Let θ (in radians) be an acute angle in a right triangle, and let x and y, respectively, be the lengths of the sides adjacent and opposite θ. suppose also that x and y vary with time.
a. how are dθ/dt, dx/dt and dy/dt related?
give steps and explain!

dθ/dt = [(cos^2 θ)*(dy/dt * x - y * dx/dt)]/(x^2)

Step-by-step explanation:

Given that x and y are the lengths of the sides adjacent and opposite θ, then they are related by:

tan θ = y/x

Differentiating respect to t, we get:

sec^2 θ * dθ/dt = (dy/dt * x - y * dx/dt)/(x^2)

dθ/dt = [(cos^2 θ)*(dy/dt * x - y * dx/dt)]/(x^2)

step-by-step explanation: yes

1. 3. can also be expressed as (22/7)

2. -4.5

3. 3.6

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