The equation r(t) = (3t + 9) i + V5t) j+ (2t) k is the position of a particle in space at time t. Find the angle between the velocity and acceleration vectors at time t=0. What is the angle? IN radians (Type an exact answer, using n as needed.)

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A: limit

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A: Given problem:- Find the derivative of f(x)=x2 e2.5x

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A: We will find the rate of change of radius. 

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A: Find your answer below 

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A: Topic:- Algebra

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A: To find the derivative

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Q: Find

A: We will find the derivative of the above function using logarithmic differentiation. 

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A: Note that: cos x cos y-sin x sin y=cos (x+y)

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A: topic - application of derivatives

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A: The objective is to solve the above question.

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A: Please refer to the image below 

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A: Consider   

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A: f(x) = 3x2 -x3  For relative maxima , f"(x) <0 For relative minima , f"(x) >0 

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A: 1st question is based on percentage application and second is on formula  (a+b)(a-b) = (a2-b2)

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A: Explanation of the answer is as follows

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A: Let's find. 

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

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Q: Solve the initial-value problem

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A: Solution:Given geometrical series1+3+9+27+81+ ......1+3+32+33+34+.....∑3nn=0∞