Answer:
Step-by-step explanation:
A 90° portion of your volume is shown below.
Let's use the shell method and decompose the solid of revolution into cylindrical shells.
The volume of each cylindrical shell is
dV = 2πrh dx
where
r = ln16 - x
h = eˣ
So
dV = 2π(ln16 - x)eˣdx
Let's integrate the two terms separately.
![\begin{array}{rcl}A &=& 2\pi \ln16 \int_{0}^{\ln16}e^{x}dx\\\\&=& 2\pi\ln16[e^{x}]_{0}^{\ln16}\\\\&=& 2\pi\ln16(16 - 1)\\&= &\mathbf{30\pi\ln1}\\\\B &=&2\pi\int_{0}^{\ln16}xe^{x}dx\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7DA%20%26%3D%26%202%5Cpi%20%5Cln16%20%5Cint_%7B0%7D%5E%7B%5Cln16%7De%5E%7Bx%7Ddx%5C%5C%5C%5C%26%3D%26%202%5Cpi%5Cln16%5Be%5E%7Bx%7D%5D_%7B0%7D%5E%7B%5Cln16%7D%5C%5C%5C%5C%26%3D%26%202%5Cpi%5Cln16%2816%20-%201%29%5C%5C%26%3D%20%26%5Cmathbf%7B30%5Cpi%5Cln1%7D%5C%5C%5C%5CB%20%26%3D%262%5Cpi%5Cint_%7B0%7D%5E%7B%5Cln16%7Dxe%5E%7Bx%7Ddx%5C%5C%5Cend%7Barray%7D)
Use the integration by parts formula
![\begin{array}{rcl}uv - \int v du &=&\\B &=& 2\pi[xe^{x}]_{0}^{\ln16} - 2\pi \int_{0}^{\ln16} e^{x}dx\\\\&=&2\pi[xe^{x}]_{0}^{\ln16}-2\pi [e^{x}]_{0 }^{\ln16}\\\\&= &2\pi(16\ln16- 0) -2\pi(16 - 1)\\&=& \mathbf{32\pi \ln16 -30\pi}\\A - B &= &30\pi\ln16 - 32\pi \ln16 +30\pi\\&=& 30\pi - 2\pi \ln16\\&=&\mathbf{2\pi(15 - \ln16)}\end{array}\\\text{The volume of the solid is $\large \boxed{\mathbf{2\pi(15 - \ln16)}}$}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7Duv%20-%20%5Cint%20v%20du%20%26%3D%26%5C%5CB%20%26%3D%26%202%5Cpi%5Bxe%5E%7Bx%7D%5D_%7B0%7D%5E%7B%5Cln16%7D%20-%202%5Cpi%20%5Cint_%7B0%7D%5E%7B%5Cln16%7D%20e%5E%7Bx%7Ddx%5C%5C%5C%5C%26%3D%262%5Cpi%5Bxe%5E%7Bx%7D%5D_%7B0%7D%5E%7B%5Cln16%7D-2%5Cpi%20%5Be%5E%7Bx%7D%5D_%7B0%20%7D%5E%7B%5Cln16%7D%5C%5C%5C%5C%26%3D%20%262%5Cpi%2816%5Cln16-%200%29%20-2%5Cpi%2816%20-%201%29%5C%5C%26%3D%26%20%5Cmathbf%7B32%5Cpi%20%5Cln16%20-30%5Cpi%7D%5C%5CA%20-%20B%20%26%3D%20%2630%5Cpi%5Cln16%20-%2032%5Cpi%20%5Cln16%20%2B30%5Cpi%5C%5C%26%3D%26%2030%5Cpi%20-%202%5Cpi%20%5Cln16%5C%5C%26%3D%26%5Cmathbf%7B2%5Cpi%2815%20-%20%5Cln16%29%7D%5Cend%7Barray%7D%5C%5C%5Ctext%7BThe%20volume%20of%20the%20solid%20is%20%24%5Clarge%20%5Cboxed%7B%5Cmathbf%7B2%5Cpi%2815%20-%20%5Cln16%29%7D%7D%24%7D)
The answer is 0.6 . 3 divide 5 is 0.6
Answer:
He can pay for the membership for 9 months.
Step-by-step explanation:
Divide 315 by 35, and then you get your answer.
Answer:
<em>Tiffany pays a total price of $9.81 for the basket of watermelons</em>
Step-by-step explanation:
<u>Percentages</u>
To increase a certain amount by a given percentage, we can first calculate the increasing amount and then add it to the original amount.
If the price of the basket of watermelons was $9 before tax, and the sales tax is 9%, we first calculate the tax amount to pay:
$9 * 9 / 100 = $0.81
Now we add it to $9 to get the total price paid by Tiffany:
Total price = $9 + $0.81 = $9.81
Tiffany pays a total price of $9.81 for the basket of watermelons
