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ad-work [718]
3 years ago
13

Help? Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y = 9.

Mathematics
2 answers:
madreJ [45]3 years ago
7 0
You plot the point of the focus and the directrix on the graph to determine where the parabola opens.
We are provided the general forms of parabola according to its opening if:
it opens upward: (x - h)<span>² = 4a(y - k)
</span>it opens downward: (x - h)<span>² = -4a(y - k)
where "h" and "k" are the coordinates of the vertex, and "a" is the focal length from the focus to the vertex.

As you plot, the directrix y = 9 is a horizontal line, and the focus at (0,-9) is below that directrix. So, it means that the parabola opens downward (and not upward because the parabola must not touch to the directrix).</span> Next, identity the vertex (h,k). Note that the vertex is the midpoint between the focus and the point of the directrix. So the vertex is (0,0). Then, the focal length "a" is 9.
Hence, the equation is
(x - 0)<span>² = -4(9)(y - 0)
x</span><span>² = -36y</span>


zvonat [6]3 years ago
3 0

Going off of the answer above:

x² = -36y

we need to make it in y= form

so the answer is y=-(1/36)*x^2

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3 years ago
An 16 16​-oz jar of peanut butter in the shape of a right circular cylinder is 7 7 in. high and 5 5 in. in diameter and sells fo
olya-2409 [2.1K]

Answer:

Step-by-step explanation:

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

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r represents the radius of the cylinder.

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π is a constant whose value is 3.14

Considering the 16 oz jar,

h = 7 inches

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Radius = diameter/2 = 5/2

r = 2.5 inches

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Considering the 29 oz jar,

h = 7.5 inches

Diameter = 5.25 inches

Radius = diameter/2 = 5.25/2

r = 2.625 inches

Volume = 3.14 × 2.625² × 7.5 = 162.27 inches³

1) If the cost is directly proportional to​ volume, then

If 137.375 inches³ cost $1.6

then 162.27 inches³ should cost

(162.27 × 1.6)/137.375 = $1.89

The price of the larger jar would be $1.89

2) If the cost is directly proportional to​ weight, then

If 16 oz cost $1.6, then

29 oz would cost

(29 × 1.6)/16 = $2.9

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7 0
3 years ago
One crate can hold 8 cases of trading cards.How many crates are needed to hold 128 cases of trading cards?
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7 0
3 years ago
to construct a parallel to a line through a point not on the line using paper folding, you can perform the _____ construction tw
adoni [48]
<span>The <u>correct answer</u> is:

The midpoint of a segment.

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Unfold the paper, and the crease made with the fold creates a line through the given point and given line. Fold this new line (crease) onto itself, making sure the given point is in the fold. This is again the same construction used to find the midpoint of a segment, and this creates our parallel line through our given point.</span></span>
6 0
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Read 2 more answers
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-1/3

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7 0
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