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3 years ago

Which of the following expressions are equal to -58? Select all that apply

Mathematics

2 answers:

liberstina [14]3 years ago

8 0

D. 34-78-14 = -58

E. -78-(-34)+(-14) = -58

both D and E are equal to -58

inysia [295]3 years ago

6 0

What are the choices? I need them to be able to answer your question.

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By the chain rule,

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}$

We have

$\dfrac{\partial w}{\partial x}=\dfrac{2x}{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial y}=\dfrac{2y}{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial z}=\dfrac{2z}{x^2+y^2+z^2}$

$\dfrac{\mathrm dx}{\mathrm dt}=7\cos t$
$\dfrac{\mathrm dy}{\mathrm dt}=-9\sin t$
$\dfrac{\mathrm dz}{\mathrm dt}=6\sec^2t$

So we have

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac2{x^2+y^2+z^2}\left(7x\cos t-9y\sin t+6z\sec^2t\right)$
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$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{8\sin t(9-16\cos^4t)}{\cos t(36+13\cos^2t+32\cos^4t)}$

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