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Equilateral triangle radius of circumcircle = \(\frac{s}{\sqrt{3}}\)

Which means \(r = 3\sqrt{3}\)

Area of a circle is Pi*r^2

Substitute to get \(\Pi ({3\sqrt{3})}^2\)

Which is equal to \(27\Pi\)

The area of the circumcircle is \(27\Pi -units^2\)

Look again at your second and third lines of "proof":  

\((2^{\sqrt2})^2 \ne 2^2\\ \text{ }\\ (2^{\sqrt2})^2 = 2^{2\sqrt2}\)

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Perhaps this graph will help:

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"If  \(log_a b=c\)  then a=?"

\(log_ab=c\Rightarrow a^c=b\Rightarrow a=b^{1/c}\)

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This is the given info:

\(g(x)=\frac{1}{4}x+\frac{3}{4}\)

\(g(x)=-\frac{3}{2}\)

thankith

the number of degrees spanned by a slice decreases at a constant rate

At 12 degrees per slice.

What is the degree measure of the fifth slice Larry eats?

42 degrees.

In triangle ABC, M and N are the midpoints of BC and AC, respectively. The perpendicular bisectors of BC and AC intersect at a point O inside the triangle. If angle C = \(\gamma \) = 47 degrees, then find the measure of angle MON = \(\omega\), in degrees. 

Hello bbelt711

The angular sum in each quadrangle is 360 °.
The angular sum in the square ONCM is 360 °.

Then is

\( \omega= 360°-2\times 90°-\gamma\\ \omega= 360°-2\times 90°-47°\\ \\ {\color{blue} \omega =133°}\)

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\(A = \frac{(b \times h)}{2}\)

\(\frac{5}{6} \times -2\)

\(\frac{5}{6} = 0.8\bar{3}\)

\(-x = x \times -1\)

\(0.8\bar{3} \times 2 = 1.\bar{6}\)

\(1.\bar{6} \times -1 = -1.\bar{6}\)

I agree, here, that the language is ambiguous, but you can specify, in words, which interpretation you want.

Generally, if you want to indicate parentheses, you will use the term "quantity of..."

\(\sqrt{-1}=i\)

\(i \times i = \sqrt{-1} \times \sqrt{-1} = {\sqrt{-1}}^{2} = -1\)

yes.

I use PEMDAS the most

Left to right:
\((1 + 5)\times10 = 60\)

PEMDAS/BODMAS:

\(1+(5\times10)=51\)

The average between the two results:

\(\frac{60+51}{2}=55.5\)

What I thought too.

It is already an improper fraction, but i'll help anyway.

How many times does 14 fit into 5 without going over?

5 10 15

2 times.

We have a leftover of 4/5.

\(2\frac{4}{5}\)is the answer.

Two ways of doing it;

(pi*7)^2 = 483.6106156533785723

pi*(7^2) = 153.9380400258998687

Please specify parentheses.

\(\pi*7^2=49\pi\approx153.93804003\)

In 12 days, Matthew will go hiking and swimming on the same day based on his current schedule.

This problem requires one to find the lowest common multiple of 2 numbers; in other words, \(lcm(6,12)=?\)

This one might be more obvious than other problems because 12 is a multiple of 6, and 12 is, of course, a multiple of itself. Therefore, \(lcm(6,12)=12\)

The result of \(lcm(6,12)\) is the fewest number of days until Matthew does both kinds of excerises again.

First, we calculate how many WITH repeating digits.

There are 90.

And then, we simply subtract how many repeating numbers are there. 9 numbers, 11, 22, 33, 44, 55, 66, 77, 88, 99.

90 - 9 = 81.

As follows:

\(y=x^3\quad \frac{dy}{dx}=3x^2\\x=y^{1/3}\quad \frac{dx}{dy}=\frac{1}{3}y^{-2/3}\rightarrow \frac{1}{3y^{2/3}} \rightarrow \frac{1}{3(y^{1/3})^2}\rightarrow \frac{1}{3x^2}\)

Now you should be able to see that dy/dx*dx/dy = 1

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Like so:

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https://web2.0calc.com

Assuming 1GB = 1000MB then possible storage = 8000/3.5 ≈ 2285.7 songs.  However, storage for complete songs is just 2285, which requires 2285*3.5 = 7997.5 MB

So domain (number of songs):  0 to 2285

Range (memory): 0 to 7997.5 MB

(NB memory = 3.5*nbr of songs)