Answer: the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.
Answer: ![3+\sqrt{2}](https://tex.z-dn.net/?f=3%2B%5Csqrt%7B2%7D)
Step-by-step explanation:
Given the following expression shown in the picture:
![\frac{7}{3-\sqrt{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B3-%5Csqrt%7B2%7D%20%7D)
You need to use a process called "Ratinalization".
By definition, using Rationalization you can rewrite the expression in its simplest form so there is not Radicals in its denominator.
Then, in order to simplify the expression, you can follow the following steps:
<em>Step 1</em>. You need to multiply the numerator and the denominator of the fraction by
, which is the conjugate of the denominator
.
<em>Step 2</em>. Then you must apply the Distributive property in the numerator.
<em>Step 3</em>. You must apply the following property in the denominator:
Therefore, applying the procedure shown above, you get:
![=\frac{(7)(3+\sqrt{2})}{(3-\sqrt{2})(3+\sqrt{2})}=\frac{21+7\sqrt{2}}{3^2-(\sqrt{2})^2}=\frac{21+7\sqrt{2}}{9-2}=\frac{21+7\sqrt{2}}{7}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%287%29%283%2B%5Csqrt%7B2%7D%29%7D%7B%283-%5Csqrt%7B2%7D%29%283%2B%5Csqrt%7B2%7D%29%7D%3D%5Cfrac%7B21%2B7%5Csqrt%7B2%7D%7D%7B3%5E2-%28%5Csqrt%7B2%7D%29%5E2%7D%3D%5Cfrac%7B21%2B7%5Csqrt%7B2%7D%7D%7B9-2%7D%3D%5Cfrac%7B21%2B7%5Csqrt%7B2%7D%7D%7B7%7D)
<em>Step 4</em>. You can observe that the expression can be simplified even more. Since:
![\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%2Bb%7D%7Bc%7D%3D%5Cfrac%7Ba%7D%7Bc%7D%2B%5Cfrac%7Bb%7D%7Bc%7D)
You get:
![\frac{21+7\sqrt{2}}{7}=\frac{21}{7}+\frac{7\sqrt{2}}{7}=3+\sqrt{2}](https://tex.z-dn.net/?f=%5Cfrac%7B21%2B7%5Csqrt%7B2%7D%7D%7B7%7D%3D%5Cfrac%7B21%7D%7B7%7D%2B%5Cfrac%7B7%5Csqrt%7B2%7D%7D%7B7%7D%3D3%2B%5Csqrt%7B2%7D)
Answer:
im not sure how the data should be interpreted but here is the distribution. It goes up by .416
Step-by-step explanation:
the average of the first 8 games is 24
the average of the 12 games is 24.416
Answer:
15 ft.
Step-by-step explanation:
The tepee is a cone and its volume
= 1/3 pi r^2 h where r = radius and h = height.
The radius r = 1/2 * 10 = 5 ft.
So we have the equation:
393 = 1/3*3.14* 5^2 * h
h = 393 / (1/3*3.14*25)
= 15.02 ft.
The probability would be
![\frac{159}{1000}](https://tex.z-dn.net/?f=%20%5Cfrac%7B159%7D%7B1000%7D%20)
,
Simplify and turn into ratio.
0.159 : 1.
I am unsure what the full question was though.
Hope this helps.