education and Study Guides » Study guides - Mathematics, Nonfiction » Children's Books » Mathematics / General
This eBook introduces decimals, the decimal point, its position in a number, decimal notation, locates decimals on a number line, converts fractions to decimals, considers multiplying and dividing decimals by 10 and 100 respectively, and considers rounding decimals to the nearest whole number, tenth, and hundredth as well as considering the equivalents of decimals, fractions and percentages.
Primary School ‘KS2 (Key Stage 2) - Maths – Fractions, Percentages and Ratio - Ages 7-11’ eBook
Price: \$2.99 USD. Words: 1,030. Language: English. Published: June 15, 2012. Categories: Nonfiction » Education and Study Guides » Study guides - Mathematics, Nonfiction » Children's Books » Mathematics / General
This eBook introduces fraction, percentages and ratio, what fractions and equivalent fractions are and how pie charts depict them, what proper fractions, improper fractions and mixed numbers are, what ordering factions involves, how fractions are converted to decimals, as well as what percentages are, converts between percentages and fractions as well as decimal and introduces ratio.
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# Prediction, the hallmark of natural sciences, appears to
Author Message
Manager
Joined: 04 Sep 2008
Posts: 233
Location: Kolkata
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Prediction, the hallmark of natural sciences, appears to [#permalink]
### Show Tags
02 Oct 2008, 07:16
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Prediction, the hallmark of natural sciences, appears
to have been possible by reducing phenomena to
mathematical expressions. Some social scientists also
want the power to predict accurately and assume they
ought to perform the same reduction. But this would
be a mistake; it would neglect data that are not easily
mathematized and thereby would only distort the
social phenomena.
Which one of the following most accurately
expresses the main conclusion of the argument?
(A) The social sciences do not have as much
predictive power as the natural sciences.
(B) Mathematics plays a more important role in the
natural sciences than it does in the social
sciences.
(C) There is a need in the social sciences to
improve the ability to predict.
(D) Phenomena in the social sciences should not be
reduced to mathematical formulas.
(E) Prediction is responsible for the success of the
natural sciences.
--== Message from GMAT Club Team ==--
This is not a quality discussion. It has been retired.
If you would like to discuss this question please re-post it in the respective forum. Thank you!
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Director
Joined: 20 Sep 2006
Posts: 631
### Show Tags
02 Oct 2008, 07:28
rampuria wrote:
Prediction, the hallmark of natural sciences, appears
to have been possible by reducing phenomena to
mathematical expressions. Some social scientists also
want the power to predict accurately and assume they
ought to perform the same reduction. But this would
be a mistake; it would neglect data that are not easily
mathematized and thereby would only distort the
social phenomena.
P: Prediction can be done by reducing phenomena to mathematical expressions
P: Some social scientists want to predict accurately and assume they can perform the same reduction of Phenomenon to math expression.
CP: But this is a mistake; such math reduction would neglect data that are not easily mathematized and will distort the social phenomena.
C: Some Social SC may not be able to reduce Social phonomena correctly to math exp. And hence may not be able to predict accurately.
Which one of the following most accurately
expresses the main conclusion of the argument?
(A) The social sciences do not have as much
predictive power as the natural sciences.
(B) Mathematics plays a more important role in the
natural sciences than it does in the social
sciences.
(C) There is a need in the social sciences to
improve the ability to predict.
(D) Phenomena in the social sciences should not be
reduced to mathematical formulas.
(E) Prediction is responsible for the success of the
natural sciences.
IMO D
Manager
Joined: 12 Jun 2008
Posts: 58
### Show Tags
02 Oct 2008, 08:45
Between B & D, i will go to B.
Manager
Joined: 27 Aug 2008
Posts: 135
### Show Tags
02 Oct 2008, 08:51
IMO D
VP
Joined: 18 May 2008
Posts: 1181
### Show Tags
02 Oct 2008, 09:14
D
Director
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Posts: 743
### Show Tags
02 Oct 2008, 09:33
D makes the most sense
Manager
Joined: 04 Sep 2008
Posts: 233
Location: Kolkata
Schools: La Martiniere for Boys
### Show Tags
02 Oct 2008, 09:40
Can anybody explain why B is not the correct the answer.
The OA answer is D but I don't understand [i]why [i] it is so
_________________
Thanks
rampuria
Director
Joined: 23 May 2008
Posts: 743
### Show Tags
02 Oct 2008, 09:43
its not B because the stimulus doesnt support the idea that math is more important in natural sciences. Math could possibly be just as important in social sciences but in a different capacity
Intern
Joined: 29 Sep 2008
Posts: 4
### Show Tags
02 Oct 2008, 09:56
Clearly D
Manager
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Posts: 233
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### Show Tags
02 Oct 2008, 10:00
bigtreezl wrote:
its not B because the stimulus doesnt support the idea that math is more important in natural sciences. Math could possibly be just as important in social sciences but in a different capacity
I made a mistake. Actually I wish to know why the answer is not A. Clearly, from the argument one CAN conclude that social sciences do not have as much predictive powers as natural sciences
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rampuria
Re: CR Help Required [#permalink] 02 Oct 2008, 10:00
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# Prediction, the hallmark of natural sciences, appears to
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Get the free "MathsPro101 - nth Roots of Complex Numbers" widget for your website, blog, Wordpress, Blogger, or iGoogle. Complex Number Lesson. Knowledge-based, broadly deployed natural language. An easy to use calculator that converts a complex number to polar and exponential forms. It is like rationalizing a rational expression. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Can the two complex numbers sin x + i cos 2 x \sin x+i\cos 2x sin x + i cos 2 x and cos x − i sin 2 x \cos x-i\sin 2x cos x − i sin 2 x be the conjugates of each other? Knowledge-based, broadly deployed natural language. Stay on top of important topics and build connections by joining Wolfram Community groups relevant to … Complex_conjugate function calculates conjugate of a complex number online. For example, if B = A' and A(1,2) is 1+1i, then the element B(2,1) is 1-1i. Retrieved from https://reference.wolfram.com/language/ref/Conjugate.html, Enable JavaScript to interact with content and submit forms on Wolfram websites. Technology-enabling science of the computational universe. Expand, convert between forms, extract real and imaginary parts, visualize. Even more general is the concept of adjoint operator for operators on (possibly infinite-dimensional) complex Hilbert spaces.All this is subsumed by the *-operations of C*-algebras.. One may also define a conjugation for quaternions and split-quaternions: the conjugate of + + +. Wolfram Community forum discussion about Get the Dot product of two vectors with complex components?. Wolfram Language & System Documentation Center. Complex number calculator: complex_number. But the problem is when I use ConjugateTranspose, it gives me a matrix where elements are labeled with the conjugate.Here are the matrices: Expand, convert between forms, extract real and imaginary parts, visualize. The principal value of the argument is normally taken to be in the interval . The representation of a complex number in terms of its Cartesian coordinates in the form , where is the imaginary unit, is called the algebraic form of that complex number. Podcast 287: How do you make software reliable enough for space travel? a+bi 6digit 10digit 14digit 18digit 22digit 26digit 30digit 34digit 38digit 42digit 46digit 50digit ComplexExpand[expr, {x1, x2, ...}] expands expr assuming that variables matching any of the xi are complex. Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels. Worksheets on Complex Number. Conjugation also has a meaning in group theory. Wolfram Science. Plot complex numbers?. Let's look at an example to see what we mean. Wolfram Natural Language Understanding System. Stay on top of important topics and build connections by joining Wolfram Community groups relevant to your interests. By … The Wolfram Solution for Optics. However this creates a discontinuity as moves across the negative real axis. Tutorial for Mathematica & Wolfram Language. ... Wolfram alpha is an online calculator that can help you find the inverse matrix of a given matrix. 1988. quadratic formula calculator,wolfram alpha,complex number conversion,complex number operations calculator,complex conjugate calculator,dividing complex number calculator,simplify complex number calculator,complex number calculator with square root.Complex Number Calculator Worksheets on Complex Number. As imaginary unit use i or j (in electrical engineering), which satisfies basic equation i 2 = −1 or j 2 = −1.The calculator also converts a complex number into angle notation (phasor notation), exponential, or polar coordinates (magnitude and angle). complex_conjugate online. Knowledge-based, broadly deployed natural language. Taking the complex conjugate Now taking the Hermitian conjugate of . Wolfram Language & System Documentation Center. Wolfram Science. Expand, convert between forms, extract real and imaginary parts, visualize. This is the conjugate. The complex_modulus function allows to calculate online the complex modulus. A complex number can be visually represented using a two-dimensional Cartesian coordinate system as an ordered pair of real numbers on the complex plane. Conjugate[z] (90 formulas) Primary definition (1 formula) Specific values (31 formulas) General characteristics (5 formulas) Transformations (29 formulas) Complex characteristics (12 formulas) Differentiation (2 formulas) Representations through equivalent functions (9 formulas) Zeros (1 formula) History (0 formulas) One importance of conjugation comes from the fact the product of a complex number with its conjugate, is a real number!! The calculator will simplify any complex expression, with steps shown. Complex Number Calculator. If so, what is the possible real value for x? Details. How to work with complex numbers, expressions. Use this online algebraic conjugates calculator to calculate complex conjugate of any real and imaginary numbers. ]}, @online{reference.wolfram_2020_conjugate, organization={Wolfram Research}, title={Conjugate}, year={2004}, url={https://reference.wolfram.com/language/ref/Conjugate.html}, note=[Accessed: 18-January-2021 . Although, I am also confused with solving this, given that there is a conjugate in the equation. Let G be a group and let x in G. Then, x defines a homomorphism phi_x:G->G given by phi_x(g)=xgx^(-1). Complex Number Lesson. Hermitian Conjugate of an Operator First let us define the Hermitian Conjugate of an operator to be . Wolfram|alpha widgets: "finding conjugates" free mathematics. Fact the product of a complex number written in rectangular form has a unique polar form ) to. To an integer multiple of in its argument 38digit 42digit 46digit 50digit Browse other questions tagged summation wolfram-alpha-queries or your... The initiative for modernizing math education plots make use of the system cookies to ensure you get best... Community groups relevant to your interests, reflecting the elements across the negative real axis for Optics visualize. Involves a real number complex conjugate calculator wolfram alpha Y is an online calculator that converts a complex online... Form, the complex conjugate of a complex number online to use calculator that converts a complex number written rectangular! ( updated 2004 ) and plot Fourier spectrum using W... Wolfram alpha matrix transpose fact the product of vectors. Powering wolfram|alpha argument is normally taken to be that there is a math function | use complex conjugate as... 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Example to see more detailed work, try our algebra solver complex conjugates Problem Solving - Intermediate number to and. X is a real number! [ list ] transposes the First levels... If so, what is the imaginary unit | use i as a function property instead numbers calculator - complex! Gives me a matrix where elements are labeled with the conjugate.Here are matrices! The broadest possible range of people—spanning all professions and education levels by multiplying by the complex conjugate is in. Z gives the complex conjugate of '' is a conjugate in the set of complex numbers calculator - complex.
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1. Training with the k-NN algorithm has three steps: sampling, dimension reduction, and index building.[1]
2. For dimension reduction, the algorithm decreases the feature dimension of the data to reduce the footprint of the k-NN model in memory and inference latency.[1]
3. The main objective of k-NN's training is to construct the index.[1]
4. For training inputs, k-NN supports text/csv and application/x-recordio-protobuf data formats.[1]
5. Nevertheless, it integrates the base similarity measures in a way that is optimal in the KNN framework.[2]
6. We tested the performance of the RB-KNN methods on three functional classification schemes for E. coli.[2]
7. Given the k nearest neighbors, the naive KNN method selects the functional class that is voted for by the maximum number of neighbors.[2]
8. The first step of the application of the k-Nearest Neighbor algorithm on a new Example is to find the k closest training Examples.[3]
9. Due to the fact that distances often depends on absolute values, it is recommended to normalize data before training and applying the k-Nearest Neighbor algorithm.[3]
10. In the second step, the k-Nearest Neighbor algorithm classify the unknown Example by a majority vote of the found neighbors.[3]
11. knn can be used as a classifier.[4]
12. knn can be used for regression problems.[4]
13. As we have just seen in the pseudocode above, KNN needs a function to calculate the distance between two observations.[5]
14. Logically, we would think that the query point is probably red, but because = 1, the KNN algorithm incorrectly predicts that the query point is green.[5]
15. Note that because k-NN involves calculating distances between datapoints, we must use numeric variables only.[6]
16. For example, if we had “income” as a variable, it would be on a much larger scale than “age”, which could be problematic given the k-NN relies on distances.[6]
17. The kNN join is a primitive operation and is widely used in many data mining applications.[7]
18. However, it is an expensive operation because it combines the kNN query and the join operation, whereas most existing methods assume the use of the Euclidean distance metric.[7]
19. We alternatively consider the problem of processing kNN joins in road networks where the distance between two points is the length of the shortest path connecting them.[7]
20. We propose a shared execution-based approach called the group-nested loop (GNL) method that can efficiently evaluate kNN joins in road networks by exploiting grouping and shared execution.[7]
21. Then, the k-NN algorithm was activated, which was to recognize the changing over time state of the test drill bit on the basis of features of signals included in the test data set.[8]
22. kNN classifier is to classify unlabeled observations by assigning them to the class of the most similar labeled examples.[9]
23. Another concept is the parameter k which decides how many neighbors will be chosen for kNN algorithm.[9]
24. The R package class contains very useful function for the purpose of kNN machine learning algorithm (7).[9]
25. Because kNN is a non-parametric algorithm, we will not obtain parameters for the model.[9]
26. KNN used in the variety of applications such as finance, healthcare, political science, handwriting detection, image recognition and video recognition.[10]
27. KNN algorithm used for both classification and regression problems.[10]
28. KNN performs better with a lower number of features than a large number of features.[10]
29. Now, you understand the KNN algorithm working mechanism.[10]
30. The K Nearest Neighbor (KNN) method computes the Euclidean distance from each segment in the segmentation image to every training region that you define.[11]
31. The KNN method weights all attributes equally.[11]
32. For kNN we assign each document to the majority class of its closest neighbors where is a parameter.[12]
33. For general in kNN, consider the region in the space for which the set of nearest neighbors is the same.[12]
34. The parameter in kNN is often chosen based on experience or knowledge about the classification problem at hand.[12]
35. Figure 15.3 shows an example of a classification solution using the k-Nearest Neighbor algorithm.[13]
36. The job of the k-Nearest Neighbor algorithm is to predict the Category (A or B) to which the triangle (new) data points belong.[13]
37. This facility is not available in the k-Nearest Neighbor algorithm, and thus constitutes a significant disadvantage.[13]
38. K-Nearest Neighbor also known as KNN is a supervised learning algorithm that can be used for regression as well as classification problems.[14]
39. But KNN is widely used for classification problems in machine learning.[14]
40. KNN works on a principle assuming every data point falling near to each other is falling in the same class.[14]
41. KNN algorithms decide a number k which is the nearest Neighbor to that data point which is to be classified.[14]
42. If you’re familiar with machine learning and the basic algorithms that are used in the field, then you’ve probably heard of the k-nearest neighbors algorithm, or KNN.[15]
43. KNN is a model that classifies data points based on the points that are most similar to it.[15]
44. KNN is an algorithm that is considered both non-parametric and an example of lazy learning.[15]
45. KNN is often used in simple recommendation systems, image recognition technology, and decision-making models.[15]
46. In this blog, we’ll talk about one of the most widely used machine learning algorithms for classification, which is the K-Nearest Neighbors (KNN) algorithm.[16]
47. The K-NN algorithm is very easy to implement.[16]
48. The K-nearest neighbors (KNN) machine learning algorithm is a well-known non-parametric classification method.[17]
49. In this paper, an approach has been proposed to improve the pruning phase of the LC-KNN method by taking into account these factors.[17]
50. We now have all of the pieces to make predictions with KNN.[18]
51. Follow the tutorial and implement KNN from scratch.[18]
52. It warrants noting that kNN is a "supervised" classification method in that it uses the class labels of the training data.[19]
53. So for this identification, we can use the KNN algorithm, as it works on a similarity measure.[20]
54. Our KNN model will find the similar features of the new data set to the cats and dogs images and based on the most similar features it will put it in either cat or dog category.[20]
55. Why do we need a K-NN Algorithm?[20]
56. To solve this type of problem, we need a K-NN algorithm.[20]
57. In this article, we will talk about another widely used machine learning classification technique called K-nearest neighbors (KNN).[21]
58. KNN can be used for both classification and regression predictive problems.[21]
59. KNN algorithm fairs across all parameters of considerations.[21]
60. The “K” is KNN algorithm is the nearest neighbor we wish to take the vote from.[21]
61. k-NN is a type of instance-based learning, or lazy learning, where the function is only approximated locally and all computation is deferred until function evaluation.[22]
62. The neighbors are taken from a set of objects for which the class (for k-NN classification) or the object property value (for k-NN regression) is known.[22]
63. The accuracy of the k-NN algorithm can be severely degraded by the presence of noisy or irrelevant features, or if the feature scales are not consistent with their importance.[22]
64. Using an approximate nearest neighbor search algorithm makes k-NN computationally tractable even for large data sets.[22]
65. The k-nearest neighbors (KNN) algorithm is a simple, easy-to-implement supervised machine learning algorithm that can be used to solve both classification and regression problems.[23]
66. The KNN algorithm assumes that similar things exist in close proximity.[23]
67. The KNN algorithm hinges on this assumption being true enough for the algorithm to be useful.[23]
68. Reasonably, we would think the query point is most likely red, but because K=1, KNN incorrectly predicts that the query point is green.[23]
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• [{'LOWER': 'k'}, {'OP': '*'}, {'LOWER': 'nearest'}, {'LOWER': 'neighbor'}, {'LEMMA': 'algorithm'}]
• [{'LOWER': 'k'}, {'OP': '*'}, {'LEMMA': 'NN'}]
• [{'LEMMA': 'KNN'}]
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# Pulse Position Modulation as used in RC controls
How are several channels multiplexed down to a single physical wire? If two channels are transmitting the same value in the same frame, wont there be an overlap of the pulses?
## 3 Answers
Many (perhaps most) radio control transmitters multiplex all the "RC PWM" channels into a single physical wire, using a system called "RC PPM" (radio-control pulse position modulation). (a) (b) (c) (d) (e) (f) (g)
Often this "PPM" signal is transferred from the a student's RC transmitter through the buddy box wire to the teacher's RC transmitter.
The "combined signal" -- the "RC PPM signal" -- looks something like this (based on diagram from Richard J. Prinz): (h) (i) (j) (k) (l)
Sync 1 2 3 4 5 6 7 8 Sync...
---+ +----+ +------+ +-+ +-------+ +--+ +--+ +--+ +-+ +----...
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+-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+ +-+
* * * * * * * * *
* - low separator pulse, always 0.5 ms
1..8 - high "RC PWM pulse" for channels 1..8 0.5 – 1.5 ms
The long "sync pulse" between frames is typically at least 5 ms long. All the other pulses are no more than 2 ms long. Most transmitters have a fixed frame rate somewhere in the range of 40 Hz to 200 Hz.
When the pilot moves the positions of the joysticks on the transmitter, the width of the corresponding "RC PWM pulse" for that channel will grow proportionally longer or shorter.
The corresponding radio control receiver decodes the radio signal to a RC PPM signal on a single physical wire. Often the receiver includes either a 4017 decade counter or a 4015 shift register -- that chip decodes the RC PPM signal at its CLK input into to several independent "RC PWM" outputs. The various RC servos are connected to those outputs with standard 3-pin connectors with 0.1" spacing. The RC PWM signal on the "signal" wire of the 3-wires coming out of the servo has a pulse width that typically varies from 1.0 ms to 2.0 ms (proportional to the position of the joystick), but only one pulse for each frame.
(The standardized "RC PWM" works differently enough from the PWM used to control DC motor speeds that some people say that RC PWM signals "are not really PWM signals" (m) (n) (o) (p) (q). Alas, none of those people give any suggestions as to what we should call these signals, so I call them "RC PWM signals" for lack of a better name. Perhaps I should call them "RC control signals" ?).
If two transmitters are transmitting at the same time, then yes, there will be an overlap of pulses. However, people at RC flying parks are very careful to assign each pilot (and the transmitter and receiver he uses) a different "frequency channel", so that the receiver in each airplane can easily pick out the signal from its own transmitter and ignore the radio signals from every other transmitter.
A 6-channel receiver uses only one "frequency channel", but it has 6 output channels (6 servo channels), i.e., it has 6 rows of output pins for up to 6 servos to plug into -- typically one channel each for pitch(elevator), roll(aileron), yaw(rudder), throttle, and some optional AUX channels.
During a single RC frame, the a 6-channel receiver cycles through every every servomotor, putting one "RC PWM" pulse at a time on each of its 6 outputs. Only one of its outputs is ever active at any one time -- there is no overlap of its pulses.
With a typical 50 Hz 6-channel transmitter, when all the control sticks are pushed to turn all the servos all the way counterclockwise, the receiver spits out
• a 1 ms pulse on channel 1, then -- as soon as that finishes -- a 1 ms pulse on channel 2, for all 6 channels -- a total of 6 ms -- and the (relatively long) sync pulse is however long it needs to be to fill out the rest of the 20 ms frame.
When all the control sticks are pushed to turn all the servos all the way clockwise, the receiver spits out
• a 2 ms pulse on channel 1, then -- as soon as that finishes -- a 2 ms pulse on channel 2, for all 6 channels -- a total of 12 ms -- and the (much shorter) sync pulse is however long it needs to be to fill out the rest of the 20 ms frame.
• Thanks for the explanation and all the links. Definitely clears up a few things. I realized I had a flawed understanding of PPM, as picked up from non-authoritative websites. Example This diagram says that the pulse width is fixed, but the position of the pulse conveys data. I was worried that two channels with the same data would have pulses in the same position. Your links show fixed pulse position (per channel) and varied pulse width.
– RaGe
Sep 2, 2014 at 15:47
• additional question: Does the sync pulse width vary per frame depending on the duty cycle of the individual channels?
– RaGe
Sep 2, 2014 at 15:49
• Yes, Oscar shows the "normal" PPM used in optical fiber and, well, everywhere except radio control "RC PPM". I feel like I'm not doing a very good job explaining, because "RC PPM" does not, in fact, have a fixed pulse position per channel. With a typical 50 Hz transmitter, the first "separator pulse" occurs at a fixed width and position every 20 ms, all the other pulses start wherever the last pulse left off, which changes every time the control sticks move. Sep 3, 2014 at 15:14
Multiple channels are time sliced onto "one-wire". The real wire count is usually three. Typically there is a positive voltage wire (may not be there depending on whether both ends have their own power or not) and always a shared ground wire.
Perhaps 40-100 times per second the transmitter broadcast the settings of all controls which map to servos on something. At the beginning of each broadcast, the voltage level on the output wire (the "one-wire") is held low for a sync'ing low pulse. After that, each servo gets a time slot. Servo #1 gets the first time slot, servo #2, the second, and so on.
Hope the illustration is clear. Although my drawing only shows 1.0, 1.5 and 2.0ms time pulses any value between 1.0 and 2.0 is valid and correlates to "proportional" values at the servo (hence the "proportional" term once used to describe these).
Multiple PWM channels generally aren't shoved into a single wire (Or I've never heard of it). If you need to send multiple data channels over the same wire then using a higher level protocol (such as UART or SPI) would be the way to go. While PWM is technically digital, it isn't like other digital protocols where data can be shoved in and expected to come out perfect on the other side. It's more like an analog signal where readings are subject to noise and infinite precision is not possible.
Also, it wouldn't matter if two channels are sending the same value or not. The way servo PWM works only the longer pulse would survive (Assuming the pulses are synchronized. If they weren't unusable garbage would most likely come out).
EDIT: As for pulse positioning, it might be possible to multiplex 2 signals depending on how they were constructed. From what I have read ppm requires either a clock pulse or a external clock, but in theory it should be possible to multiplex. Keep in mind that there won't be any real way to differentiate between the pulses sent, and both sources will need to share the same clock.
• My question is about pulse position modulation and not width modulation. I can see why it is a bad idea to multiplex two width modulated signals. Thank you for your answer nonetheless.
– RaGe
Sep 2, 2014 at 15:01
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# Why is 1 such a special number?
One, sometimes referred to as unity, is the first non-zero natural number. It is thus the integer after zero. Any number multiplied by one remains that number, as one is the identity for multiplication. As a result, 1 is its own factorial, its own square and square root, its own cube and cube root, and so on.
## Why is the number 1 so special?
The number one is far more special than a prime! It is the unit (the building block) of the positive integers, hence the only integer which merits its own existence axiom in Peano's axioms. It is the only multiplicative identity (1·a = a·1 = a for all numbers a).
## Who invented number 1?
Hindu-Arabic numerals, set of 10 symbols—1, 2, 3, 4, 5, 6, 7, 8, 9, 0—that represent numbers in the decimal number system. They originated in India in the 6th or 7th century and were introduced to Europe through the writings of Middle Eastern mathematicians, especially al-Khwarizmi and al-Kindi, about the 12th century.
## What is the perfect number?
perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128. The discovery of such numbers is lost in prehistory.
## What does 1 mean in math?
What is Number One? In mathematics, the number 1 represents a single entity, a quantity or value of 1. The whole number between 0 and 2 is 1. The number name of 1 is one.
## Is 1 a positive or negative number?
Positive numbers are any numbers greater than zero, for example: 1, 2.9, 3.14159, 40000, and 0.0005. For each positive number, there is a negative number that is its opposite. We write the opposite of a positive number with a negative or minus sign in front of the number, and call these numbers negative numbers.
## What is the spy number?
A number is said to be a Spy number if the sum of all the digits is equal to the product of all digits. Examples : Input : 1412. Output : Spy Number.
## What is a beautiful number?
A number is called beautiful if, for every digit x in the number, there are x occurrences of it in the number. Example: 1 is beautiful because 1 has 1 occurrence. 3133 is beautiful because 1 has 1 occurrence and 3 has 3 occurrences.
## What is the most greatest number?
A "googol" is the number 1 followed by 100 zeroes. The biggest number with a name is a "googolplex," which is the number 1 followed by a googol zeroes.
## What is the number for Jesus?
In some Christian numerology, the number 888 represents Jesus, or sometimes more specifically Christ the Redeemer. This representation may be justified either through gematria, by counting the letter values of the Greek transliteration of Jesus' name, or as an opposing value to 666, the number of the beast.
## What was the first number to exist?
Common intuition, and recently discovered evidence, indicates that numbers and counting began with the number one. (Even though in the beginning, they likely didn't have a name for it.) The first solid evidence of the existence of the number one, and that someone was using it to count, appears about 20,000 years ago.
## What is number 1 bathroom?
to do a "number one": to pee, to urinate. idiom. to do a "number two": to poop, to defecate. idiom. "Number one" and "number two" are expressions often used by parents and children when talking about going to the bathroom.
## Why is 1 A happy number?
A happy number is defined as a number that can be replaced by the sum of the squares of its digit repeatedly and after some repetitions, it will yield the number 1.
## What is symbolic about the number 1?
The number 1 represents newness, movement, and the possibilities that await us. In spiritual symbolism, it is the number of creation and the birth of all things -- the divine origin of the universe. In Numerology the number 1 is the root of opportunity in our lives. It is a symbol of confidence, power, and action.
## What is the happiest number?
The first few happy numbers are 1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, ... (OEIS A007770). These are also the numbers whose 2-recurring digital invariant sequences have period 1.
## What is the most loved number?
Over 30,000 people voted online for their favorite number, and the number chosen by the most people is… drum roll… 7! Almost half of all people chose numbers between 1 and 10.
## What is the number for love you?
What does 143 mean? 143 is code for I love you, especially used on pagers back in the 1990s.
## What is strong number?
Strong number is a special number whose sum of the factorial of digits is equal to the original number. For Example: 145 is strong number. Since, 1! + 4! + 5!
## What are the 4 types of spies?
Local spies are hired from among the people of a locality. Inside spies are hired from among enemy officials. Reverse spies are hired from among enemy spies. Dead spies transmit false intelligence to enemy spies.
## How can I be a spy?
Here is how to become a spy:
1. Maintain a clean record. ...
2. Earn a bachelor's degree. ...
3. Learn a foreign language. ...
4. Work on your physical fitness. ...
5. Apply to a federal agency. ...
6. Don't expect a movie. ...
7. Choose the right agency. ...
8. Be sure it's right for you.
## What is negative 1 called?
Unit Imaginary Number
The square root of minus one √(−1) is the "unit" Imaginary Number, the equivalent of 1 for Real Numbers. In mathematics the symbol for √(−1) is i for imaginary.
## Does negative 0 exist?
The negative of 0 does not exist.
## Why 1 is the greatest negative number?
The first positive integer is one greater than 0 and the number is 1. The greatest negative integer is the first negative integer from zero. The first negative integer from zero is one less than 0 and the number is – 1. Hence, the correct answer is option (c).
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EASEL BY TPT
Number of the Day for Grades 4 & 5
4th - 6th
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Description
This set of 13 Number of the Day templates comes with a set of student blackline printables and PDF Google Slides!
Each Number of the Day is open-ended and can be used with any number that fits student needs and what you're teaching in math. Templates grow change in complexity as the year goes on and students are more confident working with numbers!
These templates are also found in our Daily Brain Boosts, 180 days of Spiral Math Review for the whole year.
More from Complete Curriculum here!
These Number of the Day templates address critical focus areas in math for fourth and fifth grade:
• Place Value
• Number Sense
• Multiplication & Division
• Fractions & Decimals
• Rounding & Comparing
• Number Lines
• Story Problems
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Standards
to see state-specific standards (only available in the US).
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Understand a fraction 𝘢/𝘣 with 𝘢 > 1 as a sum of fractions 1/𝘣.
Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
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# Convert psi to pound per square foot
### One psi (pound per square inch) equals 144.0000209 pound per square foot (pound per square foot)
Please note that the value(s) of psi (pound per square inch) and pound per square foot (pound per square foot) in the corresponding base unit is (are) not exact values but approximations, therefore the above calculation is not exact.
For conversion tables, definitions and more information on the psi and pound per square foot units scroll down or use the related psi and pound per square foot quick access menus located at the top left side of the page.
psi is the symbol for pound per square inch
### From 0.10 to 4.00 psi, 40 entries
##### Accuracy of values: Note that the base equivalent value of psipound per square foot is not an exact value but an approximation, therefore the conversions in the table are approximate.
0.1 psi = 14.4000020885 pounds per square foot
0.2 psi = 28.8000041771 pounds per square foot
0.3 psi = 43.2000062656 pounds per square foot
0.4 psi = 57.6000083542 pounds per square foot
0.5 psi = 72.0000104427 pounds per square foot
0.6 psi = 86.4000125313 pounds per square foot
0.7 psi = 100.8000146198 pounds per square foot
0.8 psi = 115.2000167084 pounds per square foot
0.9 psi = 129.6000187969 pounds per square foot
1 psi = 144.0000208854 pounds per square foot
1.1 psi = 158.400022974 pounds per square foot
1.2 psi = 172.8000250625 pounds per square foot
1.3 psi = 187.2000271511 pounds per square foot
1.4 psi = 201.6000292396 pounds per square foot
1.5 psi = 216.0000313282 pounds per square foot
1.6 psi = 230.4000334167 pounds per square foot
1.7 psi = 244.8000355052 pounds per square foot
1.8 psi = 259.2000375938 pounds per square foot
1.9 psi = 273.6000396823 pounds per square foot
2 psi = 288.0000417709 pounds per square foot
2.1 psi = 302.4000438594 pounds per square foot
2.2 psi = 316.800045948 pounds per square foot
2.3 psi = 331.2000480365 pounds per square foot
2.4 psi = 345.6000501251 pounds per square foot
2.5 psi = 360.0000522136 pounds per square foot
2.6 psi = 374.4000543021 pounds per square foot
2.7 psi = 388.8000563907 pounds per square foot
2.8 psi = 403.2000584792 pounds per square foot
2.9 psi = 417.6000605678 pounds per square foot
3 psi = 432.0000626563 pounds per square foot
3.1 psi = 446.4000647449 pounds per square foot
3.2 psi = 460.8000668334 pounds per square foot
3.3 psi = 475.2000689219 pounds per square foot
3.4 psi = 489.6000710105 pounds per square foot
3.5 psi = 504.000073099 pounds per square foot
3.6 psi = 518.4000751876 pounds per square foot
3.7 psi = 532.8000772761 pounds per square foot
3.8 psi = 547.2000793647 pounds per square foot
3.9 psi = 561.6000814532 pounds per square foot
4 psi = 576.0000835418 pounds per square foot
Click here for a list of all conversion tables of psi to other compatible units.
## pound per square inch
Pound per square inch is a unit of measurement of pressure or mechanical stress. The definition for pound per square inch is the following:
A pound per square inch is equal to 1 lbf/in2.
The symbol for pound per square inch is psi
## pound per square foot
Pound per square foot is a unit of measurement of pressure or mechanical stress. The definition for pound per square foot is the following:
A pound per square foot is equal to 1 lbf/ft2.
The symbol for pound per square foot is psf
## Other people are also searching for information on psi conversions.
Following are the most recent questions containing psi. Click on a link to see the corresponding answer.
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Home | Base units | Units | Conversion tables | Unit conversion calculator
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Understand Riemannian cross-derivative on product manifolds
Suppose we have a smooth function $$f:\mathcal{M}\times\mathcal{N}\rightarrow\mathbb{R}$$ where the domain is a product of two Riemannian manifolds. The Riemannian cross-derivative ([1], section 2) is defined as: $$\mathrm{grad}_{xy}^2:= \mathrm{D}_x\mathrm{grad}_y f(x,y): \mathrm{T}_x\mathcal{M}\rightarrow \mathrm{T}_y\mathcal{N}$$
I'm trying to understand this operator. I have two specific questions:
First, to me, if we fix $$y$$ then $$\mathrm{grad}_y f(x,y):\mathcal{M}\rightarrow\mathrm{T}\mathcal{N}$$, and the differential on $$x$$ would result in an operator $$\mathrm{D}_x\mathrm{grad}_y f(x,y):\mathrm{T}\mathcal{M}\rightarrow\mathrm{T}\mathrm{T}\mathcal{N}$$, which seems not the same as the definition in the paper. Is there any point I missed here?
Second, I'm trying to understand it similar to its Euclidean counterparts. Under what curcumstances do we know that $$\mathrm{grad}_{xy}^2$$ and $$\mathrm{grad}_{yx}^2$$ are adjoints? That's to say, do we have: $$\langle \eta,\mathrm{grad}_{xy}^2(\xi) \rangle_{y} = \langle\mathrm{grad}_{yx}^2(\eta),\xi \rangle_{x}, \forall \xi\in \mathrm{T}_{x}\mathcal{M}\text{ and }\forall \eta\in \mathrm{T}_{y}\mathcal{N}$$
Any comments or references are appreciated, thanks!
References:
[1] Han, Andi, et al. "Riemannian Hamiltonian methods for min-max optimization on manifolds." SIAM Journal on Optimization 33.3 (2023): 1797-1827.
If you fix $$y$$, the function $$x \mapsto \mathrm{grad}_y f(x,y)$$ is a function mapping $$M \to T_y N$$; note that the codomain is a single, fixed vector space. So the differential in $$x$$ is a mapping $$TM \to T(T_yN)$$, but as $$T_yN$$ is a linear space its tangent space is canonically isomorphic to itself.
They should always be adjoints. You have, extending $$\eta$$ to a constant map $$M \to T_yN$$, $$\langle \eta, \mathrm{grad}_{xy}^2(\xi)\rangle_y = \xi( \langle \eta, \mathrm{grad}_y f(x,y) \rangle_y) = \xi(\eta(f))$$ So: given a vector $$\eta\in T_yN$$ and a vector $$\xi$$ in $$T_xM$$, extend them to a vector field $$\eta$$ on $$N$$ and a vector field $$\xi$$ on $$M$$, and then extend them trivially to vector fields on $$\tilde{\eta}(x,y) = (0,\eta(y))$$ and $$\tilde{\xi}(x,y) = (\xi(x),0)$$ on $$M\times N$$. Then our computation above shows that the difference between the two expression you are asking about is exactly $$[\tilde{\xi},\tilde{\eta}]f$$, but it is easy to check that this Lie Bracket vanishes.
• Another way to think about items 1 and 2: your manifold inherits a product Riemannian structure and hence a Levi-Civita connection, with respect to which you can define the Hessian of $f$. The musical operations allow you to consider the operation $H^\sharp_f: T(M\times N) \to T(M\times N)$, which is self-adjoint since the Levi-Civita connection is torsion free. The product structure gives the canonical decomposition $T_{x,y}(M\times N) = T_xM \times T_y N$ and your cross derivative is just the off-diagonal parts of $H^\sharp_f$. Commented Sep 26, 2023 at 6:07
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# The debate over bilingual education centers on the issue of
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The debate over bilingual education centers on the issue of [#permalink]
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723. The debate over bilingual education centers on the issue of whether the United States should foster the idea of single common language, an idea, some believe, that has in the past been crucial in binding diverse constituencies together.
(A) been crucial in binding diverse constituencies together
(B) been crucial as a binding together of diverse constituencies
(C) been crucial to bind together constituencies that are diverse
(D) become crucial in binding together diverse constituencies
(E) become crucial to bind together constituencies that are diverse
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03 Nov 2009, 12:17
noboru wrote:
723. The debate over bilingual education centers on the issue of whether the United States should foster the idea of single common language, an idea, some believe, that has in the past been crucial in binding diverse constituencies together.
(A) been crucial in binding diverse constituencies together
(B) been crucial as a binding together of diverse constituencies
(C) been crucial to bind together constituencies that are diverse
(D) become crucial in binding together diverse constituencies
(E) become crucial to bind together constituencies that are diverse
Excellent and confusing question. I applied MGMAT SC categorization and noticed no errors. Basically this is possibly a verb tense issue or an idiom issue. crucial-in is the correct idiom, check this http://catindiaonline.wordpress.com/200 ... notes-iii/ and browser search (Ctrl + F) for "crucial".
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11 Nov 2009, 01:18
crucial in is the correct idiom.
bilingual education is still debatable-so has been is the correct usage.
My ans is A.
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03 Aug 2010, 16:30
noboru wrote:
723. The debate over bilingual education centers on the issue of whether the United States should foster the idea of single common language, an idea, some believe, that has in the past been crucial in binding diverse constituencies together.
(A) been crucial in binding diverse constituencies together
(B) been crucial as a binding together of diverse constituencies
(C) been crucial to bind together constituencies that are diverse
(D) become crucial in binding together diverse constituencies
(E) become crucial to bind together constituencies that are diverse
The use of has become is loggically more sound here. It correctly implies that it started in the past and continues into the present.
I'll go with D. E is wordier.
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04 Aug 2010, 07:44
Still confused between answers A and D.
Can anyone please explain why you think D is wrong?
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04 Aug 2010, 18:24
I was with D, but after seeing OA as A.
Let me try to defeat D
In D "become crucial..." changes the original meaning of the sentence. "Become" indicates a change over time.
"Been crucial..." indicates an on-going situation.
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### Show Tags
05 Aug 2010, 07:37
1
"crucial in" is the correct idiom
"has been"......makes sense.
A it is.
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### Show Tags
03 Jan 2011, 09:40
no error A is good correct idiom
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Re: The debate over bilingual education centers on the issue of [#permalink]
### Show Tags
18 Mar 2014, 05:35
Can somebody please explain which is the correct idiomatic expression.. (1) Binding together xyz or (2) Binding xyz together?
Thanks, AkS
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Re: The debate over bilingual education centers on the issue of [#permalink]
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25 Aug 2018, 17:03
Unable to post link due to restrictions, just perform following search for google and follow 3rd result (Titled as Master key to Mba.....)
"The debate over bilingual education centers on the issue of whether the United States should foster the idea of single common language, an idea, some believe, that has in the past"
Check Q 18 and answer is provided after few questions
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Re: The debate over bilingual education centers on the issue of [#permalink]
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30 Aug 2018, 08:50
2
noboru wrote:
723. The debate over bilingual education centers on the issue of whether the United States should foster the idea of single common language, an idea, some believe, that has in the past been crucial in binding diverse constituencies together.
(A) been crucial in binding diverse constituencies together
(B) been crucial as a binding together of diverse constituencies
(C) been crucial to bind together constituencies that are diverse
(D) become crucial in binding together diverse constituencies
(E) become crucial to bind together constituencies that are diverse
The correct idiom is "crucial in" and with that in mind we can eliminate options B,C and E.
IMO, Option D, as it seems changes the meaning in the sentence by using "become".
Re: The debate over bilingual education centers on the issue of &nbs [#permalink] 30 Aug 2018, 08:50
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### February 26, 20142014 年 2 月 26 日 (Kurt Beschorner)
n=4539: c2806(1328896223......) = 118777574166267077360801431884976762184923 * c2765(1118810712......)
# ECM B1=1e6, sigma=2487209557
n=4585: c3093(2155169614......) = 122185863069298402655235796871 * c3064(1763845309......)
# ECM B1=1e6, sigma=2526805917
### February 25, 20142014 年 2 月 25 日 (Kurt Beschorner)
n=4441: c4435(4811400324......) = 20247286213489858061260882092946243 * c4401(2376318620......)
# ECM B1=1e6, sigma=166509083
n=4531: c4306(1052074287......) = 59152742213483330689409587717 * c4277(1778572299......)
# ECM B1=1e6, sigma=270070065
### February 18, 20142014 年 2 月 18 日 (Kurt Beschorner)
n=4501: c3839(1983275161......) = 248278749415584393018365399 * c3812(7988098726......)
# ECM B1=1e6, sigma=540093768
n=4597: c4597(1111111111......) = 49517362821841381162768425182671 * p4565(2243881838......)
# ECM B1=1e6, sigma=2596273868
```Primality testing 2243881838...... [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N-1 test using base 17
Running N+1 test using discriminant 29, base 16+sqrt(29)
Calling N-1 BLS with factored part 0.27% and helper 0.20% (1.02% proof)
2243881838...... is Fermat and Lucas PRP! (1.7816s+0.0183s)
```
# 1080 of 100000 Φn(10) factorizations were finished. 100000 個中 1080 個の Φn(10) の素因数分解が終わりました。
# 75920 of 100000 Φn(10) factorizations were cracked. 100000 個中 75920 個の Φn(10) の素因数が見つかりました。
# 116 of 9592 Rprime factorizations were finished. 9592 個中 116 個の Rprime の素因数分解が終わりました。
# 7464 of 9592 Rprime factorizations were cracked. 9592 個中 7464 個の Rprime の素因数が見つかりました。
```The following 126 probable prime factors are not certificated yet.
n=4597: p4565(2243881838......) http://factordb.com/index.php?id=1100000000645809294
n=5237: p5192(8225727009......) http://factordb.com/index.php?id=1100000000021164062
n=5323: p5277(5494980776......) http://factordb.com/index.php?id=1100000000013354497
n=6119: p5837(3754893657......) http://factordb.com/index.php?id=1100000000416753186
n=7597: p7380(2662259922......) http://factordb.com/index.php?id=1100000000476127140
n=7745: p6175(2562004991......) http://factordb.com/index.php?id=1100000000559428116
n=8223: p5371(1070563618......) http://factordb.com/index.php?id=1100000000419315002
n=10679: p10398(3212734537......) http://factordb.com/index.php?id=1100000000587092362
n=10703: p8264(5790721458......) http://factordb.com/index.php?id=1100000000596419742
n=12351: p7775(2639345918......) http://factordb.com/index.php?id=1100000000589822155
n=12413: p12382(1389253690......) http://factordb.com/index.php?id=1100000000013490240
n=14011: p13957(3202159838......) http://factordb.com/index.php?id=1100000000575379519
n=14485: p11566(1953572169......) http://factordb.com/index.php?id=1100000000615401029
n=14582: p6934(4212511300......) http://factordb.com/index.php?id=1100000000032355112
n=14825: p11812(4191829575......) http://factordb.com/index.php?id=1100000000583602914
n=15332: p7647(3599323721......) http://factordb.com/index.php?id=1100000000014723489
n=15472: p7724(6462870742......) http://factordb.com/index.php?id=1100000000014723987
n=15728: p7851(2119357982......) http://factordb.com/index.php?id=1100000000014724861
n=15934: p7655(9398162882......) http://factordb.com/index.php?id=1100000000032355349
n=16597: p14213(3389166928......) http://factordb.com/index.php?id=1100000000032433692
n=16815: p8343(8867846097......) http://factordb.com/index.php?id=1100000000032435874
n=16886: p8406(2001272104......) http://factordb.com/index.php?id=1100000000636162381
n=18170: p6846(5144476898......) http://factordb.com/index.php?id=1100000000032355788
n=18827: p18480(9000000000......) http://factordb.com/index.php?id=1100000000032454351
n=19498: p9730(8251811537......) http://factordb.com/index.php?id=1100000000014739626
n=20233: p20211(4205088806......) http://factordb.com/index.php?id=1100000000013669684
n=20581: p18686(3423440887......) http://factordb.com/index.php?id=1100000000587111590
n=21148: p9883(2211679650......) http://factordb.com/index.php?id=1100000000591597385
n=21469: p18369(2534810559......) http://factordb.com/index.php?id=1100000000615459222
n=21786: p7256(2521977139......) http://factordb.com/index.php?id=1100000000032356709
n=21858: p7276(1149947374......) http://factordb.com/index.php?id=1100000000032356727
n=21865: p17480(4725842171......) http://factordb.com/index.php?id=1100000000032485925
n=22327: p21964(1003011728......) http://factordb.com/index.php?id=1100000000032491510
n=22575: p10060(1762423748......) http://factordb.com/index.php?id=1100000000032494459
n=23572: p11466(4152899286......) http://factordb.com/index.php?id=1100000000591599582
n=24466: p11262(8383530241......) http://factordb.com/index.php?id=1100000000032357453
n=24792: p8245(7484034255......) http://factordb.com/index.php?id=1100000000015780486
n=24832: p12274(4612171090......) http://factordb.com/index.php?id=1100000000602433947
n=25722: p8564(1297186619......) http://factordb.com/index.php?id=1100000000032357932
n=25973: p24567(4967369915......) http://factordb.com/index.php?id=1100000000597306296
n=26008: p12958(2371385622......) http://factordb.com/index.php?id=1100000000615703735
n=26601: p17724(2959900507......) http://factordb.com/index.php?id=1100000000032542308
n=26982: p8951(8406608028......) http://factordb.com/index.php?id=1100000000597306316
n=27472: p12779(2206236194......) http://factordb.com/index.php?id=1100000000015790968
n=27496: p11737(5951904519......) http://factordb.com/index.php?id=1100000000015791070
n=28455: p12912(1713313150......) http://factordb.com/index.php?id=1100000000615703749
n=28952: p10998(1599236780......) http://factordb.com/index.php?id=1100000000615703752
n=29091: p19374(3948526192......) http://factordb.com/index.php?id=1100000000032553440
n=29141: p23745(4638933562......) http://factordb.com/index.php?id=1100000000615704066
n=30452: p14469(1040925734......) http://factordb.com/index.php?id=1100000000589745584
n=30650: p12224(1815469202......) http://factordb.com/index.php?id=1100000000032359447
n=30744: p8629(1825038389......) http://factordb.com/index.php?id=1100000000015803663
n=31213: p24677(2908101418......) http://factordb.com/index.php?id=1100000000615704078
n=31254: p10410(7175573812......) http://factordb.com/index.php?id=1100000000032359627
n=31590: p7768(6960331352......) http://factordb.com/index.php?id=1100000000032359729
n=32184: p10603(6671042459......) http://factordb.com/index.php?id=1100000000615704083
n=32302: p15582(7580428912......) http://factordb.com/index.php?id=1100000000615704087
n=32481: p21600(9999999999......) http://factordb.com/index.php?id=1100000000556949265
n=34278: p10955(5420339387......) http://factordb.com/index.php?id=1100000000615704117
n=34474: p15652(2718591171......) http://factordb.com/index.php?id=1100000000031223055
n=35712: p11499(1854921265......) http://factordb.com/index.php?id=1100000000615704122
n=37751: p32314(8689034915......) http://factordb.com/index.php?id=1100000000615704125
n=38673: p25763(1136317924......) http://factordb.com/index.php?id=1100000000615704126
n=41470: p13434(6631229424......) http://factordb.com/index.php?id=1100000000022717472
n=41550: p11034(3760490463......) http://factordb.com/index.php?id=1100000000022717730
n=43106: p18450(3377757599......) http://factordb.com/index.php?id=1100000000622234960
n=43566: p14139(6962562835......) http://factordb.com/index.php?id=1100000000022724114
n=44606: p22298(1019011701......) http://factordb.com/index.php?id=1100000000022727396
n=47468: p23732(9900990099......) http://factordb.com/index.php?id=1100000000022736528
n=47498: p20160(9090909091......) http://factordb.com/index.php?id=1100000000022736618
n=47520: p11504(8700248466......) http://factordb.com/index.php?id=1100000000615704186
n=47560: p17904(2209194873......) http://factordb.com/index.php?id=1100000000615704191
n=49081: p49081(1111111111......) http://factordb.com/index.php?id=1100000000013937242
n=49671: p33095(2285982058......) http://factordb.com/index.php?id=1100000000615704201
n=50131: p50068(2479448013......) http://factordb.com/index.php?id=1100000000575655925
n=51300M: p6475(1949313938......) http://factordb.com/index.php?id=1100000000022749153
n=51660M: p5754(4036177735......) http://factordb.com/index.php?id=1100000000022750359
n=52028: p25995(3330698075......) http://factordb.com/index.php?id=1100000000022751617
n=52062: p17353(1098901098......) http://factordb.com/index.php?id=1100000000022751729
n=52066: p22288(1332570450......) http://factordb.com/index.php?id=1100000000022751752
n=55315: p37998(3725063207......) http://factordb.com/index.php?id=1100000000314608933
n=55601: p43057(1000000000......) http://factordb.com/index.php?id=1100000000563716320
n=57740M: p11545(2824060999......) http://factordb.com/index.php?id=1100000000022770929
n=58962: p18944(1338567545......) http://factordb.com/index.php?id=1100000000022775164
n=59220L: p6614(4606819083......) http://factordb.com/index.php?id=1100000000022776045
n=59340M: p7393(2555229610......) http://factordb.com/index.php?id=1100000000022319751
n=59772: p18688(9901000000......) http://factordb.com/index.php?id=1100000000022320970
n=64060L: p12809(2824060999......) http://factordb.com/index.php?id=1100000000022333805
n=64410: p16115(1233544571......) http://factordb.com/index.php?id=1100000000022334904
n=65626: p28057(1459800300......) http://factordb.com/index.php?id=1100000000615704360
n=65924: p32926(4189483724......) http://factordb.com/index.php?id=1100000000636311936
n=67347: p38382(7391571857......) http://factordb.com/index.php?id=1100000000615704363
n=67366: p31075(5442877005......) http://factordb.com/index.php?id=1100000000615704364
n=68102: p32033(1099999999......) http://factordb.com/index.php?id=1100000000557665558
n=70740L: p9361(1000100005......) http://factordb.com/index.php?id=1100000000615928441
n=70842: p23613(1098901098......) http://factordb.com/index.php?id=1100000000293897389
n=71400: p15352(5670284275......) http://factordb.com/index.php?id=1100000000615704371
n=72184: p30906(6297664618......) http://factordb.com/index.php?id=1100000000615704376
n=73094: p29832(9090910000......) http://factordb.com/index.php?id=1100000000556949394
n=73808: p31585(1000000009......) http://factordb.com/index.php?id=1100000000556949493
n=74112: p24556(1016058865......) http://factordb.com/index.php?id=1100000000615704390
n=75740M: p12953(1371715669......) http://factordb.com/index.php?id=1100000000615933369
n=76537: p76529(1680243818......) http://factordb.com/index.php?id=1100000000021230909
n=77050: p29027(1553899293......) http://factordb.com/index.php?id=1100000000636541242
n=77061: p48301(1758205326......) http://factordb.com/index.php?id=1100000000615704405
n=77077: p55441(1000000000......) http://factordb.com/index.php?id=1100000000563445641
n=79560: p18417(2260354660......) http://factordb.com/index.php?id=1100000000636695277
n=79710: p21248(9100090999......) http://factordb.com/index.php?id=1100000000556949246
n=82360: p31360(9999000099......) http://factordb.com/index.php?id=1100000000556949424
n=83967: p51639(4884525227......) http://factordb.com/index.php?id=1100000000596833389
n=85113: p48339(7099610268......) http://factordb.com/index.php?id=1100000000415323025
n=86154: p28202(1821117073......) http://factordb.com/index.php?id=1100000000615720928
n=86340M: p11491(7801769750......) http://factordb.com/index.php?id=1100000000593024392
n=86453: p86453(1111111111......) http://factordb.com/index.php?id=1100000000046752372
n=87114: p29020(5179196579......) http://factordb.com/index.php?id=1100000000615720934
n=87312: p27116(5668758151......) http://factordb.com/index.php?id=1100000000615720957
n=88676: p37993(1009999999......) http://factordb.com/index.php?id=1100000000563733924
n=90312: p29116(1107149590......) http://factordb.com/index.php?id=1100000000615720958
n=92092: p31681(1009999999......) http://factordb.com/index.php?id=1100000000556949529
n=92712: p30897(1000099999......) http://factordb.com/index.php?id=1100000000556949399
n=93420L: p12372(1989086709......) http://factordb.com/index.php?id=1100000000615934614
n=93811: p93765(2592502388......) http://factordb.com/index.php?id=1100000000530981325
n=93914: p46945(2805905158......) http://factordb.com/index.php?id=1100000000022414371
n=94100L: p18788(5376763212......) http://factordb.com/index.php?id=1100000000615934625
n=96684: p27594(2048115086......) http://factordb.com/index.php?id=1100000000615721010
n=97098: p32350(1718114428......) http://factordb.com/index.php?id=1100000000536289244
```
### February 17, 20142014 年 2 月 17 日 (Propper)
n=640: c256(9999999999......) = 15426023502522488030607387700105870831428809697868716409941105675494726401 * p183(6482552031......)
# snfs
# 1079 of 100000 Φn(10) factorizations were finished. 100000 個中 1079 個の Φn(10) の素因数分解が終わりました。
# 75919 of 100000 Φn(10) factorizations were cracked. 100000 個中 75919 個の Φn(10) の素因数が見つかりました。
# n=640 was the 6th blank Phi_n(10).
# n=640 was the smallest blank Phi_n(10).
### February 11, 20142014 年 2 月 11 日 (Maksym Voznyy)
n=10455: p5109(3759996113......) is definitely prime.
# Certification is available at: http://stdkmd.com/nrr/cert/Phi/index.htm#CERT_PHI_10455_10
### February 10, 20142014 年 2 月 10 日 (Kurt Beschorner)
n=1110: c288(9100090999......) = 20405858262551036238097198927251201795324405825413199508017546361 * c224(4459548274......)
# ECM B1=26e7, sigma=2744456406
# 75918 of 100000 Φn(10) factorizations were cracked. 100000 個中 75918 個の Φn(10) の素因数が見つかりました。
# c288 was the 4th smallest blank Phi_n(10) in the list.
### February 1, 20142014 年 2 月 1 日 (Kurt Beschorner)
n=4427: c4158(8341759661......) = 9423561647642347762247901867413 * c4127(8852024291......)
# ECM B1=1e6, sigma=3556420361
n=4523: c4483(5437759358......) = 25259449262007310707041147677 * c4455(2152762438......)
# ECM B1=1e6, sigma=4000689009
plain text versionプレーンテキスト版
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# Exponents Problem (m04q20)
Author Message
Director
Joined: 16 May 2007
Posts: 548
Followers: 2
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### Show Tags
19 Jun 2007, 20:15
This topic is locked. If you want to discuss this question please re-post it in the respective forum.
What is the last digit of the following number $$2^{22} * 3^{15} * 5^{16} * 7^1$$ ?
(A) 6
(B) 5
(C) 2
(D) 1
(E) 0
[Reveal] Spoiler: OA
E
Source: GMAT Club Tests - hardest GMAT questions
Can someone please explain how to solve these kind of problems
Thanks
Intern
Joined: 10 Jun 2010
Posts: 8
Concentration: Marketing, General Management
GPA: 3.8
WE: Web Development (Investment Banking)
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Kudos [?]: 5 [4] , given: 12
### Show Tags
13 Oct 2010, 09:03
4
KUDOS
The first thing i saw in this question was a presence of a 5. That means the answer had to have either a 0 or a 5.
So now I have automatically eliminated 3 answers.
Second, all powers of 3 result in an odd number. (Check it up: 3^1=3, 3^4=81).
Third, all powers of 2 are even.
So its basically even (because of 2) mulitplied by odd (because of 3)
even*odd = even
even number*(any power of 5) = ends with a zero
eg. 2*5=10, 2*25=50, etc.
Hence E
Director
Joined: 26 Feb 2006
Posts: 900
Followers: 4
Kudos [?]: 123 [2] , given: 0
### Show Tags
19 Jun 2007, 23:05
2
KUDOS
sumande wrote:
We need to find the last digit of each term first.
2^1=2; 2^2=4; 2^3=8; 2^4=16; 2^5=32.
So the last digit of 2^x is repeated every 4th term.
so, the last digit of 2^22 will be the last digit of 2^2=4.
Similarly, for 3^x the last digit is repeated every 4th term.
3^1=3; 3^2=9; 3^3=27; 3^4=81; 3^5=243
so, the last digit of 3^15 will be last digit of 3^3=7
The last digit of 5^x is always 5 and that of 7^1 is 7.
So the last digit of the product will be the last digit of 4*3*5*7=0.
the process is perfect and result too but a small mistake: 4 x 7 x 5 x 7 = 0.
Senior Manager
Joined: 04 Jun 2007
Posts: 345
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### Show Tags
19 Jun 2007, 21:11
1
KUDOS
We need to find the last digit of each term first.
2^1=2; 2^2=4; 2^3=8; 2^4=16; 2^5=32.
So the last digit of 2^x is repeated every 4th term.
so, the last digit of 2^22 will be the last digit of 2^2=4.
Similarly, for 3^x the last digit is repeated every 4th term.
3^1=3; 3^2=9; 3^3=27; 3^4=81; 3^5=243
so, the last digit of 3^15 will be last digit of 3^3=7
The last digit of 5^x is always 5 and that of 7^1 is 7.
So the last digit of the product will be the last digit of 4*3*5*7=0.
Senior Manager
Joined: 04 Jun 2007
Posts: 345
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### Show Tags
19 Jun 2007, 23:30
1
KUDOS
Thanks for pointing that out !!
But if there is a 2 and a 5, the other numbers don't matter
Manager
Joined: 25 Apr 2007
Posts: 147
Followers: 2
Kudos [?]: 15 [1] , given: 0
### Show Tags
21 Jun 2007, 10:24
1
KUDOS
To be honest, I found this solution after reading yours. But the methodology may be helpful for solving a similar problem :
2^22*3^15*5^16*7^1 = 2*5*(2^21*3^15*5^15*7)
2^22*3^15*5^16*7^1 = 10 * integer
10 * integer ends with 0
Manager
Joined: 17 May 2007
Posts: 171
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### Show Tags
21 Jun 2007, 13:34
1
KUDOS
2^22)*(3^15)*(5^16)*(7^1)
7^1 = 7 then
5^16 will result 5 in units digit
7 * 5 reults 5 in units digit
Now 5 * 2^anything - will result in 0 as the units digit
Now 0* 3^anything - will give 0 in the units digit.
Intern
Joined: 04 Oct 2012
Posts: 12
Concentration: General Management, Human Resources
Schools: Kellogg PT '17
GMAT Date: 02-02-2013
GPA: 3.55
Followers: 0
Kudos [?]: 4 [1] , given: 7
### Show Tags
16 Oct 2012, 07:01
1
KUDOS
2*7*5*7 --- i like this thought process i would have never thought of it this way! i would have seen the 2 and 5 and thought oh it's 0 but now when i'm faced with a question like this and there is no 2 or 5 i know what to do!!!!
Current Student
Joined: 03 Oct 2006
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### Show Tags
21 Jun 2007, 19:54
I found this another way as well. However, I think the method used in the second post is the best one to follow:
(2^15)(3^15)(5^16)(7^1)
=(6^15)(5^16)(7^1)
=(6^15)(5^15)(5^1)(7^1)
=(30^15)(35^1)
30^x = the last digit will always = 0
35 * 30 = the last digit will always = 0
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12 Oct 2010, 05:14
We have 2 and 5 in the product, so last digit always be 0 irrespective of any other number.
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12 Oct 2010, 22:54
trahul4 wrote:
What is the last digit of the following number $$2^{22} * 3^{15} * 5^{16} * 7^1$$ ?
(A) 6
(B) 5
(C) 2
(D) 1
(E) 0
[Reveal] Spoiler: OA
E
Source: GMAT Club Tests - hardest GMAT questions
Can someone please explain how to solve these kind of problems
Thanks
E
2() * 3() * 5() * 7() = multiple of 10 ==> 0
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13 Oct 2010, 17:54
Look no further if you see 2 and 5 as one of the factors.
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14 Oct 2010, 07:16
take the last digit of all of them and t hen multiply and find
2^0=1;2^1=2;2^2=4;2^3=8;2^4=6;2^5=2;so it repeats after 4 times
3^0=1;3^1=3;3^2=9;3^3=7;3^4=1;3^5=3;so it repeats after 4 times
5^0=1;5^1=2;5^2=5;so it repeats after 1 times
7^1=7
2^22=22/4=2 is remainder.means it should repeat after 2 times.i.e 8
3^15=15/4=3 is remainder.means it should repeat after 3 times.i.e 7
5 and 7
so total=8*7*5*7=last digit is 0
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14 Oct 2010, 20:43
2^x will repeat the last digit 2 after each 4th power.So
2^22=(2^4)^5 * 2^2 = yyy2*4=yyy8 I am just considering the last digit.
now 3^4=y1
3^15= (3^4)^3 * 3^3 = yy1*27 =yyy7
5^16=yyy5
7^1=7
Multiplying all last digit=8*7*5*7=yy0 so last digit is 0.Ans must be E
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14 Oct 2011, 05:29
i also got the ans..which will be 4*7*5*7 which will make the unit digit 0
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14 Oct 2011, 12:44
This was easier than I thought. I did no math. This really wasn't an exponent question but a number properties question:
Since 2 is a factor the answer cannot be odd so B and D are out
Since 5 is a factor and all multiples of 5 are end in 5 or 0 then the answer is E. 0
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15 Oct 2011, 04:14
zero..
any 5 when multiplied by 2 ll result a zero as its unit digit.
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17 Oct 2011, 03:40
trahul4 wrote:
What is the last digit of the following number $$2^{22} * 3^{15} * 5^{16} * 7^1$$ ?
(A) 6
(B) 5
(C) 2
(D) 1
(E) 0
[Reveal] Spoiler: OA
E
Source: GMAT Club Tests - hardest GMAT questions
Can someone please explain how to solve these kind of problems
Thanks
This can be solved by identifying the patterns
for 2 : 2*1 = 2 , 2*2 = 4 , 2^3 = 8 , 2^4 = 16
hence it follows : 2,4,8,6 -- 4 is the count
similarly for 3 : 3,9,7,1 -- 4
for 5 : 5 -- count is 1
for 7 : 7,9,3,1 -- count is 4
Hence
2^22 = 2^(22/4) = 2^2 = 4
3^15 = 3^(15/4) = 3^1 = 3
5^16 = 5^1 = 5
7^1 = 7
4*3*5*7 = 420 .. untis digit 0
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17 Nov 2011, 23:01
2- 2,4,8,6
3 - 3,9,7,1
5- always 5
So we know that 2^22 will end in a 4 (goes through five rotations and then two more places), 3 will end on a 7 (3 rotations then 3 more places), 5 is 5, and 7 is 7.
So 4x3x7x5x7 = 0
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15 Oct 2013, 08:17
E.
2 ways to do this one.
Longer way:
We only care about the units digit ("ones" place - from here on out abbreviated as UD) of each term. So we need to figure out what the UD is of each of the terms. The best way to do this is to look for a repeating pattern.
For example, the pattern for units digit for 2 raised to a power is:
$$2^1$$ = 2
$$2^2$$ = 4
$$2^3$$ = 8
$$2^4$$ = 16 (units digit is 6)
$$2^5$$ = 32 (units digit is 2 - here the pattern begins to repeat)
So, the 2, 4, 8, 6 pattern repeats every 4 powers.
Next step to find the units digit of 2^22, we look at 22. 22 divided by 4 = 5 remainder 2. If the pattern is 2, 4, 8, 6, we need to count to the second term (remember, the remainder was 2!)...the second term in the patter is 4. So the units digit is 4.
We repeat the process for 3^15 (UD is 3), 5^16 (UD is 5), and 7^1 (UD is 7).
Finally, we multiply all the UDs together: 4 x 3 x 5 x 7 = 420. The UD of 420 is 0. So, this is the answer.
Short cut:
Since a 2 and a 5 are in the term, the UD will always be 0, no matter what else is in the term (2x5=10).
Re: Exponents Problem (m04q20) [#permalink] 15 Oct 2013, 08:17
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Tuesday April 13, 2021
AmosWEB means Economics with a Touch of Whimsy!
SAVINGS DEPOSITS: Accounts maintained by banks, savings and loan associations, credit unions, and mutual savings banks that pay interest but can not be used directly as money. These accounts, also termed transactions deposits, let customers set aside a portion of their liquid assets that COULD be used to make purchases. But to make those purchases, savings account balances must be transferred to checkable deposits or currency. However, this transference is easy enough that savings accounts are often termed near money. Savings accounts, as such constitute a sizeable portion of the M2 monetary aggregate.
SAVING FUNCTION:
A mathematical relation between saving and income by the household sector. The saving function can be stated as an equation, usually a simple linear equation, or as a diagram designated as the saving line. This function captures the saving-income relation, the flip side of the consumption-income relation that forms one of the key building blocks for Keynesian economics. The two key parameters of the saving function are the intercept term, which indicates autonomous saving, and the slope, which is the marginal propensity to save and indicates induced saving. The injections-leakages model used in Keynesian economics is based on the saving function.
The saving function is the starting point of the Keynesian economics analysis of equilibrium output determination using the injections-leakages model. It captures the relation between saving by the household sector and income. Because income is used for either consumption or saving, the saving function is a complement of the consumption function. Both reflect the fundamental psychological law put forth by John Maynard Keynes that consumption expenditures (and saving ) by the household sector depend on income and than only a portion of additional income is used for consumption, with the rest used for saving.
This function is presented either as a mathematical equation, most often as a simple linear equation, or as the graphical saving line. In either form, income is measured as disposable income, national income, or occasionally gross domestic product.
The saving function makes it easy to divide saving into two basic types. Autonomous saving is the intercept term. Induced saving is the slope. Of no small importance, the slope of the saving function is also the marginal propensity to save (MPS).
### First, The Equation
The saving function can represented in a general form as:
S = f(Y)
where: S is saving, Y is income (national or disposable), and f is the notation for a generic, unspecified functional form.
Depending on the analysis, the actual functional form of the equation can be linear, with a constant slope, or curvilinear, with a changing slope. The most common form is linear, such as the one presented here:
S = c + dY
where: S is saving, Y is income (national or disposable), c is the intercept, and d is the slope.
The two key parameters that characterize the saving function are slope and intercept.
• Slope: The slope of the saving function (d) measures the change in saving resulting from a change in income. If income changes by \$1, then saving changes by \$d. This slope is generally assumed and empirically documented to be greater than zero, but less than one (0 < d < 1). It is conceptually identified as induced saving and the marginal propensity to save (MPC).
• Intercept: The intercept of the saving function (c) measures the amount of saving undertaken if income is zero. If income is zero, then saving is \$c. The intercept is generally assumed and empirically documented to be negative (c < 0). It is conceptually identified as autonomous saving.
It is often useful to state the saving function using parameters for the consumption function.
C = a + bY
where: C is consumption expenditures, Y again is income, a is the intercept, and b is the slope.
In this case, the saving function can be specified as:
S = - a + (1-b)Y
where: S is saving and Y is income. However, now the intercept is -a rather than c and the slope is (1-b) rather than d. This alternative specification shows the connection between the saving function and the consumption function. The intercept of the saving function (-a) is the negative of the intercept of the consumption function (a). The slope of the saving function (1-b) is one minus the slope of the consumption function (b), meaning that the sum of the marginal propensity to consume (b) and the marginal propensity to save (1-b) is equal to one, which is just another way of saying that a portion of additional income is consumed and the rest is saved.
### Then, The Graph
Saving Line
The saving function is also commonly presented as a diagram or saving line, such as the one presented in the exhibit to the right. This red line, labeled S in the exhibit is positively sloped, indicating that greater levels of income generate greater saving by the household sector. The specific saving function illustrated in this exhibit is:
C = - 1 + 0.25Y
The two primary characteristics of the saving function--slope and intercept--also can be identified with the saving line.
• Slope: The slope of the saving line presented here is positive, but less than one. In this case the slope is equal to 0.25. Click the [Slope] button to highlight.
• Intercept: The saving line intersects the vertical axis at a positive value of -\$1 trillion. Click the [Intercept] button to highlight.
### And Other Factors
The saving function captures the relation between saving and income. However, income is not the only factor influencing saving.
S = f(Y, OF)
where: S is saving, Y is income (national or disposable), and now OF is specified as other factors affecting saving. These other factors are more commonly referred to as consumption expenditures determinants because the primarily influence consumption, but also subsequent affect saving. Some of the more notable consumption/saving determinants are consumer confidence, interest rates, and wealth.
Consumer confidence is the general optimism or pessimism the household sector has about the state of the economy. More optimism means more consumption, and thus less saving. Interest rates affect the cost of borrowing the funds used to purchase durable goods. Higher interest rates mean less consumption and thus more saving. Wealth is the financial and physical assets owned by the household sector. More financial wealth means more consumption and less saving, while more physical assets mean less consumption and more saving.
These determinants cause saving to change even though income does not change. Or another way of stating this, determinants cause saving to change at every level of income. For a linear saving function, this change is reflected by a change in the intercept term (-a). For a saving line, the change is seen as an upward or downward shift.
<= SAVING SAVING-INVESTMENT MODEL =>
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SAVING FUNCTION, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 2000-2021. [Accessed: April 13, 2021].
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1
IIT-JEE 1998
+2
-0.5
If $$a = i + j + k,\overrightarrow b = 4i + 3j + 4k$$ and $$c = i + \alpha j + \beta k$$ are linearly dependent vectors and $$\left| c \right| = \sqrt 3 ,$$ then
A
$$\alpha = 1,\,\,\beta = - 1$$
B
$$\alpha = 1,\,\,\beta = \pm 1$$
C
$$\alpha = - 1,\,\,\beta = \pm 1$$
D
$$\alpha = \pm 1,\,\,\beta = 1$$
2
IIT-JEE 1998
+2
-0.5
For three vectors $$u,v,w$$ which of the following expression is not equal to any of the remaining three?
A
$$\,u \bullet \left( {v \times w} \right)$$
B
$$\left( {v \times w} \right) \bullet u$$
C
$$\,v \bullet \left( {u \times w} \right)$$
D
$$\left( {u \times v} \right) \bullet w$$
3
IIT-JEE 1995 Screening
+4
-1
Let $$\overrightarrow a = \widehat i - \widehat j,\overrightarrow b = \widehat j - \widehat k,\overrightarrow c = \widehat k - \widehat i.$$ If $$\overrightarrow d$$ is a unit vector such that $$\overrightarrow a .\overrightarrow d = 0 = \left[ {\overrightarrow b \overrightarrow c \overrightarrow d } \right],$$ then $$\overrightarrow d$$ equals
A
$$\pm {{\widehat i + \widehat j - 2k} \over {\sqrt 6 }}$$
B
$$\pm {{\widehat i + \widehat j - k} \over {\sqrt 3 }}$$
C
$$\pm {{\widehat i + \widehat j + k} \over {\sqrt 3 }}$$
D
$$\pm \widehat k$$
4
IIT-JEE 1995 Screening
+4
-1
If $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c$$ are non coplanar unit vectors such that $$\overrightarrow a \times \left( {\overrightarrow b \times \overrightarrow c } \right) = {{\left( {\overrightarrow b + \overrightarrow c } \right)} \over {\sqrt 2 }},\,\,$$ then the angle between $$\overrightarrow a$$ and $$\overrightarrow b$$ is
A
$${{3\pi } \over 4}$$
B
$${{\pi } \over 4}$$
C
$$\pi /2$$
D
$$\pi$$
EXAM MAP
Medical
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### CFA Practice Question
There are 227 practice questions for this study session.
### CFA Practice Question
In the BSM model for a call option, d1 is calculated as -0.49 and d2 is 0.58. If you want to replicate the call option payoffs with stocks and zero-coupon bonds, you should long ______.
A. stocks and short bonds
B. bonds and short stocks
C. stocks and bonds
Explanation: To replicate the call options you should long stocks and short bonds. In this case you should long N(d1) stocks and short N(d2) bonds. Note N(d1) = N(-0.49) = 1 - N(0.49).
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Article
# A History of Thermodynamics: The Missing Manual
Department of Physics, Texas A&M University, College Station, TX 77843-4242, USA
Entropy 2020, 22(1), 77; https://doi.org/10.3390/e22010077
Received: 19 December 2019 / Revised: 30 December 2019 / Accepted: 31 December 2019 / Published: 7 January 2020
(This article belongs to the Collection Foundations and Ubiquity of Classical Thermodynamics)
We present a history of thermodynamics. Part 1 discusses definitions, a pre-history of heat and temperature, and steam engine efficiency, which motivated thermodynamics. Part 2 considers in detail three heat conservation-based foundational papers by Carnot, Clapeyron, and Thomson. For a reversible Carnot cycle operating between thermal reservoirs with Celsius temperatures t and $t + d t$ , heat Q from the hot reservoir, and net work W, Clapeyron derived $W / Q = d t / C ( t )$ , with $C ( t )$ material-independent. Thomson used $μ = 1 / C ( t )$ to define an absolute temperature but, unaware that an additional criterion was needed, he first proposed a logarithmic function of the ideal gas temperature $T g$ . Part 3, following a discussion of conservation of energy, considers in detail a number of energy conservation-based papers by Clausius and Thomson. As noted by Gibbs, in 1850, Clausius established the first modern form of thermodynamics, followed by Thomson’s 1851 rephrasing of what he called the Second Law. In 1854, Clausius theoretically established for a simple Carnot cycle the condition $Q 1 / T 1 + Q 2 / T 2 = 0$ . He generalized it to $∑ i Q i / T g , i = 0$ , and then $∮ d Q / T g = 0$ . This both implied a new thermodynamic state function and, with appropriate integration factor $1 / T$ , the thermodynamic temperature. In 1865, Clausius named this new state function the entropy S. View Full-Text
Keywords:
MDPI and ACS Style
Saslow, W.M. A History of Thermodynamics: The Missing Manual. Entropy 2020, 22, 77. https://doi.org/10.3390/e22010077
AMA Style
Saslow WM. A History of Thermodynamics: The Missing Manual. Entropy. 2020; 22(1):77. https://doi.org/10.3390/e22010077
Chicago/Turabian Style
Saslow, Wayne M. 2020. "A History of Thermodynamics: The Missing Manual" Entropy 22, no. 1: 77. https://doi.org/10.3390/e22010077
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Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
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# Am i moving
## Main Question or Discussion Point
In this example I make 2 assumptions
1. if an object is moving through space at time T0 it will be at point x,y,z,T0 and at a different time T1 it will be at a different position x,y,z,T1.
The other assumption I make is that light is non ballistic.
see the associated pics
Referring to fig 1
There is a box that may be moving through space. In the box is a strobe light at the red square, a mirror at the blue square and an observer with a clock at the green square. All objects are at rest wrt the box.
The strobe flashes briefly once. Light will travel from the strobe to the observer.
Light will also travel to the mirror reflect off the mirror to the observer. So the observer will see two flashes of light separated by a time period.
Using the clock the observer measures the period between the two flashes of light.
In fig 1 the light source is to the left of the direction of travel, the mirror on the right.
With this configuration the observer fires the strobe and measures the time period he sees between the two flashes of light. Lets say he gets a reading of X
The observer now changes the position of the mirror and the light. He places the mirror where the light source was and the lgiht source where the mirror was. The observer then places himslf at the psoition he was in in fig 1. The only thing that changes is the position of the mirror and the light all distances between object are the same as in fig 1.
With this configuration the observer fires the strobe and measures the time period he sees between the two flashes of light. I calculate that the observer will not get a reading of X.
Why is this or am I wrong?
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# Chapter 1 The Logic of Compound Statements. Section 1.2 – 1.3 (Modus Tollens) Conditional and Valid & Invalid Arguments.
## Presentation on theme: "Chapter 1 The Logic of Compound Statements. Section 1.2 – 1.3 (Modus Tollens) Conditional and Valid & Invalid Arguments."— Presentation transcript:
Chapter 1 The Logic of Compound Statements
Section 1.2 – 1.3 (Modus Tollens) Conditional and Valid & Invalid Arguments
Conditional Statements A conditional statement is a sentence of the form“if p then q” or p -> q (p implies q). – p is the hypothesis – q is the conclusion
Example “If you show up for work Monday morning, then you will get the job.” – p = You show up for work Monday Morning. – q = You will get the job. – p -> q When is this statement false?
Example -> p v ~q -> ~p Order of precedence: 1. ~, 2. ^,v, 3. ->, p v ~q -> ~p (pv~q) -> (~p)
Logical Equivalence -> p q -> r (p ->r) ^ (q ->r)
Equivalence -> & or p -> q ~p v q Example – ~p v q = “Either you get to work on time or you are fired.” – ~p = You get to work on time. – q = You are fired. – p = You do not get to work on time. – p -> q = “If you do not get to work on time, then you are fired.”
Negation of Conditional Negation of if p then q “p and not q” ~(p -> q) p^ ~q Derivation from Theorem 1.1.1 – ~(p -> q) ~(~p v q) – ~(~p) ^ (~q) by DeMorgan’s – p ^ ~q by the double neg law Example – If Karl lives in Wilmington, then he lives in NC. – Karl lives in Wilmington and he does not live in NC.
Contrapositive of a Conditional The contrapositive of p -> q is ~q -> ~p. Conditional is logically equivalent to its contrapositive: p -> q ~q -> ~p pq~p~qp->q~q -> ~p TTFFTT TFFTFF FTTFTT FFTTTT
Example Conditional p->q – If Howard can swim across the lake, then Howard can swim to the island. – p = “Howard can swim across the lake.” – q = “Howard can swim to the island.” Contrapositive ~q -> ~p – If Howard cannot swim to the island, then Howard cannot swim across the lake.
Converse of Conditional Converse of conditional “if p then q” (p->q) is “if q then p” (q->p) Converse is not logically equivalent to the conditional. Example – (conditional) If today is Easter, then tomorrow is Monday. – (converse) If tomorrow is Monday, then today is Easter.
Inverse of Conditional Inverse of conditional “if p then q” (p->q) is “if ~p then ~q” (~p->q) Inverse is not logically equivalent to the conditional. Example – (conditional) If today is Easter, then tomorrow is Monday. – (inverse) If today is not Easter, then tomorrow is not Monday. However, the converse and inverse are logically equivalent. pq~p~qp->qq->p~p->~q TTFFTTT TFFTFTT FTTFTFF FFTTTTT
Biconditional Biconditional is “p if, and only if q”. Biconditional is T when both p and q have the same logic value and F otherwise. Symbolically – p q
Biconditional Truth Table
Necessary & Sufficient Conditions For statements r and s, – r is a sufficient condition for s (if r then s) means “the occurrence of r is sufficient to guarantee the occurrence of s”. – r is a necessary condition for s (if not r then not s) means “if r does not occur, then s cannot occur”.
Valid & Invalid Arguments An argument is a sequence of statements. All statements in an argument, except for the final one, is the premises (hypotheses). The final statement is the conclusion. Valid argument occurs when the premises are TRUE, which results in a TRUE conclusion.
Testing Argument Form Identify the premises and conclusion of the argument form. Construct a truth table showing the truth values of all the premises and the conclusion. If the truth table reveals all TRUE premises and a FALSE conclusion, then the argument from is invalid. Otherwise, when all premises are TRUE and the conclusion is TRUE, then the argument is valid.
Example If Socrates is a man, then Socrates is mortal. Socrates is a man. :. Socrates is mortal. Syllogism is an argument form with two premises and a conclusion. Example Modus Ponens form: – If p then q. – p – :. q
Example Valid Form p v (q v r) ~r :. p v q
Example Invalid Form p -> q v ~r q -> p ^ r :. p -> r
Modus Tollens – If p then q. – ~q – :. ~p – Proves it case with “proof by contradiction” – Example: – if Zeus is human, then Zeus is mortal. – Zeus is not mortal. – :. Zeus is not human.
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# [San-Diego-pm] selective matching (was: Re: Recompiling global substitution RE?)
Anthony Foiani tkil at scrye.com
Sat Mar 20 22:36:47 PDT 2010
```Reuben Settergren <ruberad at gmail.com> writes:
>
> I should give you more clarification that my actual problem
> (still simplified) looks more like:
>
> DIST - Distance
> DISTANCE: 12.3456 ft 4.5678 m
> STD DEV: 3.4567 ft 1.2345 m
>
> AREA - Area
> AREA: 2345.6789 ft^2 345.6789 m^2
> PERIMETER: 234.5678 ft 89.0123 m
> STD DEV: 3.4567 ft 1.2345 m
>
> DIST - Distance
> DISTANCE: 12.3456 ft 4.5678 m
> STD DEV: 3.4567 ft 1.2345 m
>
> DIST - Distance
> DISTANCE: 8.9012 ft 3.0123 m
> STD DEV: 1.2345 ft 0.4567 m
>
> ...etc
To be honest, neither the original problem description, nor this
clarification, made much sense to me. I suspect that others on the
What are you actually checking against what? Where are you getting
your "good" values? Where are you getting "columns", and their
colors?
> So in any one situation, I will have a set of numbers/colors for a
> particular combination of function/metric/unit (i.e. DIST/'STD DEV'/ft:
> (3.4567,3.4567,1.2345),(red,green,yellow)). So I have to avoid the
> other functions (e.g. AREA) that might have the same numbers.
Ok, this makes a bit more sense. See below for my opinion of a good
way to tackle this problem.
> But with Mark Johnson's idea, I can chomp through my whole
> file-in-one-string bit-by-bit, something like:
>
> \$tail = \$s;
> for my \$i ( 0 .. \$#nums ) {
> \$tail =~
> s/(.*?\$function.*?\$metric.*?)(\$nums[\$i]\s+\$unit)(.*)/\$3/;
> }
>
> If there isn't already a name for this cool kind of trick, there should
> be: train cars? chewandswallow? sausage grinder? Any other ideas?
It's a very common pattern in functional and declarative languages
(lisp and prolog, if you want representative examples).
In Lisp, the pattern is to grab however many args off the front of the
list, and use the "&rest" specifier to put the remaining args into a
named list. Then you do whatever you need to do with the head args,
and call yourself on the remainder:
| (cond ((nilp tail) "")
| (process tail)))))
Prolog would do that somewhat like:
| process( [], [] ).
| process( Tail, MungedTail ).
(I'm quite rusty on both languages, but hopefully you get the idea.)
Both of these languages (and this style of programming) go back at
least into the 70s; Lisp probably goes back into the 60s. Or you
could use Mathematica, which combines the two...
My first approach was to use text matching to build domain-level
entities, and then operate on those entities. You don't have to go
full-bore OOP, but that's basically the end point of following this
line of thinking. In this case, I'll just build up a hash for each
"function", probably with some nested hashes for each metric within
the function. Then you can match those iteratively against your
criteria. (And yes, I really would write comments like this.)
You can see the result here:
http://scrye.com/~tkil/perl/reuben1.plx
I didn't care for how that forced the highlighting functions to know
the output format, though; about halfway through that implementation
(although I did finish it), I realised the the "hard part" was
encoding the criteria. Both of my programs use this structure:
| my @CRITERIA =
| (
|
| { function => 'DIST',
| metric => 'STD DEV',
| units => 'ft',
| ranges => [ 3.4567, # center value
| '' => 0.001, # center tolerance
| green => 0.01, # color => tolerance
| yellow => 0.2,
| red => -1 ] }, # default
|
| { function => 'AREA',
| metric => 'STD DEV',
| units => 'ft^2',
| ranges => [ 2.78,
| '' => 0.01,
| blue => 0.1,
| orange => 0.3,
| red => -1 ] },
|
| { function => 'DIST2',
| metric => 'DISTANCE',
| units => 'm',
| ranges => [ 3.2,
| '' => 0.01,
| green => 0.1,
| orange => 0.3,
| red => -1 ] },
|
| # if multiple criteria matches the same measurement, the
| # later criteria will be nested inside the earlier ones.
| { function => 'DIST2',
| metric => 'DISTANCE',
| units => 'm',
| ranges => [ 3.2,
| '' => 0.01,
| green2 => 0.1,
| orange2 => 0.3,
| red2 => -1 ] }
|
| ); # end of @CRITERIA
(Although only my second effort handles the stacked-rules case
described in the last criterion.)
The second one works on the individual lines as they come in, using
the latest function name as a primitive state variable. The main loop
there:
| my @cur_crit;
|
| while ( my \$line = <DATA> )
| {
| if ( \$line =~ \$func_start_re )
| {
| my \$func = \$1;
| @cur_crit = grep { \$_->{function} eq \$func } @CRITERIA;
| }
| elsif ( \$line =~ \$blank_line_re )
| {
| undef @cur_crit;
| }
| elsif ( \$line =~ \$metric_line_re )
| {
| my ( \$indent, \$metric, \$space, \$vals ) =
| ( \$1, \$2, \$3, \$4 );
|
| foreach my \$crit ( grep { \$_->{metric} eq \$metric } @cur_crit )
| {
| \$vals = highlight \$vals, \$crit;
| }
|
| \$line = join '', \$indent, \$metric, \$space, \$vals;
| }
| print \$line;
| }
The whole program can be found at:
http://scrye.com/~tkil/perl/reuben2.plx
That's the one that I think is the better code, depending on how
With this input data:
| DIST - Distance
| DISTANCE: 12.3456 ft 4.5678 m
| STD DEV: 3.4567 ft 1.2345 m
|
| AREA - Area
| AREA: 2345.6789 ft^2 345.6789 m^2
| PERIMETER: 234.5678 ft 89.0123 m
| STD DEV: 3.4567 ft 1.2345 m
|
| DIST - Distance
| DISTANCE: 12.3456 ft 4.5678 m
| STD DEV: 3.4567 ft 1.2345 m
|
| DIST - Distance
| DISTANCE: 8.9012 ft 3.0123 m
| STD DEV: 1.2345 ft 0.4567 m
|
| DIST2 - Distance
| DISTANCE: 8.9012 ft 3.0123 m
| STD DEV: 1.2345 ft 0.4567 m
And with @CRITERIA as shown above, here's the output:
| \$ ./reuben2.plx
| DIST - Distance
| DISTANCE: 12.3456 ft 4.5678 m
| STD DEV: 3.4567 ft 1.2345 m
|
| AREA - Area
| AREA: 2345.6789 ft^2 345.6789 m^2
| PERIMETER: 234.5678 ft 89.0123 m
| STD DEV: 3.4567 ft 1.2345 m
|
| DIST - Distance
| DISTANCE: 12.3456 ft 4.5678 m
| STD DEV: 3.4567 ft 1.2345 m
|
| DIST - Distance
| DISTANCE: 8.9012 ft 3.0123 m
| STD DEV: <span color="red">1.2345 ft</span> 0.4567 m
|
| DIST2 - Distance
| DISTANCE: 8.9012 ft <span color="orange"><span color="orange2">3.0123 m</span></span>
| STD DEV: 1.2345 ft 0.4567 m
The next time you hit a problem like this, you might want to spend
more time up-front on specification (and possibly writing test cases
and expected outputs) before diving right into the regexes.
(Also, remember that Perl offers many different data manipulation
techniques; regexes aren't always the right answer.)
Happy hacking,
t.
```
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# science
The acceleration due to gravity calculated this way works well for objects near the Earth’s surface. How would you have to change the above equation if the object was 100,000 meters above the ground?
(Note: this question refers to Newton’s equation for the force of gravity between two objects. How would that change if the radius of the earth or distance were increased by 100,000 meters. To help you answer this question, please review your textbook, chapter 3, Newton’s law of Gravitation section.)
F=(6.67 x10-11N.m2/kg2)(m1)(m2)
100,0002
1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. g is inversely proportional to the square of the distance from the center of the earth.
100 km above the earth's surface, g is reduced by a factor [6370/(6370+100)]^2 = 0.969
That would make it 9.51 m/s^2
6370 km is the radius of the earth.
1. 👍
2. 👎
3. ℹ️
4. 🚩
## Similar Questions
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Abacus and Vedic Maths
# Top Ten Vedic Maths Tricks You Should Know for Fast Problem-Solving
Vedic Maths is well-known for its speedy and effective problem-solving techniques that can completely transform how you view mathematics. This blog presents the top ten Vedic Maths tricks to enhance mental math prowess and simplify complex calculations – from multiplication to division; these Vedic Maths tools will enable you to solve math issues swiftly and accurately.
Contents
## Multiplication by Vertically and Crosswise Multiplication
Explore the power of Vedic Maths’ vertical and crosswise multiplication technique that simplifies expanding two or more-digit numbers.
## Squaring Numbers Ending in 5:
Use Vedic Maths’ trick of quickly squaring numbers ending in 5 to make mental calculations simpler and quicker. Multiplying Close to a Base: Simplify multiplication using Vedic Maths techniques that reduce complexity by multiplying numbers close to their bases.
## Doubling and Halving Method:
Access this Vedic Maths technique designed to simplify multiplication and division.
## Quick Division with Nikhilam Sutra:
Discover an alternative means for fast division of large numbers through Vedic Mathematics known as Nikhilam Sutra.
## Finding Percentages with Ekadhikena Purvena:
Learn how the Ekadhikena Purvena method can quickly find percentages, saving time on calculations rapidly.
## Checking Divisibility by Casting Out Nines:
Master this casting out nines technique to test divisibility quickly and detect errors in calculations rapidly.
## Discovering Fast Square Roots using Anurupyena Sutra:
Take advantage of Anurupyena Sutra to quickly locate square roots even for large numbers. Checking Fraction Equivalency using Antyayor Dasakepi: Discover this method to evaluate swiftly fraction equivalencies.
## Yavadunam Sutra to calculate cube roots
Use Yavadunam Sutra to calculate cube roots with conventional methods, saving time quickly.
## Conclusion:
With these top 10 Vedic Maths tricks, you can dramatically enhance your problem-solving skills and transform how you approach math. Leverage its speed and efficiency for fast mental calculations – enroll in our Vedic Maths program at AV to harness its incredible techniques!
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### 7.7.4 dmod_lib
Library:
dmod.lib
Purpose:
Algorithms for algebraic D-modules
Authors:
Viktor Levandovskyy, levandov@math.rwth-aachen.de
Jorge Martin Morales, jorge@unizar.es
Overview:
Let K be a field of characteristic 0. Given a polynomial ring
R = K[x_1,...,x_n] and a polynomial F in R,
one is interested in the R[1/F]-module of rank one, generated by
the symbol F^s for a symbolic discrete variable s.
In fact, the module R[1/F]*F^s has a structure of a D(R)[s]-module, where D(R)
is an n-th Weyl algebra K<x_1,...,x_n,d_1,...,d_n | d_j x_j = x_j d_j +1> and
D(R)[s] = D(R) tensored with K[s] over K.
Constructively, one needs to find a left ideal I = I(F^s) in D(R), such
that K[x_1,...,x_n,1/F]*F^s is isomorphic to D(R)/I as a D(R)-module.
We often write just D for D(R) and D[s] for D(R)[s].
One is interested in the following data:
- Ann F^s = I = I(F^s) in D(R)[s], denoted by LD in the output
- global Bernstein polynomial in K[s], denoted by bs,
- its minimal integer root s0, the list of all roots of bs, which are known
to be rational, with their multiplicities, which is denoted by BS
- Ann F^s0 = I(F^s0) in D(R), denoted by LD0 in the output
(LD0 is a holonomic ideal in D(R))
- Ann^(1) F^s in D(R)[s], denoted by LD1 (logarithmic derivations)
- an operator in D(R)[s], denoted by PS, such that the functional equality
PS*F^(s+1) = bs*F^s holds in K[x_1,...,x_n,1/F]*F^s.
References:
We provide the following implementations of algorithms:
(OT) the classical Ann F^s algorithm from Oaku and Takayama (Journal of
Pure and Applied Math., 1999),
(LOT) Levandovskyy's modification of the Oaku-Takayama algorithm (ISSAC 2007)
(BM) the Ann F^s algorithm by Briancon and Maisonobe (Remarques sur
l'ideal de Bernstein associe a des polynomes, preprint, 2002)
(LM08) V. Levandovskyy and J. Martin-Morales, ISSAC 2008
(C) Countinho, A Primer of Algebraic D-Modules,
(SST) Saito, Sturmfels, Takayama 'Groebner Deformations of Hypergeometric
Differential Equations', Springer, 2000
Guide:
- Ann F^s = I(F^s) = LD in D(R)[s] can be computed by Sannfs [BM, OT, LOT]
- Ann^(1) F^s in D(R)[s] can be computed by Sannfslog
- global Bernstein polynomial bs in K[s] can be computed by bernsteinBM
- Ann F^s0 = I(F^s0) = LD0 in D(R) can be computed by annfs0, annfs, annfsBM,
annfsOT, annfsLOT, annfs2, annfsRB etc.
- all the relevant data to F^s (LD, LD0, bs, PS) are computed by operatorBM
- operator PS can be computed via operatorModulo or operatorBM
- annihilator of F^{s1} for a number s1 is computed with annfspecial
- annihilator of F_1^s_1 * ... * F_p^s_p is computed with annfsBMI
- computing the multiplicity of a rational number r in the Bernstein poly
of a given ideal goes with checkRoot
- check, whether a given univariate polynomial divides the Bernstein poly
goes with checkFactor
Procedures:
7.7.4.0. annfs compute Ann F^s0 in D and Bernstein polynomial for a poly F 7.7.4.0. annfspecial compute Ann F^n from Ann F^s for a polynomial F and a number n 7.7.4.0. Sannfs compute Ann F^s in D[s] for a polynomial F 7.7.4.0. Sannfslog compute Ann^(1) F^s in D[s] for a polynomial F 7.7.4.0. bernsteinBM compute global Bernstein polynomial for a polynomial F (algorithm of Briancon-Maisonobe) 7.7.4.0. bernsteinLift compute a possible multiple of Bernstein polynomial via lift-like procedure 7.7.4.0. operatorBM compute Ann F^s, Ann F^s0, BS and PS for a polynomial F (algorithm of Briancon-Maisonobe) 7.7.4.0. operatorModulo compute PS via the modulo approach 7.7.4.0. annfsParamBM compute the generic Ann F^s (algorithm by Briancon and Maisonobe) and exceptional parametric constellations for a polynomial F with parametric coefficients 7.7.4.0. annfsBMI compute Ann F^s and Bernstein ideal for a polynomial F=f1*..*fP (multivariate algorithm of Briancon-Maisonobe) 7.7.4.0. checkRoot check if a given rational is a root of the global Bernstein polynomial of F and compute its multiplicity 7.7.4.0. SannfsBFCT compute Ann F^s in D[s] for a polynomial F (algorithm of Briancon-Maisonobe, other output ordering) 7.7.4.0. annfs0 compute Ann F^s0 in D and Bernstein polynomial from the known Ann F^s in D[s] 7.7.4.0. annfs2 compute Ann F^s0 in D and Bernstein polynomial from the known Ann F^s in D[s] by using a trick of Noro 7.7.4.0. annfsRB compute Ann F^s0 in D and Bernstein polynomial from the known Ann F^s in D[s] by using Jacobian ideal 7.7.4.0. checkFactor check whether a polynomial q in K[s] is a factor of the global Bernstein polynomial of F from the known Ann F^s in D[s] 7.7.4.0. arrange create a poly, describing a full hyperplane arrangement 7.7.4.0. reiffen create a poly, describing a Reiffen curve 7.7.4.0. isHolonomic check whether a module is holonomic 7.7.4.0. convloc replace global orderings with local in the ringlist L 7.7.4.0. minIntRoot minimal integer root among the roots of a maximal ideal P 7.7.4.0. isRational check whether n is a rational number
| 1,586
| 4,900
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CC-MAIN-2022-49
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http://de.metamath.org/mpegif/resspsradd.html
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text/html
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crawl-data/CC-MAIN-2020-40/segments/1600400213454.52/warc/CC-MAIN-20200924034208-20200924064208-00439.warc.gz
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Metamath Proof Explorer < Previous Next > Nearby theorems Mirrors > Home > MPE Home > Th. List > resspsradd Structured version Unicode version
Description: A restricted power series algebra has the same addition operation. (Contributed by Mario Carneiro, 3-Jul-2015.)
Hypotheses
Ref Expression
resspsr.s mPwSer
resspsr.h s
resspsr.u mPwSer
resspsr.b
resspsr.p s
resspsr.2 SubRing
Assertion
Ref Expression
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 resspsr.u . . 3 mPwSer
2 resspsr.b . . 3
3 eqid 2429 . . 3
4 eqid 2429 . . 3
5 simprl 762 . . 3
6 simprr 764 . . 3
71, 2, 3, 4, 5, 6psradd 18541 . 2
8 resspsr.s . . . 4 mPwSer
9 eqid 2429 . . . 4
10 eqid 2429 . . . 4
11 eqid 2429 . . . 4
12 fvex 5891 . . . . . . . 8
13 resspsr.2 . . . . . . . . . 10 SubRing
14 resspsr.h . . . . . . . . . . 11 s
1514subrgbas 17952 . . . . . . . . . 10 SubRing
1613, 15syl 17 . . . . . . . . 9
17 eqid 2429 . . . . . . . . . . 11
1817subrgss 17944 . . . . . . . . . 10 SubRing
1913, 18syl 17 . . . . . . . . 9
2016, 19eqsstr3d 3505 . . . . . . . 8
21 mapss 7522 . . . . . . . 8
2212, 20, 21sylancr 667 . . . . . . 7
2322adantr 466 . . . . . 6
24 eqid 2429 . . . . . . 7
25 eqid 2429 . . . . . . 7
26 reldmpsr 18520 . . . . . . . . . 10 mPwSer
2726, 1, 2elbasov 15134 . . . . . . . . 9
2827ad2antrl 732 . . . . . . . 8
2928simpld 460 . . . . . . 7
301, 24, 25, 2, 29psrbas 18537 . . . . . 6
318, 17, 25, 9, 29psrbas 18537 . . . . . 6
3223, 30, 313sstr4d 3513 . . . . 5
3332, 5sseldd 3471 . . . 4
3432, 6sseldd 3471 . . . 4
358, 9, 10, 11, 33, 34psradd 18541 . . 3
3614, 10ressplusg 15198 . . . . . . 7 SubRing
3713, 36syl 17 . . . . . 6
3837adantr 466 . . . . 5
39 ofeq 6547 . . . . 5
4038, 39syl 17 . . . 4
4140oveqd 6322 . . 3
4235, 41eqtrd 2470 . 2
43 fvex 5891 . . . . 5
442, 43eqeltri 2513 . . . 4
45 resspsr.p . . . . 5 s
4645, 11ressplusg 15198 . . . 4
4744, 46mp1i 13 . . 3
4847oveqd 6322 . 2
497, 42, 483eqtr2d 2476 1
Colors of variables: wff setvar class Syntax hints: wi 4 wa 370 wceq 1437 wcel 1870 crab 2786 cvv 3087 wss 3442 ccnv 4853 cima 4857 cfv 5601 (class class class)co 6305 cof 6543 cmap 7480 cfn 7577 cn 10609 cn0 10869 cbs 15084 ↾s cress 15085 cplusg 15152 SubRingcsubrg 17939 mPwSer cmps 18510 This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1665 ax-4 1678 ax-5 1751 ax-6 1797 ax-7 1841 ax-8 1872 ax-9 1874 ax-10 1889 ax-11 1894 ax-12 1907 ax-13 2055 ax-ext 2407 ax-rep 4538 ax-sep 4548 ax-nul 4556 ax-pow 4603 ax-pr 4661 ax-un 6597 ax-cnex 9594 ax-resscn 9595 ax-1cn 9596 ax-icn 9597 ax-addcl 9598 ax-addrcl 9599 ax-mulcl 9600 ax-mulrcl 9601 ax-mulcom 9602 ax-addass 9603 ax-mulass 9604 ax-distr 9605 ax-i2m1 9606 ax-1ne0 9607 ax-1rid 9608 ax-rnegex 9609 ax-rrecex 9610 ax-cnre 9611 ax-pre-lttri 9612 ax-pre-lttrn 9613 ax-pre-ltadd 9614 ax-pre-mulgt0 9615 This theorem depends on definitions: df-bi 188 df-or 371 df-an 372 df-3or 983 df-3an 984 df-tru 1440 df-ex 1660 df-nf 1664 df-sb 1790 df-eu 2270 df-mo 2271 df-clab 2415 df-cleq 2421 df-clel 2424 df-nfc 2579 df-ne 2627 df-nel 2628 df-ral 2787 df-rex 2788 df-reu 2789 df-rab 2791 df-v 3089 df-sbc 3306 df-csb 3402 df-dif 3445 df-un 3447 df-in 3449 df-ss 3456 df-pss 3458 df-nul 3768 df-if 3916 df-pw 3987 df-sn 4003 df-pr 4005 df-tp 4007 df-op 4009 df-uni 4223 df-int 4259 df-iun 4304 df-br 4427 df-opab 4485 df-mpt 4486 df-tr 4521 df-eprel 4765 df-id 4769 df-po 4775 df-so 4776 df-fr 4813 df-we 4815 df-xp 4860 df-rel 4861 df-cnv 4862 df-co 4863 df-dm 4864 df-rn 4865 df-res 4866 df-ima 4867 df-pred 5399 df-ord 5445 df-on 5446 df-lim 5447 df-suc 5448 df-iota 5565 df-fun 5603 df-fn 5604 df-f 5605 df-f1 5606 df-fo 5607 df-f1o 5608 df-fv 5609 df-riota 6267 df-ov 6308 df-oprab 6309 df-mpt2 6310 df-of 6545 df-om 6707 df-1st 6807 df-2nd 6808 df-supp 6926 df-wrecs 7036 df-recs 7098 df-rdg 7136 df-1o 7190 df-oadd 7194 df-er 7371 df-map 7482 df-en 7578 df-dom 7579 df-sdom 7580 df-fin 7581 df-fsupp 7890 df-pnf 9676 df-mnf 9677 df-xr 9678 df-ltxr 9679 df-le 9680 df-sub 9861 df-neg 9862 df-nn 10610 df-2 10668 df-3 10669 df-4 10670 df-5 10671 df-6 10672 df-7 10673 df-8 10674 df-9 10675 df-n0 10870 df-z 10938 df-uz 11160 df-fz 11783 df-struct 15086 df-ndx 15087 df-slot 15088 df-base 15089 df-sets 15090 df-ress 15091 df-plusg 15165 df-mulr 15166 df-sca 15168 df-vsca 15169 df-tset 15171 df-subg 16765 df-ring 17717 df-subrg 17941 df-psr 18515 This theorem is referenced by: subrgpsr 18578 ressmpladd 18616
Copyright terms: Public domain W3C validator
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CC-MAIN-2020-40
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latest
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https://www.basic-mathematics.com/algebra-worksheets.html
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crawl-data/CC-MAIN-2023-23/segments/1685224643388.45/warc/CC-MAIN-20230527223515-20230528013515-00291.warc.gz
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# Algebra worksheets
A variety of algebra worksheets that teachers can print and give to students as homework or classwork.
Integer worksheets
Worksheet about using the distributive property.
Worksheet about finding the greatest common factor of two numbers.
Least common multiple worksheet
Worksheet about finding the least common multiple of two numbers.
Writing equations worksheet
Worksheet about writing an equation when the sentence is given.
Worksheet about solving equations that have many variables.
Composition of functions worksheet
Worksheet about finding the composition of functions and also evaluating the composition of functions for some specific values.
Worksheet about factoring equations of the form ax2 + bx + c.
Worksheet about simplifying radical expressions involving the square root or the cube root.
Worksheets about solving systems of linear equations either by substitution or elimination.
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Looking for a visual puzzle really difficult? If your answer is a “Yes”You will be pleased to know that here is the challenge viral most … Read more
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When entering Facebook and other social networks, we can realize that the visual puzzles are trendy. They have really gained popularity because they generate fun. … Read more
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Do you know what you can do in your free time? Participate in a visual puzzle. Here we introduce you to one that is difficult … Read more
## Logical riddle | 97% did not claim victory in this viral challenge: you must locate the ghost in the image | Visual riddle | MEXICO
Visual puzzles have become a healthy entertainment alternative on social media. Therefore, if what you want is to have fun and test your abilities at … Read more
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https://mirror.codeforces.com/blog/Halym2007
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crawl-data/CC-MAIN-2024-33/segments/1722641086966.85/warc/CC-MAIN-20240813235205-20240814025205-00415.warc.gz
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### Halym2007's blog
By Halym2007, history, 6 months ago,
In this problem Can you explain me sample test case?How That answer comes.
• 0
By Halym2007, history, 7 months ago,
both code did same.what is the difference?
First one :
set <int> s;
s.insert (1);s.insert (3);s.insert (5);
auto tr = s.lower_bound (2);
s.erase (tr);<-----------here
--------------------------
Second one :
set <int> s;
s.insert (1);s.insert (3);s.insert (5);
auto tr = s.lower_bound (2);
s.erase (*tr);<-----------here
• +40
By Halym2007, history, 9 months ago,
• -5
By Halym2007, history, 9 months ago,
i trying to solve this problem.I tried my best I got 23 point(I got 1-st and 2-nd subtask).Can you share your idea for full score?
• -12
By Halym2007, history, 10 months ago,
In this problem.I tried greedy solution.But It didn't pass.I tried but I didn't find anti-test for my solution? Can you give me anti test for this code?
#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int N = 5e5 + 5;
ll o, a[N], seg[N], sum;
int main () {
// freopen("input.txt", "r", stdin);
int n;
cin >> n;
for (int i = 1; i <= n; ++i) {
cin >> a[i];
}
o++;
seg[o] = a[1];
for (int i = 2; i <= n; ++i) {
sum = 0;
int r;
for (int j = i; j <= n; ++j) {
sum += a[j];
if (sum >= seg[o]) {
r = j;
break;
}
}
if (sum >= seg[o]) {
o++;
seg[o] = sum;
// i bilen r aralyk
for (int j = i; j <= r; ++j) {
if (seg[o] - a[j] >= seg[o - 1] + a[j]) {
seg[o] -= a[j];
seg[o - 1] += a[j];
}
else break;
}
}
else {
seg[o] += sum;
break;
}
i = r;
}
cout << o << endl;
}
• +13
By Halym2007, history, 10 months ago,
• +16
By Halym2007, history, 11 months ago,
Will Izho 2024 be offline?
• -11
By Halym2007, history, 13 months ago,
If you has schedule or used to has schedule,Can you share?
• +8
By Halym2007, history, 13 months ago,
In this problem?We should write time complexity O(N log2(N));But i didn't understand solution proof.
#include <bits/stdc++.h>
#define ll long long int
#define pb push_back
#define ppb pop_back
#define sz size()
#define ss second
#define ff first
#define N 200001
using namespace std;
ll _, x, n, a[N];
int main(){
cin >> n;
for(int i = 1; i <= n; i++){
cin >> a[i];
}
vector <ll> v;
v.pb(a[1]);
for(int i = 2; i <= n; i++){
auto t = lower_bound(v.begin(),v.end(),a[i]) - v.begin();
if(t == v.sz) v.pb(a[i]);
else{
v[t] = a[i];
}
}
// for(auto i : v) cout << i << ' ';
cout << v.sz;
}
This code gets accepted.
• 0
By Halym2007, history, 19 months ago,
how to participate info1cup????
• +7
By Halym2007, history, 19 months ago,
my goal is to become master.
• +15
By Halym2007, history, 21 month(s) ago,
link of problem: 104052B - Lunchtime Fruits.i got 70 points but how to get 100 points.I read solution of problem but i didn't understand.Please help this problem to get 100 points
• -1
By Halym2007, history, 22 months ago,
I'm going to participate. I'm interesting about who is going to parcipate?????
• +4
By Halym2007, history, 23 months ago,
that doesn't matter junior
• +2
By Halym2007, history, 2 years ago,
which problems should i solve.or link of questions
• 0
By Halym2007, history, 2 years ago,
what is my wrong in my code. who can find my wrong please say me. [problem:https://mirror.codeforces.com/problemset/problem/916/B]. [submission:https://mirror.codeforces.com/contest/916/submission/157866266
• 0
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CC-MAIN-2024-33
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latest
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en
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http://oeis.org/A070089/internal
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crawl-data/CC-MAIN-2019-43/segments/1570987773711.75/warc/CC-MAIN-20191021120639-20191021144139-00379.warc.gz
| 148,157,979
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This site is supported by donations to The OEIS Foundation.
Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
A070089 P(n) < P(n+1) where P(n) (A006530) is the largest prime factor of n. 9
%I
%S 1,2,4,6,8,9,10,12,16,18,20,21,22,24,25,27,28,30,32,33,36,40,42,45,46,
%T 48,50,52,54,56,57,58,60,64,66,68,70,72,75,77,78,81,82,84,85,88,90,91,
%U 92,93,96,98,100,102,105,106,108,110,112,114,115,117
%N P(n) < P(n+1) where P(n) (A006530) is the largest prime factor of n.
%C Erdős conjectured that this sequence has asymptotic density 1/2.
%C There are 500149 terms in this sequence up to 10^6, 4999951 up to 10^7, 49997566 up to 10^8, and 499992458 up to 10^9. With a binomial model with p = 1/2, these would be +0.3, -0.5, -0.0, and -0.5 standard deviations from their respective means. In other words, Erdős's conjecture seems solid. - _Charles R Greathouse IV_, Oct 27 2015
%D H. L. Montgomery, Ten Lectures on the Interface Between Analytic Number Theory and Harmonic Analysis, Amer. Math. Soc., 1996, p. 210.
%H T. D. Noe, <a href="/A070089/b070089.txt">Table of n, a(n) for n = 1..1000</a>
%t f[n_] := FactorInteger[n][[ -1, 1]]; Select[ Range[125], f[ # ] < f[ # + 1] &]
%o (PARI) gpf(n)=if(n<3,n,my(f=factor(n)[,1]); f[#f])
%o is(n)=gpf(n) < gpf(n+1) \\ _Charles R Greathouse IV_, Oct 27 2015
%Y Cf. A006530, A070087.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, May 13 2002
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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)
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## Best explanation to understand and solve the problems on trains
In current mechanical world, problems on trains is the most important topic to everyone especially college students and competitive examiners, and who want to learn something about trains.
In this content has three important point that is speed, time and distance. These three play a main role in problems on trains. Here, we provide some shortcuts, formula, solved problems to overcome the problems on train. Lets we see!
### Problems on trains formulae:
The three important thing is speed, time and distance.
Now, we want to clear the definition of time, speed and distance.
Time: a duration of events expressed in terms of past, present, and future and its measured by minutes, hours, days and months.
Speed: speed is the distance traveled per unit of time. It has two types, velocity and agility.
Distance: distance is a numerical measurement of how far apart objects are.Formulas are given below:
1. Time = Distance / Speed
2. Speed = Distance / Time
3. Distance = Speed x Time
We can use this formulae in any problems on trains. It mainly focus on time management and hard work. Because, time management plays a vital role in math and logical questions. Logical thinking is the best way to reach the exact answer.
In current world every multinational companies, schools, colleges and any other industrial companies are need only smart and logical thinking people, because they can easily solve the problem with attractive mind.
So, if you know how to solve the problems on trains by using shortcuts means, the further details will help you to do so.
### Problems on trains important points to remember:
First we know the basic that is, first one is the train and the second one is an object that which crossed by the train.
When the trains are moving in the same direction means, then their speed will be added. And when the trains are moving in opposite directions means, then their speed will be subtracted.
But, everything based on time management.
### Problems on trains tips:
1. In competitive exams shortcuts are very essential to deal the logical questions. In technical world have many short and sweet ways are available, but we will put some hard work and smart work to achieve it.
2. First of all do practice and set a goal, write any 10 math questions and solve according to your basic formulae knowledge and also must focus on timing.
3. If you want to know the shortcuts of problems on trains means, first improve your time management.
4. Fix a goal, daily you want to solve at least 10 math questions, if you pickup the math with proper timing, definitely you can solve the problems on trains in an easy manner.
### Problems on trains with explanation:
Here some questions are given below with the explanation. Use this and know the secret behind that. Many examples are here check it and try it in your own way.
1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
2. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
3. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
4. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
5. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
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1 view (last 30 days)
Haya M on 24 Jan 2020
Edited: Ravi Kumar on 28 Jan 2020
I'm using the syntax [?,?]=??????(?,?,?,?.1.0,?,1.0,[−1,1]); to solve a PDE on a given domain with a given ? ,
How can I extract the matrices of the finite elements system for the PDE i.e ?
and
how I can assure that the computed eigenvalue say ?(2) corresponds to the correct eigenfunction ?(:,2)? I mean are they eigenpairs? is there any way to check that?
Thanks
Ravi Kumar on 24 Jan 2020
Edited: Ravi Kumar on 27 Jan 2020
Please use one the newer workflow like general equation based one, Structural or Thermal one. Once you setup your model in one of the newwer workflow you can get matrices using assembleFEMatrices function.
For your second question you can back substitute eigenpair into the equation and make sure the residual is near zero.
Regards,
Ravi
Show 1 older comment
Ravi Kumar on 27 Jan 2020
Knowing v1 and l1, you can compute the residual as:
res = norm(K*v1-l1*v1), this would be close to zero only if l1 and v1 are the right pair.
PS: I fixed typo in my previous comment.
Regards,
Ravi
Haya M on 28 Jan 2020
Thank you Ravi for the answer,
Do you mean that res = norm((K-l1)*v) ?
best regards,
Haya
Ravi Kumar on 28 Jan 2020
Yep, that's right. Fixed my comment again.
Ragards,
Ravi
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# MCQ Questions for Class 8 Maths Chapter 3 Understanding Quadrilaterals with Answers
If you’re looking for a way to enhance your Class 8 Maths, then look no further than the NCERT MCQ Questions for Class 8 Maths Chapter 3 Understanding Quadrilaterals with Answers. The MCQ Questions for Class 8 Maths with Answers are aligned to all topics covered so it will be helpful when preparing for your exams, no matter what subject you’re studying! Don’t forget about scoring maximum points during exam preparation by using these free Class 8 Maths Chapter 3 Understanding Quadrilaterals Objective Questions.
What are you waiting for? Get all the answers to Class 8 Maths Chapter 3 MCQs! It’s time that students power up and start practicing these MCQ Questions of Understanding Quadrilaterals Class 8 with answers. The best way of doing so would be solving them yourself in order not only to know which answer is correct but also to understand why each solution works as well.
Question 1.
The opposite sides of a parallelogram are of ________ length.
(a) not equal
(b) different
(c) equal
(d) none of these
Question 2.
In the quadrilateral ABCD, the diagonals AC and BD are equal and perpendicular to each other. What type of a quadrilateral is ABCD?
(a) A square
(b) A parallelogram
(c) A rhombus
(d) A trapezium
Question 3.
If ABCD is an isosceles trapezium, what is the measure of ∠C?
(a) ∠B
(b) ∠A
(c) ∠D
(d) 90°
Question 4.
Which of the following is true for the adjacent angles of a parallelogram?
(a) they are equal to each other
(b) they are complementary angles
(c) they are supplementary angles
(d) none of these.
Answer: (c) they are supplementary angles
Question 5.
State the name of a regular polygon of 6 sides.
(a) pentagon
(b) hexagon
(c) heptagon
(d) none of these
Question 6.
The diagonal of a rectangle is 10 cm and its breadth is 6 cm. What is its length?
(a) 6 cm
(b) 5cm
(c) 8cm
(d) 4cm
Question 7.
The perimeter of a parallelogram is 180 cm. If one side exceeds the other by 10 cm, what are the sides of the parallelogram?
(a) 40 cm, 50 cm
(b) 45 cm each
(c) 50 cm each
(d) 45 cm, 50 cm
Answer: (a) 40 cm, 50 cm
Question 8.
A _______ is both ‘equiangular’ and ‘equilateral’.
(a) regular polygon
(b) triangle
(d) none of these
Question 9.
Which of the following quadrilaterals has two pairs of adjacent sides equal and diagonals intersecting at right angles?
(a) square
(b) rhombus
(c) kite
(d) rectangle
Question 10.
Which one of the following is a regular quadrilateral?
(a) Square
(b) Trapezium
(c) Kite
(d) Rectangle
Question 11.
What do you call a parallelogram which has equal diagonals?
(a) A trapezium
(b) A rectangle
(c) A rhombus
(d) A kite
Question 12.
The sides of a pentagon are produced in order. Which of the following is the sum of its exterior angles?
(a) 540°
(b) 180°
(c) 720°
(d) 360°
Question 13.
In a square ABCD, the diagonals bisect at O. What type of a triangle is AOB?
(a) An equilateral triangle.
(b) An isosceles but not a right angled triangle.
(c) A right angled but not an isosceles triangle.
(d) An isosceles right angled triangle.
Answer: (d) An isosceles right angled triangle.
Question 14.
Which of the parallelograms has all sides equal and diagonals bisect each other at right angle?
(a) square
(b) rectangle
(c) rhombus
(d) trapezium.
Question 15.
A diagonal of a rectangle is inclined to one side of the rectangle at 25°. What is the measure of the acute angle between the diagonals?
(a) 25°
(b) 40°
(c) 50°
(d) 55°
Question 16.
The ________ of a rhombus are perpendicular bisectors of one another.
(a) angles
(b) sides
(c) diagonals
(d) none of these
Question 17.
ABCD is a parallelogram. The angle bisectors of ∠A and ∠D meet at O. What is the measure of ∠AOD?
(a) 45°
(b) 90°
(c) 75°
(d) 180°
Question 18.
he sum of the measures of the three angles of a triangle is ______.
(a) 360°
(b) 210°
(c) 180°
(d) none of these
Question 19.
How many diagonals does a rectangle have?
(a) 2
(b) 1
(c) 0
(d) none of these
Question 20.
Which of the following quadilaterals has two pairs of adjacent sides equal and diagonals intersecting at right angles?
(a) square
(b) rhombus
(c) kite
(d) rectangle
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