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3 years ago

Find the equation for the circle with a diameter whose endpoints are (-5, -3) and (3,2).

Mathematics

1 answer:

densk [106]3 years ago

3 0

Answer:

(x +1)^2 +(y +0.5)^2 = 22.25

Step-by-step explanation:

The center of the circle is the midpoint of the diameter, so is ...

(h, k) = ((-5, -3) +(3, 2))/2 = (-5+3, -3+2)/2 = (-1, -1/2)

The circle formula is then ...

(x -h)^2 +(y -k)^2 = r^2

(x -(-1))^2 +(y -(-1/2))^2 = r^2

We can find r^2 by substituting one of the points for (x, y).

(3 +1)^2 +(2 +1/2)^2 = r^2 = 16 +6.25 = 22.25

Then the circle equation is ...

(x +1)^2 +(y +0.5)^2 = 22.25

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Step-by-step explanation:

Previous concepts

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Solution to the problem

Part a

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the standard error for the mean would be:

$\sigma_{\bar X}= \frac{140}{\sqrt{100}} =14$

Part b

We want this probability:

$P(\bar X >120)$

And we can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And replacing we got:

$z = \frac{120-90}{\frac{140}{\sqrt{100}}}= 2.143$

And we can find this probability with the complement rule and the normal standard deviation or excel and we got:

$P( z>2.143) = 1-P(Z$

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