Answer:
c)3/2(8/7)^x
Step-by-step explanation:
Evaluate the functions.
1. Because 7/4 > 1 and the exponent is positive,
the function does not decay.
2.Because 4/5 < 1 and the exponent is negative,
the function does not decay.
3. Because 8/7 > 1 and the exponent is negative,
the function decays.
4. Because 9/2 > 1 and the exponent is positive,
the function does not decay.
A composite plot the functions verifies the answer.
If all the x's are exponents, then 3/2 (8/7)^-x is the only one that decays as x gets bigger. That's because the base is greater than 1 and the x is negative.
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Answer:
288 pi or 904.22
Step-by-step explanation:
(4/3) × pi × r³
(4/3) × pi × 6³
288pi or
288 × 3.14 = 904.32 units³
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.
