Answer:
13.3 cm
Step-by-step explanation:
Apply the Pythagorean Theorem:
hyp² = (2nd longest side)² + (shortest side)². Here the numbers are:
(24 cm)² = (20 cm)² + (shortest side)², or
576 - 400 = 176 = hyp²
Taking the square root of both sides, we get (shortest side) = 13.3 cm
Answer:
y(0) = 0.25 feet
![y(\frac{1}{4}) = 0.0789 \text{ feet}](https://tex.z-dn.net/?f=y%28%5Cfrac%7B1%7D%7B4%7D%29%20%3D%200.0789%20%5Ctext%7B%20feet%7D)
![y(\frac{1}{2}) =-0.2003 \text{ feet}](https://tex.z-dn.net/?f=y%28%5Cfrac%7B1%7D%7B2%7D%29%20%3D-0.2003%20%5Ctext%7B%20feet%7D)
Step-by-step explanation:
We are given the following information in the question:
The displacement from equilibrium of an oscillating weight suspended by a spring =
![y(t) = \displaystyle\frac{1}{4} \cos(5t)](https://tex.z-dn.net/?f=y%28t%29%20%3D%20%5Cdisplaystyle%5Cfrac%7B1%7D%7B4%7D%20%5Ccos%285t%29)
where y is the displacement in feet and t is the time in seconds.
Here, cos is in radians.
1) t = 0
![y(0) = \displaystyle\frac{1}{4} \cos(5(0)) = \frac{1}{4} \cos(0) = \frac{1}{4}(1) = \frac{1}{4}](https://tex.z-dn.net/?f=y%280%29%20%3D%20%5Cdisplaystyle%5Cfrac%7B1%7D%7B4%7D%20%5Ccos%285%280%29%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D%20%5Ccos%280%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D%281%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D)
y(0) = 0.25 feet
2) t = ![\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D)
![y(\displaystyle\frac{1}{4}) = \displaystyle\frac{1}{4} \cos(5(\frac{1}{4})) = \frac{1}{4} \cos(1.25) = \frac{1}{4}(0.31532236) =0.07883059](https://tex.z-dn.net/?f=y%28%5Cdisplaystyle%5Cfrac%7B1%7D%7B4%7D%29%20%3D%20%5Cdisplaystyle%5Cfrac%7B1%7D%7B4%7D%20%5Ccos%285%28%5Cfrac%7B1%7D%7B4%7D%29%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D%20%5Ccos%281.25%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D%280.31532236%29%20%3D0.07883059)
![y(\frac{1}{4}) = 0.0789 \text{ feet}](https://tex.z-dn.net/?f=y%28%5Cfrac%7B1%7D%7B4%7D%29%20%3D%200.0789%20%5Ctext%7B%20feet%7D)
3) t = ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
![y(\displaystyle\frac{1}{2}) = \displaystyle\frac{1}{4} \cos(5(\frac{1}{2})) = \frac{1}{4} \cos(2.5) = \frac{1}{4}(-0.80114362) = -0.200285905](https://tex.z-dn.net/?f=y%28%5Cdisplaystyle%5Cfrac%7B1%7D%7B2%7D%29%20%3D%20%5Cdisplaystyle%5Cfrac%7B1%7D%7B4%7D%20%5Ccos%285%28%5Cfrac%7B1%7D%7B2%7D%29%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D%20%5Ccos%282.5%29%20%3D%20%5Cfrac%7B1%7D%7B4%7D%28-0.80114362%29%20%3D%20-0.200285905)
![y(\frac{1}{2}) =-0.2003 \text{ feet}](https://tex.z-dn.net/?f=y%28%5Cfrac%7B1%7D%7B2%7D%29%20%3D-0.2003%20%5Ctext%7B%20feet%7D)
The negative sign indicates the opposite direction of displacement.
It would be a 2:1 ratio because sides AC and DF are 8:4 which simplifies to 2:1
Hope this helps!
Answer:
question
Step-by-step explanation:
what was the question? <3