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Problem 3.178 · medium

1. Let x be the distance from the wall to the bottom and y the height of the top. The ladder is the hypotenuse: x² + y² = 169.
   Reviewed
2. Differentiate with respect to t: 2x dx/dt + 2y dy/dt = 0, so dy/dt = -(x/y) dx/dt.
   Reviewed
3. \[ \left. \sqrt{169 - x^{2}} \right|_{\substack{ x=5 }} = 12 \]
   When x = 5, y = √(169 − 25).✓ Proved
4. \[ \left. - \frac{v x}{y} \right|_{\substack{ x=5\\ y=12\\ v=3 }} = - \frac{5}{4} \]
   dy/dt = −(x/y)(dx/dt) with x = 5, y = 12, dx/dt = 3.✓ Proved