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.
Answer:
y = 4 or y = 6
Step-by-step explanation:
2log4y - log4 (5y - 12) = 1/2
2log_4(y) - log_4(5y-12) = log_4(2) apply law of logarithms
log_4(y^2) + log_4(1/(5y-12)) = log_4(/2) apply law of logarithms
log_4(y^2/(5y-12)) = log_4(2) remove logarithm
y^2/(5y-12) = 2 cross multiply
y^2 = 10y-24 rearrange and factor
y^2 - 10y + 24 = 0
(y-4)(y-6) = 0
y= 4 or y=6
Answer:
1232
Step-by-step explanation:
Step 1: 8x14 to find the base
Step 2: Base times Height
Good Luck! And have a great day!
First, we need to equalize the denominator. If the denominator multiplies by (x+1), so does the numerator. If the denominator multiplies by (x-1), so does the numerator.
Look into my attachment at the second row.
Second, because the first fraction and the second fraction have the same denominator, you can join them into one fraction.Look into my attachment at the third row.
Third, simplify the numerator.Look into my attachment at the fourth to the fifth row
Fourth, simplify the denominator.Look into my attachment at the sixth to the seventh row.