Two airplanes are flying in the air at the same height: airplane A is flying east at 250 mi/h and airplane B is flying north at 300 mi/h. 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 is the distance between the airplanes changing?

  decreasing at 390 miles per hour

Step-by-step explanation:

Airplane A's distance in miles to the airport can be written as ...

  a = 30 -250t . . . . . where t is in hours

Likewise, airplane B's distance to the airport can be written as ...

  b = 40 -300t

The distance (d) between the airplanes can be found using the Pythagorean theorem:

  d^2 = a^2 + b^2

Differentiating with respect to time, we have ...

  2d·d' = 2a·a' +2b·b'

  d' = (a·a' +b·b')/d

__

To find a numerical value of this, we need to find the values of its variables at t=0.

  a = 30 -250·0 = 30

  a' = -250

  b = 40 -300·0 = 40

  b' = -300

  d = √(a²+b²) = √(900+1600) = 50

Then ...

  d' = (30(-250) +40(-300))/50 = -19500/50 = -390

The distance between the airplanes is decreasing at 390 miles per hour.

c

step-by-step explanation:

part a

in a city ice cream is mostly only bought when the temperature is very high as ice cream cools down our

so we can derive the conclusion that as the temperature increases the number of ice creams sold also increases

part b

y intercept is 5

slope is 2

happy to

pls mark as brainliest