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3 years ago

What is the equation of the circle with center (4, 4) that passes through the point (10, 14)?

Mathematics

2 answers:

zhuklara [117]3 years ago

7 0

Answer:

The answer to your question is (x - 4)² + (y - 4)² = 136

Step-by-step explanation:

Data

C (4, 4)

P (10, 14)

Process

1.- Calculate the distance from the center to the point

dCP = $\sqrt{(10 - 4)^{2} + (14 - 4)^{2}}$

dCP = $\sqrt{6^{2} + 10^{2}}$

dCP = $\sqrt{36 + 100}$

dCP = $\sqrt{136}$

2.- Calculate the equation of the circle

( x - 4)² + (y - 4)² = ( $\sqrt{136}$ )²

(x - 4)² + (y - 4)² = 136

Anna11 [10]3 years ago

3 0

Answer:

(x - 4)² + (y - 4)² = 136 is the answer.

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Andru [333]

Answer:

x (Falafel) = $5.50

y (Turkey BLT) = $7.50

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Step-by-step explanation:

Step 1: Write out systems of equations

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There are multiple ways to solve for this systems of equations. I will use an augmented matrix for this:

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4 0

3 years ago

Read 2 more answers

A professor at a university wants to estimate the average number of hours of sleep students get during exam week. The professor

kotegsom [21]

Answer:

$n=(\frac{1.64(6.995)}{1.939})^2 =35.003 \approx 36$

So the answer for this case would be n=36 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma =6.995$ represent the population standard deviation

n represent the sample size

Solution to the problem

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$