Explanation:
First, we need to find the values of the sine and cosine of x knowing the value of tan x and x being in the 3rd quadrant. Since tan x = 5/12, using Pythagorean theorem, we know that
Note that both sine and cosine are negative because x is in the 3rd quadrant.
Recall the addition identities listed below:
Therefore, the expression reduces to
It would be y=x+3 because you have a slope of 1 and a y-intercept at 3
Answer:
Step-by-step explanation:
![CI=\left[\begin{array}{ccc}1&6&0\\0&1&2\\1&-1&3\end{array}\right] \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]](https://tex.z-dn.net/?f=CI%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%266%260%5C%5C0%261%262%5C%5C1%26-1%263%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C0%261%260%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D)
Subtract row 3 from row 1:
![\left[\begin{array}{ccc}1&6&0\\0&1&2\\0&7&-3\end{array}\right] \left[\begin{array}{ccc}1&0&0\\0&1&0\\1&0&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%266%260%5C%5C0%261%262%5C%5C0%267%26-3%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C0%261%260%5C%5C1%260%26-1%5Cend%7Barray%7D%5Cright%5D)
Subtract row 3 from 7 times row 2:
![\left[\begin{array}{ccc}1&6&0\\0&1&2\\0&0&17\end{array}\right] \left[\begin{array}{ccc}1&0&0\\0&1&0\\-1&7&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%266%260%5C%5C0%261%262%5C%5C0%260%2617%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C0%261%260%5C%5C-1%267%261%5Cend%7Barray%7D%5Cright%5D)
Divide row 3 by 17:
![\left[\begin{array}{ccc}1&6&0\\0&1&2\\0&0&1\end{array}\right] \left[\begin{array}{ccc}1&0&0\\0&1&0\\\frac{-1}{17} &\frac{7}{17} &\frac{1}{17} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%266%260%5C%5C0%261%262%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C0%261%260%5C%5C%5Cfrac%7B-1%7D%7B17%7D%20%26%5Cfrac%7B7%7D%7B17%7D%20%26%5Cfrac%7B1%7D%7B17%7D%20%5Cend%7Barray%7D%5Cright%5D)
Subtract 2 of row 3 from row 2:
![\left[\begin{array}{ccc}1&6&0\\0&1&0\\0&0&1\end{array}\right] \left[\begin{array}{ccc}1&0&0\\\frac{2}{17} &\frac{3}{17} &\frac{-2}{17} \\\frac{-1}{17} &\frac{7}{17} &\frac{1}{17} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%266%260%5C%5C0%261%260%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C%5Cfrac%7B2%7D%7B17%7D%20%26%5Cfrac%7B3%7D%7B17%7D%20%26%5Cfrac%7B-2%7D%7B17%7D%20%5C%5C%5Cfrac%7B-1%7D%7B17%7D%20%26%5Cfrac%7B7%7D%7B17%7D%20%26%5Cfrac%7B1%7D%7B17%7D%20%5Cend%7Barray%7D%5Cright%5D)
Subtract 6 of row 2 from row 1:
![\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right] \left[\begin{array}{ccc}\frac{5}{17}&\frac{-18}{17}&\frac{12}{17}\\\frac{2}{17} &\frac{3}{17} &\frac{-2}{17} \\\frac{-1}{17} &\frac{7}{17} &\frac{1}{17} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C0%261%260%5C%5C0%260%261%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B5%7D%7B17%7D%26%5Cfrac%7B-18%7D%7B17%7D%26%5Cfrac%7B12%7D%7B17%7D%5C%5C%5Cfrac%7B2%7D%7B17%7D%20%26%5Cfrac%7B3%7D%7B17%7D%20%26%5Cfrac%7B-2%7D%7B17%7D%20%5C%5C%5Cfrac%7B-1%7D%7B17%7D%20%26%5Cfrac%7B7%7D%7B17%7D%20%26%5Cfrac%7B1%7D%7B17%7D%20%5Cend%7Barray%7D%5Cright%5D)
![C^{-1}=\frac{1}{17} \left[\begin{array}{ccc}5&-18&12\\2&3&-2\\-1&7&1\end{array}\right]](https://tex.z-dn.net/?f=C%5E%7B-1%7D%3D%5Cfrac%7B1%7D%7B17%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-18%2612%5C%5C2%263%26-2%5C%5C-1%267%261%5Cend%7Barray%7D%5Cright%5D)
![C^{-1}b=\frac{1}{17} \left[\begin{array}{ccc}5&-18&12\\2&3&-2\\-1&7&1\end{array}\right]\left[\begin{array}{c}10&1&3\end{array}\right]=\left[\begin{array}{c}4&1&0\end{array}\right]](https://tex.z-dn.net/?f=C%5E%7B-1%7Db%3D%5Cfrac%7B1%7D%7B17%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-18%2612%5C%5C2%263%26-2%5C%5C-1%267%261%5Cend%7Barray%7D%5Cright%5D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D10%261%263%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D4%261%260%5Cend%7Barray%7D%5Cright%5D)
Answer:
Minimum hour = 177 hour
Step-by-step explanation:
Given:
Paddle boats rent = $8
Paddles rent = $5 Per 24 hours
Total amount = $45
Find:
Number of hour David rent paddle boat
Computation:
8 + (5/24)n = 45
(5/24)n = 37
n = 177.6 hour
Minimum hour = 177 hour
