Using washers, the volume is given by

$\displaystyle\pi\int_{x=1}^{x=e}((1+3)^2-(\ln x+3)^2)\,\mathrm dx$
$=\displaystyle\pi\int_{x=1}^{x=e}(7-6\ln x-(\ln x)^2)\,\mathrm dx$

5 0

3 years ago

If a club charges an initial fee of $99 to join, and a monthly fee of $45. Write an equation that represents the cost of being a

ANEK [815]

Equation: 99 + 45x, with x as how many ever months.

After five months:
99 + 45(5) = 99 + 225 = $324.

8 0

3 years ago

A pharmacist has a 12% solution and a 20% solution of boric acid. How much of each should she use to make 80 grams of a 15% solu

nlexa [21]

Step-by-step explanation:

If x = the amount of 12% and y = the amount of 20%, then x + y = 80

Since we need 80 grams of 15%, 80(.15) = 12.

We are given that .12x + .20y = 12.

We can solve the first equation for x or y. Let's do x.

x = 80 - y

.12(80 - y) + .20y = 12

9.6 - .12y + .20y = 12

.08y = 2.4

y = 30

x = 80 - 30 = 50

5 0

3 years ago

Read 2 more answers