Let C be the curve of intersection of the parabolic cylinder x2 = 2y, and the surface 3z = xy. Find the exact length of C from the origin to the point 5, 25 2 , 125 6 .
Added by David M.
Step 1
Given: x^2 = 2y 3z = xy From the first equation, we have y = x^2/2. Let's denote x as t, then y = t^2/2. Substitute the values of x and y into the second equation: 3z = t(t^2/2) z = t^3/2 Therefore, the parametric equation of the curve is r(t) = (t, t^2/2, Show more…
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