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MArishka [77]
2 years ago
10

Use cylindrical coordinates. find the volume of the solid that lies within both the cylinder x2 y2 = 9 and the sphere x2 y2 z2 =

16.
Mathematics
1 answer:
marissa [1.9K]2 years ago
6 0
In Cartesian coordinates, the region is given by -3\le x\le3, -\sqrt{9-x^2}\le y\le\sqrt{9-x^2}, and -\sqrt{16-x^2-y^2}\le z\le\sqrt{16-x^2-y^2}. Converting to cylindrical coordinates, using

\begin{cases}\mathbf x(r,\theta,\zeta)=r\cos\theta\\\mathbf y(r,\theta,\zeta)=r\sin\theta\\\mathbf z(r,\theta,\zeta)=\zeta\end{cases}

we get a Jacobian determinant of r, and the region is given in cylindrical coordinates by 0\le\theta\le2\pi, 0\le r\le3, and -\sqrt{16-r^2}\le z\le\sqrt{16-r^2}.

The volume is then

\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=3}\int_{z=-\sqrt{16-r^2}}^{z=\sqrt{16-r^2}}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta=\dfrac{4(64-7\sqrt7)\pi}3
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If the pressure is 6 pounds per inch when the temperature is 440 F, find the pressure exerted when the temperature of the gas is
SVEN [57.7K]

4.18

(380*6)/440=4.18

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3 years ago
Write a number sentence that<br> equals 4/6​
Arturiano [62]

when you have a function that is 4/6 think of it as reversed the number its going to be 4/6=6×4.

7 0
3 years ago
A polling organization asked a nation-wide random sample of 1600 new brides (those who got married in the past 2 years) the foll
iren [92.7K]

Answer:

It has millions of tickets. On each ticket is written a number a dollar amount. The exact average and SD are unknown but are estimated from the sample to be $20,000 and $5,000 respectively.

Step-by-step explanation:

Given that:

sample size n = 1600

sample mean \overline x = 20000

standard deviation = 5000

The objective is to choose from the given option about what most closely resembles the relevant box model.

The correct answer is:

It has millions of tickets. On each ticket is written a number a dollar amount. The exact average and SD are unknown but are estimated from the sample to be $20,000 and $5,000 respectively.

However, if draws are made without replacement, the best estimate of the average amount for the bride will be $20,000

Similarly, the standard error for the sample mean = \dfrac{s}{\sqrt{n}}

= \dfrac{5000}{\sqrt{1600}}

= \dfrac{5000}{40}}

the standard error for the sample mean = 125

4 0
3 years ago
*Silly and/or spam answers will not be tolerated*
stepladder [879]

Answer:

-1/8

Step-by-step explanation:

lim x approaches -6     (sqrt( 10-x) -4) / (x+6)

Rationalize

   (sqrt( 10-x) -4)      (sqrt( 10-x) +4)

    ------------------- * -------------------

       (x+6)                 (sqrt( 10-x) +4)

We know ( a-b) (a+b) = a^2 -b^2

a= ( sqrt(10-x)   b = 4    

(10-x) -16

-------------------

(x+6) (sqrt( 10-x) +4)    

-6-x

-------------------

(x+6) (sqrt( 10-x) +4)

Factor out -1 from the numerator

-1( x+6)

-------------------

(x+6) (sqrt( 10-x) +4)

Cancel x+6 from the numerator and denominator

-1

-------------------

(sqrt( 10-x) +4)

Now take the limit

lim x approaches -6    -1/ (sqrt( 10-x) +4)

                                      -1/ (sqrt( 10- -6) +4)

                                      -1/ (sqrt(16) +4)

                                      -1 /( 4+4)

                                        -1/8

5 0
3 years ago
Read 2 more answers
What is the surface area?​
Alchen [17]

Answer:

SA: 1575.2

Step-by-step explanation:

(22)(22) + (26)(22) = (23.6)(22)

484 + 572 + 519.2 = 1575.2

I hope I helped you ;)

6 0
2 years ago
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