All Parallelograms are ___

Evaluate the integral Find the volume of material remaining in a hemisphere of radius 2 after a cylindrical hole ofradius 1 is d

algol13

You want to find the volume inside the hemisphere $x^2+y^2+z^2=4$ (i.e. inside the sphere but above the plane $z=0$ ) and outside the cylinder $x^2+y^2=1$ . Call this region $R$ .

In cylindrical coordinates, we have

$\displaystyle\iiint_R\mathrm dV=\int_0^{2\pi}\int_1^2\int_0^{\sqrt{4-r^2}}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$

$\displaystyle=2\pi\int_1^2 r\sqrt{4-r^2}\,\mathrm dr$

$\displaystyle=-\pi\int_3^0\sqrt u\,\mathrm du$

(where $u=4-r^2$ )

$\displaystyle=\pi\int_0^3\sqrt u\,\mathrm du$

$=\dfrac{2\pi}3u^{3/2}\bigg|_0^3=2\sqrt3\,\pi$

7 0

3 years ago

(9, 19) (2, 16)<br> Write the coordinates as decimals or integers.

9966 [12]

Answer:

In decimal 0.428571428

Step-by-step explanation:

The slope = (y2 - y1)/(x2 - x1) y2 = 16, y1 = 19x2=2 and x1=9

The slope = (16 - 19)/(2 -9)

The slope = (-3)/(-7)

The slope = 0.428571428

So in decimal form the coordinates are going to be written as 0.428571428

Slope is the steepness of a line, it is the difference between the y coordinates divided by the difference in x coordinates.

6 0

3 years ago

A rectangular shoebox has a volume of 728 cubic inches. The base of the shoebox measures 8 inches by 6.5 inches. How long is the

bagirrra123 [75]

Divide the volume by the two measures. 728 ÷ 8 = 91 ÷ 6.5 = 14 so, the shoe box is we inches long.

8 0

3 years ago

The following are the last 7 days adjusted closing stock prices (in $) for Citigroup: 22, 25, 20, 15, 40, 55, 28 A) Compute the

son4ous [18]

Answer:

(A) The 25th percentile is 20.

(B) The mean of the data set is 20 and the median of the data set is 25. The data set is left-skewed.

Step-by-step explanation:

The data set arranged in ascending order is:

S = {15, 20, 22, 25, 28, 40, 55}

(A)

Compute the 25th percentile as follows:

$25^{th} \text{Percentile}=[\frac{n+1}{4}]^{th}obs.\\\\=[\frac{7+1}{4}]^{th}obs.\\\\=2^{nd}obs.\\\\=20$

Thus, the 25th percentile is 20. This value implies that exactly 25% of the observations are less than 20.

(B)

Compute the sample mean as follows:

$\text{Mean}=\frac{22+25+20+15+40+55+28}{7}=\frac{205}{7}=29.29$

Compute the median as follows:

For a set with odd number of observations, the median value if the middle value.

The middle value is 25.

Thus, the mean of the data set is 20 and the median of the data set is 25.

The Mean < Median.

This implies that the data set is left-skewed.

4 0

2 years ago

MR is the angle bisector of

Otrada [13]

Answer:

∠NMP, so m∠1 = m∠2.

Step-by-step explanation:

6 0

3 years ago

All Parallelograms are ____