The Angle of rotation of the given regular pentagon after undergoing rotational transformation is; 72°
<h3>How to find the angle of rotation?</h3>
We are told that the image is a perfect pentagon that all its' sides are all equal with no uneven sides.
Now, A figure is said to have rotational symmetry if it looks exactly the same after rotating it some angle less than 360° which is a full rotation.
Now, a regular pentagon will have a rotational symmetry of order 5 because it will look the same after 5 turns.
Thus;
Angle of rotation = 360/5
Angle of rotation = 72°
Read more about Angle of Rotation at; brainly.com/question/2078551
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The given series is ![-1 + -3 + -5 + -7 +...](https://tex.z-dn.net/?f=%20%20-1%20%2B%20-3%20%2B%20-5%20%2B%20-7%20%2B...%20)
Alternatively it can be written as , say s then
![S= -1 -3 -5 -7 ...\\ \\ S=-(1+3+5+7+........)\\ \\ \text{This is an arithmetic series with first term=a=1 and }\\ \text{common diffrence=d=3-1=2}\\ \\ \text{Using the arithmetic series sum formula we can say}\\ \\ S_n=\frac{n}{2}[2a+(n-1)d]\\ \\ S_{15}=\frac{15}{2}[2*1+(15-1)*2]\\ \\ S_{15}=\frac{15}{2}[2+28]\\ \\ S_{15}=\frac{15}{2}*30\\ \\ S_{15}=225\\ \\ \text{Hence the sum of the given sequence is }= -225\\](https://tex.z-dn.net/?f=%20S%3D%20-1%20-3%20-5%20-7%20...%5C%5C%20%5C%5C%20S%3D-%281%2B3%2B5%2B7%2B........%29%5C%5C%20%5C%5C%20%5Ctext%7BThis%20is%20an%20arithmetic%20series%20with%20first%20term%3Da%3D1%20and%20%7D%5C%5C%20%5Ctext%7Bcommon%20diffrence%3Dd%3D3-1%3D2%7D%5C%5C%20%5C%5C%20%5Ctext%7BUsing%20the%20arithmetic%20series%20sum%20formula%20we%20can%20say%7D%5C%5C%20%5C%5C%20S_n%3D%5Cfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D%5C%5C%20%5C%5C%20S_%7B15%7D%3D%5Cfrac%7B15%7D%7B2%7D%5B2%2A1%2B%2815-1%29%2A2%5D%5C%5C%20%20%20%5C%5C%20S_%7B15%7D%3D%5Cfrac%7B15%7D%7B2%7D%5B2%2B28%5D%5C%5C%20%5C%5C%20S_%7B15%7D%3D%5Cfrac%7B15%7D%7B2%7D%2A30%5C%5C%20%5C%5C%20S_%7B15%7D%3D225%5C%5C%20%5C%5C%20%5Ctext%7BHence%20the%20sum%20of%20the%20given%20sequence%20is%20%7D%3D%20-225%5C%5C%20)
Answer: 100 ft^2
Step-by-step explanation:
Replace s with 5 in your equation and solve:
![4s^2](https://tex.z-dn.net/?f=4s%5E2)
![4(5)^2](https://tex.z-dn.net/?f=4%285%29%5E2)
![4(25)](https://tex.z-dn.net/?f=4%2825%29)
= ![100\\](https://tex.z-dn.net/?f=100%5C%5C)