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
LUCKY_DIMON [66]
3 years ago
5

Find the average value of the function f(x, y, z) = 5x2z 5y2z over the region enclosed by the paraboloid z = 9 − x2 − y2 and the

plane z = 0.
Mathematics
1 answer:
Katyanochek1 [597]3 years ago
4 0
The paraboloid meets the x-y plane when x²+y²=9. A circle of radius 3, centre origin. 

<span>Use cylindrical coordinates (r,θ,z) so paraboloid becomes z = 9−r² and f = 5r²z. </span>

<span>If F is the mean of f over the region R then F ∫ (R)dV = ∫ (R)fdV </span>

<span>∫ (R)dV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] rdrdθdz </span>

<span>= ∫∫ [θ=0,2π, r=0,3] r(9−r²)drdθ = ∫ [θ=0,2π] { (9/2)3² − (1/4)3⁴} dθ = 81π/2 </span>


<span>∫ (R)fdV = ∫∫∫ [θ=0,2π, r=0,3, z=0,9−r²] 5r²z.rdrdθdz </span>

<span>= 5∫∫ [θ=0,2π, r=0,3] ½r³{ (9−r²)² − 0 } drdθ </span>

<span>= (5/2)∫∫ [θ=0,2π, r=0,3] { 81r³ − 18r⁵ + r⁷} drdθ </span>

<span>= (5/2)∫ [θ=0,2π] { (81/4)3⁴− (3)3⁶+ (1/8)3⁸} dθ = 10935π/8 </span>

<span>∴ F = 10935π/8 ÷ 81π/2 = 135/4</span>
You might be interested in
Please help!! This is so confusing! 100 points!!
masya89 [10]

Answer:

The value of the expression given is:

  • 4

Step-by-step explanation:

First, you must divide the expression in three, and to the final, you can multiply it:

  1. [(3^8)*(2^(-5))*(9^0)]^(-2)
  2. [(2^(-2))/(3^3)]^4
  3. 3^28

Now, we can solve each part one by one:

<em>First part. </em>

  • 3^8 = 6561
  • 2^(-5) = 0.03125
  • 9^0 = 1 (Whatever number elevated to 0, its value is 1)
  • (6561 * 0,03125 * 1) = 205.03125

And we elevate this to -2:

  • 205.03125^-2 = 2<u>.378810688*10^(-5)</u> or <u>0.00002378810688 </u>

<em>Second part. </em>

  • 2^(-2) = 0.25
  • 3^3 = 27
  • 0.25 / 27 = 9.259259259 * 10^(-3) or 0.00925925925925

And we elevate this to 4:

  • 0.00925925925925^4 = <u>7.350298528 * 10^(-9)</u> or <u>0.000000007350298528 </u>

<em>Third Part. </em>

  • 3^28 = <u>2.287679245 * 10^13</u> or <u>22876792450000</u>

At last, we multiply all the results obtained:

  • 0.00002378810688 * 0.000000007350298528 * 22876792450000 = <u>3.999999999999999999</u> approximately <u>4</u>

<u><em>We approximate the value because the difference to 4 is minimal, which could be obtained if we use all the decimals in each result</em></u>.

3 0
3 years ago
Read 2 more answers
How many meters are in a millimeter
Naddika [18.5K]
There are 1000 millimeters in a meter and 0.001 meters in a millimeter
7 0
3 years ago
Read 2 more answers
What is the slope of the line whose equation is 2x−4y=10 ? Enter your answer in the box. NEED HELP ASAP PLEASE WILL GIVE BRAINLI
stich3 [128]

Answer:

The slope of the line is 1/2.

Step-by-step explanation:

2 x − 4 y = 10 (Subtract  2 x from both sides.)

− 4 y = − 2 x + 10 (Divide both sides by -4.)

y = − 2 x − 4 + 10 − 4  (Simplify.)

y = 1/2 x − 5 /2

y=1/2


4 0
3 years ago
Read 2 more answers
If the length of a rectangle is 4.3 feet and its width is 2.7 feet what is its are and its perimeter
Dvinal [7]
The area is 11.61 square feet and the perimeter is 14 feet. i hope this helps :)

Area=Length times width

Perimeter=Length+Length+width+width
7 0
3 years ago
Read 2 more answers
1+1= help will give brainlist
zvonat [6]

Answer:

2

Step-by-step explanation:

1 + 1 =2

Hope this helps! Have a good day! :)

7 0
1 year ago
Read 2 more answers
Other questions:
  • Elizabeth uses 23.25 ounces of granola and 10.5 ounces of raisins for 15 servings of trail mix. In each serving contains the sam
    12·1 answer
  • In referring to snipers what is 2 minutes left mean
    7·1 answer
  • Fill in the blank. In the triangle below, zº =
    13·2 answers
  • A store manager is accepting applications for part-time workers. he can hire no more than 14 people. so far,he has hired 9 peopl
    5·1 answer
  • What is the point slope form of (7,-4) and (-1,3)
    6·2 answers
  • I need help with this I put this out 3 times I need help
    14·1 answer
  • The cost of a car rental is ​$35 per day plus 21 cents per mile. You are on a daily budget of ​$98. Write and solve an inequalit
    15·1 answer
  • A cylinder with a height of 4 m has a volume of approximately
    11·1 answer
  • Given that cos(x)=−0.65, what is cos(−x)
    11·1 answer
  • Find 4 geometric means between -5 and -125.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!