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
bezimeni [28]
3 years ago
6

Use spherical coordinates to evaluate the

Mathematics
1 answer:
kotykmax [81]3 years ago
5 0

Answer:

4096π / 5

Step-by-step explanation:

∫∫∫ (x² + y² + z²) dV

In spherical coordinates, x² + y² + z² = r², and dV = r² sin φ dr dθ dφ.

E is the range 0 ≤ r ≤ 4, 0 ≤ φ ≤ π, 0 ≤ θ ≤ 2π.

∫₀ᵖⁱ∫₀²ᵖⁱ∫₀⁴ (r²) (r² sin φ dr dθ dφ)

∫₀ᵖⁱ∫₀²ᵖⁱ∫₀⁴ (r⁴ sin φ) dr dθ dφ

Evaluate the first integral.

∫₀ᵖⁱ∫₀²ᵖⁱ (⅕ r⁵ sin φ)|₀⁴ dθ dφ

∫₀ᵖⁱ∫₀²ᵖⁱ (¹⁰²⁴/₅ sin φ) dθ dφ

¹⁰²⁴/₅ ∫₀ᵖⁱ∫₀²ᵖⁱ (sin φ) dθ dφ

Evaluate the second integral.

¹⁰²⁴/₅ ∫₀ᵖⁱ (θ sin φ)|₀²ᵖⁱ dφ

¹⁰²⁴/₅ ∫₀ᵖⁱ (2π sin φ) dφ

²⁰⁴⁸/₅ π ∫₀ᵖⁱ sin φ dφ

Evaluate the third integral.

²⁰⁴⁸/₅ π (-cos φ)|₀ᵖⁱ

²⁰⁴⁸/₅ π (-cos π + cos 0)

²⁰⁴⁸/₅ π (1 + 1)

⁴⁰⁹⁶/₅ π

You might be interested in
Pleas answer this fast <br><br> i dont under stand
Lorico [155]

Answer:

196ft^2

Step-by-step explanation:

direct the diagram as shown in my image attachment

A = 1/2 x (18-(9-7)) x (6+8) = 112ft^2

B = 2 x (6+8) = 28ft^2

C = 7 x 8 = 56ft^2

total area = 112 + 28 + 56 = 196ft^2

for more math tips do check out my insta: learntionary

5 0
3 years ago
Read 2 more answers
What is the answer to this question 1.6x + 30
PolarNik [594]
What are you trying to find ?
5 0
2 years ago
$44 bag pack,with a <br> 30% discount
lesya [120]

Answer:

Answer: $30.80

Step-by-step explanation:

4 0
2 years ago
A newsletter publisher believes that more than 79% of their readers own a personal computer. Is there sufficient evidence at the
Katarina [22]

Answer:

Please see attachment

Step-by-step explanation:

Please see attachment

6 0
3 years ago
Read 2 more answers
Please help!
Lostsunrise [7]

Answer:

Using the provided formula, the amount of money Jamal have after 4 years:

A = 4253 x (1 + 1/100)^4 = 4425.69$

Hope this helps!

:)

8 0
3 years ago
Other questions:
  • PLEASE HELP ASAP!!
    12·1 answer
  • I SHALL NAME THEE BRAINLIEST!! (: Pls help me. (#1) 4A - 1 = 3A + 8 solve and check (#2) 1 + F + 3 + F = F + 5 solve and check (
    7·1 answer
  • jayden and carson are selling t-shirts and sweatshirts for a fundraiser. jayden sells 9 t-shirts and 3 sweatshirts for $288. car
    14·1 answer
  • What is sin45 degrees divided by 20
    12·2 answers
  • Last month, he sold 50 chickens and 30 ducks for $550. This month, he sold 44 chickens and 36 ducks for $532. How do you solve t
    11·2 answers
  • The graph of f(x)=3•2^x -3 is shown below. G(x) is a transformation of f(x). How would you write the equation for the function g
    12·1 answer
  • A landscaper is comparing the costs of potted plants from two nurseries. Nursery P charges $15 per plant plus a $50 delivery fee
    8·1 answer
  • I don’t need a explanation, I just need to know if these 3 graphs are growth or decay. This needs to be in within a hour
    15·2 answers
  • Find the product mentally.
    12·2 answers
  • Use distributive property. 4 x 63 = ??
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!