First convert the numbers to get the same denominator
1/3=4/12
5/6=10/12
5/12
Then add them all together
4/12+10/12+5/12= 19/12
Then reduce
1 7/12
Your answer is 1 ton and 7/12 of a ton

8 0

3 years ago

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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

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

7 0

3 years ago