Answer:
Step-by-step explanation:
25.12 inches around means diameter. So radius = 12.56 inches
volume ![= \pi r^2 \times h =\pi \times 12.56^2 \times 66 = 32709.44 \ in^3](https://tex.z-dn.net/?f=%3D%20%5Cpi%20r%5E2%20%5Ctimes%20h%20%3D%5Cpi%20%5Ctimes%2012.56%5E2%20%5Ctimes%2066%20%3D%2032709.44%20%5C%20in%5E3)
Answer:
False
Step-by-step explanation:
They are two different points. A way to check it is changing to cartesian coordinates, the formula to change from polar to cartesian is:
![x = rcos(\theta)\\y = rsin(\theta)](https://tex.z-dn.net/?f=x%20%3D%20rcos%28%5Ctheta%29%5C%5Cy%20%3D%20rsin%28%5Ctheta%29)
For the point ![(-4, \pi)](https://tex.z-dn.net/?f=%28-4%2C%20%5Cpi%29)
![x_1=-4cos(\pi)=4\\y_1=-4sin(\pi)=0](https://tex.z-dn.net/?f=x_1%3D-4cos%28%5Cpi%29%3D4%5C%5Cy_1%3D-4sin%28%5Cpi%29%3D0)
For the point ![(4,-\pi)](https://tex.z-dn.net/?f=%284%2C-%5Cpi%29)
![x_2=4cos(-\pi)=-4\\y_2=4sin(-\pi)=0](https://tex.z-dn.net/?f=x_2%3D4cos%28-%5Cpi%29%3D-4%5C%5Cy_2%3D4sin%28-%5Cpi%29%3D0)
![(4,0)\neq (-4,0)](https://tex.z-dn.net/?f=%284%2C0%29%5Cneq%20%28-4%2C0%29)
Answer:B.) 1.74%
Step-by-step explanation:
Answer:
Step-by-step explanation:
In order to find the value of y, first we need to find the length of the perpendicular dropped from one of the vertices of the triangle to its opposite side.
By geometric mean theorem:
Length of the perpendicular
Next, by Pythagoras theorem:
![{y}^{2} = {9}^{2} + {( \sqrt{27} )}^{2} \\ \\ {y}^{2} = 81 + 27 \\ \\ {y}^{2} = 108 \\ \\ y = \sqrt{108} \\ \\ y = \sqrt{36 \times 3} \\ \\ y = \sqrt{ {6}^{2} \times 3} \\ \\ y = 6 \sqrt{3} \: units](https://tex.z-dn.net/?f=%20%7By%7D%5E%7B2%7D%20%20%3D%20%20%7B9%7D%5E%7B2%7D%20%20%2B%20%20%7B%28%20%5Csqrt%7B27%7D%20%29%7D%5E%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%20%7By%7D%5E%7B2%7D%20%20%3D%2081%20%2B%2027%20%5C%5C%20%20%5C%5C%20%20%7By%7D%5E%7B2%7D%20%20%3D%20108%20%5C%5C%20%20%5C%5C%20y%20%3D%20%20%5Csqrt%7B108%7D%20%20%5C%5C%20%20%5C%5C%20y%20%3D%20%20%5Csqrt%7B36%20%5Ctimes%203%7D%20%20%5C%5C%20%20%5C%5C%20y%20%3D%20%20%5Csqrt%7B%20%7B6%7D%5E%7B2%7D%20%20%5Ctimes%203%7D%20%20%5C%5C%20%20%5C%5C%20y%20%3D%206%20%5Csqrt%7B3%7D%20%20%5C%3A%20units)
For this case we have the following vector:
u = (1, -3)
When multiplying by the scalar 1/3 we have:
1 / 3u = (1/3) (1, -3)
Rewriting the new vector we have:
1 / 3u = (1/3, -3/3)
1 / 3u = (1/3, -1)
Answer:
1 / 3u = (1/3, -1)