Thread: differentiation

differentiate
(X^2 + 200^2)^(1/2) multiplied by (1/4), and substitute X=200tanY

and

((500-X)^2 + 200^2)^(1/2) multiplied by (1/3), and substitute
X= -200tanZ+500

then combine equations and show that the minimum time occurs when (sinY)/m = (sinZ)/n where m and n are constants

Originally Posted by asian5

differentiate
(X^2 + 200^2)^(1/2) multiplied by (1/4), and substitute X=200tanY

and

((500-X)^2 + 200^2)^(1/2) multiplied by (1/3), and substitute
X= -200tanZ+500

then combine equations and show that the minimum time occurs when (sinY)/m = (sinZ)/n where m and n are constants

So after making the substitution we have equations 1 and 2.

#1)

#2) (The 500's cancel out.)

Now a little bit of trig comes in.

#1)
Factor out the 400, then take it out of the square-root function.



Now make the trig substitution

This should simplify things a lot and use the same process for equation #2.

the other part of the question is tricky.. could you continue