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ELEN [110]
3 years ago
7

1 pt) If a parametric surface given by r1(u,v)=f(u,v)i+g(u,v)j+h(u,v)k and −4≤u≤4,−4≤v≤4, has surface area equal to 1, what is t

he surface area of the parametric surface given by r2(u,v)=5r1(u,v) with −4≤u≤4,−4≤v≤4?
Mathematics
1 answer:
natta225 [31]3 years ago
8 0

The area of the surface given by \vec r_1(u,v) is 1. In terms of a surface integral, we have

1=\displaystyle\int_{-4}^4\int_{-4}^4\left\|\frac{\partial\vec r_1(u,v)}{\partial u}\times\frac{\partial\vec r_1(u,v)}{\partial v}\right\|\,\mathrm du\,\mathrm dv

By multiplying each component in \vec r_1 by 5, we have

\dfrac{\partial\vec r_2(u,v)}{\partial u}=5\dfrac{\partial\vec r_1(u,v)}{\partial u}

and the same goes for the derivative with respect to v. Then the area of the surface given by \vec r_2(u,v) is

\displaystyle\int_{-4}^4\int_{-4}^425\left\|\frac{\partial\vec r_1(u,v)}{\partial u}\times\frac{\partial\vec r_1(u,v)}{\partial v}\right\|\,\mathrm du\,\mathrm dv=\boxed{25}

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mariarad [96]

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Which is the same as saying 70 cents per cookie

=============================================================

Explanation:

The unit rate is the cost of one cookie. The term "unit" means "one".

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3 years ago
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Setler79 [48]

Answer:

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Step-by-step explanation:

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==================

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7 0
3 years ago
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Fofino [41]

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Step by step solution :

Step  1  :

Equation at the end of step  1  :

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Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :


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Equation at the end of step  3  :

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Step  4  :

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Hope this helps you, Have a nice day.

4 0
3 years ago
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saul85 [17]

Answer:

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