Assume a spring is oscillating and the length of the spring can be described as sin (t) L (t)=- What is the formula for the instantaneous rate of change of L(t)?

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A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: y' – y = 2te',

A: Laplace transform: L(y'(t))=py(p)-y(0) L(y(t))=y(p) L(2tet)=2(p-1)2

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A: Find gradient of f(x,y). Find compute the point . Take the magnitude of the same .

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Q: 1. Find the rate of y with respect to x at the point (5, 8) if 7y-ry 4. dy da

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Q: Find the general solution of the differential equation for interest compounded continuously,dA/dt =…

A: dA/dt=kA

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Q: Give the number of complete oscillations that will occur over 1 minute for a mass- spring system…

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Q: A particle is traveling upward and to the right along the curve y = ln x. Its x-coordinate is…

A: Given a particle is travelling upward and to the right long the curve y=lnx. It is given that dxdt=x…

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Q: The differential equation of the family of curves orthogonal to x² + y? = C² is

A: Solve the above questions.

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

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A: Instantaneous velocity of a particle is the velocity at a particular time.

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Q: The differential equation for cooling of a cup of coffee is given by dT dt = -(T – Tenu)/T where T…

A: final answer is  T = 200 C at t =5 minutes detailed solution with explanation is given below

Q: "Differentiate both sides of the equation V = Tr*with respect to t AP (using the chain rule on the…

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Q: 24. What does it mean to say that dV is an exact differential?

A: What do you mean by dV is an exact differential.

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Q: Let -sin (y-4x) Find the rate of change of z with respect to y at the point (2, 1) with x held…

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Q: 1 - Find a formula for the rate of change dv/dt of the volume of a balloon being inflated such that…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…