1. Find the value of c so that the lines 5x+cy = 4 (A) c = -3 (B) c=15 x-3y=9 and x- (C) C=-15 (D) are perpendicular. 5 C =- 3 (E) C = 5/3

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A: The given differential equation is; y''+2y'+y=e-tln(t).

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A: The Solution is given below

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A: Topic = Trigonometry

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A: We can find the answer as below.

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A: We need to find P(x).

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A: Given the curve r(t)=1+t i+t3 j, t0=1

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A: Solution is given below:

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Q: (a) Verify that y=tan(x + c) is one-parameter family of solutions of the differential equation y'= 1…

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A: In this question we are going to fill these blank up.

Q: 1) Simplify the expression for f(x + 1) - f(x) where f(x) = e2x - 1) . ) 0 (2 - 1) b) O (2-1)(2 - 1)…

A: option (b) is correct. see below the calculation

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A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

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A: We can find f(x) as below, by finding the derivative.

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A: Given :- u =(3,2) , w=(2,-1),v=(-6,-4)  Write v as linear combination of u and w

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Q: Calculate the following antiderivatives: (a) ∫ 8t− 6t^6 −5dt =  +C. (b) ∫ 1/u^7/4 + 3.5 sqrt u du…

A: a) Given:       ∫8t-6t6-5dt  =∫8t dt-∫6t6 dt-∫5 dt taking constant out     =8∫t dt-6∫t6dt-5∫ dt…

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A: Here we will find whether given vectors are orthogonal or not,

Q: J (2) Ten thousand dollars is invested at 645 intrest Compound Continously. → when will the…

A: We can find the required time as below.

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A: The given double integral:∫y=-3y=3∫x=-9-y2x=9-y225-x2-y2dxdyWe need to evaluate the above integral.

Q: Determine whether the series is convergent or divergent by expressing s as a telescoping sum. If it…

A: answer is in next step.

Q: Using [ y = e^(2x) (c1 + c2) + 3/2x2 (2x) ] and [ y = ( c1 + c2x ) e^(2x) + 3x/25 sinx + 4x/25 cnx +…

A: The given differential equation is;  y'' - 4y' + 4y = 3e2x + xsinx

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A: We have to complete the proof of property 4.

Q: (a) Use the Midpoint Rule with n = 6 to approximate integral 8 x-6 S8 dx 6 x+8 ?

A: As per the instruction, we will be answering the first question. Given:

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Q: 08 06 04- 02- }} ye y=0x=y² 02 yer* dxdy = 36 38

A: To switch the order of integration and then evaluate the value of integration.

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A: Given the diagram of a tank. To find the total work to lift the fluid of the tank.

Q: Solve the given IVP using Laplace Transforms. Solve for x(s) and STOP! (Express x(s) as a single…

A: Given IVP is x'' + 9x = cos3t,  x0=0,  x'0=2

Q: Match the equation with its graph. r(t) = cos(nt)i + sin(лt)j + t²k, Need Help? + 2 Z -2 Read It N₂…

A: Given problem:- r(t)=cos(πt)i+sin(πt)j+t2k  To find:- Draw the graph of given curve

Q: Q.1: Solve the differential equation below; xy' + 4y = 8 x¹

A: We have to solve above differential equations