a hot-air balloon is tethered to the ground and only moves up and down. You and a friend take a ride on the balloon for approximately 25 minutes. On this particular ride the velocity of the balloon, v(t) in feet per minute, as a function of time, t in minutes, is represented by the function v(t)= -t^3 + 34t^2 - 284t + 490. At what times is the velocity of the balloon 50 feet per minute?

Answer 1

so
50 = -t^3 + 34t^2 - 284t + 490
t^3 - 34t^2 + 284t - 440 = 0

I tried t = ± 1, ± 2
and sure enough when t = 2, I had a solution
using synthetic division,
(t-2)(t^2 - 32t+ 220) = 0
(t-2)(t-10)(t-22) = 0

t = 2 or t = 10 or t = 22

Since the ride lasted 25 minutes, all three answers are valid.

Answer 2

thank you soooo much!!!