Prove that for all integers, n , n^3-n is divisible by 3.

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Q: P(A | B) = 0.1, P(B) = 0.7, P(A | B') = 0.4. Find P(B | A).

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Q: Find the norm of i and the unit vector i in the direction of a if ||7|| =

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Q: What are the steps in solving problems involving direct proportion?

A: Concept: When the ratio of the things remains constant, it is said to be direct proportion.

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A: The below function is defined on the interval (0,2]. fx=4x+2 To find the Fourier series of even…

Q: Q2) Solve the D.E xy(x² + 1)dy -(y² + 1)dx = 0 %3D

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Q: If R is symmetric, then R 1 is symmetric. True False

A: We have determined that if R is symmetric then R-1 is symmetric or not. If R is symmetric, then R-1…

Q: What is the minimum number of edges of a spanning tree for this graph? A В E D. C.

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Q: How many distinct equivalence classes exist in the relation R defined as below: x Ry + 3| (2x - )

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Q: 1.5 3-y Q1) Evaluate the integral S dx dy using polar coordinate 'y

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Q: To find: the whether the given telescopic series converges or not by finding the limit of the sum of…

A: Given series is ∑k=1∞1k0.1 - 1(k+1)0.1

Q: | 10re", | 2:r3 + 3x² – 12x, r>0 * <0 Given: f(r) = (a) Identify all critical numbers of f. (b)…

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Q: Evaluate the triple integral z dV, where E is bounded by the cylinder y + z? = 16 and the planes E x…

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Q: Directions: Study the horizontal double bar graph and answer the questions that follow. Write your…

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A: Given McJester's Burger Hut plans to expand by opening several new restaurants.  The chain operates…

Q: 1. ÿ + 6ÿ + 11ý + 6y(t) = 0; y(0) = 2, y(0) = 1, ÿ(0) = -1 %3D %3D

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Q: If n is a positive integer, then [2 -168 -4 -2]^n  is [ ]  (Hint: Diagonalize the matrix first. Note…

A: Given that,  A=2-168-4-2 let A=21-84-2-1=2B Then An=2Bn                         1, where nis a…

Q: Exercises: 1) Determine the eigenvalues and the corresponding eigenvectors for the following…

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Q: 14. Briefly explain why || d || == || c || when d=axb and || a ||=1. a b d

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Q: 2. What is the last digit in the product of 31x3 x3x --x32018 x32019x320207

A: Given, 31×32×33× · · · ×32018 ×32019×32020 = 3(1+2+3+ . . . +2020) = 32020(1+2020)2     since…

Q: Q18: Select the incorrect step while evaluating . , dx. e x2-7x+10 x-8 8. I: Let I = S; ;dx = ; odx…

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Q: Solve the cubic equation in two different ways: 1 – 4x – 4x2 + 8x³ = 0. - %3D

A: The function given is as follows: fx=8x3-4x2-4x+1=0 We are asked to solve the cubic equation using…

Q: (b) Compute two iterations (x2, va) of Newton's method starting with (xo, yo) = (1, 1) to estimate…

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Q: The shaded region R is bounded by the lines y = 0, x = 5, and the curve y = Vx – 1 as shown in…

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Q: Q: Solve by iteration methods the following 2X + Y+ 6z= 9 8X + 3Y + 2Z= 13 X + 5Y + Z= 7 X=2 Y=4…

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Q: Find the solution. y'+=V5. y v(1) = 0 3 x2– 3x +2 (A) у 9x x-3+ 2x y = 9x x3 – 2x 2 +1 9x II

A: Given differential equation:y'+yx=y, y(1)=0To find: Solution of the differential equation.

Q: Find the curvature of the function y=ln(3x) at x=3x=3. Find the radius of curvature at x=3x=3.…

A: Given function is:  y = ln(3x) First we will calculate the radius of curvature : Radius of curvature…

Q: Let the characteristic equation of a 3 X 3 Matrix A be X3 + ad² + 47) – eigenvalue of A is 4 and a…

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Q: у (0) %3D —2, у(0) ||

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Q: . i. Is 221 – 1 a prime? Give your reason. Note 21 = 3 x 7 is not prime. ii. Is 219 – 1 a prime?…

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Q: Q42. The value of p and q respectively when (p + q) V p is false is? (a) T, T (b) T, F (c) F, T- (d)…

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Q: Q Use Newton methad to find f(s), f'ca) 9. 8. to 8. 10

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Q: Solve the following IVPS using LT method. 3) y" + 16y = 1, y(0) = 1, y(0) = 2;

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Q: Let the characteristic equation of a 3 X 3 Matrix A be X3 + aX? + 47A eigenvalue of A is 4 and a is…

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Q: Q10: Following are the differential equations and their respective solutions. Select the incorrect…

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Q: D is the region enclosed by Sx² + y? <9 and y <0, then vhich of the following is the setting of he…

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Q: Let V = (3, 00). For u, v e V and a e R define vector addition by u H v := uv – 3(u + v) + 12 and…

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Q: he function f(x) = e – 1 is to be solved using lewton-Raphson method. If the initial value of o is…

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Q: 2x; . The graph X;+1 ° (Continue) Consider the discrete time dynamical system X1+1 = of the updating…

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Q: Determine whether the following series converges. Justify your answer. (- 15)* 00 Σ k! k= 1 Select…

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Q: 14. Briefly explain why || d || == || c || when d=axb and || a ||=1. a b d

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Q: A ship is traveling from a port located at (-2, -2) to a destination located at (10, 10). It decides…

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Q: Let T:R R' be linear transformation defined by T. (-3rs+4) (a) Find the standard matrix ofT. Find a…

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Q: Q10: Following are the differential equations and their respective solutions. Select the incorrect…

A: We have to check whether the given solution is solution of actual differential equation or not.

Q: True / False (no work needed): Approximating the integral x* – 5x² +x dx with Composite Simpson's…

A: TRUE , because error in the Simpson's 1/3 rule us of order h4.

Q: Q4. Find the value of the cubic root V48 using Bisection method, the root lies between 3.5 and 3.75.…

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Q: ) Solve the D.E xy(x²+ 1)dy- (y2 + 1)dx 0 %3D

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Q: How Fnd the Goneral soluhomfor dhe following %3D

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Q: 1. Draw the graph of the following relations and/or functions. Make sure that all "important" points…

A: Given are some functions in (a), (b) and (c)   To Graph the function, then find the domain, Range,…

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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