1) y = x
2) y = -(1/5)x + 4
3) y = -6x + 2
4) y = x + 2
5) y = (1/2)x + 2
6) y = -x + 4
7) y = -x + 1
8) y = (3/2)x + 2
9) y = -(3/2)x - 2
10) y = 2x - 1
Test each
if angle is increased, rock will go further
if the angle starts at 0, then increases to 90 degrees (straight up) the rock will go up then bounce off of the launcher going either front or back, but vastly shorter than if it were pointed straight ahead
2nd one
changing angle change the distance
we see that is true
Answer:
1.35
Step-by-step explanation:
I believe this is right but it could be wrong. Hope this helps! <3
Answer:
![\cos{\theta} = \frac{\sqrt{15}}{4}](https://tex.z-dn.net/?f=%5Ccos%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B15%7D%7D%7B4%7D)
Step-by-step explanation:
For any angle
, we have that:
![(\sin{\theta})^{2} + (\cos{\theta})^{2} = 1](https://tex.z-dn.net/?f=%28%5Csin%7B%5Ctheta%7D%29%5E%7B2%7D%20%2B%20%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%201)
Quadrant:
means that
is in the first quadrant. This means that both the sine and the cosine have positive values.
Find the cosine:
![(\sin{\theta})^{2} + (\cos{\theta})^{2} = 1](https://tex.z-dn.net/?f=%28%5Csin%7B%5Ctheta%7D%29%5E%7B2%7D%20%2B%20%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%201)
![(\frac{1}{4})^{2} + (\cos{\theta})^{2} = 1](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B4%7D%29%5E%7B2%7D%20%2B%20%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%201)
![\frac{1}{16} + (\cos{\theta})^{2} = 1](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B16%7D%20%2B%20%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%201)
![(\cos{\theta})^{2} = 1 - \frac{1}{16}](https://tex.z-dn.net/?f=%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%201%20-%20%5Cfrac%7B1%7D%7B16%7D)
![(\cos{\theta})^{2} = \frac{16-1}{16}](https://tex.z-dn.net/?f=%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%20%5Cfrac%7B16-1%7D%7B16%7D)
![(\cos{\theta})^{2} = \frac{15}{16}](https://tex.z-dn.net/?f=%28%5Ccos%7B%5Ctheta%7D%29%5E%7B2%7D%20%3D%20%5Cfrac%7B15%7D%7B16%7D)
![\cos{\theta} = \pm \sqrt{\frac{15}{16}}](https://tex.z-dn.net/?f=%5Ccos%7B%5Ctheta%7D%20%3D%20%5Cpm%20%5Csqrt%7B%5Cfrac%7B15%7D%7B16%7D%7D)
Since the angle is in the first quadrant, the cosine is positive.
![\cos{\theta} = \frac{\sqrt{15}}{4}](https://tex.z-dn.net/?f=%5Ccos%7B%5Ctheta%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B15%7D%7D%7B4%7D)