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Alexus [3.1K]
3 years ago
9

Can someone pls help? i dont understand this

Mathematics
1 answer:
Akimi4 [234]3 years ago
5 0

Answer:

b

Step-by-step explanation:

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Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.
qwelly [4]

Answer:

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\displaystyle \frac{dy}{dt}=-\frac{33}{8}

B)

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Step-by-step explanation:

<em>x</em> and <em>y</em> are differentiable functions of <em>t, </em>and we are given the equation:

xy=6

First, let's differentiate both sides of the equation with respect to <em>t</em>. So:

\displaystyle \frac{d}{dt}\left[xy\right]=\frac{d}{dt}[6]

By the Product Rule and rewriting:

\displaystyle \frac{d}{dt}[x(t)]y+x\frac{d}{dt}[y(t)]=0

Therefore:

\displaystyle y\frac{dx}{dt}+x\frac{dy}{dt}=0

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:

\displaystyle (4)y=6\Rightarrow y=\frac{3}{2}

Therefore:

\displaystyle \frac{3}{2}\left(11\right)+(4)\frac{dy}{dt}=0

Solve for dy/dt:

\displaystyle \frac{dy}{dt}=-\frac{33}{8}

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:

(1)y=6\Rightarrow y=6

Therefore:

\displaystyle (6)\frac{dx}{dt}+(1)\left(-9)=0

Solve for dx/dt:

\displaystyle \frac{dx}{dt}=\frac{3}{2}

5 0
3 years ago
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