The depth in feet of a crater lake is given by f(x,y)= 100-0.015x^2-0.001y^2 whe
ID: 2980290 • Letter: T
Question
The depth in feet of a crater lake is given by f(x,y)= 100-0.015x^2-0.001y^2 where x and y are measured in feet from the center of the lake. Josh, who is not a very good swimmer, is in the water at point (25,90). a) How deep is the water at Josh's location? b) Find the instantaneous rate at which the depth is changing (at the point (25,90)) if he begins swimming toward the point (50,90). Make sure you label your answer with correct units. c) Find the instantaneous rate at which the depth is changing (at the point (25,90)) if he begins swimming toward a diving platform located at (45,70). d) Still assuming he is at the point (25,90), in which direction would the depth of the water increase most rapidly for Josh? e) Since Josh is not a very good swimmer, in which direction away from the point (25,90) should he begin swimming to reach shallow water as quickly as possible? NOTE: Please explain in detail, i care about the steps! 5 stars are given for correct and good explanation.Explanation / Answer
a>. f(x,y)= 100-0.015x^2-0.001y^2.... thus put x=25 and y=90 we get 82.525 b)since y coordinate is 90 constant his instantaneous rate at which the depth is changing (at the point (25,90)) if he begins swimming toward the point (50,90) is zero. c)df/dt=df/dx*dx/dt+df/dy*dy/dt=-.015*2*x*dx/dt-.001*2*y*dy/dt=-.03 *dx/dt-.002*dy/dt. now assume for time period dx/dt=45-25=20 and dy/dt=90-70=20.so put this in above and get the answer d)depth of the water will increase if x decreases or y deceases or both decreses. e) he will reach shallow water as quickly as possible if he if x increases or y increases or both increases.