The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the diameter is 100 mm?

157,143 mm/s

Step-by-step explanation:

Formula for the volume of a sphere is;

V = 4/3 * pi * r^3

dv/dr = 4 pi r^2

dv/dt = dv/dr * dr/dt

dr/dt = 5 mm/s

dr/dt = 4 * pi * r^2

r = d/2 = 100/2 = 50 mm

dr/dt = 4 * 22/7 * 50^2 = 220,000/7

dv/dr = 220,000/7 * 5 = 157,142.8571428571

Approximately 157,143 mm/s

take it another

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: