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1 answer:
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Answer:
A)
B)
Step-by-step explanation:
<em>x</em> and <em>y</em> are differentiable functions of <em>t, </em>and we are given the equation:
First, let's differentiate both sides of the equation with respect to <em>t</em>. So:
By the Product Rule and rewriting:
Therefore:
A)
We want to find dy/dt when <em>x</em> = 4 and dx/dt = 11.
Using our original equation, find <em>y</em> when <em>x</em> = 4:
Therefore:
Solve for dy/dt:
B)
We want to find dx/dt when <em>x</em> = 1 and dy/dt = -9.
Again, using our original equation, find <em>y</em> when <em>x</em> = 1:
Therefore:
Solve for dx/dt: