Problem 1. Show that, if v1, U2, U3 are perpendicular in R", then |||v₁ + V2 + v3||² = ||v1||² + ||v2||² + ||v3||² (Hint: first show that the analogous formula is true for two perpendicular vectors.)

Q: Exercise III Use the method Laplace transform to solve the following. (a) y"-10y +9y = 5t, y(0) =…

A: a)

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A: Here according to the definition,       R = {(x,y) : x = y mod 3} Then if y = 7, then x must be 7…

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Q: dy 7. Find by implicit differentiation. dx 8. Use logarithmic differentiation to find y'. 4x4y6 = y…

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Q: 1 Зі -5 A = | ₁/ i

A: Given matrix is A = 13ii-5

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A: Given that y=x2+4x−5. We have to evaluate the first derivative of y=x2+4x−5 at x=0 using a value of…

Q: 7) Find the value of a retirement savings account with a monthly contribution of $50 (contributions…

A: Monthly investment  = $50 Interest rate = 4.8% per year i.e. 0.4% per month

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A: Given,  x f(x) f'(x) 0.5 0.4794   0.6 0.5646   0.7 0.6442

Q: Solve using Laplace transforms y''+2y'-6y=7e-3t, where y(0)=1, and y'(0)=-2

A: Solution

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Q: prove:   If n is not prime, then {1, 2, 3,..., n-1} is not a group under multiplication mod n.

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Q: 5. Write the equation of the tangent line to the curve of y = e³x + cos(-x) at the point (0,2).

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Q: (a) y(t) = x(1²) Deterr

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Q: the system of linear equations. (If the system is depende 2x + y + 3z = 40 -X - 7z=-66 3x + 2y z =…

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Q: 1 0 Let R be the region in the first quadrant bounded by the graphs of y = 4 cos () andy = (x - 2)²,…

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Q: 10 h Let aj = -15 a, = -13 and az = -7 -5 -5 The set {aj, a2, az } will span R' unlessh = (If there…

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Q: Numerical solution of Ordinary differential equations Consider the following initial value problem…

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Q: From Rogawski 2e section 5.5, exercise 2. A population of insects increases at a rate of 290 +6t +…

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Q: -92 -20 -32 - -424 -90 -154 512 110 182 What is A5? . A = 1 -3 -2 1 5 :) ( 7 0 4 0 0 8 10 0 (39 8…

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Q: Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

A: Hope this is useful

Q: Exercise II Use the method Laplace transform to solve the following. (a) = 1₂-1₁ +1₁ 2²₂2 = 1₂.

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Q: Suppose m, n ∈ Z + are relatively prime. The function f : Zmn → Zm × Zn defined by  f([Z]mn) =…

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Q: The population of a town is given by the equation  P = 1500(20.2t),   here t is the time in years

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Q: 23) Suppose that you roll a pair of honest dice. If you roll a total of 6, you win $18; if you roll…

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Q: 2. Solve the initial-boundary value problem du 3 au 0 0 10 Əx? ди (0, t) ди (4т, t) — 0 t >0 0, 0 <…

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Q: 2. Solve, 6 0 1-0 10 OC

A: To find the matrix multiplication :-

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Q: ii, Find the area under the graph y=5x4 between the limits x= 1 and x=3.

A: Given y = 5x4

Q: dx, y) Find the Jacobian du, v) x=9u cos 6v, y=9u sin 6v, z = 3w 1458v 972v 972u 1458u or dx, y, z)…

A: Given x = 9u cos 6v,   y = 9u sin 6v,   z = 3w

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Q: Problem 3 Using Variable Separable, solve x² (y + 1) dx + y² (x - 1) dy = 0

A: Given differential equation is x2(y+1)dx + y2(x-1)dy = 0

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A: Given the function fx,y,z=x4y4z7 reaches the maximum value for x,y,z≥0 on the unit sphere x2+y2+z2=1

Q: (c) Show that for 2" > 4n for n ≥ 5.

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Q: Find the coordinates of the intersection points A and B, between the closed curve (x + 1)² + 4(y-1)²…

A: In this question, we can find the intersection points of the given curve. Using the equation of…

Q: Solve the initial-boundary value problem ди 3 д и Ət 10 дх2 ди (0, t) = ди дх дх u(x, 0) - = (4п,t)…

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Q: (b) Define fo = 0, f₁ = 1 and fn = fn-1 + fn-2 for n ≥2. Show that 3 fak for all k ≥ 0.

A: As per the guidelines we shall solve one question only as you have asked more than one different…