Answer: 1. y = 2(x + 4)² - 3
<u>Step-by-step explanation:</u>
Notes: The vertex form of a parabola is y = a(x - h)² + k
- (h, k) is the vertex
- p is the distance from the vertex to the focus
1)
Now input a = 2 and (h, k) = (-4, -3) into the equation y = a(x - h)² + k
y = 2(x + 4)² - 3
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2)
Now input a = -1/3 and (h, k) = (-8, -7) into the equation y = a(x - h)² + k
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3)
The midpoint of the focus and directrix is the y-coordinate of the vertex:
The x-coordinate of the vertex is given in the focus as 7
(h, k) = (7, 1)
Now let's find the a-value:
Now input a = -1/2 and (h, k) = (7, 1) into the equation y = a(x - h)² + k
Step-by-step explanation:
<u>So the domain of f(x) := tanx is all real numbers except x = π 2 + kπ, k an integer.</u>
Answer:
1st and 3rd choices
Step-by-step explanation:
1st:
The graph follows the y=mx+b pattern, which if fits will always be a straight line.
This expression will be used throughout to explain answers.
3rd:
The y-intercept, or b, is -2. In the y-intercept, the x value is 0, so a point in the line is (0, -2).
The rest:
The 2nd is wrong because the y-intercept is -2. The line is two units below the origin when the x value is zero.
The 4th is wrong, because the slope, m, is 1/3, which is less than 3.
The 5th is wrong, because as explained in the 3rd choice, the y-intercept is -2, not 2.
By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 12 in. long and 10 in. wide, find the dimensions of the box that will yield the maximum volume. (Round your answers to two decimal places.)
in (smallest value)
in
in (largest value)