1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
borishaifa [10]
3 years ago
15

Let the region R be the area enclosed by the function f(x)=ln(x) and g(x)= 1/2x-2. Find the volume of the solid generated when t

he region R is revolved about the line y=-5.
Mathematics
1 answer:
Neporo4naja [7]3 years ago
3 0

Answer:

V=61.66

Step-by-step explanation:

This problem can be solved by using the expression for the Volume of a solid with the washer method

V=\pi \int \limit_a^b[R(x)^2-r(x)^2]dx

where R and r are the functions f and g respectively (f for the upper bound of the region and r for the lower bound).

Before we have to compute the limits of the integral. We can do that by taking f=g, that is

f(x)=g(x)\\ln(x)=\frac{1}{2}x-2

there are two point of intersection (that have been calculated with a software program as Wolfram alpha, because there is no way to solve analiticaly)

x1=0.14

x2=8.21

and because the revolution is around y=-5 we have

R=ln(x)-(-5)\\r=\frac{1}{2}x-2-(-5)\\

and by replacing in the integral we have

V=\pi \int \limit_{x1}^{x2}[(lnx+5)^2-(\frac{1}{2}x+3)^2]dx\\

V=\pi [28x+\frac{1}{x}+xln^2x-12xlnx-6lnx]  

and by evaluating in the limits we have

V=61.66

Hope this helps

regards

You might be interested in
Answer pls in standard form too
romanna [79]

Answer:

a)

Slope form y=2x+3

Standard form 2x-y=-3

b)

Slope y=3/5x-6

Standard 3x-5y=30

c)

slope y=-3/2x+9

standard 3x+2y=18

d)

slope y=-3x+0

standard = 3x+y=0

Step-by-step explanation:

a)

Slope form y=2x+3

Standard form 2x-y=-3

b)

Slope y=3/5x-6

Standard 3x-5y=30

c)

slope y=-3/2x+9

standard 3x+2y=18

d)

slope y=-3x+0

standard = 3x+y=0

7 0
2 years ago
ABC is similar to XYZ. The length of AB is 3 inches. The length of BC is 5 inches. The length of YZ is 13 inches. What is the le
Marrrta [24]

Answer:

7.8

Step-by-step explanation:

5 0
3 years ago
I Need Help Asappp! So Pls answerrr!
lisabon 2012 [21]

Answer:

y= -3x+6

Step-by-step explanation:

3 0
2 years ago
A fruit stand has to decide what to charge for their produce. They need $10, for 4 apples and 4 oranges. They also need $15 for
slega [8]

Answer:

Here I think you need to do $15-50%=7.5 and $10-50=5

4 0
3 years ago
What is the answer to x+y=2
Ahat [919]

Answer:

u need 2 equation to solve

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • I shall brainliest you. Use the distributive property to expand the following expression.
    9·2 answers
  • The area of the conference table in Mr. Nathan’s office must be no more than 175 ft2. If the length of the table is 18 ft more t
    7·1 answer
  • What’s the value of 2 quarters 4 dimes and 6 pennies
    11·2 answers
  • How to find the distance between two pairs of points
    11·1 answer
  • I WILL AWARD BRAINLIEST!! PLEASE HELP!!
    7·1 answer
  • Can someone help me out on this :P
    15·2 answers
  • 13. Car Depot rents a car for an initial fee of $20
    7·1 answer
  • Question 14 (5 points)
    15·1 answer
  • You roll a 6-sided die.<br> What is P(not odd)?<br> Write your answer as a percentage.
    8·1 answer
  • in 2001 the average yearly wage was 21842 on average people spent £1644 on their family holiday what percentage of the average y
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!