Question

Coughing forces the trachea to contract, which affects the velocity v of the air passing through the trachea. Suppose the velocity of the air during coughing is v = k(R-r)r2 where k and R are constants, R is the normal radius of the trachea, and r is the radius during coughing. What radius will produce the maximum air velocity? @Calculus1

Answer 1

v = k(R - r)r^2 - is this the formula?

Answer 2

yes

Answer 3

\[v=k(R-r)r^2\]\[v=kRr^2-kr^3\]\[v'=2kRr-2kr^2=r(2kR-2kr)=0\]since r can't be zero,\[2kR-2kr=0\]\[r=\frac{2kR}{2k}=R\]thus a radius of R will produce the max air velocity

Answer 4

wait, miscalc

Answer 5

1/2R, 2/3R, 3/2R, or 4/9 R are choices

Answer 6

\[r=\frac{2}{3}R\]***

Answer 7

howd you get that mahone?

Answer 8

dv/dr = 2kRr - 3kr^2
= 0

r (2kR - 3kr) = 0
r = 2R / 3

Answer 9

\[v=k(R-r)r^2\]\[v=kRr^2-kr^3\]\[v'=2kRr-3kr^2=r(2kR-3kr)=0\]\[r=\frac{2}{3}R\]

Answer 10

just tell your teacher that \[\lim r\to0=\infty\]infinite air velocity ftw

Answer 11

mahone i dont care what anyone says... u are the man.
You too jimmy

Answer 12

lol 0- ty treyhud