Question

A road perpendicular to a highway leads to a farmhouse located 8 mile away. An automobile traveling on the highway passes through this intersection at a speed of 40mph. How fast is the distance between the automobile and the farmhouse increasing when the automobile is 7 miles past the intersection of the highway and the road? The distance between the automobile and the farmhouse is increasing at a rate of miles per hour.

Answer 1

B Z y n smile 0 A farm house AQs 8 miles e ob- y & AB 2 Giren dy 40mile NOW 17² = 82 + y2 shery at y = 1 =) Z?: 82+72) L : 1113 Now from us 22: 82 + y2 3) d (22) = (82 + y2) di :) 22 dz 사 0 +2y dy at 2 d² dt 2 X 7 X 40 &x 113 126 34 miles/ho wy fox)= x-31nu 225 pl X 1-3 bet f'mo 20 x sign t'in 5 + + 0 3 May min f(12= 3.629 f1375 -0.2958 $6512 0.1716 Absolut marm value is 3.629 at this occurs at x eluals V3

Absolute minimum value is - 0.2958 and this occurs at x elleabs 3 felis y : 522 o frl: 502 X= 10, DX = 0.4 5) Dy: fl 24DX) +12) f(0.4) - 110 5*10-4.) ² - 5x10² =) 40.8 -) 1 Dys 40.8 Ans dy dx 16x in dy a lox da 2 dy lon 3x0.4 12 0 Idy=12