3 years ago

Simplify when it is possible 10 x^2 - y + x^2

Mathematics

1 answer:

Romashka-Z-Leto [24]3 years ago

5 0

Combine like terms
11x^2 - y

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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

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

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

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

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

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

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3 years ago

Jenna and Corey solved the equation, 4(x+4) = 2( 2x+5) +6, and came up with two different solutions.

iogann1982 [59]

Answer: C

Step-by-step explanation:

They both end up equaling 4x+16 so they cancel each other out

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3 years ago

Which of these nonterminating decimals can be converted into a rational number?

ValentinkaMS [17]

A can be converted since it is a repeating decimal

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Find the equation of the line that contains the point (-4,-1) and is perpendicular to the line 4x+5y=15. Write the line in slop

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