Sketch the situation if necessary and use related rates to solve. two airplanes are flying in the air at the same height. airplane a is flying east at 250 mph and airplane b is flying north at 300 mph. if they are both heading to the same airport, located 30 miles east of airplane a and 40 miles north of airplane b, at what rate (in mph) is the distance between the airplanes changing?

  -390 mph

Step-by-step explanation:

Let a and b represent, respectively, the distances of A and B from the airport. The distance d between the planes is then given by the Pythagorean theorem as ...

  d² = a² + b²

Differentiating with respect to time, we have ...

  2d·d' = 2a·a' +2b·b'

Solving for d', we get ...

  d' = (a/d)a' +(b/d)b'

The value of d at the time of interest is ...

  d = √(a² +b²) = √(30² +40²) = √2500 = 50

Then the rate of change of separation is ...

  d' = (30/50)(-250 mph) +(40/50)(-300 mph) = (-150 -240) mph

  d' = -390 mph

The distance between planes is decreasing at 390 miles per hour.

(5x-1)^2= (5x)^2-2(5x)×1+(1)^2=25x^2-10x+1

idk

step-by-step explanation: