(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.
Answer:
the y-intercept is (0,-6)
the x-intercept is (8,0)
Step-by-step explanation:
<em>Solving for the y-intercept:</em>
Since the equation 'y=3/4x - 6' is in the 'y=mx + c' form (where m is the slope and c is the y-intercept):
3/4 is m (which is the slope)
-6 is c (which is the y-intercept)
<em>Solving for the x-intercept:</em>
When the line intersects with the x-axis, the y-value is 0. Hence, the coordinate is (x,0). Substituting this into 'y=3/4x - 6':
0 = 3/4x - 6
3/4x - 6 + 6 = 6
3/4x = 6
x = 4/3 * 6
= 8
Hence,
the y-intercept is (0,-6)
the x-intercept is (8,0)
<em>Hope this helps and be sure to have a wonderful time ahead at Brainly! :D</em>
Answer:
The distance from Endnville to Concord = 14.8 miles
Step-by-step explanation:
∵ Westfalls is 7 miles South of Endnville
∵ Concord is 13 miles West of Westfalls
∵ South and West are ⊥
∴ The distance from Endnville to Concord = √(7)² + (13)²
= 14.8 miles
Answer:
D: x=12
Step-by-step explanation:
Answer:
Step-by-step explanation:
The Caucasus Mountains