Answer: D. -y-x
Step-by-step explanation: combine like terms
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:
9
Step-by-step explanation:
90 divided by 10 =9
Answer:
The correct answer is:
The graph will be the same width as the parent graph f(x) = x², but the vertex has been shifted to (1, 2).
Step-by-step explanation:
Since the value of a, the coefficient of x², is 1, this means the graph has not been stretched or shrunk. However, since the function is different than f(x)=x², we know that the vertex is not at (0, 0). We can write the function in vertex form to find the new vertex.
To write the function in vertex form, we find the value of b/2. The value of b in this function is -2; -2/2 = -1. We then square this: (-1)² = 1. This is what we add and subtract to the function (we must do both to preserve equality), giving us:
f(x) = x²-2x+1+3-1
The first three terms of this function can be written as the square (x+(b/2))²; this is (x-1)², and gives us f(x) = (x-1)²+3-1. Combining like terms, we have:
f(x) = (x-1)²+2
This is vertex form, f(x) = a(x-h)²+k, where (h, k) is the vertex. This means the vertex is at (1, 2) instead of (0, 0).
