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3 years ago

7

I don’t get how you do this please help

1 answer:

Tpy6a [65]3 years ago

6 0

What are the directions?

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Tom brought 7/8 gallons of water to a party and his friends drank2/3 of it. How many gallons of water did they drink?

natka813 [3]

In plain and short, what's 2/3 of 7/8? well, is just their product.

$\bf \cfrac{7}{8}\cdot \cfrac{2}{3}\implies \cfrac{7\cdot 2}{8\cdot 3}\implies \cfrac{14}{24}\implies \stackrel{simplified}{\cfrac{7}{12}}$

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3 years ago

Evaluate the integral Find the volume of material remaining in a hemisphere of radius 2 after a cylindrical hole ofradius 1 is d

algol13

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 $u=4-r^2$ )

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

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

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4 years ago

30, 16, 49, 25 find the median

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Harlamova29_29 [7]

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63 Degrees

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