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Verizon [17]
3 years ago
12

Which is the equation of a parabola with a directrix at y = −3 and a focus at (5, 3)?

Mathematics
1 answer:
kramer3 years ago
3 0

Answer:

y = 1/12 (x − 5)²

Step-by-step explanation:

We can solve this graphically without doing calculations.

The y component of the focus is y = 3.  Since this is above the directrix, we know this is an upward facing parabola, so it must have a positive coefficient.  That narrows the possible answers to A and C.

The x component of the focus is x = 5.  Since this is above the vertex, we know the x component of the vertex is also x = 5.

So the answer is A. y = 1/12 (x−5)².

But let's say this wasn't a multiple choice question and we needed to do calculations.  The equation of a parabola is:

y = 1/(4p) (x − h)² + k

where (h, k) is the vertex and p is the distance from the vertex to the focus.

The vertex is halfway between the focus and the directrix.  So p is half the difference of the y components:

p = (3 − (-3)) / 2

p = 3

k, the y component of the vertex, is the average:

k = (3 + (-3)) / 2

k = 0

And h, the x component of the vertex, is the same as the focus:

h = 5

So:

y = 1/(4×3) (x − 5)² + 0

y = 1/12 (x − 5)²

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Answer:

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Step-by-step explanation:

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5 0
2 years ago
Speeding: On a stretch of Interstate-89, car speed is a normally distributed variable with a mean of 69.1 mph and a standard dev
Alborosie

Answer: 11.9%

Step-by-step explanation:

Given :  On a stretch of Interstate-89, car speed is a normally distributed variable with \mu=69.1 mph and \sigma=3.3 mph.

Let x be a random variable that represents the car speed.

Since , z=\dfrac{x-\mu}{\sigma}

z-score corresponds x = 73 , z=\dfrac{73-69.1}{3.3}\approx1.18

Required probability :

\text{P-value }: P(x>73)=P(z>1.18)\\\\=1-P(z

[using z-value table.]

Hence, the approximate percentage of cars are traveling faster than you = 11.9%

8 0
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Answer:

Step-by-step explanation:

a) = 46.2 X 10∧-1

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b) = 5.7 x 10∧-6

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