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Let C be the curve of intersection of the parabolic cylinder x2 = 2y, and the...

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)

Solutions

Expert Solution

Step 1)

Hence we can say that,

Hence,

Step 2)

we have,

Hence we can say that,

(x,y,z) = (0,0,0) corresponds to t = 0

(x,y,z) = (5,25/2,125/6) corresponds to t = 5

Hence we can say that t ranges form t = 0 to t = 5

we know that length of parametric curve r(t) is given by,

we have,

we have a = 0 and b = 5 hence,

Hence we can say that length of C from origin to the point (5,25/2,125/6) is L = 155/6

milcah answered 2 years ago
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