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borishaifa [10]
2 years ago
8

Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the paraboloid z = 9x2 y2 and the p

arabolic cylinder y = 2x2
Mathematics
1 answer:
dolphi86 [110]2 years ago
7 0

The vector function is, r(t) =  \bold{ < t,2t^2,9t^2+4t^4 > }

Given two surfaces for which the vector function corresponding to the intersection of the two need to be found.

First surface is the paraboloid, z=9x^2+y^2

Second equation is of the parabolic cylinder, y=2x^2

Now to find the intersection of these surfaces, we change these equations into its parametrical representations.

Let x = t

Then, from the equation of parabolic cylinder,  y=2t^2.

Now substituting x and y into the equation of the paraboloid, we get,

z=9t^2+(2t^2)^2 = 9t^2+4t^4

Now the vector function, r(t) = <x, y, z>

So r(t) = \bold{ < t,2t^2,9t^2+4t^4 > }

Learn more about vector functions at brainly.com/question/28479805

#SPJ4

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