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3 years ago

Find the volume of the given solid: Bounded by the cylinder y^2+z^2=4 and the planes x = 2y, x = 0, z = 0 in the first octant.

Mathematics

1 answer:

rodikova [14]3 years ago

3 0

The solution would be like this for this specific problem:

V = ∫ dV 
= ∫0→2 ∫ 0→π/2 ∫ 0→ 2·r·sin(φ) [ r ] dzdφdr 
= ∫0→2 ∫ 0→π/2 [ r·2·r·sin(φ) - r·0 ] dφdr 
= ∫0→2 ∫ 0→π/2 [ 2·r²·sin(φ) ] dφdr 
= ∫0→2 [ -2·r²·cos(π/2) + 2·r²·cos(0) ] dr 
= ∫0→2 [ 2·r² ] dr 
= (2/3)·2³ - (2/3)·0³ 
= 16/3

So the volume of the given solid is 16/3. I am hoping that these answers have satisfied your query and it will be able to help you in your endeavors, and if you would like, feel free to ask another question.

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A college conducts a common test for all the students. For the Mathematics portion of this test, the scores are normally distrib

Jet001 [13]

Using the normal distribution, it is found that 58.97% of students would be expected to score between 400 and 590.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

$\mu = 502, \sigma = 115$

The proportion of students between 400 and 590 is the p-value of Z when X = 590 subtracted by the p-value of Z when X = 400, hence:

X = 590:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{590 - 502}{115}$

Z = 0.76

Z = 0.76 has a p-value of 0.7764.

X = 400:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{400 - 502}{115}$

Z = -0.89

Z = -0.89 has a p-value of 0.1867.

0.7764 - 0.1867 = 0.5897 = 58.97%.

58.97% of students would be expected to score between 400 and 590.

More can be learned about the normal distribution at brainly.com/question/27643290

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6 0

1 year ago

Answer this question!

aksik [14]

Answer:

I would tell you

Step-by-step explanation:

you need to put 2 y and 2 x and that you need to divide

8 0

2 years ago

Please help me how to figure this out I’m trying to figure out the area ASAP please

Natasha2012 [34]

Answer:

$1230.88m^{2}$

Step-by-step explanation:

Shown is one-fourth of a circle. Also, according to the picture, the radius is 28 meters.

The area for a whole circle is $2\pi r^{2}$ .

Using that information, we can find the area as if the circle was whole instead of just the fourth.

$2(\pi)(28m)^2 = 2(3.14)(784m^{2} ) = 4923.52m^{2}$

Now that we know the area of the whole circle, we just have to divide it by four to find the area of the fourth of the circle.

$4923.52m^{2} / 4 = 1230.88m^{2}$

That means that the area of the shape shown is $1230.88m^{2}$ .

I hope this helps!

4 0

3 years ago

How do I figure this out??

goldenfox [79]

The function is divided by 12, you would find it out by dividing 120 by 10 and getting 12, if you wanted to check your answer, you would do 84 divided by 7 which is 12. the answer to 12 is 1 and 24 is 2. hope this helped :))

7 0

3 years ago

What is y = x2 + 4x + 7 in vertex form

Makovka662 [10]

Answer:

$y = (x + 2)^{2} + 3$

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3 years ago