Let p be an odd prime. Suppose p5 mod 8. Show p-1 p? – 1 mod 2. 5

Q: Find in side r=2 aren oul sde r=l+ Ges 6

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Q: Find plane area inside polar function r 2 and outside polar function r= -2sint in thisd quurter.

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Q: Maximize: z = 2x, + X2 Use the simplex method to solve the linear programming problem. X+5x2 s 12…

A: The given linear programming problem is…

Q: Maximize. z= 2x, + X2 Use the simplex method to solve the linear programming problem. X, +5x2 s 12…

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Q: Let f be the function defined by f (x) = cos(/x). OS sin() (c) It is known that f' (x) = cos() and…

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Q: Q5/ Use Linear Regression to fit the following data: 2 4 5 6. Y 4 9 10 10 8

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Q: 3.r – 21 – 4r - 3 dr 12(x² + x +1)

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Q: Determine whether the following series converges or diverges. If the series converges, determine the…

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Q: Use the Alternating Series Remainder Theorem to determine the number of terms required to…

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Q: Q4) Find plane area inside the polar function r 2 and outside polar function r = 2 sin +e) in second…

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Q: 3+ V9 – 4(3 – i) 21 = 3+ V4i – 3 2 How do you solve for the equation above ?

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Q: Let E be solid bounded below by the xy-plane, bounded above by the cylinder z = 1- y?. On the sides,…

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Q: Q5) Find volume of body bounded by z = -y? from below and z = x? from above inside y = 0,y = x,x 1.

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Q: Q4) Find plane area inside polar function r = 2 and outside polar function r = -2sine in third…

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Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z2 by the yz-plane. Do…

A: Surface area in yz-plane

Q: 2. For each of the following, find the values of r for which the series converges. (a) ". Also, find…

A: We have to find the value of x for which series converges.

Q: Let V = R? and let H be the subset of V of all points on the line -3x + 4y = -12. Is H a subspace of…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: The approximation of f, xin(x + 3) dx using two points Gaussian quadrature formula is:

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Q: Q1) Evaluate the integral N 4-y2 dx dy using polar coordinate

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Q: 3+ V9 – 4(3 – i) 21 = 3+ V4i – 3 2

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Q: Given the powers of a transition matrix T and its square below, find the probability of moving from…

A: given powers of a transition matrix and its square T=    A   B  C    ABC0.20.30.50.20.30.50.10.20.7…

Q: #2. Let S be the set of all strings of O's and 1's of length 3. Define a relation R on S as follows:…

A: Given is a set S of strings.   Also, given a relation R of set S.   To Prove: R is an equivalence…

Q: (b) The diagr cubic fune it passes t

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Q: Consider an 2n +1 2n + 3 for n EN = {1,2,3,...}. 1. Find a general formula for the kth partial sum…

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Q: (1+x)-3=1-3x+6x2-10x3........ with ex= 1+x +x2/2 +x3/6............

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Q: In Exercises 1-4, find the vector x determined by the given coor- dinate vector [x ]g and the given…

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Q: Estimate the error in using the partial sum of 65 terms of the series k=1 Error DII * @ # $ & 2 4 5…

A: We have to find the error of series.

Q: Q4) Find plane area inside the polar function r = 2 and outside polar function r= -2cose in second…

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Q: line re gment corine tin g tuo pents pick a peut in the unit ciscle that are randomdy unit a a cherd…

A: The CDF for r here is obtained as:F(r) = P(R <= r) As the point is uniformly distributed over the…

Q: Q3) Evaluate triple integral , S S2(x² – y²)dz dy dx .

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Q: There are red balls, white balls, and black balls in a bag. A ball is chosen at random and the color…

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Q: Q3) Evaluate triple integral S S dz dy dx.

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Q: Suppose the amount of a certain radioactive substance in a sample decays from 3.60 mg to 800. pg…

A: We have to find the half life of substance.

Q: Find plane area inside the polar function r = 2 and outside polar function r = 2 sin ( + 0) in…

A: Area using polar coordinates is given by A=∫∫A r dr dθ

Q: QI) Evaluate the integral , S, dy dx using polar coordinate

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Q: n(A U B) = 155, n(A N B) = 30, and n(A) = 105 %3D What is n(B) ?

A: We have given the values n(AUB)=155 , n(AnB)=30 and n(A)=105 . Then to find n(B) .

Q: Q4) Find plane area inside the polar function r = 2 and outside polar function r = 2 sin ( + 0) in…

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Q: O Evaluate the following integral using Partial Fractions Method: x3 + x2 y : dx x2 1

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Q: O Find plane area inside the polar function r = 2 and outside polar function r = 2 sin (+ 0) in…

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Q: Aーy? QI) Evaluate the integral dx dy using polar coordinate

A: To find integral using polar coordinate .

Q: Q1/ Estimate f (1.72) from the given data using Newton's Backward Difference Formula: 1.7 1.8 1.9 2…

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Q: Q4/ solve the equation by Newton -Raphson Method: F(x) = x* - 5x + 65 , start at x =2, accuracy…

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Q: Q3) Evaluate triple integral S, y(x2 - y²)dz dx dy.

A: To Evaluate: ∫01∫y1∫-y2x2x2-y2dz dx dy

Q: 22 – 9a? = 1 4,

A: We have to sketch the graph of given equation.

Q: a. ž Ātsink) (use integral test n2 b. here 2n Ma

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Q: /1- y?)dx = 0

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Q: 3. Compute the product M()M() as a 2 x 2 matrix. What kind of isometry is this product? If it is a…

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Q: Q2) Evaluate the following integral using Trigonometric Substitutions Method: dx 19x2 + 16 y

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Q: Prove that between any two rational numbers, there is an irrational number via (i) the…

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Q: A card is drawn at random from a box of 20 cards numbered from 1 to 20. Find the probability of…

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