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aallyssabrown0120
08.07.2019 •
Mathematics
Aheap of rubbish in the shape of a cube is being compacted into a smaller cube. given that the volume decreases at a rate of 4 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 125 cubic meters.
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Ответ:
V = s^3
Given:
dV/dt = -4 cubic meters per minute
V = 125 cubic meters
Required: ds/dt (rate of change of edge per minute) at V = 125 m^3
Solution:
Differentiate, equation below
V = s^3
dV/dt = 3*s^2 (ds/dt)
-4 = 3*s^2 (ds/dt)
ds/dt = -1.33/s^2 > eq. (1)
V = s^3
(125)^0.33 = (s^3)^0.33
s = 5 > eq. (2)
Substitute eq. (2) to eq. (1), we get
ds/dt = -1.33/(5)^2 = -0.053 meters per minute
ANSWER: -0.053 meters per minute
Ответ:
Using implicit differentiation, it is found that the rate of change of an edge is of -0.0533 meters per minute.
---------------------
The volume of a cube of edge e is given by:
In this problem, the volume is of 125 m³, thus, we solve the above equation to find the length of an edge, in metres.
Now, for the rate of change, we need to apply the implicit differentiation, thus:
Volume decreases at a rate of 4 cubic meters per minute, thus:
The rate of change of an edge is
. Then:
The rate of change is of -0.0533 cubic meters per minute.
A similar problem is given at link
Ответ: