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
The next three terms of the sequence 20, 40, 80, 160,… are 320, 640, and 1280.
hram777 [196]
Correct

Its a geometric sequence with common ratio 2.
5 0
3 years ago
What is the area? Bit confused on this one.
Nutka1998 [239]

Answer:

A = 9x² + 12x

Step-by-step explanation:

The area (A) of the rectangle is calculated as

A = height × width

  = 3(3x² + 4x) ← distribute parenthesis by 3

   = 9x² + 12x

7 0
3 years ago
Read 2 more answers
2,500 calories in 24 hours
Klio2033 [76]

what do mean what are you looking for

5 0
3 years ago
At a university, 60​% of the students who apply. Of the students the university​ accepts, 25% actually enroll If 2000 students​
sweet-ann [11.9K]

Answer:

300 students are enrolled.

Step-by-step explanation:

As the university accepts 60% of the students who apply.

As 2000 students apply, it means that:

2000 × 60% ⇒ 2000 × 0.6 = 1200 students are accepted

Out of these 1200, 25% enrolled

1200 × 25% ⇒ 1200 × 0.25 = 300 students are enrolled

Therefore, 300 students are enrolled.

5 0
3 years ago
Pls help me .question no 14
Alex_Xolod [135]

Question 14, Part (i)

Focus on quadrilateral ABCD. The interior angles add to 360 (this is true for any quadrilateral), so,

A+B+C+D = 360

A+90+C+90 = 360

A+C+180 = 360

A+C = 360-180

A+C = 180

Since angles A and C add to 180, this shows they are supplementary. This is the same as saying angles 2 and 3 are supplementary.

==================================================

Question 14, Part (ii)

Let

x = measure of angle 1

y = measure of angle 2

z = measure of angle 3

Back in part (i) above, we showed that y + z = 180

Note that angles 1 and 2 are adjacent to form a straight line, so we can say

x+y = 180

-------

We have the two equations x+y = 180 and y+z = 180 to form this system of equations

\begin{cases}x+y = 180\\y+z = 180\end{cases}

Which is really the same as this system

\begin{cases}x+y+0 = 180\\0+y+z = 180\end{cases}

The 0s help align the y terms up. Subtracting straight down leads to the equation x-z = 0 and we can solve to get x = z. Therefore showing that angle 1 and angle 3 are congruent. We could also use the substitution rule to end up with x = z as well.

4 0
3 years ago
Other questions:
  • Use the substitution method to solve the system of equations. Choose the correct ordered pair.
    13·2 answers
  • Need help with 1 through 5 please!
    12·1 answer
  • What's the perimeter for this
    7·1 answer
  • Cavalries principles states that two solids with equal heights and base areas have equal volumes true or false?
    12·1 answer
  • Solve the system of equations. <br><br> -5x+2y=9 <br><br> y=7x
    15·2 answers
  • What is the missing Angel
    9·2 answers
  • Find the sum of the first 7 terms of the following series, to the nearest integer. 125,50,20,...
    9·1 answer
  • HELP!!!!!!!!!!!!!!! <br> PLEASE THE PICTURE IS BELOW
    14·1 answer
  • Last month, a basketball team scored 83, 84, 85, 87, 89, 88, 67, 79, and 81 points in their games. Which data value(s) are outli
    8·1 answer
  • The method of least squares of residuals is commonly used to get the best fit with linear regression. The reason why the absolut
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!