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

4+n=5

step-by-step explanation:

this is because the four is four hours and the n represents the 1 extra hour over the weekend.

b= i'm srry i don't know that one.

4+n=5 n=1 because if vernon plays 5 hours a week then 4+1=5 hours.

hope this : )