Obtain the Laplace transform of the given functions. Simplify answers, whenever possible. Show complete solutions and box your final your final answers. 1. F(t) = (e"t + 3)2

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A: I am attaching image so that you understand each and every step.

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A: To solve this question we need to apply the condition of continuity of a function at a given point.

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Q: Q1- Solve the linear system using Inverse matrix method 5x1 + 4x2 = 13 2x1 - 3x2 = -4

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Q: State whether the function is a probability mass function or not. If not, explain why not. f= {(2,0....

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Q: A company produces a special new type of TV. The company has fixed costs of $494,000, and it costs $...

A: Find your answer below 

Q: 1. f(x) = x2- 6x + 3 is continuous on the interval [- 3,2].

A: As per the company guidelines we can solve first question. I hope that the given solution will help ...

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Q: Find the Jacobian of the transformation x = r cos θ, y = r sin θ.

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Q: 5. Use the Gram-Schmidt procedure to find a QR decomposition of the matrix [1 -1 1 1

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Q: Question 11 d²y is Blank 1. Find the second derivative of y= (x+5)² The dx- Blank 1 Add your answer

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Q: Find lower bound for f(n) = 5n².

A: f(n)=5n2f(1)=f(-1)=5f(2)=f(-2)=5×4=20f(3)=f(-3)=5×9=45f(4)=f(-4)=5×16=80... ⇒ f(n)={5,20,45,80,........

Q: state if these are true or false

A: True. 

Q: Find the most general antiderivative. 7 9) SWi-Zndt

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Q: 100 venicies showed that 00 Tlad Tes with low press with Dald lore, 30 Tiad tires WILIT DOlI and bal...

A: We will find the number of vehicles with such tires. 

Q: 4x + 4 if r 8 36 if r= 8 Is f(x) continuous at z = 8? O Yes • No Cannot Be Determined

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Q: 6 The coefficient of Sin(x) in the antiderivative of F(x) =|cos is Blank 1 (use fraction form not de...

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Q: If a and b are unit vectors in R', show that ||a x b||? + (a · b)² = 1. %3D

A: On solving this we will get:-

Q: Evaluate the integral and check your answer by differentiating. NOTE: Enter the exact ansuwer. [1+si...

A: Given problem:- ∫ [1+ sin2(θ) csc(θ)] dθ 

Q: 1. Which of the following functions have a derivative of zero? a) y = 9.8 b) y= 11 c) y=-4+x d) y = ...

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Q: Find f"(x). If f (x) %3D 3x3 — Зx2 + х + 1 3x3 - 3x2 + x + 1 А) 3х- 4 (в) 9х- 6 (с) 18х - 6 D 6x -5

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Q: Activity II Direct ona: Match each solid figure in column A with its surface column B. Write the cor...

A: We will find the surface area of all the five solid figure as following.

Q: | (о + 1) In (») da

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Q: Find a power series representation for the function. (Give your power series representation centered...

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Q: F(t) = (2t + 8) u(t – 6)

A: Note that: L{u(t-c)g(t)}=e-csL{g(t+c)}

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A: topic- functions

Q: Find the radius of convergence, R, of the series. 5n – 1 n = 1 R = Find the interval, I, of converge...

A: The radius of convergence is R = 1 and, The interval of convergence is (-1, 1)

Q: Find the derivative of y = 3 sin x A 6 sin x B 6 cos 2x (c) 6 tan x

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Q: - х e con 2x dx

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Q: If f(1) = 12 and f '(x) ≥ 1 for 1 ≤ x ≤ 6, how small can f(6) possibly be?

A: The Mean Value theorem says, If a function is continuous on some closed interval [a,b] and different...

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Q: Given cost function C(g) = q° - 125g + 25000q, what is the minimum average cost? ty Ce It would be S...

A: Given query is to find minimum average cost.

Q: From the following equation  2x^3+2x^2-16x-20 Find the following  Increasing and decreasing inter...

A: Solved below

Q: Given cost function C(q) = q° - 125q + 25000q, what is the minimum average cost? It would be $ per i...

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Q: A sform z (pa, + zaz) to spherical form. Simplify your answer.

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Q: IDSION may beTEcorded via any device capable of producing a digital video file, or can be recorded d...

A: Since you have posted multiple questions i can do first three subparts as per our company guidelines...