A ladder 10 ft long rests against a vertical wall. Let theta be the angle between the top of the ladder and the wall and let be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to theta when theta=pi/3?

Question

Mathematics

Jimena Thompson

29 July, 11:49

A ladder 10 ft long rests against a vertical wall. Let theta be the angle between the top of the ladder and the wall and let be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from the wall, how fast does x change with respect to theta when theta=pi/3?

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Answers (1)

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Regina Murphy · Answer 1

5 ft/s

Step-by-step explanation:

Let L be the length of the ladder. The relation between the angle and distance X is:

X = L * sin θ the change of X will be:

dX/dt = L * cos θ If we evaluate the expression when θ = π/3, we get the change of X:

dX/dt = 10 * cos (π/3)

dX/dt = 5 ft/s