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3 years ago

Match each expression to its simplified form 5(2x+6)

Mathematics

1 answer:

wel3 years ago

4 0

5(2x + 6)
10x + 30
divide 2 on both
5x + 15
divide 5 on both
x + 3

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shtirl [24]

Answer:

$\frac{dy}{dx} =-\sqrt[3]{\frac{y}{x} }$

Step-by-step explanation:

Recall that using the chain rule we can state:

$\frac{dy}{dt} =\frac{dy}{dx}*\frac{dx}{dt}$

and therefore solve for dy/dx as long as dx/dt is different from zero.

Then we find dy/dt and dx/dt,

Given that

$x=sin^3(t)\\dx/dt = 3 sin^2(t)* cos(t)$

And similarly:

$y=cos^3(t)\\dy/dt=-3\,cos^2(t)*sin(t)$

Therefore, dy/dx can be determined by the quotient of the expressions we just found:

$\frac{dy}{dx} =\frac{dy/dt}{dx/dt} =\frac{-3\,cos^2(t)*sin(t)}{3\,sin^2(t)*cos(t)} =-\frac{cos(t)}{sin(t)}$

now notice that we can find $cos(t) = \sqrt[3]{y}$ from the expression for y,

and $sin(t) = \sqrt[3]{x}$ from its expression for x.

Therefore dy/dx can be written in terms of x and y as:

$\frac{dy}{dx} =-\frac{cos(t)}{sin(t)}=-\sqrt[3]{\frac{y}{x} }$

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Alex_Xolod [135]

Answer:

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Step-by-step explanation:

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