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3 years ago

Which of the following functions is graphed below? Please help ASAP

Mathematics

1 answer:

amid [387]3 years ago

4 0

Answer:

its not very clear can you take a picture again?

Step-by-step explanation:

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Use cylindrical coordinates. find the volume of the solid that is enclosed by the cone z = x2 + y2 and the sphere x2 + y2 + z2 =

sashaice [31]

Let $R$ be the solid. Then the volume is

$\displaystyle\iiint_R\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta$

which follows from the facts that

$\begin{cases}x=r\cos\theta\\y=r\sin\theta\\z=\zeta\end{cases}\implies\mathrm dx\,\mathrm dy\,\mathrm dz=r\,\mathrm dr\,\mathrm d\theta\,\mathrm d\zeta$
(by computing the Jacobian)

and

$z=x^2+y^2=r^2\implies z+z^2=72\implies z=-9\text{ or }z=8$
(we take the positive solution, since it's clear that $R$ lies above the $x$ - $y$ plane)
$r^2+z^2=72\implies z=\pm\sqrt{72-r^2}$
(again, taking the positive root for the same reason)
$z=r^2\implies 8=r^2\implies r=\sqrt8$

$\displaystyle\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}\int_{\zeta=r^2}^{\zeta=\sqrt{72-r^2}}r\,\mathrm d\zeta\,\mathrm dr$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}r(\sqrt{72-r^2}-r^2)\,\mathrm dr$
$=\displaystyle2\pi\int_{r=0}^{r=\sqrt8}(r\sqrt{72-r^2}-r^3)\,\mathrm dr$
$=\dfrac{32(27\sqrt2-35)\pi}3$

7 0

3 years ago

John is working part-time in an office. He works 30 hours per week and earns $600 each week. He currently has $2,700 in a saving

amm1812

He will have 3800 inhis balance i belive

4 0

3 years ago

Last Wednesday, students could choose ham or turkey sandwiches for lunch. The cafeteria made 500 sandwiches in all, 270 of which

Gelneren [198K]

Answer:

54%

Step-by-step explanation:

270/500

4 0

3 years ago

Factorize 3x to second power minus 6x

Ulleksa [173]

Answer:

3x( 3x -2)

Step-by-step explanation:

(3x) ^2 - 6x

9x^2 -6x

The greatest common factor is 3x

3x( 3x -2)

5 0

3 years ago

3( + 4) + 8 = —3<br> solve

egoroff_w [7]

3x4 to 12
12+8
Answer 20

5 0

3 years ago