Answer:
3.9 units
Step-by-step explanation:
We are given that,
Time taken by each swing = 2.2 seconds
The pendulum formula is given by,
, where T is the time taken and L is the length of the swing.
So, we have,
![2.2= 2\pi \sqrt{\frac{L}{32}}](https://tex.z-dn.net/?f=2.2%3D%202%5Cpi%20%5Csqrt%7B%5Cfrac%7BL%7D%7B32%7D%7D)
i.e. ![\frac{2.2}{2\pi}=\sqrt{\frac{L}{32}}](https://tex.z-dn.net/?f=%5Cfrac%7B2.2%7D%7B2%5Cpi%7D%3D%5Csqrt%7B%5Cfrac%7BL%7D%7B32%7D%7D)
i.e. ![(\frac{2.2}{2\pi})^{2}=\frac{L}{32}](https://tex.z-dn.net/?f=%28%5Cfrac%7B2.2%7D%7B2%5Cpi%7D%29%5E%7B2%7D%3D%5Cfrac%7BL%7D%7B32%7D)
i.e. ![L=32\times (\frac{2.2}{2\pi})^{2}](https://tex.z-dn.net/?f=L%3D32%5Ctimes%20%28%5Cfrac%7B2.2%7D%7B2%5Cpi%7D%29%5E%7B2%7D)
i.e. ![L=32\times \frac{4.84}{4 \pi^2}](https://tex.z-dn.net/?f=L%3D32%5Ctimes%20%5Cfrac%7B4.84%7D%7B4%20%5Cpi%5E2%7D)
i.e. ![L=32\times \frac{1.21}{\pi^2}](https://tex.z-dn.net/?f=L%3D32%5Ctimes%20%5Cfrac%7B1.21%7D%7B%5Cpi%5E2%7D)
i.e. ![L=\frac{38.72}{9.87}](https://tex.z-dn.net/?f=L%3D%5Cfrac%7B38.72%7D%7B9.87%7D)
i.e. L = 3.923 units
So, rounded to tenths, the length of the swing is 3.9 units.
Well you have a 50% chance to get even balls, you could choose at least 4 to be sure I would say, but there's also the universalistic reality of possibility
The coordinates of U after the reflection are: (-5, -3)
<h3>
How to get the coordinates after the reflection?</h3>
By looking at the graph, we can see that the coordinates of point U are:
U = (-1, -3)
And we want to reflect it across the line x = -3.
Notice that because this is a vertical line, the y-component does not change by the reflection. Only changes the x-component, such that the distance between the original coordinates and the final coordinates to the line don't change.
The original x-component is x = -1, the distance to the line is:
d = |-3 - (-1)| = 2 units.
Then the new x-component will also be at 2 units of the line, but in the other direction:
new x-component: x = -3 - 2 = -5
The coordinates of U after the reflection are:
(-5, -3)
If you want to learn more about reflections:
brainly.com/question/4289712
#SPJ1
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▹ Answer
<em>a = 8</em>
▹ Step-by-Step Explanation
a/4 + 4 = 6
Multiply both sides:
a + 16 = 24
Subtract 16 from both sides:
16 - 16 = a
24 - 16 = 8
a = 8
Hope this helps!
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