You want to find the volume inside the hemisphere $x^2+y^2+z^2=4$ (i.e. inside the sphere but above the plane $z=0$ ) and outside the cylinder $x^2+y^2=1$ . Call this region $R$ .

In cylindrical coordinates, we have

$\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_1^2\int_0^{\sqrt{4-r^2}}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$

$\displaystyle=2\pi\int_1^2 r\sqrt{4-r^2}\,\mathrm dr$

$\displaystyle=-\pi\int_3^0\sqrt u\,\mathrm du$

(where $u=4-r^2$ )

$\displaystyle=\pi\int_0^3\sqrt u\,\mathrm du$

$=\dfrac{2\pi}3u^{3/2}\bigg|_0^3=2\sqrt3\,\pi$

7 0

3 years ago

Question 1 (Essay Worth 10 points)

Shalnov [3]

✿————✦————✿————✦————✿

The answer is: <u>2(k2−4k)(2c+5)</u>

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Step:

* Consider 2ck2+5k2−8ck−20k. Do the grouping 2ck2+5k2−8ck−20k=(2ck2+5k2) +(−8ck−20k), and factor out k2 in the first and −4k in the second group.

* Factor out the common term 2c+5 by using the distributive property.

* Rewrite the complete factored expression.

✿————✦————✿————✦————✿

6 0

2 years ago

HEY PLEASE HELP I AM STRUGGLING!!

Maksim231197 [3]

Answer:

Step-by-step explanation:

ok the first box is linear

the 2nd isnt

the 3rd isnt either

the fourth is

not sure about 5th but im sure it isnt

8 0

3 years ago

PLEASE HELP TIMED TEST!!!! I WILL REPORT YOU IF YOU GIVE ME A LINK!!

Elenna [48]

Answer:

x=40

Step-by-step explanation:

you have to get a answer of 60

(40)+20=60

and 2(40)-20=60

5 0

3 years ago