Check the picture below.
so the volume will simply be the area of the hexagonal face times the height.
![\textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\stackrel{\qquad degrees}{\cot\left( \frac{180}{n} \right)}~~ \begin{cases} n=\stackrel{number~of}{sides}\\ s=\stackrel{length~of}{side}\\[-0.5em] \hrulefill\\ n=6\\ s=12 \end{cases}\implies A=\cfrac{1}{4}(6)(12)^2\cot\left( \frac{180}{6} \right) \\\\\\ A=216\cot(30^o)\implies A=216\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the hexagon}}{(216\sqrt{3})}~~\stackrel{height}{(10)}\implies 2160\sqrt{3}~~\approx ~~3741.2~cm^3](https://tex.z-dn.net/?f=%5Ctextit%7Barea%20of%20a%20regular%20polygon%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7B1%7D%7B4%7Dns%5E2%5Cstackrel%7B%5Cqquad%20degrees%7D%7B%5Ccot%5Cleft%28%20%5Cfrac%7B180%7D%7Bn%7D%20%5Cright%29%7D~~%20%5Cbegin%7Bcases%7D%20n%3D%5Cstackrel%7Bnumber~of%7D%7Bsides%7D%5C%5C%20s%3D%5Cstackrel%7Blength~of%7D%7Bside%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20n%3D6%5C%5C%20s%3D12%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Ccfrac%7B1%7D%7B4%7D%286%29%2812%29%5E2%5Ccot%5Cleft%28%20%5Cfrac%7B180%7D%7B6%7D%20%5Cright%29%20%5C%5C%5C%5C%5C%5C%20A%3D216%5Ccot%2830%5Eo%29%5Cimplies%20A%3D216%5Csqrt%7B3%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20the%20hexagon%7D%7D%7B%28216%5Csqrt%7B3%7D%29%7D~~%5Cstackrel%7Bheight%7D%7B%2810%29%7D%5Cimplies%202160%5Csqrt%7B3%7D~~%5Capprox%20~~3741.2~cm%5E3)
Answer:
False solution; [1⅐, -3 3⁄7]
Step-by-step explanation:
{x - 2y = 8
{4x - y = 8
-¼[4x - y = 8]
{x - 2y = 8
{-x + ¼y = -2 >> New Equation
____________
-1¾y = 6
y = -3 3⁄7 [Plug this back into both equations to get the x-coordinate of 1⅐]; 1⅐ = x
I am joyous to assist you anytime.
Answer:
The mean reflects the best measure of the center
Step-by-step explanation:
12, 13, 13, 14, 21, 22, 23
Median: 14
Mean: 16.86
The mean reflects the best measure of the center
Answer:
B.
Step-by-step explanation:
f(x - c) shift the function <em>c</em> units to the right.
In this case, if (x - 1) was substituted in place of the x, the graph would shift 1 unit to the right.
If you want to graph the new function and know the graph of the previous one, this relationship avoids you the substitution of (x - 1) into the function and expansion of the expression to obtain a new quadratic formula.
Answer:
A. 30 : 54
Step-by-step explanation:
If you divide 30 by 6 and 54 by 6, you'll get a ratio of 5 : 9, which is the same ratio shown in the problem
Hope this helps :)
