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drek231 [11]
2 years ago
14

Write the equation of a parabola whose directrix is y=9.75 and has a focus at (8, 0.25).

Mathematics
1 answer:
lana [24]2 years ago
6 0

Answer:

y = (-1/19)(x - 8)² + 1521/76

Step-by-step explanation:

A parabola moves in such a way that it's distance from it's focus and directrix are always equal.

Now, we are given that directrix is y = 9.75 and focus is at (8, 0.25). Focus can be rewritten as (8, ¼) and directrix can be rewritten as y = 39/4

If we consider a point with the coordinates (x, y), it means the distance from this point to the focus is;

√((x - 8)² + (y - ¼)²)

Distance from that point to the directrix is; (y - 39/4)

Thus;

√((x - 8)² + (y - ¼)²) = (y - 39/4)

Taking the square of both sides gives;

((x - 8)² + (y - ¼)²) = (y - 39/4)²

(x - 8)² + y² - ½y + 1/16 = y² - (39/2)y + (39/4)²

Simplifying this gives;

(x - 8)² - (39/4)² = (½ - 39/2)y

(x - 8)² - 1521/4 = -19y

(x - 8)² - 1521/4 = -19y

Divide both sides by -19 to get;

y = (-1/19)(x - 8)² + 1521/76

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An animal shelter spends 5.50 per day to care for each bird and 8.50 per Day to care for each cat and a notice that the shelter
Deffense [45]

Answer:

19 birds

Step-by-step explanation:

First, I wrote my two equations:

5.5x +8.5y = 291.5

x + y = 41

Next, I got the variable y by itself in the second equation. Subtract x to get y = -x + 41. Then, I substituted what y equaled into the first equation. It should look like this: 5.5x + 8.5(-x+41) = 291.5. Distribute 8.5 to get 5.5x -8.5x + 348.5 = 291.5. Subtract 5.5x and 8.5x to get -3x. It should look like this: -3x + 348.5= 291.5. Subtract 348.5 from 291.5 to get -57. Now, you should have -3x = -57. Divide -3 from both sides, to get x = 19. So, there are 19 birds. If you want to go even further, 41-19= 22, which means there are 22 cats. Hope this helped!

6 0
3 years ago
Vera is using her phone. Its battery lifw is down to 2/5 and it drains another 1/9 fraction every hour. How long will her batter
just olya [345]

Battery is down currently = 2/5

Battery drains at the rate of 1/9 every hour.

Remaining battery life of Vera = 1 -2/5 = 3/5

Let y we the number of hours battery will last.

So, 1/9 y = 3/5

y = 27/5

y = 5 + 2/5 hours

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So battery will last another 5 hrs and 24 mins.

hope this helps:)

4 0
3 years ago
ILL BRAINLIEST YOU PLEASE HELP ME
svetoff [14.1K]
5 hope that helps you
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3 years ago
The resting heart rate of 60 patients is shown in the frequency table below.
Murrr4er [49]

The standard deviation is 9.27. The typical heart rate for the data set varies from the mean by an average of 9.27 beats per minute.

<h3>How to determine the standard deviation of the data set?</h3>

The dataset is given as:

Heart Rate  Frequency

60 1

65 3

70 4

75 12

80 8

85 15

90 9

95 5

100 3

Calculate the mean using

Mean = Sum/Count

So, we have

Mean = (60 * 1 + 65 * 3 + 70 * 4 + 75 * 12 +  80 * 8 +  85 * 15 +  90 * 9 +  95 * 5 + 100 * 3)/(1 + 3 + 4 + 12 + 8 + 15 + 9 + 5 + 3)

Evaluate

Mean = 82.25

The standard deviation is

\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f -1}}

So, we have:

SD = √[1 * (60 - 82.25)^2 + 3 * (65 - 82.25)^2 + 4 * (70 - 82.25)^2 + 12 * (75 - 82.25)^2 + 8 * (80 - 82.25)^2 +  15 * (85 - 82.25)^2 +  9 * (90  - 82.25)^2 + 5 * (95 - 82.25)^2 + 3 * (100 - 82.25)^2)]/[(1 + 3 + 4 + 12 + 8 + 15 + 9 + 5 + 3 - 1)]

This gives

SD = √85.9533898305

Evaluate

SD = 9.27

Hence. the standard deviation is 9.27. The typical heart rate for the data set varies from the mean by an average of 9.27 beats per minute.

Read more about standard deviation at:

brainly.com/question/4079902

#SPJ1

5 0
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The Orlando Solar Bears had a successful season on the ice winning 80% of their games. They won a record of 32 games. How many g
Makovka662 [10]

Answer:

Step-by-step explanation:

You'd do 80% times 32. You have to move the 80 to the left 2 times. then multiply.

7 0
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