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3 years ago

3x + 2y = 12 y = x - 9 solve by substitution

Mathematics

1 answer:

mezya [45]3 years ago

7 0

Point form: (6,-3)
equation form: x=6, y=-3

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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:

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

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Step-by-step explanation:

x and y are differentiable functions of t, and we are given the equation:

$xy=6$

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

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

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

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Using our original equation, find y when x = 4:

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Therefore:

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

Solve for dy/dt:

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Again, using our original equation, find y when x = 1:

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Therefore:

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Solve for dx/dt:

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3 years ago

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