Triple integral spherical coordinates.

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The discussion focuses on solving a triple integral using spherical coordinates, specifically addressing the variables p, theta, and phi. The user has defined p as the square root of the sum of squares of x, y, and z, and is trying to determine the restrictions for the angles theta and phi. It is suggested to visualize the problem by drawing a picture to better understand the ranges of these angles. The typical ranges for phi and theta in spherical coordinates are also mentioned as part of the guidance. Understanding these ranges is crucial for correctly setting up the integral.
Kuma
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Homework Statement



Here is the question given:

jZVUZ.png



Homework Equations





The Attempt at a Solution



So i set p as x^2 + y^2 + z^2

so p lies in between b and a.

But how do i find the restrictions on the two angles, theta and phi?
 
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Kuma said:

Homework Statement



Here is the question given:

jZVUZ.png



Homework Equations





The Attempt at a Solution



So i set p as x^2 + y^2 + z^2

so p lies in between b and a.

But how do i find the restrictions on the two angles, theta and phi?

Hopefully you mean \rho=\sqrt{x^2+y^2+z^2}. Draw a picture. What do \phi\hbox{ and }\theta usually range through for spheres?
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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