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
GenaCL600 [577]
3 years ago
12

A solid lies between planes perpendicular to the x-axis at x tox=. The cross sections perpendicular to the x-axis are circular d

isks with diameters running from the curve y cotx to the curve y csc x.
Find the volume of the solid.
A. +1) OA 6 2 O
B. (2/3-2)-3 n2 O
C. (3-1)x+ (3-1)
D. 2 12
Mathematics
1 answer:
cluponka [151]3 years ago
3 0

It's unclear what the planes are supposed to be, so I'll take x=a and x=b with 0\le a.

The cross sections are disks with diameter \csc x-\cot x, so each disk of thickness \Delta x has a volume of

\dfrac{\pi(\csc x-\cot x)^2}4\Delta x

Then taking infinitesimally thin disks, we find the solid has a volume of

\displaystyle\frac\pi4\int_a^b(\csc x-\cot x)^2\,\mathrm dx

Since

(\csc x-\cot x)^2=2\csc^2x-2\csc x\cot x-1

and

\dfrac{\mathrm d(\csc x)}{\mathrm dx}=-\csc x\cot x

\dfrac{\mathrm d(\cot x)}{\mathrm dx}=-\csc^2x

it follows that the volume is

\displaystyle\frac\pi4\left(-2\cot x+2\csc x-x\right)\bigg|_a^b

=\dfrac\pi4(2(\cot a-\cot b)+2(\csc b-\csc a)+a-b)

=\dfrac\pi4\left(2\tan\dfrac b2-2\tan\dfrac a2+a-b\right)

You might be interested in
The answer to the question please​
Jlenok [28]

Answer:

the answer is -2x^9

Step-by-step explanation:

i know this because of photomath lolll

8 0
3 years ago
Trina invited 60 people to her party and 42 said they would attend. What percent of people said they were NOT able to attend? Pl
Llana [10]
1. simplify 42/60 to 7/10 (42/60 divided by 2 is 21/30, 21/30 divided by 3 is 7/10)
2. if 10 x 10 = 100 than 7 x 10 = 70 so that would make it 70/100 which is 70%
so 70% is the answer

Hope this helps ;)
Please don't forget to mark as brainliest answer!
5 0
3 years ago
Read 2 more answers
Need help with math homework who can help ?
Softa [21]
What's the problem ?
7 0
3 years ago
G(n)=-4n+2; find g(8)<br>​
yarga [219]

Answer:

-30

Step-by-step explanation:

In g(8) the 8 = n.  So, substitute 8 in for n in the expression -4n + 2

g(8)  =  -4(8) + 2 = -32 + 2 = -30

4 0
3 years ago
Read 2 more answers
Choose all the factors of 12. (Check all that apply.)
SSSSS [86.1K]
ANSWER: 1,2,3,4,6,12
EXPLANATION: When a question asks you the factors of a number it is basically just asking you what number are in the multiplication of 12. The numbers all tie in with the number 12 when they are multiplied
EX:
-1 * 12 = 12
-2*6=12
-3*4=12
-6*2=12

7 0
3 years ago
Read 2 more answers
Other questions:
  • Mrs Morrison’s math class starts at 11:30 If the class ends at 1:00 how long is Mts.Morrison teaching
    9·2 answers
  • A deep sea diving bell is being lowered at a constant rate. After 12 minutes, the bell is at a depth of 600 ft. After 30 minutes
    14·2 answers
  • Solve 5x=125.<br> X=25<br> x=3
    6·1 answer
  • Algebra II Help??? Subtracting Fractions<br><br> (2x)/(y^2-x^2) - (x)/(y-x)
    13·1 answer
  • Evaluate the expression: 2 ⋅ 6^2 *
    5·2 answers
  • Thomas made 8700 ml of tomato soup.he packed 1.6L of the soup in his kids lunches .he then froze half of the remaining soup.
    5·1 answer
  • Which equations are true for the values of x, y, and z? Select three options.
    8·1 answer
  • Is 4.47214 a rational number
    11·2 answers
  • You put 100$ in a savings account for six months at a rate of 0.2%
    5·1 answer
  • No bots answer fast plz 1. (4x + 8) + (7x + 3) =
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!