Answer:
C. 8
Step-by-step explanation:
The average rate of change is the slope of the line between the two points of interest. It is given by the formula ...
m = (y2 -y1)/(x2 -x1)
For points (1, 2) and (3, 18), the average rate of change is ...
m = (18 -2)/(3 -1) = 16/2 = 8
The average rate of change between x=1 and x=3 is 8.
Here bro this should help
9514 1404 393
Answer:
8000π mm^3/s ≈ 25,133 mm^3/s
Step-by-step explanation:
The rate of change of volume is found by differentiating the volume formula with respect to time.
V = 4/3πr^3
V' = 4πr^2·r'
For the given numbers, this is ...
V' = 4π(20 mm)^2·(5 mm/s) = 8000π mm^3/s ≈ 25,133 mm^3/s
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<em>Additional comment</em>
By comparing the derivative to the area formula for a sphere, you see that the rate of change of volume is the product of the area and the rate of change of radius. This sort of relationship will be seen for a number of different shapes.
