(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:
I think it is A but not 100% sure.
Step-by-step explanation:
If I understand the drawing correctly than yes, because
6 9/12 + 6 9/12 = 12 and 18/12 = 13 and 6/12 or 13 and 1/2.
13 1/2 + 4 8/12 = 13 6/12 + 4 8/12 = 17 and 14/12 = 18 2/12 or 18 and 1/6.
Answer:
John is 17,
Susan is 14,
and Khalid is 9.
Step-by-step explanation:
a = John's age
b = Susan's age
c = Khalid's age
Let's set our rules from the given information.
a = b + 3
c = b - 5
a + b + c = 40
Now, we can solve for b through substitution.
(b + 3) + b + (b - 5) = 40
3b - 2 = 40
3b = 42
b = 14
So, now that we have Susan's age, we can follow the rules and see if it holds.
17 + 14 + 9 = 40 Viola!
Answer:
11.
A) EZ Pay Plan=0.15x
B) 40 to Go Plan=0.05x+40
12.
0.15x=0.05x+40
13.
x=400 minutes
14. The solution is the amount of minutes that it takes for both plans to cost the same amount. X has one solution, so it accounts for both equations.
15. EZ Pay Plan
Step-by-step explanation:
For 11, what you need to know is that the slope (coefficient of x) is the price per minute. 0.15 per minute and 0.05 per minute are charged, and therefore are the slope for those equations. The 40 on B is because it is the y intercept. No matter how long you use the object, you will always pay at least 40 dollars.
For 12, you have to find x for the minutes used.
For 13, if you do the process algebraically,
0.15x=0.05x+40
0.10x=40 (subtracted 0.05x from both sides)
x=400 (divided 0.10x and 40 by 0.10)
For 14, (no explanation)
For 15, if you substitute 200 as x, you would see that the EZ Pay Plan would make you pay 30 dollars while the 40 To Go Plan would make you pay 10+40 dollars, which 30<50.
(sorry for late response)
