2 years ago

A

Mathematics

1 answer:

LekaFEV [45]2 years ago

3 0

Answer: 31.5 in.

Answer:

the answer is 13 cm

Step-by-step explanation:

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Let w = x2 + y2 + z2, x = uv, y = u cos(v), z = u sin(v). use the chain rule to find ∂w ∂u when (u, v) = (9, 0).

jasenka [17]

By the chain rule,

$\dfrac{\partial w}{\partial u}=\dfrac{\partial w}{\partial x}\cdot\dfrac{\partial x}{\partial u}+\dfrac{\partial w}{\partial y}\cdot\dfrac{\partial y}{\partial u}+\dfrac{\partial w}{\partial z}\cdot\dfrac{\partial z}{\partial u}$
$\dfrac{\partial w}{\partial u}=2xv+2y\cos v+2z\sin v$

We also have $x(9,0)=0$ , $y(9,0)=9$ , and $z(9,0)=0$ , so at this point we get

$\dfrac{\partial w}{\partial u}(9,0)=2\cdot9\cdot\cos0=18$

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