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)

2^y = ln 5, or   y(ln 2) = ln 5.   solving for y,   y = (ln 5) / (ln 2).   y=5

step-by-step explanation:

step-by-step explanation: i dont