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3 years ago

Find the standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2.

Mathematics

2 answers:

Anit [1.1K]3 years ago

7 0

Answer:

$y=-\frac{1}{8}x^2$

Step-by-step explanation:

Find the standard form of the equation of the parabola with a focus at (0, -2) and a directrix at y = 2

The distance between the focust and the directrix is the value of 2p

Distance beween focus (0,-2) and y=2 is 4

$2p=4, p=2$

The distance between vertex and focus is p that is 2

Focus is at (0,-2) , so the vertex is at (0,0)

General form of equation is

$y-k=-\frac{1}{4p}(x-h)^2$

where (h,k) is the vertex

Vertex is (0,0) and p = 2

The equation becomes

$y-0=-\frac{1}{4(2)}(x-0)^2$

$y=-\frac{1}{8}x^2$

anyanavicka [17]3 years ago

5 0

Hello,
The parabola having like focus (0,p/2) and as directrix y=-p/2 has as equation x²=2py

Here -p/2=2==>p=-4

x²=-8y is the equation.

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3 years ago

How would the expression x^3+64 be rewritten using sum off cubes

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$\bf \textit{difference of cubes}
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a^3+b^3 = (a+b)(a^2-ab+b^2)\qquad
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\boxed{64=4^3}\qquad x^3+64\implies x^3+4^3\implies (x+4)(x^2-x4+4^2)
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3 years ago

Read 2 more answers

The yearly cost y for driving a certain car is $7,800 for 10,000 miles

Licemer1 [7]

Answer:

y = 0.36x + 4200.00

15100.00 miles.

Step-by-step explanation:

If the yearly cost for driving x miles is given by y dollars then the two ordered pairs to find the linear relation between x and y are (10000,7800) and (20000,11400).

So, the equation will be

$\frac{y - 11400}{11400 - 7800} = \frac{x - 20000}{20000 - 10000}$

⇒ $\frac{y - 11400}{3600} = \frac{x - 20000}{10000}$

⇒ $y - 11400 = \frac{9}{25}(x - 20000)$

⇒ $y - 11400 = \frac{9}{25}x - 7200$

⇒ $y = \frac{9}{25}x + 4200$

⇒ y = 0.36x + 4200.00 ........... (1) (Answer)

Now, for y = $9636.00, from equation (1),

9636 = 0.36x + 4200

⇒ 0.36x = 5436

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3 years ago

A field is a rectangle with a perimeter of 1220 feet. The length is 100 feet more than the width. Find the width and length of t

rosijanka [135]

To start, let x represent the width and x+100 represent the length. Since the perimeter of a figure is the sum of all the measurements of the side which can be represented by (x+100)+(x+100)+x+x and since you know your perimeter is 1220, you can set the expression equal to 1220. This would look like this:
(x+100)+(x+100)+x+x=1220

Once you have done that, combine any like terms (combine terms with the same variables and raised to the same power together) which would simplify to this:
4x+200=1220

Now that you have your like terms simplified, subtract 200 from both sides to get 4x=1020 and finally, to solve for x, or find the width, divide both sides by 4 to get x=255.

Now that you have your width, now you must find your length as the question asks to find the dimensions of the rectangular field. To find the length, add 100 to the width, 255 since according to the information given, the length is 100 more than the width. When you add 100 to 255, you should get that your length is 355.

Now that you have your length and width, you can conclude that the dimensions of the field is 255 by 355 feet, which is your answer :)

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3 years ago

Events A and B are independent. Find the missing probability.

STALIN [3.7K]

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