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
In a circle, chords ST and RA intersect at Y such that SY is perpendicular to RY. The value of mSA + mRT is: a. 90º b. 180º c. 2
pshichka [43]

Answer:

a. 90º

Explanation:

The chords ST and RA intesect at Y, so that SY is now perpendicular to RY and they form an angle 90 degrees at that point. However angles mSA and mRT are both at the circumference of the circle(a chord is a line from point of a circle's circumference to the other) and are both 90 degrees because angle at the circumference is half of angle at the centre in same arc.

6 0
2 years ago
Find the length of the missing sides, round your answers to the nearest hundredth.
azamat
90 round to the nearest hundredth
5 0
3 years ago
Plant A: A graph has time (weeks) on the x-axis, and height (inches) on the y-axis. A line goes through points (0, 3), (1, 4.8),
butalik [34]

Answer:

The correct option is;

No, The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks

Step-by-step explanation:

The parameters given are;

Plant A:

Weeks,    Height

0,               3

1,                4.8

2,               6.6

3,               8.4

The rate of change of height, H per week, t,\left (\dfrac{dH}{dt} \right )  for plant A per week is therefore;

\dfrac{dH}{dt} =  \dfrac{H_n - H_{(n-1)} }{t_n - t_{(n-1)}} = \dfrac{8.4 - 3 }{3 - 0} = \dfrac{5.4}{3} = 1.8 \ inches/week

Therefore we have;

H = 1.8 × t + 3

At week 6,

H = 3 + 6×1.8 = 13.8 inches

Plant B

Weeks,    Height

2,               7.3

3,               8.7

4,               10.1

The rate of change of height, H per week, t,\left (\dfrac{dH}{dt} \right )  for plant B per week is given as follows;

\dfrac{dH}{dt} =  \dfrac{H_n - H_{(n-1)} }{t_n - t_{(n-1)}} = \dfrac{10.1 - 7.3 }{4 - 2} = \dfrac{2.8}{2} = 1.4 \ inches/week

Therefore we have;

When t = 2, H = 7.3 hence, 7.3 = 2 × 1.4 + H₀

Where:

H₀ = H at t = 0

H₀ = 7.3 - 2 × 1.4 = 4.5

At week 6 we have;

H = 4.5 + 6×1.4 = 12.9 inches

Which indicates that Plant A will be 0.9 inches taller than Plant B at week 6.

The correct option is therefore;

No, The greater rate of change of Plant A will result in it being 0.9 inches taller in 6 weeks.

5 0
3 years ago
Read 2 more answers
Help with these math questions please help me thank you!
Reptile [31]

Step-by-step explanation:

1.(2,3)

2.No

3.1st quadrant

4.5

5.Yes

6.Quadrant-4

7.(2,-3)

6 0
3 years ago
I need help with the coordinate plane
alexira [117]

Answer:

The -7 changes to 7 and the ordered pair of the new point is (4,7)

The -2 changes to 2 and the ordered pair of the new point is (2,-5)

Step-by-step explanation:

Hope this helped.

7 0
3 years ago
Other questions:
  • One batch of walnut muffins uses 1 cups of walnuts. How many cups of
    6·1 answer
  • Factor out the GCF from the terms of the polynomial −2x5 − 6x3 − 16x2. A. −2x(x4 + 3x2 + 8x) B. −2x2(x3 + 3x + 8) C. −2x2(−x3 −
    6·1 answer
  • Find the area of the rhombus if AE = 20 m and DE = 32 m
    15·1 answer
  • What value is missing
    13·2 answers
  • Sinxcos y = }(sin(x + y) + sin(x-y))<br> O<br> A. True<br> O<br> B. False
    8·1 answer
  • The points (12,23) and (14,45) lie on a line.<br> What is the slope of the line?
    6·1 answer
  • Please help me with this i dont know wht im doing
    7·2 answers
  • How many<br> students play a sport but are<br> not in the band? (Look at the photo!)
    8·2 answers
  • 3x6-2x4 in Bidmas someone please help
    15·1 answer
  • A bakery is collecting data to investigate how changing the price charged for a loaf of bread affects the bakery’s daily profit.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!