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3 years ago

Explain how the pythagorean theorem is used to derive the equation of a circle

1 answer:

4 0

Its a bit tricky to explain without a diagram bot if we take a point (a, b) on the coordinate plane as the center of the circle and another point (x,y) on the circumference then the distance between (a,b) and (x,y) is the radius of the circle.

Now create a triangle by drawing a line horizontally from (a,b) to the circumference and another line prerpendicular to this line from the point (x,y) to make a right angled triangl.e

Applying the pythagoras theorem to this triangle gives

(x - a)^2 + (y - b)^2 = r^2 which is the standard form of equation of a circle.

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Jack’s bill at a restaurant came to $52.31. He wants to leave a 15% tip. How much will the new total be, including tip?

blondinia [14]

52.31*1.15=60.1565

round it to the nearest penny and you will get $60.16

4 0

4 years ago

Taylor purchased 9 pints of ice cream for a party. If each guest will be served exactly 1 2 2 1 pint of ice cream, how many gu

Neporo4naja [7]

Complete question :

Carly purchased 9 1/2 pints of ice cream for a party. If each guest will be served exactly 3/5 pint of ice cream, what is the greatest number of gusts that Carly can serve

Answer:

15 guests

Step-by-step explanation:

Given that:

Total pints of icecream = 9 1/2

Fraction of ice cream pints per guest = 3/5 pints

Number of guest that can be served :

Total pints / fraction per guest

9 1/2 ÷ 3/5

19/2 * 5/3

95 / 6

= 15.8 guest

Hence, greatest Number of guest that can be served = 15

8 0

3 years ago

5 13/20 as a decimal

aniked [119]

5 13/20

turns into 113/20

answer: 5.65

4 0

3 years ago

Read 2 more answers

Figure ABCD is a parallelogram, if point C lies on the line x = -1, what is the y value of point c?

brilliants [131]

Answer:

y = 0

Step-by-step explanation:

A parallelogram is a quadrilateral with opposite sides parallel. Then segment CD must be parallel to AB, and CB must be parallel to DA. Two different segments are parallel if they have the same slope.

slope of DA = (yA - yD)/(xA - xD) = (4 - 2)/(1 - (-1)) = 1

slope of CB = (yB - yC)/(xB - xC) = (2 - yC)/(1 - (-1)) = 1

(2 - yC) = 2 * 1

2 - 2 = yC

0 = yC

Note: coordinates of A are (xA, yA), of B are (xB, yB), of C are (xC, yC) and of D are (xD, yD)

6 0

3 years ago

(1 point) The cost of unleaded gasoline once followed an unknown distribution with a mean of $4.59 and a standard deviation of $

marin [14]

Answer:

a) unknown

b) 1.43% probability that the average price for 30 gas stations is less than $4.55.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 4.59, \sigma = 0.1$

a) What's the approximate probability that the average price for 16 gas stations is over $4.69?

Sample size less than 30 and unknow distribution. Therefore, the central limit theorem cannot be applied and the answer is unknown.

b) Find the probability that the average price for 30 gas stations is less than $4.55.

Now $n = 30, s = \frac{0.1}{\sqrt{30}} = 0.0183$

This probability is the pvalue of Z when X = 4.55. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{4.55 - 4.59}{0.0183}$

$Z = -2.19$

$Z = -2.19$ has a pvalue of 0.0143

1.43% probability that the average price for 30 gas stations is less than $4.55.

5 0

4 years ago