Use the Laplace transform to solve the given system of differential equations. dx dy + 7x + dt = 1 dt dy x + dt dx y = et dt x(0) = 0, y(0) = 0

Q: (c) y = 2

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Q: F(x)= 4x -8 x intercept.     (X,y)=.  (.    ) y intercept.      (x,y)=.   (.   )

A: Given:         f(x) =4x-8 This is in the form of y=mx+b is the equation of the straight line…

Q: x(t) = ?

A: Given: x'=3-22-2x+12e-t comparing this by  x'=Ax+b The homogeneous solution:…

Q: Find f (VF + xJ dx

A:

Q: Let f(x) = 9-5x. Find f(t). f(t) =|

A: given that                                 f(x)=9-5x we have to find f(t). we can find f(t) by…

Q: b 11. Find the vertex of f (x) = x² – 8x + 16. Use x = 2a A. (4,0) (- 4,0) С. (0,4) D. (0, -4) B.

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Q: The functions u and w are defined as follows. u (x) = -2x-1 w (x) = 2x²-2 Find the value of u (w…

A: u(w(3))=-33

Q: Find f′(x) and f′(c).

A:

Q: x+2 Determine the (x,y) location of the hole for f(x)=- x² - 4

A: Holes occur when a duplicate factor is cancelled in the numerator/denominator of f(x).

Q: Find スeso and its oder for the function f(z) = 1-x +Z + ě. %3D

A:

Q: (x*2)+(y*1.5)+(z*0.5)=20 find the values of X, Y, & Z

A: Please see the below answer.

Q: (27) Let X = P(2) and )E(5-5x) finc

A: Given X≈Pλ That is, EX=λ

Q: Z = (1 + i)(2-1)-¹, find |Z|.

A:

Q: Find all values of t for which

A: Given that: t-223t-3=0

Q: If ƒ(2)=z²+1 then u(x,y) = 3+y² 3- y² + 1 83+y²-1 3- y²

A: Given  f(z) = z2+1 We know that z = x+iy Hence f = (x+iy)2+1 = x2+2ixy+i2y2+1= x2+2ixy-y2+1

Q: If u(x) = 4x² — 7 and v(x) = x³ – 9, find u(x) · v(x). . u(x) · v(x) =

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Q: x2 + x3 Define T:R3 - R° by T 2x1 + x2 12 - x1 – x2 + 3x3 | Then we can write T(v) Av where A =

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Q: x(t) = ?

A: Taking Laplace transform:…