Related Rates
1 answer:
Answer:
- 0.382 m/min
- 8 1/3 ft/s
Step-by-step explanation:
1. The rate of change of volume is ...
V = πr^2h
V' = πr^2h'
h' = V'/(πr^2) = (3 m^3/min)/(π(5 m)^2) = 0.12/π m/min
h' ≈ 0.382 m/min
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2. In the attached, ∆PCM ~ ∆MXS, so we can write the proportion ...
x/9 = s/15 . . . . where x = BX and s = BS in the diagram
Multiplying by 15 gives ...
s = (15/9)x = (5/3)x
Then the rate of change is ...
s' = (5/3)x' = (5/3)(5 ft/s)
s' = 8 1/3 ft/s
The tip of the shadow is moving at 8 1/3 feet per second.
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Answer: m = 0
Step-by-step explanation: To find the slope of the line, we can use the graphing method. To do this, we start by plotting our two points.
Let's label (6, 1) as point A and (-6, 1) as point B.
Now, graph our line through the 2 points.
Now remember that the slope, or m, is equal to
the rise over run from point A to point B.
To get from point A to point B, we rise o units and run -12 units.
So our slope or rise / run is 0/-12 which simplifies to 0.
This should make sense because we have a horizontal or flat line and
remember that the slope of any horizontal or flat line is 0.
Image attached.
