A hot air ballon rising vertically is tracked by an observer located 3 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is π 5 , and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment?

0.458 mi/min

Step-by-step explanation:

We are given that

Distance of observer from lift-off point=3 miles

We have to find the rate at which the balloon rising at this moment.

Using the formula

Differentiate w.r.t t

Using the formula

step-by-step explanation:

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !