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2 years ago

I need help with a proof. i only need number 3, 6, & 7. please help!!!

Mathematics

1 answer:

lesya692 [45]2 years ago

3 0

Answer:

boottytff tgggfgv dugddcv

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Can i please get help with this question?

Westkost [7]

41 years old as 47 take away 6 makes 41

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3 years ago

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Rewrite the following integral in spherical coordinates.

lora16 [44]

In cylindrical coordinates, we have $r^2=x^2+y^2$ , so that

$z = \pm \sqrt{2-r^2} = \pm \sqrt{2-x^2-y^2}$

correspond to the upper and lower halves of a sphere with radius $\sqrt2$ . In spherical coordinates, this sphere is $\rho=\sqrt2$ .

$1 \le r \le \sqrt2$ means our region is between two cylinders with radius 1 and $\sqrt2$ . In spherical coordinates, the inner cylinder has equation

$x^2+y^2 = 1 \implies \rho^2\cos^2(\theta) \sin^2(\phi) + \rho^2\sin^2(\theta) \sin^2(\phi) = \rho^2 \sin^2(\phi) = 1 \\\\ \implies \rho^2 = \csc^2(\phi) \\\\ \implies \rho = \csc(\phi)$

This cylinder meets the sphere when

$x^2 + y^2 + z^2 = 1 + z^2 = 2 \implies z^2 = 1 \\\\ \implies \rho^2 \cos^2(\phi) = 1 \\\\ \implies \rho^2 = \sec^2(\phi) \\\\ \implies \rho = \sec(\phi)$

which occurs at

$\csc(\phi) = \sec(\phi) \implies \tan(\phi) = 1 \implies \phi = \dfrac\pi4+n\pi$

where $n\in\Bbb Z$ . Then $\frac\pi4\le\phi\le\frac{3\pi}4$ .

The volume element transforms to

$dx\,dy\,dz = r\,dr\,d\theta\,dz = \rho^2 \sin(\phi) \, d\rho \, d\theta \, d\phi$

Putting everything together, we have

$\displaystyle \int_0^{2\pi} \int_1^{\sqrt2} \int_{-\sqrt{2-r^2}}^{\sqrt{2-r^2}} r \, dz \, dr \, d\theta = \boxed{\int_0^{2\pi} \int_{\pi/4}^{3\pi/4} \int_{\csc(\phi)}^{\sqrt2} \rho^2 \sin(\phi) \, d\rho \, d\phi \, d\theta} = \frac{4\pi}3$

4 0

1 year ago

What’s the answer 6x=4x+140

dmitriy555 [2]

1) given 6x = 4x + 140

2) subtract 4x from both sides => 6x - 4x = 4x - 4x + 140

=> 2x = 140

3) divide both members by 2 => 2x / 2 = 140 / 2

=> x = 70

4) Answer: x = 70

6 0

3 years ago

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Linda is making a mosaic stepping stone to place in

Lorico [155]

Answer:

D 565.2 in

Step-by-step explanation:

First you need to find the area of the stepping stone. The rule for area of circle is pi times radius squared. To find the radius you divide 12 by 2 = 6. After you do 6 times 6= 36 you multiply 36 times pi (3.14) = 113.04. After we find the are of the stepping stone we multiply it by five to get how many inches we have to cover. 113.04 times 5= 565.2 in.

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2 years ago

Vanessa draws one side of equilateral AABC on the coordinate plane at points A(-2, 1) and B(4,1). What are the possible coordina

natulia [17]

Answer:

Step-by-step explanation:

Answer E is the only one that is close

7 0

2 years ago

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