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Alex
2 years ago
13

If the diameter of a circle is 80 ft., find the area A 5,024 ft2 B 20,096 ft2 C 251.2 ft2 D 125.6 ft2

Mathematics
1 answer:
Dmitry [639]2 years ago
3 0
A. 5,024

If the diameter is 80 feet, the radius is 40 ft.

Area of a circle = (pi)(r^2)
A = 3.14 x 40^2
A = 5,042
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A) Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given cur
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(b) See the other attached sketch. (The text is a bit cluttered, but hopefully you'll understand what is drawn.) Each shell has a radius 9 - <em>x</em> (this is the distance between a given <em>x</em> value in the orange shaded region to the axis of revolution) and a height of 8 - <em>x</em> ³ (and this is the distance between the line <em>y</em> = 8 and the curve <em>y</em> = <em>x</em> ³). Then each shell has a volume of

2<em>π</em> (9 - <em>x</em>)² (8 - <em>x</em> ³) = 2<em>π</em> (648 - 144<em>x</em> + 8<em>x</em> ² - 81<em>x</em> ³ + 18<em>x</em> ⁴ - <em>x</em> ⁵)

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\displaystyle 2\pi \int_0^2 (648-144x+8x^2-81x^3+18x^4-x^5)\,\mathrm dx = \boxed{\frac{24296\pi}{15}}

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Answer:

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The <em>x-</em>intercepts are (-1/4, 0) and (4, 0).

Part B)

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Step-by-step explanation:

The function given is:

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To find the <em>x-</em>intercepts of the function, set the function equal to 0 and solve for <em>x: </em>

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Note that the leading coefficient of our function is negative.

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Hence, our vertex will be the maximum.

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