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3 years ago

Which sets of numbers are closed under subtraction?

1 answer:

3 0

I'm pretty sure it is only b because <span>when you subtract two rational numbers, you always get back a rational number.</span>

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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

Pls help ill mark brainliest

JulsSmile [24]

Answer:

mhm thats great points man pointsssss idc

5 0

3 years ago

Read 2 more answers

What is the volume of the cynlinder?

vova2212 [387]

The volume of a cylinder can be found using the formula V=(pi)(r)^2(h)

V=(3.14)(8)^2(10)
V = 2010.62 Ft^3

I think that is the answer

8 0

3 years ago

A video game was originally priced at $20.it is on sale for 20% off.How much did you pay for the game?

Allushta [10]

20+ 20(0.2)
20+ 4
24 dollars

7 0

3 years ago

The Reunion Tower is one of the most recognizable landmarks in Dallas, Texas due to the giant sphere that sits atop the structur

ValentinkaMS [17]

The volume of a sphere uses the following formula:

$V = \frac{4}{3}\pi r^{3}$

Because the question asks to use 3.14 in place of pi, the formula will now look like this:

$V = (\frac{4}{3})(3.14)r^{3} = 4.18\overline{66} r^{3}$

We are given a diameter of 118 feet. The radius is half of the diameter, so divide the diameter by 2 to find the radius:

$118 \div 2 = 59$
$r = 59$

Plug this value into the formula, and solve with a calculator:

$4.18\overline{66} \times 59^3 = 4.18\overline{66} \times 205379 = 859853.413$

Although our result is one cubic foot off, the answer is <span>A. 859,852ft^3.

(859,852 is the result if the constant in the given formula is 4.18666, but the result with infinitely repeating numbers is 859,853.)</span>

6 0

3 years ago