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3 years ago

Whats the answer.......................

Mathematics

1 answer:

scZoUnD [109]3 years ago

4 0

Answer:

Step-by-step explanation:

Cory is 5 times as far as kira. that makes it 5 times 5. tina is 5 times as far as cory. that makes it 5 times 5 times 5

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Evaluate the surface integral:S

rjkz [21]

Assuming $S$ does not include the plane $z=0$ , we can parameterize the region in spherical coordinates using

$\mathbf r(u,v)=\left\langle3\cos u\sin v,3\sin u\sin v,3\cos v\right\rangle$

where $0\le u\le2\pi$ and $0\le v\le\dfrac\pi/2$ . We then have

$x^2+y^2=9\cos^2u\sin^2v+9\sin^2u\sin^2v=9\sin^2v$
$(x^2+y^2)=9\sin^2v(3\cos v)=27\sin^2v\cos v$

Then the surface integral is equivalent to

$\displaystyle\iint_S(x^2+y^2)z\,\mathrm dS=27\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^2v\cos v\left\|\frac{\partial\mathbf r(u,v)}{\partial u}\times \frac{\partial\mathbf r(u,v)}{\partial u}\right\|\,\mathrm dv\,\mathrm du$

We have

$\dfrac{\partial\mathbf r(u,v)}{\partial u}=\langle-3\sin u\sin v,3\cos u\sin v,0\rangle$
$\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle3\cos u\cos v,3\sin u\cos v,-3\sin v\rangle$
$\implies\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle-9\cos u\sin^2v,-9\sin u\sin^2v,-9\cos v\sin v\rangle$
$\implies\left\|\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}\|=9\sin v$

So the surface integral is equivalent to

$\displaystyle243\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv\,\mathrm du$
$=\displaystyle486\pi\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv$
$=\displaystyle486\pi\int_{w=0}^{w=1}w^3\,\mathrm dw$

where $w=\sin v\implies\mathrm dw=\cos v\,\mathrm dv$ .

$=\dfrac{243}2\pi w^4\bigg|_{w=0}^{w=1}$
$=\dfrac{243}2\pi$

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3 years ago

25 x 170 x 6.350<br> please help

m_a_m_a [10]

Answer:

26,987.5

Step-by-step explanation:

hope it's helpful to you ☺️

$\sf{}$

♛┈⛧┈┈•༶♛┈⛧┈┈•༶

✌️

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2 years ago

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Which angel is a right angle (Choose One)(100 Points)

lorasvet [3.4K]

$\huge\mathsf\blue{Answer}:-$

Hey mate,

Attachment 3 is a right angle because a right angle makes a straight line ( 90 degree angle)

that's why it's a right angle

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2 years ago

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5.1+2.3x=23.5..solve for x

erastovalidia [21]

Answer:

see beleow

Step-by-step explanation:

Let's solve your equation step-by-step.

5.1+2.3x=23.5

Step 1: Simplify both sides of the equation.

2.3x+5.1=23.5

Step 2: Subtract 5.1 from both sides.

2.3x+5.1−5.1=23.5−5.1

2.3x=18.4

Step 3: Divide both sides by 2.3.

2.3x

2.3

18.4

2.3

x=8

Answer:

x=8

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3 years ago

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Alja [10]

Answer:

20 square meters

Step-by-step explanation:

To do this continue the line of the top of the rectangle so you split the figure into a triangle and a rectangle. The dimensions of the rectangle would be 8 by 2, so 8 * 2 = 16. Next, the dimensions of the triangle would be (4 - 2) by (8 - 4) = 2 by 4. The area would then be 2 * 4 = 8/2 = 4.

All you have to do now is add those two areas together, 16 + 4 = 20 square meters.

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3 years ago

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