We will have the following:
First, we write the both equations: the line and the circle:
![\begin{gathered} y=3x \\ \\ and \\ \\ x^2+y^2=4 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D3x%20%5C%5C%20%20%5C%5C%20and%20%5C%5C%20%20%5C%5C%20x%5E2%2By%5E2%3D4%20%5Cend%7Bgathered%7D)
This can be seeing as follows:
Now, we determine the point where the line intersects the circle in the first quadrant, so first, we determine the positive part of the circle, that is:
![\begin{gathered} x^2+y^2=4\Rightarrow y^2=-x^2+4 \\ \\ \Rightarrow y=\sqrt{-x^2+4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5E2%2By%5E2%3D4%5CRightarrow%20y%5E2%3D-x%5E2%2B4%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20y%3D%5Csqrt%7B-x%5E2%2B4%7D%20%5Cend%7Bgathered%7D)
Now, we equal this expression and the line:
![\begin{gathered} 3x=\sqrt{-x^2+4}\Rightarrow(3x)^2=(\sqrt{-x^2+4})^2 \\ \\ \Rightarrow9x^2=-x^2+4\Rightarrow10x^2-4=0 \\ \\ \Rightarrow5x^2=2\Rightarrow x^2=\frac{2}{5} \\ \\ \Rightarrow x=\pm\sqrt{\frac{2}{5}} \\ \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%203x%3D%5Csqrt%7B-x%5E2%2B4%7D%5CRightarrow%283x%29%5E2%3D%28%5Csqrt%7B-x%5E2%2B4%7D%29%5E2%20%5C%5C%20%20%5C%5C%20%5CRightarrow9x%5E2%3D-x%5E2%2B4%5CRightarrow10x%5E2-4%3D0%20%5C%5C%20%20%5C%5C%20%5CRightarrow5x%5E2%3D2%5CRightarrow%20x%5E2%3D%5Cfrac%7B2%7D%7B5%7D%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20x%3D%5Cpm%5Csqrt%7B%5Cfrac%7B2%7D%7B5%7D%7D%20%5C%5C%20%20%5Cend%7Bgathered%7D)
From this, we take the positive value, since it the only one that makes sense under the parameters required, now we find the value of y:
![y=3(\sqrt{\frac{2}{5}})\Rightarrow y=\frac{3\sqrt{10}}{5}](https://tex.z-dn.net/?f=y%3D3%28%5Csqrt%7B%5Cfrac%7B2%7D%7B5%7D%7D%29%5CRightarrow%20y%3D%5Cfrac%7B3%5Csqrt%7B10%7D%7D%7B5%7D)
So, the solution is at the point:
![(\sqrt{\frac{2}{5}}\frac{}{},\frac{3\sqrt{10}}{5})](https://tex.z-dn.net/?f=%28%5Csqrt%7B%5Cfrac%7B2%7D%7B5%7D%7D%5Cfrac%7B%7D%7B%7D%2C%5Cfrac%7B3%5Csqrt%7B10%7D%7D%7B5%7D%29)
This can be seeing as follows:
Answer:
0.9
Step-by-step explanation:
20/23 = 0.869565217, which rounded to the nearest tenth is 0.9
Answer:
Step-by-step explanation:
Let's look at this in this perspective. There are 60 minutes in 1 hour. What I would do first is get rid of the 39 minutes at the end of 8:39. Now you have 8:00. Count until you get to 7 AM. 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7. That's 11 hours from 8 PM to 7 AM. 60 x 11 = 660. Now, there are 11 minutes more on that 7-o clock and the 39 minutes we got rid of in the beginning. 11 + 39 = 40. 660 + 40 = 700.
Answer: Kenny's energy was off for 700 minutes, or 11 hours and 40 minutes.