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noname [10]
3 years ago
9

A circle is centered at the point (5, -4) and passes through the point (-3, 2).

Mathematics
1 answer:
Sedbober [7]3 years ago
8 0

Answer:

The equation of the circle is (x + -5)² + (y + 4)² = 100

Step-by-step explanation:

* Lets revise the standard form of the equation of the circle

- If the center of the circle is point (h , k) and the length of its radius is r,

 then the equation of the circle is (x - h)² + (y - k)² = r² in standard form

* Now lets solve the problem

- The center of the circle is point (5 , -4)

∴ h = 5 and k = -4

∴ The equation of the circle is (x - 5)² + (y - -4)² = r²

∴ The equation of the circle is (x - 5)² + (y + 4)² = r²

- The circle passes through the point (-3 , 2)

- To find r substitute the x-coordinate and the y-coordinate of the

  point in the equation of the circle

∵ Point (-3 , 2) is on the circle

∴ x = -3 and y = 2

∴ (-3 - 5)² + (2 + 4)² = r² ⇒ simplify it

∴ (-8)² + (6)² = r² ⇒ solve power 2

∴ 64 + 36 = r² ⇒ add the like terms

∴ 100 = r²

∵ The equation of the circle is (x - 5)² + (y + 4)² = r²

∴ The equation of the circle is (x - 5)² + (y + 4)² = 100

- To complete the form

∴ The equation of the circle is (x + -5)² + (y + 4)² = 100

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Read 2 more answers
Assume that the paired data came from a population that is normally distributed. using a 0.05 significance level and dequalsxmin
Artemon [7]
"<span>Assume that the paired data came from a population that is normally distributed. Using a 0.05 significance level and d = (x - y), find \bar{d}, s_{d}, the t-test statistic, and the critical values to test the claim that \mu_{d} = 0"

You did not attach the data, therefore I can give you the general explanation on how to find the values required and an example of a random paired data.

For the example, please refer to the attached picture.

A) Find </span><span>\bar{d}
You are asked to find the mean difference between the two variables, which is given by the formula:
\bar{d} =  \frac{\sum (x - y)}{n}

These are the steps to follow:
1) compute for each pair the difference d = (x - y)
2) sum all the differences
3) divide the sum by the number of pairs (n)

In our example: 
</span><span>\bar{d} =  \frac{6}{8} = 0.75</span>

B) Find <span>s_{d}
</span><span>You are asked to find the standard deviation, which is given by the formula:
</span>s_{d} =  \sqrt{ \frac{\sum(d - \bar{d}) }{n-1} }

These are the steps to follow:
1) Subtract the mean difference from each pair's difference 
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3) sum the squares
4) divide by the degree of freedom DF = n - 1

In our example:
s_{d} = \sqrt{ \frac{101.5}{8-1} }
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C) Find the t-test statistic.
You are asked to calculate the t-value for your statistics, which is given by the formula:
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SE =  \frac{ s_{d} }{ \sqrt{n} }

These are the steps to follow:
1) calculate the standard error (divide the standard deviation by the number of pairs)
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3) calculate the mean value of y (sum all the values of y and then divide by the number of pairs)
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In our example:
SE = 3.81 / √8
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The problem gives us <span>\mu_{d} = 0, therefore:
t = [(9.75 - 9) - 0] / 1.346</span>
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We find <span>t_{\alpha / 2} = 1.895</span>

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