Answer:
The partial sum is 561
Step-by-step explanation:
Given:
The arithmetic series = 9+12+15...+51+54+57
Partial sum between 9 and 57, with d=3
To Find :
The partial sum = ?
Solution
The given series is a arithmetic series with difference 3.
So the series is
9,12,15,18,21,24,27,30,33,36,29,42,45,48,52,51,54,57
Thus There are 17 terms,
Here the is a middle term is the the ninth,
The 9 term is
![a_ 9 = a_0 +(n-1)d](https://tex.z-dn.net/?f=a_%209%20%20%3D%20%20a_0%20%2B%28n-1%29d)
![a_ 9 = 9 +(9-1)3](https://tex.z-dn.net/?f=a_%209%20%20%3D%20%209%20%2B%289-1%293)
![a_ 9 = 9 +(8)3](https://tex.z-dn.net/?f=a_%209%20%20%3D%20%209%20%2B%288%293)
![a _9 = 33](https://tex.z-dn.net/?f=a%20_9%20%3D%2033)
Now the
The partial sum is 33 x 17 = 561
The simplified form of the given expression is 2tanx. Option C is correct.
<h2>Trigonometry identity</h2>
Given the following trigonometry identity:
![\frac{cosx}{1-sinx} -\frac{cosx}{1+sinx}](https://tex.z-dn.net/?f=%5Cfrac%7Bcosx%7D%7B1-sinx%7D%20-%5Cfrac%7Bcosx%7D%7B1%2Bsinx%7D%20)
<h3>Simplify the expression</h3>
Find the LCM of the expression to have:
![=\frac{cosx}{1-sinx} -\frac{cosx}{1+sinx} \\ =\frac{cosx(1+sinx)-(cosx(1-sinx)}{(1-sinx)(1+sinx)} \\ =\frac{cosx+cosxsinx-cosx+cosxsinx}{1-sin^2x}\\ =\frac{2cosxsins}{cos^2x } \\ =\frac{2cosxsinx}{cos^2x}\\ ](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bcosx%7D%7B1-sinx%7D%20-%5Cfrac%7Bcosx%7D%7B1%2Bsinx%7D%20%5C%5C%0A%3D%5Cfrac%7Bcosx%281%2Bsinx%29-%28cosx%281-sinx%29%7D%7B%281-sinx%29%281%2Bsinx%29%7D%20%5C%5C%0A%3D%5Cfrac%7Bcosx%2Bcosxsinx-cosx%2Bcosxsinx%7D%7B1-sin%5E2x%7D%5C%5C%0A%20%3D%5Cfrac%7B2cosxsins%7D%7Bcos%5E2x%20%7D%20%5C%5C%0A%3D%5Cfrac%7B2cosxsinx%7D%7Bcos%5E2x%7D%5C%5C%0A%20)
This can be simplified further to have:
![=\frac{2sinxcosx}{cos^2x}\\ =\frac{2sinx}{cosx}\\ =2tanx](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2sinxcosx%7D%7Bcos%5E2x%7D%5C%5C%0A%20%3D%5Cfrac%7B2sinx%7D%7Bcosx%7D%5C%5C%0A%20%3D2tanx)
Therefore the simplified form of the given expression is 2tanx.
Learn more on trigonometry function here: brainly.com/question/4515552
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Answer:
If you wanted it to be converted to ft, then her height would be: 4 ft , 5 inches
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Step-by-step explanation: