A car leaves an intersection traveling west. Its position 4 sec later is 20 ft f

Question

A car leaves an intersection traveling west. Its position 4 sec later is 20 ft from the intersection. At the same time, another car leaves the same intersection heading north so that its position 4 sec later is 30 ft from the intersection. If the speeds of the cars at that instant of time are 8 ft/sec and 12 ft/sec, respectively, find the rate at which the distance between the two cars is changing. (Round your answer to one decimal place ft/s Need Help? LRead LTak to Tutor My Notes o Ask Your Teache -1 points TanApCalcBr10 3.6.044 Suppose the wholesale price of a certain brand of medium-sized eggs p (in dollars/carton) is related to the weekly supply x (in thousands of cartons) by the following equation. If 36000 cartons of eggs are available at the beginning of a certain week and the price is falling at the rate of at what rate is the supply chan (Round your answer to nearest whole number.) (Hint: To find the value of p when X 36, solve the supply equation for p when x 36 cartons per week. 1 points TanApCalcBr10 3.6.050 My Notes o Ask Your Teache The volume V of a cube with sides of length x in. is changing with respect to time. At a certain instant of time, the sides of the cube are 5 in ong and increasing at the rate of 0.3 in How fast is the volume of the cube changing at that instant of time? cu in/sec. Need Help? LRead LTak to Tutor My Notes o Ask Your Teache 1 points TanApCalcBr10 3.6.052. Two ships leave the same port at noon. Ship A sails north at 18 mph, and ship B sails east at 10 mph. How fast is the distance between them changing at 1 p.m.? (Round your answer to one decimal place mph

Explanation / Answer

let the car travelling north is A and car travelling west is b.

abter 4 secs distance travelled by A is 30ft

and after 4 secs distance travelled by B is 20 ft

AB= sqrt(900+400)=10sqrt13

AB^2 =OA^2 +OB^2

2AB d(AB)/dt =2OAd(OA)/dt +2OBd(OB)/dt

10sqrt13d(AB)/dt=30*12+20*8

d(AB)/dt=52/sqrt13 =14.4ft

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