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

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.

answer: 0,6

step-by-step explanation:

this would make it the y intercept.