A point $P(x,y)$ moves in the first quadrant on $$x^2+y^2=25.$$ At the instant when $x=3$,

Question

A point $P(x,y)$ moves in the first quadrant on $$x^2+y^2=25.$$ At the instant when $x=3$, $x$ increases at $0.4\text{ cm/s}$. Find: $y$; $\dfrac{\mathrm{d}y}{\mathrm{d}t}$, and describe the vertical motion.

Accepted Answer

(a) $y=4\text{ cm}$; (b) $\frac{\mathrm{d}y}{\mathrm{d}t}=-0.3\text{ cm/s}$, moving down.

Differentiation

Differentiation

Solution:

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