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
GrogVix [38]
2 years ago
12

Find the area of the surface. The part of the surface z = xy that lies within the cylinder x2 + y2 = 36.

Mathematics
1 answer:
rewona [7]2 years ago
3 0

Answer:

Step-by-step explanation:

From the given information:

The domain D of integration in polar coordinates can be represented by:

D = {(r,θ)| 0 ≤ r ≤ 6, 0 ≤ θ ≤ 2π) &;

The partial derivates for z = xy can be expressed  as:

y =\dfrac{\partial z}{\partial x} , x = \dfrac{\partial z}{\partial y}

Thus, the area of the surface is as follows:

\iint_D \sqrt{(\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2 +1 }\ dA = \iint_D \sqrt{(y)^2+(x)^2+1 } \ dA

= \iint_D \sqrt{x^2 +y^2 +1 } \ dA

= \int^{2 \pi}_{0} \int^{6}_{0} \ r  \sqrt{r^2 +1 } \ dr \ d \theta

=2 \pi \int^{6}_{0} \ r  \sqrt{r^2 +1 } \ dr

= 2 \pi \begin {bmatrix} \dfrac{1}{3}(r^2 +1) ^{^\dfrac{3}{2}} \end {bmatrix}^6_0

= 2 \pi \times \dfrac{1}{3}  \Bigg [ (37)^{3/2} - 1 \Bigg]

= \dfrac{2 \pi}{3} \Bigg [37 \sqrt{37} -1 \Bigg ]

You might be interested in
An area of 4 square yards is equal to 36 square feet. 10 square yards is equal to how many square feet? sq feet
lora16 [44]

Answer: 90 square feet

Step-by-step explanation:

5 0
3 years ago
Unit rate 40 meters in 60 seconds
gavmur [86]
The answer is .6 repeating.
7 0
3 years ago
For each equation below , determine the value of y if x = 2 .
Fynjy0 [20]
You simply plug in the value of x in each equation to find y.

1)
y = 7 - 3(2)
y = 7 - 6
y = 1

2)
y = 18/2
y = 9

hope this helped, blessings!
3 0
3 years ago
Read 2 more answers
Rewrite the equation 7-y=5x+11 to standard form
Zielflug [23.3K]
Rewriting this <span>7-y=5x+11 in standard form involves only changing the order in which the terms appear:

</span><span>7-y=5x+11 becomes 5x + y  + 11 - 7 = 0, or 5x + y + 4 = 0, or 5x + y = -4.</span>
4 0
3 years ago
Can you help me find the LCM of 6 and 15
PIT_PIT [208]
The LCM of 6 and 15 is 30:)
7 0
3 years ago
Read 2 more answers
Other questions:
  • (01.02 MC)The number line shows the distance in meters of two divers, A and B, from a shipwreck located at point X:
    9·1 answer
  • If a woman making $31,000 a year receives a cost-of-living increase of 2.4%, what will her new salary be?
    5·1 answer
  • Henry is making a corn grits recipe that calls for 1/4 cup of corn grits for every /12 cup of water. How much water will he need
    7·1 answer
  • jamal runs 1 2/5 miles a day to train a race. If he runs the same distance for 3 days a week, what is the distance he runs in on
    14·1 answer
  • Can you please help me? as much as you can is greatly appreciated &lt;333 pt 1
    8·1 answer
  • Help me out guys I’ll give u a star
    7·1 answer
  • 3) The perimeter of a triangle is 28x-7. 2 of the sides are 5X-3 and 12x+8. What is the third
    11·1 answer
  • Pls help!!!! Urgent pls answer 19-36
    10·2 answers
  • Help please I’ll give the highest point ! :)))) tysm I need it done by 10:20
    13·2 answers
  • What is the role of a conservator?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!