The general form of a parabola when using the focus and directrix is:
(x - h)² = 4p(y - k) where (h, k) is the vertex of the parabola and 'p' is distance between vertex and the focus. We use this form due to the fact we can see the parabola will open up based on the directrix being below the focus. Remember that the parabola will hug the focus and run away from the directrix. The formula would be slightly different if the parabola was opening either left or right.

Given a focus of (-2,4) and a directrix of y = 0, we can assume the vertex of the parabola is exactly half way in between the focus and the directrix. The focus and vertex with be stacked one above the other, therefore the vertex will be (-2, 2) and the value of 'p' will be 2. We can now write the equation of the parabola:
(x + 2)² = 4(2)(y - 2)
(x + 2)² = 8(y - 2) Now you can solve this equation for y if you prefer solving for 'y' in terms of 'x'

5 0

2 years ago

Assume the upper arm length of males over 20 years old in the United States is approximately Normal with mean 39.2 centimeters (

MAVERICK [17]

Answer:

The interval [32.6 cm, 45.8 cm]

Step-by-step explanation:

According with the <em>68–95–99.7 rule for the Normal distribution:</em> If $\large \bar x$ is the mean of the distribution and s the standard deviation, around 68% of the data must fall in the interval

$\large [\bar x - s, \bar x +s]$

around 95% of the data must fall in the interval

$\large [\bar x -2s, \bar x +2s]$

around 99.7% of the data must fall in the interval

$\large [\bar x -3s, \bar x +3s]$

So, the range of lengths that covers almost all the data (99.7%) is the interval

[39.2 - 3*2.2, 39.2 + 3*2.2] = [32.6, 45.8]

<em>This means that if we measure the upper arm length of a male over 20 years old in the United States, the probability that the length is between 32.6 cm and 45.8 cm is 99.7%</em>

3 0

2 years ago

Debra Arthur earns a weekly salary of $625 at All Sports.

Tcecarenko [31]

She earns $825 more as a head buyer than a assistant buyer

7 0

2 years ago