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Diagonals If x, y, and z are lengths of the edges of a
Chapter 3, Problem 18E(choose chapter or problem)
Problem 18E
Diagonals If x, y, and z are lengths of the edges of a rectangular box, the common length of the box’s diagonals is s = .
a. Assuming that x, y, and z are differentiable functions of t, how is ds/dt related to dx/dt , dy/dt and dz/dt ?
b. How is ds/dt related to dy/dt and dz/dt if x is constant?
c. How are dx/dt , dy/dt and dz/dt related if s is constant?
Questions & Answers
QUESTION:
Problem 18E
Diagonals If x, y, and z are lengths of the edges of a rectangular box, the common length of the box’s diagonals is s = .
a. Assuming that x, y, and z are differentiable functions of t, how is ds/dt related to dx/dt , dy/dt and dz/dt ?
b. How is ds/dt related to dy/dt and dz/dt if x is constant?
c. How are dx/dt , dy/dt and dz/dt related if s is constant?
ANSWER:
Solution:-
Step 1 of 4
Given that
a. We have to find how is ds/dt related to dx/dt , dy/dt and dz/dt ?