Irfan Islam stion 7 Read the following related rates problem and possible solution. et answered Two very well trained cats start at the same location and travel in perpendicular (right angle, 90 degree) directions. Sunshine Cat travels due north at a rate of 6 km/hour. Snoopy Cat travels east at a rate of 2 km/hour. At what rate is the distance between the kitties changing after 3 hours? ked out of 1.0 Flag question We draw a picture of the given information. dc at 3 hours? north dt a 6 km/h 2 km/h Let all variables be as labeled in the diagram. After 3 hours Sunshine Cat has traveled 6-3 18 kilometers northward. After 3 hours, Snoopy Cat has traveled 2-3 6 kilometers eastward. By Pythagorean theorem, at 3 hours, then 2-a +b 2- 18 + 6 360 Also, by Pythagorean theorem, and taking the derivatives w.r.t. time t: 26 2c 2a 2t da =6 and dt db = 2. Subbing those in, along with a 18, 6 6, and c=360, we get and we are given that dt 26 +26 26 2a dt 2V300d 2(18)(6) + 2(6)(2) dt de 240 dt 2/300 120 va60 120 Therelore the distance Lebiben the tO cats is increasing kmh at 3 hoUrS 300 Seloct a reaporse beiow. Select one a The distacie e t decreacing not inaeasng 9 The pped her calcudang io agorean heoen 0I