The radius of a cylinder is increasing at a constant rate of 2 inches per minute. The volume remains a constant 440 cubic inches. At the instant when the radius of the cylinder is 44 inches, what is the rate of change of the height? The volume of a cylinder can be found with the equation V= Round your answer to three decimal places.

The rate of change of the height is approximately .

Step-by-step explanation:

From Geometry we know that volume of cylinder (), measured in cubic inches, is expressed by:

(1)

Where:

- Radius, measured in inches.

- Height, measured in inches.

Given that volume remains constant, the expression for the rate of change of the height (), measured in inches per minute, is:

(2)

Where is the rate of change of the radius, measured in inches per minute.

If we know that , and , then the rate of change of the height is:

The rate of change of the height is approximately .

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.  

step-by-step :