3 years ago

Line e has a slope of –5/8.Line f is perpendicular to e.What is the slope of line f?

Mathematics

1 answer:

Varvara68 [4.7K]3 years ago

3 0

Answer:

8/5

Step-by-step explanation:

opposite reciprocal

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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

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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

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

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