Given the following acceleration function of an object moving along a line, find the position function with the given initial velocity and position. a(t) = 0.4t; v(0)= 0, s(0) = 1 ... s(t) = (Type an expression using t as the variable.)

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A: Given problem:-

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A: Put x=2cost , y=2sint

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A: Topic = Geometry

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A: See the answer below

Q: oriented

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A: Explanation of the answer is as follows

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A: the process of finding the derivative of a dependent variable in an implicit function by…

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A: We have to find a point on line which is closest to the origin.

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A: Given query is to find the the function of the graph.

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A: This question can be solved using the concept of integration by substitution.

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A: This is a problem related to simple interest. Based on the general formula of simple interest we…

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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A: As per as our guidelines i am supposed to answer only one question please repost remaining question…

Q: Let F(x) = f(f(x)) and G(x) = (F(x))² . You also know that f(6) 7, f(7) = 2, f'(7) = 13, f'(6) = 6…

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A: We will find the derivative of the given function in the following step.

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A: Topic = Series

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Q: So what is the square units

A: Apologies for the inconvenience. The correct solution is given below: Given function is: fx=ex7 from…

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A: Given query is to find the derivative of the function.

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A: To find the derivative of  y=(tan-1(x))23

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Q: Solve the given initial-value problems. 4.43. xe" dx +(y-1)dy 0; y(0) 0

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A: A detailed solution is given below

Q: 2) Evaluate the following line integral: . 0+z)dx + (x + z)dy + (x + y)dz where C consists of the…

A: C1: (0,0,0) to (1, 0, 1)x-01-0=y-00-0=z-01-0=tx=t, y=0, z=tdx=dt, dy=0, dz=dtI1=∫01[(0+t)+(t+0)]…

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A: see below the answer and calculation

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A: see below the answer  and calculation