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Harlamova29_29 [7]
2 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]2 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
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farmer joe is enclosing a rectangular area on his arm for his chicken with 200 feet of fencing that he recently acquired in a tr
Llana [10]
For this case, the area is given by:
 A = x * (200-2x)
 Rewriting:
 A = 200x-2x ^ 2
 Deriving the expression we have:
 A '= 200-4x
 Equaling zero we have:
 200-4x = 0
 We clear x:
 4x = 200
 x = 200/4
 x = 50 feet
 Then, the maximum area is:
 A (50) = 50 * (200-2 * 50)
 A (50) = 5000 feet ^ 2
 Answer:
 
the maximum possible area that can be enclosed with his 200ft of fencing is:
 A
 (50) = 5000 feet ^ 2
8 0
3 years ago
On a number line, point D is at -6, and point E is at 8. Point F lies between points D and E. If DF: FEis 3: 1, where does point
Vadim26 [7]

F is located on the numbe<u>r 4.5</u><u> </u>on the number line.

<h3></h3><h3>Where does point F lie on the number line?</h3>

We know that point D is at -6

Point E is at 8.

Point F is between D and E, such that the ratio:

DF:FE is 3:1

So if we divide the distance between D and E in 4 parts, 3 of these parts are DF, and one of these parts is FE.

First, the distance between E and D is:

distance = 8 - (-6) = 14 units.

Now, if we divide that by 4, we get:

14/4 = 3.5

Then we have:

DF = 3*(3.5) = 10.5

This means that F is at 10.5 units to the right of D, then:

F = D + 10.5 = -6 + 10.5 = 4.5

F is located on the numbe<u>r 4.5</u><u> </u>on the number line.

If you want to learn more about ratios:

brainly.com/question/2328454

#SPJ1

7 0
1 year ago
454 / 762 = ?
Maslowich

Answer:

huh-

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Select the correct answer.
gizmo_the_mogwai [7]

Answer:

Factors are (x-1), (x+1), and (x+2).

Step-by-step explanation:

g(x)=x^{3}+2x^{2} -x-2\\g(x)=(x - 1) (x + 1) (x + 2)

7 0
2 years ago
Ellie borrows money at a year simple rate of 6 1/2% after 4 years ellie owes 39 interest
kupik [55]

Answer: Ellie borrowed $150.

Step-by-step explanation:

I = PRT

39 = P x 0.065 x 4

39 = P x 0.26

Divide both sides by 0.26

150 = P

6 0
2 years ago
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