Ahot air balloon 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/3 , and it is changing at a rate of 0.1 rad/min. how fast is the balloon rising at this moment?

The observer and the balloon form a right triangle (see attachment).

The balloon is rising at 1.2 rad per min

Using tangent rule, we have:

Substitute 3 for x

Differentiate both sides with respect to time (t)

Make dy/dt, the subject

Substitute

So, we have:

Using a calculator, we have:

Multiply

Hence, the balloon is rising at 1.2 rad per min

Read more about rates at:

link

can you make your screen more see able?

then i might be able to .

75%

step-by-step explanation: