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3 years ago

23/6 as a mixed number

Mathematics

2 answers:

Kobotan [32]3 years ago

7 0

3 5/6 would be the answer to your question

jenyasd209 [6]3 years ago

6 0

3 5/6 is 23/6 as a mixed number

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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

These types of lines have a zero slope

mamaluj [8]

The lines with a slope of 0 are horizontal lines because all the points on the line have the same y-coordinate on a graph. Using the slope formula on the line will give you 0.

7 0

3 years ago

If the hypotenuse of a right triangle measures 15 cm and one of the legs measures 12 cm, what is the length of the other leg?

Mama L [17]

Step-by-step explanation:

12 to the 2nd power=144

15 to the 2nd power =225

225-144=81

square root of 81 is 9

5 0

3 years ago

Given a right triangle with legs a, b and hypotenuse c, solve for a if b= 20 and c= 29

pantera1 [17]

Answer:

C) 21

Step-by-step explanation:

a² + 20² = 29² Use Pythagorean Theorem to solve for a

a² + 400 = 841 Solve for the exponents

- 400 - 400 Subtract 400 from both sides

a² = 441 Take the square root of both sides

a = 21

8 0

2 years ago

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How is 40 gummy bears for 5 dollars written as a fraction?

Marina86 [1]

40/5 because to find the answer you would divided them

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2 years ago

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