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boyakko [2]
2 years ago
6

A parabola can be drawn given a focus of (0,−6) and a directrix of y=−2. Write the equation of the parabola in any form.

Mathematics
1 answer:
topjm [15]2 years ago
7 0

Answer:

y = x^2 - 4

Step-by-step explanation:

The vertex of a parabola is exactly halfway between the focus and the directrix.  If the focus is at (0, -6) and the directrix is the line y = -2, then we do this to locate the vertex:  Draw a vertical line through (0, -6) also crossing the line y = -2.  The y value halfway between y = -6 and y = -2 is y = -4, and the vertex is thus (0, -4).

Using the vertex method, write out the equation of this parabola, starting with the general form y - k = (x-h)^2, where (h, k) is the vertex.  Here h = 0 and k = -4

We get:  y + 4 = (x - 0)^2, or y + 4 = x^2, or y = x^2 - 4.  As a check, let x = 0; y = -4, which is the y-coordinate of the vertex.

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Step-by-step explanation

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7 0
3 years ago
You randomly select an integer from 0 to 19 ​(inclusively) and then randomly select an integer from 0 to 24 ​(inclusively). What
Mila [183]

Answer:

The probability of selecting 5 both​ times is 0.002.

Step-by-step explanation:

We are given that you randomly select an integer from 0 to 19 ​(inclusively) and then randomly select an integer from 0 to 24 ​(inclusively).

And we have to find the probability of selecting 5 both​ times.

As we know that the probability of an event is given by;

                Probability = \frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}

Now, here between integer from 0 to 19 ​(inclusively);

Number of times 5 comes = 1

Total number of integers = 20

Similarly, between integer from 0 to 24 ​(inclusively);

Number of times 5 comes = 1

Total number of integers = 25

So, the required probability = \frac{1}{20}\times \frac{1}{25}

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Hence, the probability of selecting 5 both​ times is 0.002.

5 0
3 years ago
Solve the following inequality: 3-5x-x^2>=0
Dennis_Churaev [7]

Answer:

-5/2+-1/2√37≤x≤-5/2+1/2√37

Step-by-step explanation:

Step 1: Find the critical points

-x^2-5x+3=0

For this equation: a=-1, b=-5, c=3

−1x^2+−5x+3=0

x=−b±√b2−4ac/2a

x=−(−5)±√(−5)2−4(−1)(3)/2(-1)

x=5±√37 /−2

x=-5/2+1/2√37

Step 2: Check intervals in between critical points

x≤-5/2+1/2 √37 (Doesn't work in original inequality)

-5/2+-1/2√37≤x≤-5/2+1/2√37 (Works in original inequality)

x≥-5/2+1/2 √37 (Doesn't work in original inequality)

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3 years ago
Find the volume of each prism. Round to the nearest tenth if necessary
bekas [8.4K]
The volume is 216 :)
3 0
3 years ago
Which are like terms to the term 2x.
Anvisha [2.4K]
X2, or 2X or X times 2, or X•2.
4 0
2 years ago
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