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# Car 1 is 10 miles east of car 2.

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Car 1 is 10 miles east of car 2. Car 1 is driving at 10 mph eastward, car 2 is driving north at a speed of 20 mph. how fast is the distance changing after 2 hours of driving?

Apr 5, 2021

#5
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Why does it say 4 replys when theres 0? Glitch?

Apr 5, 2021
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It's not a glitch, it is because someone previously spammed on here, and then I flagged the post and the admin came on and took down the spam posts. There were 2 spam posts and 2 of my replies. They are still there, just only visible to the mods and the admin.

RiemannIntegralzzz  Apr 5, 2021
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Related rates and the pythagorean theorem

x = car 1 = 2 hrs * 10 m/hr = 20 miles     and      dx/dt = 10  m/hr

y = car 2 = 2hrs * 20 m/hr = 40 miles      and      py/dt = 20 m/hr

Pythagorean theorem for the distance between the two cars :

x^2 + y^2 = s^2                        s^2 = 2000      now differentiate with respect to time (using chain rule)

2x dx/dt     +    2y dy/dy   =   2s ds/dt           We have all of these variables except   ds/dt (which we are looking for) ...so plug in

2(20)  * 10          + 2 (40)  *20  =   2 (sqrt(2000)  * ds/dt

ds/dt = 2000/(2 sqrt(2000))  = 1000/sqrt(2000) = 22.36 m/hr

Apr 5, 2021
edited by ElectricPavlov  Apr 5, 2021
edited by ElectricPavlov  Apr 5, 2021