Find the Rectangular equation. X-5cos() and y=53in(6)

Q: 46 a Show that cos x+ =-sinx. = -sinx. d" (cosx) = cosx + drn b Prove that

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Q: Question 1 Consider the following IVP: y"-2y'= -4; y(0) = 0, y'(0) = 4 Find the general solution. A…

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Q: In Exercises 19–22, let R³ have the Euclidean inner product. a. Find the orthogonal projection of u…

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Q: Identify and sketch the graph of the following equations in R. (a) r2+2y? + z2 – 8r + 12y - 2z + 35…

A: The given equation for part (a) is x2+2y2+z2-8x+12y-2z+35=0. The given equation for part (b) is…

Q: 1. Use a triple integral to find the volume of the solid that lies under the plane z = 1++y, and…

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Q: [2 - 3 2 - 3 and be express as A = LU as below L4 – 1 - 2 1 c) Let A = |1 | 01 [u11 U12 U13 [2 - 3 2…

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Q: Check that P ˅(Q ˅ R) is equal to ┐(R ˄ Q ˄ P) → P

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Q: Relationship y= (ax+bX) - Find the Linearizationof Nonlinear

A: This is the question from linearization techniques. It involves the application of differential…

Q: 2. Find the power series representation of the following functions. And then write out their I.O.C..…

A: we have to find the power series representation of following f(x).

Q: . Describe ALL transformations from the parent function f(x) = x² to the function g(x) = -(x + 3)´ +…

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Q: Which of the following is the general solution to the differential equation (x + 2y)dx + (x + 2y +…

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Q: Find: 8 cos/1+x dx . V1+x

A: Given integral is ∫08cos1+x1+xdx. We have to solve the given integral. Substitute 1+x=u…

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: f(x) = 2x5 + 15x4 - 3x3-4x2+ 7x+ 14 1)Trapeaoidal rule 2) Trape20idal rule with n=2 3) 1/3 Simpson…

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Q: 2. List the amplitude, midline, and period of each of the following functions: (a) 3 cos(T/4 * x) –…

A: We will use standard form of equation  For y= a sin (bx+c) +d           or     y= a cos (bx+c) +d…

Q: Find the general solution of this ODE: d'y dy + 12 + 37y = - 6e-4t dt2 dt The solution will be of…

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Q: Evaluate the integral shown using Simpson's 3/8 Rule with 9 panels. 12 4arctan () dx O 32.52020854 O…

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Q: Find the solution. dy x3– 2y dx х A x= -+ 5 3x3 2y2 5 x3 C x2 5 D xy = + 3 B

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Q: KA spherical tank with radius of 125m can hold a volume of 25m'3 Use Bisection and Regula Falsi…

A: Given that a spherical tank with radius R=12.5 m can hold a volume V of 25 m3. The volume of liquid…

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: Find the solution. dy +y= dx 1+e* A y = ce¯*+e¯*In(1+e*) B В y = ce¯ – e ¯*In(1-e*) се © y =…

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Q: Given the function f (x,y) =- Vx+y² which ONE of the following statements is CORRECT? O A. f is only…

A: Given function: f(x,y)=5x+y2 To find: Correct option

Q: Find the distance between m [-2, 3, 2,0,3, – 13, –5] and n = [4, –1,1, –5, 0, 11, –3].

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Q: Given the function f (x,y) =V(x2-4)(y²-9). Which ONE of the following statements is TRUE? A. If x> -…

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Q: Compute the Fourier Transform of f(x) = e-ax-

A: Fourier transform of a function fx is defined as  Ffx=∫-∞∞fxeisx dx Gamma function =∫0∞e-x xn-1 dx

Q: . ndS over the 2 = 9, where F = is the unit outw

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Q: Use variation of parameters to solve the given nonhomogeneous system. X' = -7t e X(t) =

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Q: 5. Assume that n is a positive integer. Then, use the Cauchy formula to calculate the following…

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Q: 1 3 a) Consider a set of vectors, x = |3 |,y = | 2 and z = L4 Can we express the vector, v = 4 as a…

A: The solution is given as

Q: What is the particular solution to the differential equation dx 1 + y = 2e-* with y = 1, dy -1 when…

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Q: Q2: Use vector to check whether the points A (4,3,2), B (4,3,0), C (4,0,0), and D (4,0,2) are…

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Q: .Use the Monotone Convergence Theorem to show that the (2n)! {a)" is convergent.

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Q: If z=x²sinh then %3D дхду O A. (-x3– 3x2y +2xy2 – 32x)/16+x²– 2xy + y2 (16+x2- 2xy +y?) ² O B. (x3–…

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Q: 9. Prove that if {fn(x)} converges uniformly to the function f(x) on each of the sets A1, A2, ...,…

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Q: Se-2t if 0 3,

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Q: eVx² +y?+z? T(e4 – e)(x² +y² + z?) Let f(x, y,z) Let S be the solid bounded by the xz plane and the…

A: Here we can use spherical coordinates to find the value of the integral. In spherical coordinates…

Q: Integrate f(x) from x = 0 to 10 using Three-Point Gauss-Legendre Quadrature. f(x) = 5000 + 24583x –…

A: Gauss's three-point formula to evaluate the integral I=∫abfxdx is: I=b-a2w1fx1+w2fx2+w3fx3 Here we…

Q: Given the function f (x,y) =/(x2– 4)(y²– 9). Which ONE of the following statements is TRUE? O A. If…

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Q: Which of the following is the general solution to the differential equation (3s – 2t + 1)ds = -(3s –…

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Q: Find the solution. y" - 2y'- 2y = 0

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Q: ()* + dy What is the general solution to the differential equation y = 0 ? dx In(1+ Ay) = Ax + B y2…

A: We have yd2ydx2-dydx2+dydx=0 Let dydx=p Then d2ydx2=pdpdy So, yd2ydx2-dydx2+dydx=0 becomes:…

Q: . (a) Show that if a, is a series of nonnegative terms that diverges to o, then any

A: Answer :-

Q: rt, 0<t< 2 2. Find the Laplace transform of the function f(t) = {0 r

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Q: he price-demand equation of the particular brand of shampoo át á šúþérmarket chai hen the demand is…

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 2x y'' – 3y' – 10y = 7e y(0) = 1, y'(0) = - 17 - %3D %3D

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Q: You are designing an RPG (role-playing game) for a gaming console and have decided to use an open…

A: Given that the function dx,y=e-x2y is to be minimised and maximised on the unit disc x2+y2≤900. We…

Q: Show that the lines L1 : x = 1 – t, y = 2t, z = 4+t and L2 : x = 1+ 4t, y = 3 – 8t, z = 5 – 4t are…

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Q: 3. Use zero- through third-order Taylor series expansions to predict f(3) for f(x) = 25x³ 6x2 + 7x –…

A: Given below clear explanation

Q: Use variation of parameters to solve the given nonhomogeneous system. X' X - -7t e X(t)

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

A: This is a problem of differential equation.