Reyes Simpson
12/05/2023 · Junior High School
Both \( x \) and \( y \) denote functions of \( t \) that are related by the equation \( x^{2}+y^{2}=6 x+8 y \). Use this equation and the given derivative to find the specified derivative. NoTE: Enter the exact answers. (a) Given that \( \frac{d x}{d t}=-6 \), find \( \frac{d y}{d t} \) when \( (x, y)=(7,3) \). \( \frac{d y}{d t}= \) (b) Given that \( \frac{d y}{d t}=15 \), find \( \frac{d x}{d t} \) when \( (x, y)=(3+\sqrt{3}, 4+\sqrt{5}) \). \( \frac{d x}{d t}= \)
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(a) \( \frac{dy}{dt} = -24 \)
(b) \( \frac{dx}{dt} = -15 \frac{\sqrt{5}}{\sqrt{3}} \)
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