Question

(1 point) A car is driving northwest at v mph across a sloping plain whose height, in feet above sea level, at a point N miles north and E miles east of a city is given by h(N, E) = 1750 50N 25E (a) At what rate is the height above sea level changing with respect to distance in the direction the car is driving? rate = (b) Express the rate of change of the height of the car with respect to time in terms of v rate

Answer 1

Guen hCNE) tere Ni the number of miles fTom morlh 1TSO+50N+25E E is the number of miles from east Northwest is 45° nosth of west Let The Nrthuest distance of the car be xmiles So,its morthery Com penent gains m ts eastery co mponent losse mile and Thus The resultant haight is h=1750 +50 Ca) Difterentiak fhe fmchon ho) 1750 +2 2 wilh Tagpect to 25 2 Thus, the rate of the change of height with epect to 25 dh distance is XP with reapect change of height bThe rate of the the to time is, dt ctt 25 dt 25