The positions of two airplanes approaching an airport are plotted in a coordinate plane with the airport located at (0,0). The locations of the planes are given by the coordinates (7, 2) and (-1, -8). Each grid square is 1 mile wide. How far apart are the approaching airplanes? Round your answer to the
nearest tenth of a mile.

  12.8 miles

Step-by-step explanation:

The distance is given by the distance formula:

  d = √((x2 -x1)^2 +(y2 -y1)^2)

  d = √((-1 -7)^2 +(-8-2)^2) = √((-8)^2 +(-10)^2) = √(64 +100)

  d = √164 ≈ 12.8

The planes are about 12.8 miles apart.

1) slope of the line = derivative of the of the function at the given point.

y' = cosx - x cosx

Evaluate for x = pi => y' = cos(pi) - pi*cos(pi) = -1 - (pi*cos(pi)) = -1 + pi

Then slope = -1 + pi

Given point: (pi, -pi)

Equation:

y - (-pi) = [-1+ pi] (x - pi)

y + pi = -x +pi + xpi -pi^2

y = (pi-1)x - pi^2      this is the answer