Find the distance from the point (4,2) to the line y= −2.

Mathematics

1 answer:

riadik2000 [5.3K]3 years ago

6 0

Answer:

The distance is 4.

Step-by-step explanation:

The shortest distance from the point (4,2) to the line y=-2, in this case, would be a straight line perpendicular to y=-2.

For each and every value of "x" on the line, y = -2. The shortest distance occurs at y(4) = - 2.

At this point the distance is:

$d^{2} =(4 - 4)^{2} + (2-(-2))^{2} \\d^{2} =4 ^{2}\\\\d = 4$

The distance is 4.

You might be interested in

amanda read 15 pages of her 150-page book in 2 hours. At this rate, how long will it take her to read the entire book?

irina [24]

20 hours. You find this by dividing 150 by 10 and then multiplying that by 2.

7 0

3 years ago

Read 2 more answers

The sugar content of the syrup in canned peaches is normally distributed. A random sample of n = 10 cans yields a sample standar

Serggg [28]

Answer:

The 95% confidence interval is given by:

3.30<σ<8.76

Step-by-step explanation:

1) Data given and notation

s=4.798 represent the sample standard deviation

$\bar x$ represent the sample mean

n=10 the sample size

Confidence=95% or 0.95

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 mean or variance 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.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=10-1=9$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical values.