The and answer is going to be 3 because when you multiply 5 and 3 you get 15
In this item, we are given with the slope, m = 2/3 and intercept of (1,1). The equation of the line that contains these properties is,
y - y₁ = m(x - x₁)
Substituting the known values,
y - 1 = (2/3)(x - 1)
Simplifying,
3y - 3 = 2x - 2
Further simplifying,
<em> 2x - 3y = -1</em>
The answer would be sas or conguernt angle
Answer = (A) about 30
1000/200 = 5
5 x 6 = 30
(a) See the attached sketch. Each shell will have a radius <em>y</em> chosen from the interval [2, 4], a height of <em>x</em> = 2/<em>y</em>, and thickness ∆<em>y</em>. For infinitely many shells, we have ∆<em>y</em> converging to 0, and each super-thin shell contributes an infinitesimal volume of
2<em>π</em> (radius)² (height) = 4<em>πy</em>
Then the volume of the solid is obtained by integrating over [2, 4]:

(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)
so that the overall volume of the solid would be

I leave the details of integrating to you.