Let (in radians) be an acute angle in a right triangle,and let x and y, respectively, be
Chapter 3, Problem 9(choose chapter or problem)
Let \((in radians) be an acute angle in a right triangle, and let \(x\) and \(y\), respectively, be the lengths of the sides adjacent to and opposite \(θ\). Suppose also that \(x\) and \(y\) vary with time.
(a) How are dθ/dt, dx/dt, and \(dy/dt\) related?
(b) At a certain instant, \(x = 2\) units and is increasing at 1 unit/s, while \(y = 2\) units and is decreasing at unit/s. How fast is \(θ\) changing at that instant? Is \(θ\) increasing or decreasing at that instant?
Equation Transcription:
Text Transcription:
theta
x
y
d theta / dt
dx/dt
dy/dt
x = 2
y = 2
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