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3 years ago

Please answer this correctly

Mathematics

2 answers:

Serga [27]3 years ago

8 0

Answer:

1/6 chance

Step-by-step explanation:

There is only one number on the die, 6.

There are 6 faces on the die so there is $\frac{1}{6}$ chance rolling a 6.

nikdorinn [45]3 years ago

3 0

Answer:

1/6

Step-by-step explanation:

A six sided die is numbered 1 through 6. Since we're looking for the probability that the outcome is greater than 5, only one number suits that, which is 6.

Only 1 out of the 6 numbers work so therefore the probability of it happening is 1/6

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Evaluate the surface integral:S

rjkz [21]

Assuming $S$ does not include the plane $z=0$ , we can parameterize the region in spherical coordinates using

$\mathbf r(u,v)=\left\langle3\cos u\sin v,3\sin u\sin v,3\cos v\right\rangle$

where $0\le u\le2\pi$ and $0\le v\le\dfrac\pi/2$ . We then have

$x^2+y^2=9\cos^2u\sin^2v+9\sin^2u\sin^2v=9\sin^2v$
$(x^2+y^2)=9\sin^2v(3\cos v)=27\sin^2v\cos v$

Then the surface integral is equivalent to

$\displaystyle\iint_S(x^2+y^2)z\,\mathrm dS=27\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^2v\cos v\left\|\frac{\partial\mathbf r(u,v)}{\partial u}\times \frac{\partial\mathbf r(u,v)}{\partial u}\right\|\,\mathrm dv\,\mathrm du$

We have

$\dfrac{\partial\mathbf r(u,v)}{\partial u}=\langle-3\sin u\sin v,3\cos u\sin v,0\rangle$
$\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle3\cos u\cos v,3\sin u\cos v,-3\sin v\rangle$
$\implies\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}=\langle-9\cos u\sin^2v,-9\sin u\sin^2v,-9\cos v\sin v\rangle$
$\implies\left\|\dfrac{\partial\mathbf r(u,v)}{\partial u}\times\dfrac{\partial\mathbf r(u,v)}{\partial v}\|=9\sin v$

So the surface integral is equivalent to

$\displaystyle243\int_{u=0}^{u=2\pi}\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv\,\mathrm du$
$=\displaystyle486\pi\int_{v=0}^{v=\pi/2}\sin^3v\cos v\,\mathrm dv$
$=\displaystyle486\pi\int_{w=0}^{w=1}w^3\,\mathrm dw$

where $w=\sin v\implies\mathrm dw=\cos v\,\mathrm dv$ .

$=\dfrac{243}2\pi w^4\bigg|_{w=0}^{w=1}$
$=\dfrac{243}2\pi$

4 0

3 years ago

Please helpppppp!!!!!!!!

likoan [24]

Answer:

Step-by-step explanation:

6 0

3 years ago

Select two ratios that are equivalent to 4:18

steposvetlana [31]

Answer:

2:9

Step-by-step explanation

4:18 divided by 2 is the lowest it can go so 4 divided by 2 is 2

18 divided by 2 is 9 so,

2:9

4 0

3 years ago

Read 2 more answers

Compute using long division: 1,234÷68

Kruka [31]

Answer:

Quotient = 18

Remainder = 10

Step-by-step explanation:

1234/68

=> 68 x 1 = 68

=> 123 - 68 = 55

=> Take the 4 down

=> 554/68

=> 68 x 8 = 544

=> 554 - 544 = 10

So, the quotient = 18.

Remainder = 10

4 0

3 years ago

2 equivalent rations for 6/5 ? please help !!!

quester [9]

Answer: 12/10 and 24/20
Explanation if you simplify these fractions it’s becomes 6/5

7 0

3 years ago