96(over)100 in a fraction form
Answer:
t=0.93 seconds or t=0.07 seconds
Step-by-step explanation:
If ![h=-16t^2+8t-1](https://tex.z-dn.net/?f=h%3D-16t%5E2%2B8t-1)
The time when the projectile lands on the ground is when its height, h=0.
![-16t^2+8t-1=0](https://tex.z-dn.net/?f=-16t%5E2%2B8t-1%3D0)
Using Factoring by Perfect Squares
![-16t^2+8t=1\\\text{Divide all through by the coefficient of t^2}\\\frac{-16t^2}{-16} +\frac{8t}{-16}=\frac{1}{-16}\\t^2-\frac{1}{2}t=-\frac{1}{16}](https://tex.z-dn.net/?f=-16t%5E2%2B8t%3D1%5C%5C%5Ctext%7BDivide%20all%20through%20by%20the%20coefficient%20of%20t%5E2%7D%5C%5C%5Cfrac%7B-16t%5E2%7D%7B-16%7D%20%2B%5Cfrac%7B8t%7D%7B-16%7D%3D%5Cfrac%7B1%7D%7B-16%7D%5C%5Ct%5E2-%5Cfrac%7B1%7D%7B2%7Dt%3D-%5Cfrac%7B1%7D%7B16%7D)
Divide all through by the coefficient of ![t^2](https://tex.z-dn.net/?f=t%5E2)
![\frac{-16t^2}{-16} +\frac{8t}{-16}=\frac{1}{-16}\\t^2-\frac{1}{2}t=-\frac{1}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B-16t%5E2%7D%7B-16%7D%20%2B%5Cfrac%7B8t%7D%7B-16%7D%3D%5Cfrac%7B1%7D%7B-16%7D%5C%5Ct%5E2-%5Cfrac%7B1%7D%7B2%7Dt%3D-%5Cfrac%7B1%7D%7B16%7D)
Next, divide the coefficient of t by 2, square it and add it to both sides.
![t^2-\frac{1}{2}t+(-\frac{1}{2})^2=-\frac{1}{16}+(-\frac{1}{2})^2\\(t-\frac{1}{2})^2=-\frac{1}{16}+\frac{1}{4}\\(t-\frac{1}{2})^2=\frac{3}{16}\\](https://tex.z-dn.net/?f=t%5E2-%5Cfrac%7B1%7D%7B2%7Dt%2B%28-%5Cfrac%7B1%7D%7B2%7D%29%5E2%3D-%5Cfrac%7B1%7D%7B16%7D%2B%28-%5Cfrac%7B1%7D%7B2%7D%29%5E2%5C%5C%28t-%5Cfrac%7B1%7D%7B2%7D%29%5E2%3D-%5Cfrac%7B1%7D%7B16%7D%2B%5Cfrac%7B1%7D%7B4%7D%5C%5C%28t-%5Cfrac%7B1%7D%7B2%7D%29%5E2%3D%5Cfrac%7B3%7D%7B16%7D%5C%5C)
Taking square roots of both sides
![t-\frac{1}{2}=\sqrt{\frac{3}{16}}\\t=\frac{1}{2} \pm \sqrt{\frac{3}{16}}\\t=\frac{1}{2} \pm \frac{\sqrt{3}}{4}](https://tex.z-dn.net/?f=t-%5Cfrac%7B1%7D%7B2%7D%3D%5Csqrt%7B%5Cfrac%7B3%7D%7B16%7D%7D%5C%5Ct%3D%5Cfrac%7B1%7D%7B2%7D%20%5Cpm%20%5Csqrt%7B%5Cfrac%7B3%7D%7B16%7D%7D%5C%5Ct%3D%5Cfrac%7B1%7D%7B2%7D%20%5Cpm%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B4%7D)
Therefore:
![t=\frac{1}{2} + \frac{\sqrt{3}}{4} \: OR \: t=\frac{1}{2} - \frac{\sqrt{3}}{4}\\t=\frac{2+\sqrt{3}}{4} \: OR \: \frac{2-\sqrt{3}}{4}\\t=0.93seconds \: OR \: 0.07 seconds](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B1%7D%7B2%7D%20%2B%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B4%7D%20%5C%3A%20OR%20%5C%3A%20t%3D%5Cfrac%7B1%7D%7B2%7D%20-%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B4%7D%5C%5Ct%3D%5Cfrac%7B2%2B%5Csqrt%7B3%7D%7D%7B4%7D%20%5C%3A%20OR%20%5C%3A%20%5Cfrac%7B2-%5Csqrt%7B3%7D%7D%7B4%7D%5C%5Ct%3D0.93seconds%20%5C%3A%20OR%20%5C%3A%200.07%20seconds)
Y = 14 If it’s equilateral then the bottom 2 are the same so it would be 50 + 50 = 100 and because a triangle adds up into 180 then the last angle is 80 degrees and we would then make 5y + 10= 80 we would simplify
5y + 10 - 10 = 80 - 10
5y/5 = 70/5
y = 14
Answer:
2:1 or 2
Step-by-step explanation:
<em>*** </em>(Ratios can be written as " a : b", or can be written as a fraction " a / b".
>> therefore 10/5 can be simplified to 2/1 )<em>***</em>
For every 10 notebooks, there are 5 ballpens.
Therefore, for every 2 notebooks there is 1 ballpen (The simplification).
<u><em>EXTRA: </em></u>
**Also remember that the ratio of notebooks to ballpens cannot be reversed into ballpen to notebook ratio, because this would change the meaning.
2/1 is not the same as 1/2 **