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 April 8th, 2018, 10:54 PM #1 Newbie   Joined: Feb 2018 From: Burnaby Posts: 5 Thanks: 0 Chain rule Car A is traveling north on Highway 152 and car B is traveling west on Highway 251. Each car is approaching the intersection of these two highways. At a certain moment, car A is 0.7 km from the intersection and traveling 95 km/h while car B is 0.7 km from the intersection and traveling at 80 km/h. How fast is the distance between the cars changing at that moment? Please could i get help on this, I don't know what I'm doing wrong i got an answer of 102.9kmph apparently somehow i must use partial derivatives Last edited by moody; April 8th, 2018 at 11:31 PM. April 9th, 2018, 03:31 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 102.9 is the correct answer! Why would you think you are doing this wrong? April 12th, 2018, 03:03 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 Since moody has not responded- You don't use "partial derivatives" since there is only one independent variable, the time, t. But you do use the "chain rule". Let x be the distance from the intersection to car A and let y be the distance from the intersection to car B. Then the straight line distance between cars, z, satisfies $\displaystyle z^2= x^2+ y^2$. Differentiating but sides by t (using the chain rule), $\displaystyle 2d\frac{dz}{dt}= 2x\frac{dx}{dt}+ 2y\frac{dy}{dt}$. The "2"s cancel to give $\displaystyle d\frac{dz}{dt}= x\frac{dx}{dt}+ y\frac{dy}{dt}$. You are told the values for x, y, [/math]\frac{dx}{dt}[/math], and $\displaystyle \frac{dy}{dt}$. Tags chain, rule Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post nbg273 Calculus 4 March 2nd, 2017 10:03 PM Ku5htr1m Calculus 2 November 30th, 2016 03:55 PM ungeheuer Calculus 1 July 30th, 2013 05:10 PM unwisetome3 Calculus 4 October 19th, 2012 01:21 PM Peter1107 Calculus 1 September 8th, 2011 10:25 AM

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