Asked by Chris P Bacon
The radius r, in inches, of a spherical balloon is related to the volume V by r(V)= cubed√3V/4pi
Air is pumped into the balloon so the volume after t seconds is given by V(t)=12+20t.
a. Find the expression for the composite function r(V(t)).
b. What is the exact time in seconds when the radius reaches 16 inches?
Air is pumped into the balloon so the volume after t seconds is given by V(t)=12+20t.
a. Find the expression for the composite function r(V(t)).
b. What is the exact time in seconds when the radius reaches 16 inches?
Answers
Answered by
oobleck
r = ∛(3V/(4π)) = ∛(3(12+20t)/(4π)) = ∛(3(3+5t)/π)
∛(3(3+5t)/π) = 16
3(3+5t)/π = 4096
3+5t = 4096π/3
t = (4096π - 9)/15
∛(3(3+5t)/π) = 16
3(3+5t)/π = 4096
3+5t = 4096π/3
t = (4096π - 9)/15
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.