Consider the initial value problem my" + cy' + ky = F(t), y(0) = 0, y'(0) = 0 modeling the motion of a spring-mass-dashpot system initially at rest and subjected to an applied force F(t), where the unit of force is the Newton (N). Assume that m = 2 kilograms, c = 8 kilograms per second, k = 80 Newtons per meter, and the applied force in Newtons is if 0 7/2. F(t) = {0 S40 a. Solve the initial value problem, using that the displacement y(t) and velocity y'(t) remain continuous when the applied force is discontinuous. For 0 7/2, y(t) =

Q: Farmer Lindsey estimates that after t days, her crop will be increasing at a rate of r(t)  =  15t8 +...

A: Solution ) r (t) = 15t8 + e-0.76t when t = 0 r(0) = 15×(0)8 + e--0.76×0 r(0) = 0 + e0 r(0) = 0 + 1 r...

Q: Provide an appropriate response. If xy + x = 12 and dx/dt = -3, then what is dy/dt when x = 2 and y ...

A: We will find the value of dy/dt with the help of the given data x=2 ,y=5 and dX/dt=-3 as following.

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A: Differentiable

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A: To find out the area of the region bounded by the curves. 

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A: Given query is to find the are of the region bounded by the curve.

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A: Question- A pharmaceutical company is testing a new drug. After a person takes A0 mg of the drug, th...

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Q: Evaluate f'(-2) if f(x) = x* – 5+ x-2 + 4x-4.

A: The detailed solution is given below Thank you 

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A: Given integral ∫0π sin8x2 cos2x2 dx

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A: (a) Given: - The condition is the same direction as -2i+9j. To find: - The unit vectors that satisfy...

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A:

Q: Week 8 Online Homework Introdu Score: 26.67/31 28/31 answered Question 9 Let g(x) = log,(x). Find g...

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A: We want to choose correct statement from given options.

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A: We can find the volume as below

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Q: 2x ²-11)dx x3+3x²-4

A: To evaluate the integral.

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Q: Evaluate: " sin7 cos4 dx

A:

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A: The curve x=13y2+232 from y=0 to y=5

Q: dder the folowing. TX) - V 30 - tch the graph of the function. Use a praphing utlty to vertfy your g...

A: Given query is graph the function and find domain and range.

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Q: What the twice amount of 375.00 dollars

A: The objective is to find the twice amount of 375.00 dollars .

Q: t Determine f'(1) if ƒ (t) = log10 %3D t+1

A: Given: - The function is, f(t)=log10tt+1 To determine: - The solution of f'(1).

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A: This question can be solved using the concept of rate of change of physical quantities.

Q: 2. An open box will be made by cutting a square from each corner of a 6-ft by 6-ft piece of cardboar...

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Q: What is the amplitude and period of the function shown below? 5- 4- 3- 2- 1- -2 -1 -1 -3 2 3 4 6. -2...

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Q: Suppose the sales of potato chips generates a profit at the rate P′(t)  =  10t ln(7t) dollars per we...

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Q: Use A = P(1+ where: n A = the amortized amount (total loan/investment amount over the life of the lo...

A: Given query is to find the amount to get double.

Q: Which of the following best describes the function below? S(x)={3r if.rs2 |x³ if 2<x f(x) =: A. Cont...

A: To check continuity we find left hand limit and Right hand limit. If they are equal then function is...

Q: find eigen value of matrix A 3 -2 A %3D -니 2. 2.

A:

Q: The derivative of the function y = ecos²(x) is: y' = - sin(2x)eCos² (x) y' = sin(2x)eCos²(x) the abo...

A: We will find the derivatives of the given function y=ecos2x in the following step.

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A:

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A: This question can be solved using the concept of integration of trigonometric function.

Q: Determine the slope of the tangent line to the graph of ƒ (x) =- at the point(4, -4).

A: Use differentiation for finding the slope.