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3 years ago

What is the answer of 11-(-2) 14?

Mathematics

1 answer:

blondinia [14]3 years ago

4 0

11-(-2)14=
11-((-2).14)=
11-(-28)=11+28=39

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Find the volume of the solid formed by revolving the region bounded by LaTeX: y = \sqrt{x} y = x and the lines LaTeX: y = 1 y =

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Answer:

The volume is:

$\displaystyle\frac{37\pi}{10}$

Step-by-step explanation:

See the sketch of the region in the attached graph.

We set the integral using washer method:

$\displaystyle\int_a^b\pi r^2dx$

Notice here the radius of the washer is the difference of the given curves:

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$\displaystyle\int_1^4\pi(x-\sqrt{x})^2dx$

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$\displaystyle\pi\int_1^4x^2-2x\sqrt{x}+x\,dx$

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$\displaystyle\pi\int_1^4x^2-2x^{3/2}+x\,dx$

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Simplifying a bit:

$\displaystyle\pi\left[\frac{x^3}{3}-\frac{4x^{5/2}}{5}+\frac{x^2}{2}\right|_1^4$

Then plugging the limits of the integral:

$\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(4)^{5/2}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]$

Taking the root (rational exponents):

$\displaystyle\pi\left[\frac{4^3}{3}-\frac{4(2)^{5}}{5}+\frac{4^2}{2}-\left(\frac{1}{3}-\frac{4}{5}+\frac{1}{2}\right)\right]$

Then doing those arithmetic computations we get:

$\displaystyle\frac{37\pi}{10}$

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3 years ago

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3 years ago

Derive the equation of the parabola with a focus at (_5, 5) and a directrix of y = -1.

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Answer: Option D is correct.

Step-by-step explanation:

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focus = (-5,5)

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