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
Harlamova29_29 [7]
3 years ago
7

(6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Use an iterated integral to compute the vo

lume of the ellipsoid x^2/a^2 + y^2/b^2 + z^2/c^2 = 1. The a, b, and c are positive constants.
Mathematics
1 answer:
kipiarov [429]3 years ago
8 0
Let R be the ellipsoid with equation

\left(\dfrac xa\right)^2+\left(\dfrac yb\right)^2+\left(\dfrac zc\right)^2=1

so that the volume of R is given by the triple integral

\displaystyle\iiint_R\mathrm dV

Consider the augmented spherical coordinates given by the identities

\begin{cases}x=ar\cos u\sin v\\y=br\sin u\sin v\\z=cr\cos v\end{cases}

Computing the Jacobian, we find that the volume element is given by

\mathrm dV=\mathrm dx\,\mathrm dy\,\mathrm dz=abcr^2\sin v\,\mathrm dr\,\mathrm du\,\mathrm dv

so that the volume integral can be written as

\displaystyle\iiint_R\mathrm dV=abc\int_{v=0}^{v=\pi}\int_{u=0}^{u=2\pi}\int_{r=0}^{r=1}r^2\sin v\,\mathrm dr\,\mathrm du\,\mathrm dv=\frac{4abc\pi}3
You might be interested in
Solve the inequaility - x/4 <2
IrinaK [193]

❄ Hi there,

let us start by considering this: What should we do to get x all by itself?

Since it's

  • divided by 4
  • multiplied by -1

we should

  • multiply (both sides) by 4
  • divide (both sides) by -1

So, let's start.

\sf{\dfrac{-x}{4}\times4 < 2\times4}}

\sf{-x < -8}

\sf{x > 8}

When we divide both sides of an inequality by a negative number, we do "the inequality flip" and <em>flip the inequality sign</em>.

❄

8 0
1 year ago
Determine the value of x<br> 2.12 units<br> 2.02 units<br> 12.38 units<br> 0.49 units
Olin [163]
I believe the answer is 2.02
8 0
3 years ago
Lots took one hour to drive from his apartment to philips arena and back. the return drive took 8 minutes less than the trip to
noname [10]

The equation would use to determine how long he drove each way is 2x - 8 = 60.

<h3>What is the equation?</h3>

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

We have been given that Lots took one hour to drive from his apartment to Philips arena and back. the return drive took 8 minutes less than the trip to the arena.

Since the return trip took 8 minutes less, the complete equation must be written in minutes.

Here x - 8 represents the time it took to return to Philips Arena.

The total travel time, including both directions, was 60 minutes;

thus, add x and x - 8 and set them both equal to 60.

So 2x - 8 = 60

Therefore, the equation would use to determine how long he drove each way is 2x - 8 = 60.

Learn more about the equation here:

brainly.com/question/10413253

#SPJ4

6 0
2 years ago
But I said not to do that-​
harkovskaia [24]

Answer:

Some people just put those links for virus so don't click on them, and i don't think they actually read the question.

5 0
3 years ago
Solving Equations Discussion
olya-2409 [2.1K]
1.   Equations are:    

3x + 2 = 5x + 8      and     7x + 2 = 7x - 4

2.   The equation is:

2(32x - 2) = 2x + 36

64x - 4 = 2x + 36

3. You have to choose a classmate's question and answer.

4. You have to look at responses and comments.
3 0
3 years ago
Other questions:
  • El radio del círculo es 4 ,pulgadas cuál es el diámetro ?
    10·1 answer
  • Umm how do I solve this
    8·2 answers
  • How would I set this problem up?
    12·1 answer
  • Three years ago, the annual tuition at a university was $2,000. The following year, the tuition was $2,200, and last year, the t
    9·2 answers
  • What is the value of x in the equation x – y = 30, when y = 15?
    7·2 answers
  • Which unit (mm, cm, m, or km) would be the most appropriate for each measurement? a Distance across Lake Michigan b Length of a
    6·1 answer
  • Find value of x so that f(x)=7​
    8·1 answer
  • The Drama Club sold 450 tickets for the spring play. An adult ticket cost $5 and a student ticket cost $3. Total ticket sales eq
    15·1 answer
  • The exponential decay function A = A0(1/2)^t/P can be used to determine the amount A, of a radioactive substance present at time
    9·1 answer
  • I need help please!
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!