Express each as ratio in the simplest form.:
1 answer:
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Answer:
a) he rate of change of the volume of a snowball (due to melting) is proportional to the square of the volume at time t. Initially, the snowball has a volume of 900 cm3
and V(0) = 900
where A is a real constant, it appears because it says that the change i volume (dV/dt) is "proportional" to . Furthermore, we should assume that A is a negative number, because the volume of the snowball will decrease as the time pasese by.
(b) For an insect moving along some path, the velocity at time t is proportional to the square root of its position.
Here again appears a constant B for the "proportional" part. And i wrote the velocity as "the rate of change of the position with respect to te time".
Hmmm the object, is at rest, when dropped, so it has a velocity of 0 ft/s
the only force acting on the object, is gravity, using feet will then be -32ft/s²,
was wondering myself on -32 or 32.. but anyhow... we'll settle for the negative value, since it seems to be just a bit of convention issues
so, we'll do the integral to get v(t) then
when will it reach the ground level? let's set s(t) = 0
part B) check the picture below
the only force acting on the object, is gravity, using feet will then be -32ft/s²,
was wondering myself on -32 or 32.. but anyhow... we'll settle for the negative value, since it seems to be just a bit of convention issues
so, we'll do the integral to get v(t) then
when will it reach the ground level? let's set s(t) = 0
part B) check the picture below