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
seraphim [82]
3 years ago
14

Find the volume of the wedge-shaped region contained in the cylinder x2 + y2 = 49, bounded above by the plane z = x and below by

the xy-plane.
Mathematics
1 answer:
fiasKO [112]3 years ago
4 0
\displaystyle\iiint_R\mathrm dV=\int_{y=-7}^{y=7}\int_{x=-\sqrt{49-y^2}}^{x=0}\int_{z=x}^{z=0}\mathrm dz\,\mathrm dx\,\mathrm dy

Converting to cylindrical coordinates, the integral is equivalent to

\displaystyle\iiint_R\mathrm dV=\int_{\theta=\pi/2}^{\theta=3\pi/2}\int_{r=0}^{r=7}\int_{z=r\cos\theta}^{z=0}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta
=\displaystyle\int_{\theta=\pi/2}^{\theta=3\pi/2}\int_{r=0}^{r=7}-r^2\cos\theta\,\mathrm dr\,\mathrm d\theta
=-\displaystyle\left(\int_{\theta=\pi/2}^{3\pi/2}\cos\theta\,\mathrm d\theta\right)\left(\int_{r=0}^{r=7}r^2\,\mathrm dr\right)
=\dfrac{2\times7^3}3=\dfrac{686}3
You might be interested in
Nine times the sum of a number and 4 is 3. Use the variable w for the unknown number
DENIUS [597]
9(w+4)=3
9w+36=3
w=-33/9
6 0
3 years ago
What's the answer to this question??​
laiz [17]

Answer:

b=8

Step-by-step explanation:

b=√(10²-6²)=√(100-36)=√64=8

7 0
3 years ago
Can someone please help me answer this question asap thank you
Marianna [84]
Ross would be the correct answer. To figure it out you would divide 27/3 which is 9 and then 49/7 which is 7. So 9>7.
4 0
2 years ago
the ratio of boys to girls in a class is 5:4 there are 36 students in the class how many students are girls
Alina [70]
First add up the total parts in the ratio.
5 + 4 = 9
Now we need to know the value of each part
36 / 9 = 4
The girls has total of 4 parts, therefore we can just multiply the number of parts by the amount in each part
4 x 4 = 16
So there r 16 girls in the class
4 0
3 years ago
Determine if the sequence below is arithmetic or geometric and determine the
Brrunno [24]
The sequence is arithmetic since the common difference that is equal
d=11-15=7-11=-4
a(n) = a1 +(n-1)d
a1=15
=
a(n) = 15+(n-1)-4
5 0
3 years ago
Other questions:
  • Jake ate 4/8 of a pizza. Millie ate 2/8 of a pizza. How much pizza was eaten by Jake and Millie? Write in the simplest form
    8·1 answer
  • How do you Simplify this <br> 10+13i/-8i
    13·2 answers
  • What is the measure of
    5·1 answer
  • mrs. houston puts 5 ounces of snack mix in each bag how many pounds of snack mix does she need to fill 32 bags
    7·1 answer
  • Julie has a part time job after school she gets paid at a constant rate of dollars per hour.Julie works 12$ per month . Use this
    13·1 answer
  • 75,4,3,100 form of proportion<br><br>​
    9·1 answer
  • Pls answer soon!!!!!
    7·2 answers
  • What is 12 to the exponent 263845
    6·2 answers
  • What is the answer???????
    6·1 answer
  • −9−(−12) as an addition expression
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!