At time t, a particle moving in the xy-plane is at position (x(t), y(t)), where x(t) and y(t) are not explicitly dx = 4t +1 and dt dy = sin(r). At time t = 0, x(0) = 0 and y(0) = -4. dt given. For t 2 0, %3D (a) Find the speed of the particle at timet 3, and find the acceleration vector of the particle at timet = 3. (b) Find the slope of the line tangent to the path of the particle at time t = 3. (c) Find the position of the particle at time t = 3.

Q: b) Use the Laplace Transform to solve the following differential equation given the initial…

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A: Given:y=x+52x-5Differentiation formula:ddxxn=n.xn-1ddxuv=vdudx-udvdxv2

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Q: 1. Solve for x(t) and y(t), given that x(0)=4 and y(0)=3 dy - y = 0 dx + x + 4y dt — 10%; х - | dt

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Q: (a) Find the differential dy of y = e#/5. (b) Evaluate dy for a = 0, dx = .1. (a) dy = dx (b) dy =

A: Solved below

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Q: . The exact differential d(xy)= xdy + ydx, what is the d( = 4x²y'dy+2xy*dx.

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Q: 1. Solve for x(t) and y(t), given that x(0)=4 and y(0)=3 dy dx + x + 4y = 10; æ dt - y = 0 dt

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A: since we know that L[y''] = p2Y(s)-py(0)-y(0)

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A: Laplace transferom, solve the differential equation by using Laplace transferom

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Q: 87. Find the value of dy/dt at t = 0 if y = 3 sin 2x and x = t+pai

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Q: Find the differential dy of the function y Provide your answer below: dy= dx = 5x4 + 4 4x + 3

A: y=5x4+44x+3Differentiate w.r.t xdydx=4x+320x3-5x4+444x+32

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A: Topic  =Differential equation Correct option  = A

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A: NOTE: Refresh your page if you can't see any equations. . take the derivative with respect to t

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A: To Find the differential dy of the function y=(cos(x))(7x)

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.