Question 7 Find the solution. (D² - 2D - 3)y = 0; when x = 0, y = 0, y'= 4 - 3x – e 2x A y = - „3x By = e-e³ y = e-3x - e* y = e+e3x

Q: 12. In a standard deck of 52 cards, each card has a suit and a rank. There are four suits (spades…

A: We have to find the probability that the 5 cards in this hand consist of 3 Aces and 2 Queens.

Q: Q.3- Prove that: 2n 1 (cos =0 +i sin €) + 10 2cosne eine

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Q: Find the Laplace transform of x(t) using differentiation theorem. d2 d a1z x(t) + 6x(t) + 5x(t) =…

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Q: exercise Find the laplace of each f(t) 2. sin8t sin6t

A: We have to find the Laplace transform of ft=sin8tsin6t

Q: Consider the following IVP: y' = et; y(0) = 2 Find the general solution. y(t) = 1 – e¯ 1- A В y(t) =…

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Q: The table shows the total assets (in trillions) held in a foreign bank for the given years. Complete…

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Q: Question 27 A box contains three coins: two regular coins and one fake two-headed coin(P(H)=1). You…

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Q: 3s – 2 Find the Inverse Laplace Transform of G (s) 2s2 – 6s – 2

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Q: H13. estimate intervals to the approximate the Minimam number of Sub Velue of (ax 4) dx with an…

A: (a) We have fx = 2x2+4 then f'(x) = 4x, and f''(x) = 4 Note: We have second degree function.

Q: 10. A game of chance involves a spinner marked with mimbers from 1-30. The game costs $10 to play.…

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Q: Find the solution, (D3+3D2+3D+1)y = 0 A y = c,e*+ (c,x+czx²)e-* y = c,+c,e"+c;e¯ B C D y =…

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Q: Let A be a subset of a topological space X. Show that bd(A) = Ø iff A is open and closed in X.

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Q: What value of t ensures the following system of equations has infinitely many solutions? 3r + (t² –…

A: System of linear equations, using Matrix augmented Matrix

Q: Solve the system of first-order linear differential equations. (Use C1 and C2 as constants.) Yı' =…

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Q: You are given: (i) H; 1 for 0 Sx <110. 110-x (ii) 8= 0.05

A: We need to find average cost of life insuranceafor a person aged x after 10 years from now. Which is…

Q: What value of t ensures the following system of equations has infinitely many solutions? ... 3r + (*…

A: Given system of equation is 3x + (t2 - 4)y = 1ty = 2

Q: 7 similar cars are entered in a race. The cars all have an equal chance of winning and there are no…

A: Given 7 similar cars are entered in a race. To select 1st position ,7C1= 7 choices. To select 2nd…

Q: Consider the following IVP: x" - 4x' + 4x = 4e2t; x(0) = -1, x'(0) = -4 %3D %3D

A: We have to solve the given differential equation,(IVP).

Q: What is the result of applying the row operations –3R1 + R2 → R2 and -R1 + R3 → R3 to the matrix 2…

A: Row operations are calculations we can do using the rows of a matrix in order to solve a system of…

Q: Jse the Limit Comparison Test to determine the convergence or divergence of the series. 1 8) n/n +1

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Q: Question 16 Find the Laplace Transform of e4t + 5 A + s- 4 B s+4 C s-4 D) s+4 s2 - + +

A: The solution is given as

Q: 16. Prove that an integer (a,-1an-2 · . . ao)10 is divisible by 11 if and only if ao + a2 + a4 + . .…

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Q: Evaluate f (x) = 300z 1+e from 0 to 10 using 6- segment Simpson's % rule. If the true value is…

A: Given f(x) = 300x1 + ex

Q: What is the arithmetic mean of 6, 8, 12,13,9,7,11 and 15?

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Q: Use the following information to sketch the graph of a continuous function with the following…

A: The given conditions are : (a) f-3=5, f0=2, f3=0 (b) f'x&gt;0 on -∞,-3∪3,∞and f'x&lt;0 on -3,3…

Q: 7hat is the result of applying the row operations -3R1 + R2 → R2 and –R1+ R3 → R3 to the natrix [1 2…

A: Given matrix is 12-13-22abc

Q: For the system below, solve using Jacobi and Gauss-Seidel methods with error of below 5%. 5x, – x,…

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Q: Which of the following row operations on a matrix may not be an elementary operation Replace one row…

A: We want to find true option

Q: 40 The above graph is planar OTrue OFalse

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Q: TRUE OR FALSE? A. Let A and B be n x n matrices. If AB = [0], then BA = [0]? B. If A and B are n x…

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Q: (2x + y + 1)y' = 1 %3D

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Q: -1 4 6 2 0 -1 0 0 Let A = so that A4(t) = (t+ 1)²(t – 2)². Define T : Rª → Rª by 2 2 1 6 0 2 T(x) =…

A: We have to find a basis for the generalized eigenspace and we can proceed further.

Q: The Taylor polynomial of degree 100 for the function fabout x = 3 is given by P (x) = (x – 3)? –…

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Q: 12. Start with the identities x2 1 P, (x) = xPn-1(x) + *P(x) n P, (x) = xP-1(x) + nP,-1(x ) (a) Show…

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Q: Question 3: a. Find the derivative of the function 2x +1(x - dx b. Given that y = 4x' -*, find dy…

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Q: Consider the following IVP: у" + у'%3D -сos x; у(0) %3D а, у'(0) 3b Find the general solution. 1 1…

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Q: Question 8 (2 marks) The graph of (=) + (2) + (-) = 1 is a plane for any nonzero numbers a, b, and…

A: Solution

Q: Question 1: 1- Evaluate xp 1+ x

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Q: Prove the following using the mathematical induction Let c and d be integers. For every natural…

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Q: 3. Give the parametric and symmetric equations of the line that passes through the point (4,-3,5)…

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Q: If A and B be 2 x 2 matrices, then (A +B)(A – B) = A² – B². A True B False

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Q: Find the solution. dy y -xy? dx

A: This is a problem of differential equation.

Q: For the following relation ~ on set X, determine whether it is symmetric, transitive or reflexive.…

A: For all x in X, x2 ≠ x2 + 1,hence x ~ x Hence ~ is reflexive.  Now consider the equation          x2…

Q: Using the Divergence Theorem, evaluate I= F-dS where S is the sphere of radius 2 centered at the…

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Q: If A and B be 2 x 2 matrices, then (A + B)(A – B) = A² – B?. A True False

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Q: 1. Let a and b be real numbers such that a < b. Apply the Mean Value Theorem to f(x) = In(cosh x) to…

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Q: If A and B be 2 x 2 matrices, then (A +B)(A – B) = A² – B². True B False

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Q: Given the following data: 8, 3, 3, 17, 9, 22, 19, find the median.

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Q: Consider the following IVP: y"+a?y = 0; y(0) = 1, y'(0) = 0 Find the general solution. A) y(t) = sin…

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Q: Question 5 Find the solution. (D2 + D- 6)y = 0 y = c,e* +c,e2 3x (A) y = c,e* +c,e-2* B – 3x -2r y =…

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