Plz help I’ll mark you

A) Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given cur

Leno4ka [110]

(a) See the attached sketch. Each shell will have a radius y chosen from the interval [2, 4], a height of x = 2/y, and thickness ∆y. For infinitely many shells, we have ∆y converging to 0, and each super-thin shell contributes an infinitesimal volume of

2π (radius)² (height) = 4πy

Then the volume of the solid is obtained by integrating over [2, 4]:

$\displaystyle 4\pi \int_2^4 y\,\mathrm dy = 2\pi y^2\bigg|_{y=2}^{y=4} = 2\pi (4^2-2^2) = \boxed{24\pi}$

(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 - x (this is the distance between a given x value in the orange shaded region to the axis of revolution) and a height of 8 - x ³ (and this is the distance between the line y = 8 and the curve y = x ³). Then each shell has a volume of

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

so that the overall volume of the solid would be

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

I leave the details of integrating to you.

3 0

3 years ago

Ellen purchased a dishwasher, which cost $315 before the 9.22% sales tax. She used the machine an average of 10 times per week f

Natasha2012 [34]

Given:
Cost of dishwasher : 315 before sales tax
sales tax : 9.22%

Total cost = 315 * 1.0922 = 344.043

Average of 10 uses per week for the next 6 years before replacing it.
There are 52 weeks in a year.

10 uses per week * 52 weeks per year * 6 years = 3120 average uses

cost for water = 0.09 ; cost for electricity = 0.13 ; total cost per use = 0.22

0.22 * 3120 = 686.40 cost of use

purchase cost = 344.043
cost of use = 686.40
lifetime cost 1,030.443

5 0

3 years ago

Read 2 more answers

Jake has decided to invest in three business ventures. The total cost of investing in all three ventures is $15,000. The combine

Arte-miy333 [17]

X = first venture, y = second venture, z = third venture

x + y + z = 15,000
x + z = y + 7000
3x + 2y + 2z = 39,000
these are ur equations.....

x + y + z = 15,000
x - y + z = 7000
--------------------add
2x + 2z = 22,000

x + y + z = 15,000....multiply by -2
3x + 2y + 2z = 39,000
-------------------
-2x - 2y - 2z = - 30,000 (result of multiplying by -2)
3x + 2y + 2z = 39,000
------------------add
x = 9,000

2x + 2z = 22,000
2(9000) + 2z = 22000
18,000 + 2z = 22000
2z = 22000 - 18000
2z = 4000
z = 4000/2
z = 2,000

x + y + z = 15,000
9000 + y + 2000 = 15,000
11,000 + y = 15,000
y = 15,000 - 11,000
y = 4,000

first venture (x) = 9,000 <==
second venture (y) = 4,000 <==
third venture (z) = 2,000 <==

7 0

3 years ago

Read 2 more answers

PLEASE PLEASE I WILL MARK AS BRAINLIEST!!!!!!!

SOVA2 [1]

4t+6s=4524
t+s=925

Multiply the second equation by -4 to cancel the variable t
4t+6s=4524
-4t-4s=-3700
2s = 824
Divide both sides by 2
S= 412

925-412= 513
T=513

7 0

3 years ago

I dont understand this

algol13

Answer:0,3 for y and 4,0 for x

the second one is 0,6 for y and for the x it will be -3,0

Step-by-step explanation:

8 0

3 years ago