Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The paraboloid z = 6x2 + y2 and the parabolic cylinder y = 5x2.

Step-by-step explanation:

Given that:

The paraboloid surface z = 6x² + y² and the parabolic cylinder y = 5x²

Let assume that:

x = t

then from y = 5x², we have:

y = 5t²

Now replace y = 5t² and x = t into z = 6x² + y²

z = 6t² + (5t²)²

z = 6t² + 25t⁴

Hence, the curve of intersection is illustrated by the set of equations:

x = t, y = 5t², and z = 6t² + 25t⁴

As a vector equation:

.

step-by-step explanation:

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.