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3 years ago

The circumference of a circular garden is approximately 30 feet. What is the approximate area inside the circular garden?

Mathematics

1 answer:

kakasveta [241]3 years ago

5 0

Answer:

$\frac{225}{\pi }$ or 71.6197

Step-by-step explanation:

This just manipulating formulas.

The formula for the circumference of a circle is $2\pi r$ , and we know this is equal to 30. That means $\pi r=15$ . The formula for the area of a circle is $\pi r^2$ , so we know the area of the circle must be $15r$ ( $\pi r*r$ , and we found $\pi r$ to be 15 earlier).

Now, using this information, let's find r in terms of $\pi$ .

$\pi r=15$

$r=\frac{15}{\pi }$

Now let's plug in r to the expression we found for area.

$15(\frac{15}{\pi } )$

$\frac{225}{\pi }$

The area of the circle is approximately $\frac{225}{\pi }$ or 71.6197.

Edit- Apparently there is a formula for this:

$\frac{c^{2} }{4\pi }$ where $c$ is the circumference of the circle.

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Step-by-step explanation:

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3 years ago

The sum of three numbers is 26. Twice the first minus the second is the third less 2. The third is the second minus 3 times the

Agata [3.3K]

Let a, b, c represent the three numbers. The problem statement gives rise to three equations:

a +b +c = 26
2a -b = c -2
-3a +b = c

Adding the first two equations gives

... (a +b +c) +(2a -b) = (26) +(c -2)

... 3a +c = 24 +c . . . . . simplify

... 3a = 24 . . . . . . . . . . subtract c

... a = 8 . . . . . . . . . . . . divide by 3

Adding the second and third equations gives ...

... (2a -b) +(-3a +b) = (c -2) +(c)

... -a = 2c -2 . . . . simplify

... -6 = 2c . . . . . . add 2, substitute for a

... -3 = c . . . . . . . . divide by 2

Using the third equation we can find b.

... -3·8 +b = -3 . . . . substitute for a and c

... b = 21 . . . . . . . . .add 24

The numbers are 8, 21, -3.

_____

The method above is sort of "ad hoc", taking advantage of the numbers in this particular set of equations. You can use more formal methods of Gaussian elimination or Cramer's Rule to solve these by just following a procedure. Or, your graphing calculator can do it for you.

6 0

3 years ago

Which of the following is a polynomial?

Zanzabum

Answer:

I'm pretty sure A is the correct answer :)

(x-2)(x^4+3) is a polynomial

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3 years ago

You recently took a statistics exam in a large class. The instructor tells the class that the scores were Normally distributed,

Lunna [17]

Answer:

b. the area to the right of 2

Step-by-step explanation:

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, which is also the area to the left of Z. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X, which is the area to the right of Z.

In this problem:

$X = 96, \mu = 72, \sigma = 12$