A cylinder’s radius is reduced to two-fifths its original size and the height is quadrupled. How has the volume of the cylinder
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The vector function is, r(t) =
Given two surfaces for which the vector function corresponding to the intersection of the two need to be found.
First surface is the paraboloid,
Second equation is of the parabolic cylinder,
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, .
Now substituting x and y into the equation of the paraboloid, we get,
Now the vector function, r(t) = <x, y, z>
So r(t) =
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Answer:
Step-by-step explanation:
Required
The graph equation
From the graph, we have:
The slope of the graph is:
So, the graph equation is:
In standard form, we have: