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miskamm [114]
3 years ago
8

What does this mean I don’t quite get it.

Mathematics
1 answer:
vampirchik [111]3 years ago
4 0
The circumference of a circle is the length of the line making the circle.

To find circumference, the formula is

2\pi \times r
So, the answer to this problem would be 31.42
You might be interested in
Please give me the answers to all three I will mark u brilliant
elixir [45]

Answer:

First know the formula for the area of a circle;

<h2>A = πr^{2}</h2>

Where 'π' represents pi(3.14 or 22/7), and 'r' stands for the radius being squared.

For the first problem, we can see that 12 is our <u>diameter</u>.

And to find the radius, we need to find 1/2 of the diameter (half of the diameter), so;

D/2 = R

Replace with actual values;

12/2 = 6, <u>6</u> is our <u>radius</u>.

Now we plug this into our formula:

A = πr^{2}

A = 3.14(6^2)

A = 3.14(36)

A = <u>113.04 centimetres</u> is the area of the circle.

For the second problem, we can see that 18 is our <u>diameter</u>.

And to convert the diameter into the radius, we do what we did to the past problem, find 1/2 of the diameter.

So;

D/2 = R

18/2 = 9, <u>9</u> is our <u>radius</u>.

Now we plug this into our formula:

A = πr^{2}

A = 3.14(9^2)

A = 3.14(81)

A = <u>254.34 inches</u> is the area for this circle.

For the third problem, we can see that our radius is already given, 5.

So now we just simply and easily plug this into our formula;

A = πr^{2}

A = 3.14(5^2)

A = 3.14(25)

A = <u>78.5 meters</u> is the area for this circle.

4 0
1 year ago
Find the exact value of the expression.<br> tan( sin−1 (2/3)− cos−1(1/7))
Sonja [21]

Answer:

\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}

Step-by-step explanation:

I'm going to use the following identity to help with the difference inside the tangent function there:

\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}

Let a=\sin^{-1}(\frac{2}{3}).

With some restriction on a this means:

\sin(a)=\frac{2}{3}

We need to find \tan(a).

\sin^2(a)+\cos^2(a)=1 is a Pythagorean Identity I will use to find the cosine value and then I will use that the tangent function is the ratio of sine to cosine.

(\frac{2}{3})^2+\cos^2(a)=1

\frac{4}{9}+\cos^2(a)=1

Subtract 4/9 on both sides:

\cos^2(a)=\frac{5}{9}

Take the square root of both sides:

\cos(a)=\pm \sqrt{\frac{5}{9}}

\cos(a)=\pm \frac{\sqrt{5}}{3}

The cosine value is positive because a is a number between -\frac{\pi}{2} and \frac{\pi}{2} because that is the restriction on sine inverse.

So we have \cos(a)=\frac{\sqrt{5}}{3}.

This means that \tan(a)=\frac{\frac{2}{3}}{\frac{\sqrt{5}}{3}}.

Multiplying numerator and denominator by 3 gives us:

\tan(a)=\frac{2}{\sqrt{5}}

Rationalizing the denominator by multiplying top and bottom by square root of 5 gives us:

\tan(a)=\frac{2\sqrt{5}}{5}

Let's continue on to letting b=\cos^{-1}(\frac{1}{7}).

Let's go ahead and say what the restrictions on b are.

b is a number in between 0 and \pi.

So anyways b=\cos^{-1}(\frac{1}{7}) implies \cos(b)=\frac{1}{7}.

Let's use the Pythagorean Identity again I mentioned from before to find the sine value of b.

\cos^2(b)+\sin^2(b)=1

(\frac{1}{7})^2+\sin^2(b)=1

\frac{1}{49}+\sin^2(b)=1

Subtract 1/49 on both sides:

\sin^2(b)=\frac{48}{49}

Take the square root of both sides:

\sin(b)=\pm \sqrt{\frac{48}{49}

\sin(b)=\pm \frac{\sqrt{48}}{7}

\sin(b)=\pm \frac{\sqrt{16}\sqrt{3}}{7}

\sin(b)=\pm \frac{4\sqrt{3}}{7}

So since b is a number between 0 and \pi, then sine of this value is positive.

This implies:

\sin(b)=\frac{4\sqrt{3}}{7}

So \tan(b)=\frac{\sin(b)}{\cos(b)}=\frac{\frac{4\sqrt{3}}{7}}{\frac{1}{7}}.

Multiplying both top and bottom by 7 gives:

\frac{4\sqrt{3}}{1}= 4\sqrt{3}.

Let's put everything back into the first mentioned identity.

\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}

\tan(a-b)=\frac{\frac{2\sqrt{5}}{5}-4\sqrt{3}}{1+\frac{2\sqrt{5}}{5}\cdot 4\sqrt{3}}

Let's clear the mini-fractions by multiply top and bottom by the least common multiple of the denominators of these mini-fractions. That is, we are multiplying top and bottom by 5:

\tan(a-b)=\frac{2 \sqrt{5}-20\sqrt{3}}{5+2\sqrt{5}\cdot 4\sqrt{3}}

\tan(a-b)=\frac{2\sqrt{5}-20\sqrt{3}}{5+8\sqrt{15}}

4 0
3 years ago
An equilateral triangle has a perimeter of 51x + 3. What is the length of each side of the triangle?
Blababa [14]

First subtract 3 from 51 which gives you 48, then divide 48 by 3 which gives you the answer of 16.

3 0
3 years ago
Read 2 more answers
Need help finding D=___
lesya692 [45]
A straight line is 180 degrees and 144 is on a straight line. So, 180-144 which is 36. So, now we know 2 angles and the Degrees of a triangle is 180 degrees.
36+76+d= 180 D= 68
4 0
3 years ago
Okay it might be simple but can yall help and give me a real answer plz UwU
ad-work [718]

Answer:

6 cubic cm

Step-by-step explanation:

3 · 3 · 2 = 18

18 · 1/3 = 6

7 0
2 years ago
Read 2 more answers
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