Mathematics, 12.10.2019 08:30 freddhendrickss

Find the volume of the solid in the first octant bounded by the parabolic cylinder z = 4 − x2 and the plane y = 2.

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Answer from: hayesvolcano

We use triple integration to find volume of solid.

Volume of the solid in the first octant is 32/ 3

To solve this, it is important to set up the boundaries of double integral correctly.

First, notice that the cylinder we are given intersects the XY plane at the line given by the equation x = 2

Hence our boundaries of the integral with respect to x is the segment [0,2]. Since the other plane is y=2 . so, boundaries of the integral with respect to y is the segment [0,2].

Now , integrate that

$\int\limits^2_0 \int\limits^2_0 (4-x^{2} )dxdy\\\\\frac{16}{3} \int\limits^2_0 \, dy\\\\\frac{16}{3}*2\\\\=\frac{32}{3}$

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Answer from: angelrenee2000

The volume is given by the triple integral,

$\displaystyle\int_0^2\int_0^2\int_0^{4-x^2}\mathrm dz\,\mathrm dx\,\mathrm dy$

Easy enough to compute. Since the integrand is independent of

, you can compute that integral right away to get

$2\displaystyle\int_0^2\int_0^{4-x^2}\mathrm dz\,\mathrm dx$

Next, with respect to

,

$2\displaystyle\int_0^2z\bigg|_{z=0}^{z=4-x^2}\,\mathrm dx=\int_0^2(4-x^2)\,\mathrm dx$

which results in a volume of

$2\displaystyle\left(4x-\frac13x^3\right)\bigg|_{x=0}^{x=2}=2\left(8-\frac83\right)=\dfrac{32}3$

Answer from: Quest

see below

step-by-step explanation:

7. there are 10 data points in the set. the middle point is between 5 and 6. the middle point in the top half is 8 and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term point 8 = 100 point 3 = 88

iqr = 100-88 = 12

final point 8 = 93 point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6. b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical . there is an outlier for the males that skews the data

5. the iqr is a better measure of spread for the movies and basketball games. since the basketball game has an outlier, we do not want to use standard deviation for measurement.

3. the exam median is much higher than the class median. the median line is farther to the right on the exams

2. there is no way to tell what the means are from the box and whisker plots.

Answer from: Quest

step-by-step explanation:

deez nut

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Find the volume of the solid in the first octant bounded by the parabolic cylinder z = 4 − x2 and th...

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