SophomoreSareke
26.12.2020 •
Mathematics
a conical tank with vertex down is 10 feet across the top and 12 feet deep. If water is flowing out of the tank at a rate of 12 cubic feet per minute, find the rate at which the water level is dropping when radius of water level is 4ft.
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Ответ:
The water level is dropping at a rate of 0.24 ft/s
Step-by-step explanation:
Here, we simply want to calculate the change in depth (height of the cone) , given the volume change
Mathematically, we have the volume of a cone as;
V = 1/3 * π * r^2 * h
we are given dv/dt as 12 ft^3/m
dv/dh = 1/3 * π * r^2
Substituting the value for the radius, we have
dv/dh = 1/3 * 22/7 * 4^2 = 50.29
dh/dt = dh/dv * dv/dt
dh/dv = 1/(dv/dh) = 1/50.29
Thus,
dh/dt = 1/50.29 * 12
dh/dt = 0.24 ft/s
Ответ:
(3,-7)
Step-by-step explanation:
You can use desmos.com to find intersecting points (it's a graphing calculator).