### Finding cylindrical coordinates

(See attached file for full problem description) --- Given a point P with spherical coordinates (4, pi/6, pi/4). Find the xyz coordinates and cylindrical coordinates for P. ---

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(See attached file for full problem description) --- Given a point P with spherical coordinates (4, pi/6, pi/4). Find the xyz coordinates and cylindrical coordinates for P. ---

I would like for you to complete an optimization project. Examples include: the optimum number of hours to study for an exam, the best time to leave for work to avoid traffic, the optimum speed to drive a dirt bike up a hill to achieve the longest jump. I would like you to follow "The Process of Problem Solving" found below

Assume that the distance from New York to Miami is d and that half the distance is traveled at 45mph and half the distance is traveled at 55mph. If the average velocity is given by d/T=d/[0.5d/45+0.5d/55] I'm drawing a complete disconnect between the line above and this: =99/2=49.5(mph) I'm canc

I'm trying to find the average velocity from New York to Miami if half the distance is covered at 45mph and half the distance is covered at 55 mph.

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1. Which of the following defines a function f for which f(-x)=-f(x)? Please see attached.

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Pls see attachment

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Q. Show directly that the function {see attachment}, is integrable on R = [0,1] x [0,1] and find {see attachment} (Hint: Partition R into {see attachment} squares and let N ... {see attachment})

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Solve the following equation ... (see attachment)

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A mothball loses mass by evaporation at a rate proportional to its instantaneous surface area. If half the mass is lost in 100 days, how long will it be before the radius has decreased to one-half its initial value? How long before the mothball disappears completely?