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dezoksy [38]
3 years ago
6

Given the function g(x)=x^2-2 find the range for the domain (-2,-1,1,3)

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
5 0

Answer:

(-2,2)

(-1,-1)

(1,-1)

(3,7)

If you graph it with a graphing calc. and pinpoint the X's(domains) then you can see the Y's(ranges)

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Answer:

The volume of the solid is π/40 cubic units.

Step-by-step explanation:

Please refer to the graph below.

Recall that the area of a semi-circle is given by:

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The volume of the solid will be the integral from <em>x</em> = 0 to <em>x</em> = 1 of area A. Since the diameter is given by <em>y</em>, then the radius is <em>y/2</em>. Hence, the volume of the solid is:

\displaystyle V=\int_0^1\frac{1}{2}\pi \left(\frac{y}{2}\right)^2\, dx

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\displaystyle V=\frac{1}{2}\pi\int_0^1\left(\frac{x^2}{2}\right)^2\, dx

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Integrate:

\displaystyle V=\frac{1}{2}\pi \left[\frac{x^5}{20}\Big|_0^1\right]

Evaluate:

\displaystyle V=\frac{\pi}{40}\left((1)^5-\left(0\right)^5\right)=\frac{\pi}{40}\text{ units}^3

The volume of the solid is π/40 cubic units.

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