Answer:
I dont get it
Step-by-step explanation:
Cory gains 3 cars a year and Roger 1.
Cory - 18 (6 x 3) : Roger - 6 (6 x 1)
I Cory was to stop receiving cars for 3 years, while Roger kept getting them for 3 then they would have the same amount.
Answer: -66.67%, but if the answer is supposed to positive then the answer is 66.67%.
<em>* Hopefully this helps:) </em>
Answer:
S is not the subspace of ![R^2](https://tex.z-dn.net/?f=R%5E2)
Step-by-step explanation:
Let us suppose two vectors u and v belong to the S such that the property of xy≥0 is verified than
![v=\left[\begin{array}{c}0 \\1\end{array}\right]](https://tex.z-dn.net/?f=v%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%20%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
Both the vectors satisfy the given condition as follows and belong to the S
![x_u y_u=-1\times 0=0 \geq 0\\x_v y_v=1\times 0=0 \geq 0\\](https://tex.z-dn.net/?f=x_u%20y_u%3D-1%5Ctimes%200%3D0%20%5Cgeq%200%5C%5Cx_v%20y_v%3D1%5Ctimes%200%3D0%20%5Cgeq%200%5C%5C)
Now S will be termed as subspace of R2 if
- u+v also satisfy the condition
- ku also satisfy the condition
Taking u+v
![u+v=\left[\begin{array}{c}-1 \\0\end{array}\right]+\left[\begin{array}{c}0 \\1\end{array}\right]\\u+v=\left[\begin{array}{c}-1+0 \\0+1\end{array}\right]\\u+v=\left[\begin{array}{c}-1 \\1\end{array}\right]](https://tex.z-dn.net/?f=u%2Bv%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-1%20%5C%5C0%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%20%5C%5C1%5Cend%7Barray%7D%5Cright%5D%5C%5Cu%2Bv%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-1%2B0%20%5C%5C0%2B1%5Cend%7Barray%7D%5Cright%5D%5C%5Cu%2Bv%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-1%20%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
Now the condition is tested as
![\\x_{u+v} y_{u+v}=-1\times 1=-1](https://tex.z-dn.net/?f=%5C%5Cx_%7Bu%2Bv%7D%20y_%7Bu%2Bv%7D%3D-1%5Ctimes%201%3D-1%20%3C0%5C%5C)
This indicates that the condition is not satisfied so S is not the subspace of ![R^2](https://tex.z-dn.net/?f=R%5E2)
The sine ratio is basically a fraction of the opposite side over the hypotenuse. Since the hypotenuse is always the longest side, this means the fraction cannot exceed 1. If it did,then that would lead to the opposite side being larger than the hypotenuse but again the hypotenuse is the longest side. The largest the sine ratio can get is 1.