All categories

3 years ago

The endpoints of a diameter of a circle are A(1,2) and (7.10). Find the area of the circle in terms of pi

Mathematics

1 answer:

OLEGan [10]3 years ago

7 0

Answer:

25pi

Step-by-step explanation:

To solve this, create a right triangle between the two points. We know the distance of one leg is 6, and the distance of the other leg is 8. Use the Pythagorean theorem to solve for the diameter. You substitute 6 and 8 into the values of A and B. Once you get this, you get (6^2)+(8^2)=c^2. Once you further simplify this, you get 36 + 64 = c^2, which is 100 = c^2. Take the square roots of both sides to get the diameter as 10. Divide the diameter by 2 to get the radius. Square the radius and multiply it by pi to get the area. Doing this will get the result of 25 pi.

You might be interested in

The product of two positive consecutive numbers is 42. What is the smaller number?

Temka [501]

X = first integer, y = second integer (right after x)

since y is right after x, we can say
y = x+1

If the product of the two integers (x and y) is 42, then
x*y = 42
x*( y ) = 42
x*( x+1 ) = 42 ... y is replaced with x+1
x*x + x*1 = 42
x^2 + x = 42
x^2 + x - 42 = 0
(x + 7)(x - 6) = 0 ... factor
x + 7 = 0 or x - 6 = 0
x = -7 or x = 6

The result must be positive as the problem states it, so we toss out x = -7
The only answer is x = 6

If x = 6, then
y = x+1
y = 6+1
y = 7

The two consecutive numbers are 6 and 7

The final answer is 6

Sure enough, 6*7 = 42 checks out

8 0

3 years ago

How to write a fraction or mixed number as a decimal pre algebra?

Oksanka [162]

If you had the number 4 1/4 you would divide the numerator (1) by the denominator (4) and then take the decimal number (0.25) you get and add the decimal to the whole number on your mixed number (4+0.25) and that would give you the decimal.

4 0

3 years ago

For a certain river, suppose the drought length Y is the number of consecutive time intervals in which the water supply remains

AnnZ [28]

Answer:

a) There is a 9% probability that a drought lasts exactly 3 intervals.

There is an 85.5% probability that a drought lasts at most 3 intervals.

b)There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

Step-by-step explanation:

The geometric distribution is the number of failures expected before you get a success in a series of Bernoulli trials.

It has the following probability density formula:

$f(x) = (1-p)^{x}p$

In which p is the probability of a success.

The mean of the geometric distribution is given by the following formula:

$\mu = \frac{1-p}{p}$

The standard deviation of the geometric distribution is given by the following formula:

$\sigma = \sqrt{\frac{1-p}{p^{2}}$

In this problem, we have that:

$p = 0.383$

$\mu = \frac{1-p}{p} = \frac{1-0.383}{0.383} = 1.61$

$\sigma = \sqrt{\frac{1-p}{p^{2}}} = \sqrt{\frac{1-0.383}{(0.383)^{2}}} = 2.05$

(a) What is the probability that a drought lasts exactly 3 intervals?

This is $f(3)$

$f(x) = (1-p)^{x}p$

$f(3) = (1-0.383)^{3}*(0.383)$

$f(3) = 0.09$

There is a 9% probability that a drought lasts exactly 3 intervals.

At most 3 intervals?

This is $P = f(0) + f(1) + f(2) + f(3)$

$f(x) = (1-p)^{x}p$

$f(0) = (1-0.383)^{0}*(0.383) = 0.383$

$f(1) = (1-0.383)^{1}*(0.383) = 0.236$

$f(2) = (1-0.383)^{2}*(0.383) = 0.146$

Previously in this exercise, we found that $f(3) = 0.09$

$P = f(0) + f(1) + f(2) + f(3) = 0.383 + 0.236 + 0.146 + 0.09 = 0.855$

There is an 85.5% probability that a drought lasts at most 3 intervals.

(b) What is the probability that the length of a drought exceeds its mean value by at least one standard deviation?

This is $P(X \geq \mu+\sigma) = P(X \geq 1.61 + 2.05) = P(X \geq 3.66) = P(X \geq 4)$ .

We are working with discrete data, so 3.66 is rounded up to 4.

Either a drought lasts at least four months, or it lasts at most thee. In a), we found that the probability that it lasts at most 3 months is 0.855. The sum of these probabilities is decimal 1. So:

$P(X \leq 3) + P(X \geq 4) = 1$

$0.855 + P(X \geq 4) = 1$

$P(X \geq 4) = 0.145$

There is a 14.5% probability that the length of a drought exceeds its mean value by at least one standard deviation

8 0

3 years ago

What is the equation of the line shown in this graph? <br><br> The points are (-2, 2) and (-2, -3)

KengaRu [80]

$\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-3-2}{-2-(-2)}\implies \cfrac{-3-2}{-2+2}\implies \stackrel{und efined}{\cfrac{-5}{0}}$

so our slope is undefined, that means a vertical line, check the picture below

5 0

3 years ago

After selecting 180 of its employees to from a new division, a company discovers that engineers outnumber analysts by a 3:1 rati

nikdorinn [45]

Answer:

I think its 90

Step-by-step explanation:

3x plus 1x is 4x divide 180 but 4 and get 45 so that meab there are 135 and 45

you need 90 more analysts to have a 1 to 1 ratio

3 0

3 years ago