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Bezzdna [24]
3 years ago
12

What is the equation of a parabola that has a focus at (0, −3) and a directrix,y = 3 ?

Mathematics
2 answers:
KiRa [710]3 years ago
8 0
Refer to the diagram shown.

At an arbitrary point P (x,y) on the parabola, the distance from the focus should be equal to the distance from the directrix.
The distance of P from the focus is
d₁ = √[x² + (y+3)²]
The distance from P to the directrix is
d₂ = 3 - y

Therefore
d₁ = d₂.
That is,
x² + (y+3)² = (3 - y)²
x² + y² + 6y + 9 = 9 - 6y + y²
x² + 12y = 0
y = - (1/12) x²

Answer: y=- \frac{1}{12} x^{2}


lianna [129]3 years ago
7 0

Answer:

D)

Step-by-step explanation:

<em>no time to explain, just answer it</em>

You might be interested in
Find the surface area of the triangular prism shown below.
VikaD [51]

Answer:

136

Step-by-step explanation:

5*7 = 35

5*7 = 35

4*6/2 = 12

4*6/2 = 12

7*6 = 42

Add them all up

5 0
2 years ago
9 ft 8 ft 5 ft 13 ft What is the area of this figure? ​
Vlad1618 [11]

Answer:

D. 98 ft.^2

Step-by-step explanation:

A= b*h

=13*8

=104 ft.^2

Because there is a piece missing, we know it must be under 104 ft.^2. They didn't give us enough information to find the complete area of the missing triangle, so I used the process of elimination. With the responses given and this information, we can assume that the answer is 98 ft.^2.

8 0
3 years ago
Simplify (3s^8)^-5 write your answer using only positive exponents. help please!!
loris [4]

Answer:

1 / ( 243s^40 )

Step-by-step explanation:

For this problem, we need to know that a negative exponent simply can be rewritten in the opposing part of the fraction, for this case, the denominator.  So we can simplify as shown:

(3s^8)^-5

= 1 / (3s^8)^5

= 1 / 3^5 * s^8^5

= 1 / 243 * s^40

= 1 / ( 243s^40 )

Cheers.

3 0
2 years ago
The n sequence question
MaRussiya [10]

Answer:

a) in order

-3;-2;-1

b) 6

1-4=-3

2-4=-2

3-4=-1

4-4=0

5-4=1

6-4=2

7-4=3

8-4=4

9-4=5

10-4=6

5 0
3 years ago
1) f(x) = 2x + 4, g(x) = 4x2 + 1; Find (g ∘ f)(0).
Sholpan [36]

Answer:

<h2>(g \: \circ \: f)(0) = 17</h2>

Step-by-step explanation:

f(x) = 2x + 4

g(x) = 4x² + 1

In order to find (g ∘ f)(0) we must first find

(g ° f )(x)

To find (g ° f )(x) substitute f(x) into g(x) that's for every x in g(x) replace it with f(x)

That's

<h3>(g \: \circ \: f)(x) = 4( ({2x + 4})^{2} ) + 1 \\  = 4(4 {x}^{2}  + 16x + 16) + 1 \\  =  {16x}^{2}  + 64x + 16 + 1</h3>

We have

<h3>(g \: \circ \: f)(x) =  {16x}^{2}  + 64x + 17 \\</h3>

Now to find (g ∘ f)(0) substitute the value of x that's 0 into (g ∘ f)(0)

We have

<h3>(g \: \circ \: f)(0) = 16( {0})^{2}  + 64(0) + 17 \\</h3>

We have the final answer as

<h3>(g \: \circ \: f)(0) = 17</h3>

Hope this helps you

8 0
3 years ago
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