Answer:
40
Step-by-step explanation:
Answer:
5400 mi²
Step-by-step explanation:
The area is half the absolute value of the sum of the determinants of the points taken pairwise in some consistent order around the polygon. For a triangle, this sum of determinants can also be written as the determinant of a 3×3 matrix of the coordinates with the third column being 1.
... Area = (1/2)|D|
where D = ...
![\left|\begin{array}{ccc}0&-1&1\\-3&-9&1\\3&-2&1\end{array}\right|=\left|\begin{array}{cc}0&-1\\-3&-9\end{array}\right|+\left|\begin{array}{cc}-3&-9\\3&-2\end{array}\right|+\left|\begin{array}{cc}3&-2\\0&-1\end{array}\right|\\\\=-3+33-3=27](https://tex.z-dn.net/?f=%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D0%26-1%261%5C%5C-3%26-9%261%5C%5C3%26-2%261%5Cend%7Barray%7D%5Cright%7C%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D0%26-1%5C%5C-3%26-9%5Cend%7Barray%7D%5Cright%7C%2B%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D-3%26-9%5C%5C3%26-2%5Cend%7Barray%7D%5Cright%7C%2B%5Cleft%7C%5Cbegin%7Barray%7D%7Bcc%7D3%26-2%5C%5C0%26-1%5Cend%7Barray%7D%5Cright%7C%5C%5C%5C%5C%3D-3%2B33-3%3D27)
Then the area is (in grid squares) ...
... Area = (1/2)|27| = 13.5 . . . . grid squares
Each grid square is (20 mi)² = 400 mi², so 13.5 grid squares is ...
... 13.5 × 400 mi² = 5400 mi²
Virgil has 1/6 of the original cake, which he wants to divide into 4 parts. Thus:
1/6 / 4
= 1/6 x 1/4
= 1/24
Each person will receive 1/24 of the original cake.
5(0)-4(0)^2+3
Answer:
=3
Best of wishes and good luck!!
Answer:
2308.39 m³
Step-by-step explanation:
The formula of volume of sphere
![= \frac{4}{3} \pi {r}^{3}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%7Br%7D%5E%7B3%7D%20)
The volume of the sphere
![= \frac{4}{3} \times 3.14 \times {(16.4 \div 2)}^{3}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20%20%5Ctimes%203.14%20%5Ctimes%20%20%7B%2816.4%20%5Cdiv%202%29%7D%5E%7B3%7D%20)
![= \frac{4}{3} \times 3.14 \times {8.2}^{3}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B4%7D%7B3%7D%20%20%5Ctimes%203.14%20%5Ctimes%20%20%7B8.2%7D%5E%7B3%7D%20)
![= \frac{6925.18208}{3}](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B6925.18208%7D%7B3%7D%20)
![= 2308.394027...](https://tex.z-dn.net/?f=%20%3D%202308.394027...)
= 2308.39 m³ (rounded to the nearest hundredth)