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2 years ago

Minimize Q=3x2+3y2, where x+y=6.

Mathematics

1 answer:

weeeeeb [17]2 years ago

5 0

Answer:

$+(x + y) {}^{2} = 6 {}^{2} \\ x {}^{2} + 2xy + y {?}^{2} = 36$

$x {}^{2} + y {}^{2} = 36 - 2xy$

$q = 3(x {}^{2} + y {}^{2} )$

$q = 3(36 - 2xy) = 108 - 6xy$

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G find the area of the surface over the given region. use a computer algebra system to verify your results. the sphere r(u,v) =

Svetach [21]

Presumably you should be doing this using calculus methods, namely computing the surface integral along $\mathbf r(u,v)$ .

But since $\mathbf r(u,v)$ describes a sphere, we can simply recall that the surface area of a sphere of radius $a$ is $4\pi a^2$ .

In calculus terms, we would first find an expression for the surface element, which is given by

$\displaystyle\iint_S\mathrm dS=\iint_S\left\|\frac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv$

$\dfrac{\partial\mathbf r}{\partial u}=a\cos u\cos v\,\mathbf i+a\cos u\sin v\,\mathbf j-a\sin u\,\mathbf k$
$\dfrac{\partial\mathbf r}{\partial v}=-a\sin u\sin v\,\mathbf i+a\sin u\cos v\,\mathbf j$
$\implies\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}=a^2\sin^2u\cos v\,\mathbf i+a^2\sin^2u\sin v\,\mathbf j+a^2\sin u\cos u\,\mathbf k$
$\implies\left\|\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}\right\|=a^2\sin u$

So the area of the surface is

$\displaystyle\iint_S\mathrm dS=\int_{u=0}^{u=\pi}\int_{v=0}^{v=2\pi}a^2\sin u\,\mathrm dv\,\mathrm du=2\pi a^2\int_{u=0}^{u=\pi}\sin u$
$=-2\pi a^2(\cos\pi-\cos 0)$
$=-2\pi a^2(-1-1)$
$=4\pi a^2$

as expected.

6 0

3 years ago

Luca made a scale drawing of the auditorium. in real life, the stage is 45 feet long. it is 18

ollegr [7]

Answer:

30:1

Step-by-step explanation:

45*12 = 540

540/18 = 30

8 0

2 years ago

He needs to purchase some work clothes and notices that J.C. Penney is having a 25% off of your total purchase sale. He decides

SVETLANKA909090 [29]

First, lets determine the regular price of his purchase :

16.99 (3) + 34.99 (3) + 52.99 (2) + 5.99 (5) = 50.97 + 104.97 + 105.98 + 29.95 = 291.87

Therefore, the regular price of his purchase is $291.87 before sales tax.

If he receives 25% off of his total purchase, then the price is now :

291.87 * .75 = $218.90

We multiply by 75% because we are only paying 75% of the total purchase price since we received a 25% discount.

The total savings is

291.87 - 218.90 = $72.97

If sales tax is 10%, the total purchase price after sales tax is :

218.90 * 1.10 = $240.79

The sales tax is $21.89 since

240.79 -218.90 = 21.89

If he pays with 3 $100 bills, we should receive :

300 - 240.79 = $59.21

in change.

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3 years ago

The model represents an equation.

madreJ [45]

Answer:

9/5

Step-by-step explanation:

solve the original equation for x

-4× + 3 = 1x +(-6)

-1x

-5x + 3 = -6

-3

-5x = -9

/-5

x = 9/5

CHECK

-4(9/5) + 3 = 1(9/5) +(-6)

-21/5 = -21/5

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2 years ago

What is the product?

gavmur [86]

Answer:

Step-by-step explanation:

3 0

3 years ago

Minimize Q=3x2+3y2​, where x+y=6.

Minimize Q=3x2+3y2, where x+y=6.