Answer:
![PQ = 8.83](https://tex.z-dn.net/?f=PQ%20%3D%208.83)
Step-by-step explanation:
Given
![P = (8,1,4)](https://tex.z-dn.net/?f=P%20%3D%20%288%2C1%2C4%29)
![Q = (3,8,6)](https://tex.z-dn.net/?f=Q%20%3D%20%283%2C8%2C6%29)
Required
Determine distance PQ
This is calculated as:
![PQ = \sqrt{(x_2- x_1)^2+(y_2- y_1)^2+(z_2- z_1)^2}](https://tex.z-dn.net/?f=PQ%20%3D%20%5Csqrt%7B%28x_2-%20x_1%29%5E2%2B%28y_2-%20y_1%29%5E2%2B%28z_2-%20z_1%29%5E2%7D)
Where
![(x_1,y_1,z_1) = (8,1,4)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%2Cz_1%29%20%3D%20%288%2C1%2C4%29)
and
![(x_2,y_2,z_2) = (3,8,6)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%2Cz_2%29%20%3D%20%283%2C8%2C6%29)
So, we have:
![PQ = \sqrt{(3- 8)^2+(8- 1)^2+(6- 4)^2}](https://tex.z-dn.net/?f=PQ%20%3D%20%5Csqrt%7B%283-%208%29%5E2%2B%288-%201%29%5E2%2B%286-%204%29%5E2%7D)
![PQ = \sqrt{-5^2+7^2+2^2}](https://tex.z-dn.net/?f=PQ%20%3D%20%5Csqrt%7B-5%5E2%2B7%5E2%2B2%5E2%7D)
![PQ = \sqrt{25+49+4}](https://tex.z-dn.net/?f=PQ%20%3D%20%5Csqrt%7B25%2B49%2B4%7D)
![PQ = \sqrt{78}](https://tex.z-dn.net/?f=PQ%20%3D%20%5Csqrt%7B78%7D)
![PQ = 8.83](https://tex.z-dn.net/?f=PQ%20%3D%208.83)
we know the perimeter is 24, and is an equilateral triangle, so it has three equal sides, so each side is 24 ÷ 3 = 8.
![\bf \textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4}~~ \begin{cases} s=side's\\ \qquad length\\ \cline{1-1} s = 8 \end{cases}\implies A=\cfrac{8^2\sqrt{3}}{4}\\\\\\ A=16\sqrt{3}\implies A\approx 24.71](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20an%20equilateral%20triangle%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7Bs%5E2%5Csqrt%7B3%7D%7D%7B4%7D~~%20%5Cbegin%7Bcases%7D%20s%3Dside%27s%5C%5C%20%5Cqquad%20length%5C%5C%20%5Ccline%7B1-1%7D%20s%20%3D%208%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Ccfrac%7B8%5E2%5Csqrt%7B3%7D%7D%7B4%7D%5C%5C%5C%5C%5C%5C%20A%3D16%5Csqrt%7B3%7D%5Cimplies%20A%5Capprox%2024.71)
Answer:
Step-by-step explanation:
circumference=2πr
=2*3.14*2
=12.56 km
Each pave stone is 0.15. You can put 44 into 66 1 time. Then you get 22 then put a decimal point after 66 and after the decimal point put a zero. Then bring the 0 down to 22 and that makes 220. 44 x 5 is 220. Subtract 220 from 220 and there’s the answer.