Hello ppl. This is the problem:
I'm really confused, was rummaging over it for hours this morning, I've got the F equation, the constant, but simply cant find dr/dt. Plus my friend was saying that F=dV/dt but i said no F=V/t. I'm now confused about the whole question, someone please help asap.A section of blood vessel has a flow-rate F in cubic millimetres per
minute proportional to the fourth power of its radius, R. The blood vessel can be considered perfectly cylindrical and is expandable. At some instant the
flow rate is 30 cubic millimetres per minute when the radius is 0.5 millimetres. At that same instant the flow-rate is increasing at rate of 0.24 cubic millimetres per minute squared.
(i) What is the rate of increase of the radius at that instant?
(ii) If the rate of increase of the radius is constant how long after the time when the radius is 0.5 mm is the radius 1 mm?
F=kr^4
k=1/480 from values (0.5, 30)
I'm confused with whether F = V/t or dv/dt, i was thinking the former (by looking at the units)
Other equation: V= (pi)(r^4)h, where h is, i was thinking, the length of the vessel? :s
tha main part of the question is: dV/dt = dV/dr * dr/dt
I was trying to even use Volume=Ft.
all the variable have confused me.
Think about what an increasing flow rate means. It means that the flow rate is increasing with respect to time (ie: dF/dt).
This is also agreed by the units as flow rate would be in whereas this is given in which means a dt must be there something
Using the chain rule as you said:
(I didn't check your working for k )
edit: I get k = 480 instead of 1/480
Hello, kangaroo!
A section of blood vessel has a flow-rate in mm³/min
. . is proportional to the fourth power of its radius,
The blood vessel can be considered perfectly cylindrical and is expandable.
At some instant the flow rate is 30 mm³/min when the radius is 0.5 mm.
At that same instant, the flow-rate is increasing at rate of 0.24 mm³/min²
(a) What is the rate of increase of the radius at that instant?
We have: .
We are told: .
. . Hence: .
The function is: .
Differentiate with respect to time: .
. . We have: . mm/min.
Am I misreading the question?(b) If the rate of increase of the radius is constant,
how long after the time when the radius is 0.5 mm is the radius 1 mm?
The radius increases from 0.5 mm to 1.0 mm ... an increase of 0.5 mm.
If the radius increases at a constant 0.001 mm/min,
. . it will take: .
Is it really that simple?