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2 years ago

Please help me with this problems before my head explodes

Mathematics

1 answer:

Orlov [11]2 years ago

4 0

Answer:

1: c over 3

2: 9

3: 15 square root of 3

4: 5 + 2√6

Sorry but that's all I got

Step-by-step explanation:

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1 year ago

Find the surface area of the prism 9mm 12mm 8mm

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We are asked in this problem the surface area of the prism given the dimensions: <span>9mm by 12mm by 8mm. Surface area is the sum of the areas of each face of the prism. The formula for surface area is 2*lw+2*lh+ 2*wh. In this case, upon substitution, SA = 2*9*12+2*9*8+2*12*8 equal to a total of 552 mm2. </span>

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3 years ago

Read 2 more answers

Suppose z equals f (x comma y ), where x (u comma v )space equals space 2 u plus space v squared, y (u comma v )space equals spa

barxatty [35]

$z=f(x(u,v),y(u,v)),\begin{cases}x(u,v)=2u+v^2\\y(u,v)=3u-v\end{cases}$

We're given that $f_x(6,1)=3$ and $f_y(6,1)=-1$ , and want to find $\frac{\partial z}{\partial v}(1,2)$ .

By the chain rule, we have

$\dfrac{\partial z}{\partial v}=\dfrac{\partial z}{\partial x}\dfrac{\partial x}{\partial v}+\dfrac{\partial z}{\partial y}\dfrac{\partial y}{\partial v}$

and

$\dfrac{\partial x}{\partial v}=2v$

$\dfrac{\partial y}{\partial v}=-1$

Then

$\dfrac{\partial z}{\partial v}(1,2)=\dfrac{\partial z}{\partial x}(6,1)\dfrac{\partial x}{\partial v}(1,2)+\dfrac{\partial z}{\partial y}(6,1)\dfrac{\partial y}{\partial v}(1,2)$

(because the point $(x,y)=(6,1)$ corresponds to $(u,v)=(1,2)$ )

$\implies\dfrac{\partial z}{\partial v}(1,2)=3\cdot2\cdot2+(-1)\cdot(-1)=\boxed{13}$

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2 years ago