SOLUTION: V = C(Ro – R)R^2 where C > 0 is a constant based on individual body characteristics, Ro is the radius of the windpipe before the cough, and R is the radius of the windpipe dur

Algebra ->  Expressions-with-variables -> SOLUTION: V = C(Ro – R)R^2 where C > 0 is a constant based on individual body characteristics, Ro is the radius of the windpipe before the cough, and R is the radius of the windpipe dur      Log On


   



Question 38533: V = C(Ro – R)R^2
where C > 0 is a constant based on individual body characteristics,
Ro is the radius of the windpipe before the cough, and R is the
radius of the windpipe during the cough. Find the value of R that
maximizes the velocity, and state the resulting maximum velocity.
I just want to confirm that I am on the right track?
V = C(Ro – R)R^2
= C Ro R^2 - CR^3
V'(R)= 0
CR(2Ro - 3R) = 0,
R = 0 or 2/3.
I think the elgebra may not be right?
Can someone please tell me if this is the right idea.
Thankyou.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Well, Your initial steps are OK but I think that your final statement lost an Ro.
V+=+CRoR%5E2-CR%5E3
dV%2FdR+=+2CRoR-3CR%5E2
Setting dV%2FdR+=+0
2CRoR-3CR%5E2+=+0 Solve for R. Factor CR.
CR%282R0-3R%29+=+0 Apply the zero products principle.
CR+=+0 and/or %282Ro-3R%29+=+0
If CR+=+0 then R+=+0 Since C%3E0
If 2Ro-3R+=+0 then 3R+=+2Ro and R+=+%282%2F3%29Ro