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Calculus question. Pls help.

Calculus question. Pls help.-example-1
User Jedierikb
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call eastward plane A and westward plane B

speed from west is 450

speed from south is 275

the distance between them is defined by pythagorean theorem


(s_A)^2+(s_B)^2=s^2 where s is distance between

when sA=sB=100, then find speed of change in distance

first find distance


100^2+100^2=s^2


d=100√(2)


if we look at
(s_A)^2+(s_B)^2=s^2 and take the derivitive of both side with respect to time, we get


2(s_A)(ds_A)/(dt)+2(s_B)(ds_B)/(dt)=2(s)(ds)/(dt)


(ds_A)/(dt) is speed of plane A


(ds_B)/(dt) is speed of plane B

we are solving for
(ds)/(dt)

subsituting


2(100)(450)+2(100)(275)=2(100√(2))(ds)/(dt)

solving


(ds)/(dt)=512.652

User Ptimson
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