# calculus

A plane flies horizontally with a speed Of 600km/h at an altitude of 10km and pasess directly over th town of quinton .find the rate at which the distance from the plane to quinton is increasing when its 20km away from quinton ?

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1. let the horizontal distance from Quinton be x km
let the distance between plane and Quinto by y km

x^2 + 10^2 = y^2
2x dx/dt = 2y dy/dt
dy/dt = (x dx/dt)/y

when x=20
y^2 = 400 + 100 = 500
y = √500 = 10√5
dx/dt = 600 km/h
dy/dt = 20(600)/10√5 = appr. 536.7 km/h

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2. But did u use pythagoram theorom an how did u manipulate it ? And thanks because the answer is right .

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3. yes, you can see in my first line of the solution that I used the Pythagorean theorem.
I then differentiate with respect to time, since we were talking about "rates" in the question and I saw a rate given as 600 km/h

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4. Thank you !

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5. how did you get dy/dt to be (x dx/dt)/y

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