Check the picture below.
so if y = 2, then 2y = 4, thus
![\textit{area of a segment of a circle}\\\\A=\cfrac{r^2}{2}\left(\cfrac{\pi \theta }{180}~~ - ~~sin(\theta ) \right)~~\begin{cases}r=radius\\\theta =\stackrel{degrees}{angle}\\[-0.5em]\hrulefill\\r=4\\\theta =60\end{cases}\\\\\\A=\cfrac{4^2}{2}\left(\cfrac{\pi (60) }{180}~~ - ~~sin(60^o ) \right)\implies A=8\left( \cfrac{\pi }{3}~~ - ~~\cfrac{\sqrt{3}}{2} \right)\\\\\\A=\cfrac{8\pi }{3}~~ - ~~4\sqrt{3}\implies A\approx 1.45](https://tex.z-dn.net/?f=%5Ctextit%7Barea%20of%20a%20segment%20of%20a%20circle%7D%5C%5C%5C%5CA%3D%5Ccfrac%7Br%5E2%7D%7B2%7D%5Cleft%28%5Ccfrac%7B%5Cpi%20%5Ctheta%20%7D%7B180%7D~~%20-%20~~sin%28%5Ctheta%20%29%20%20%5Cright%29~~%5Cbegin%7Bcases%7Dr%3Dradius%5C%5C%5Ctheta%20%3D%5Cstackrel%7Bdegrees%7D%7Bangle%7D%5C%5C%5B-0.5em%5D%5Chrulefill%5C%5Cr%3D4%5C%5C%5Ctheta%20%3D60%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5CA%3D%5Ccfrac%7B4%5E2%7D%7B2%7D%5Cleft%28%5Ccfrac%7B%5Cpi%20%2860%29%20%7D%7B180%7D~~%20-%20~~sin%2860%5Eo%20%29%20%20%5Cright%29%5Cimplies%20A%3D8%5Cleft%28%20%5Ccfrac%7B%5Cpi%20%7D%7B3%7D~~%20-%20~~%5Ccfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%20%5Cright%29%5C%5C%5C%5C%5C%5CA%3D%5Ccfrac%7B8%5Cpi%20%7D%7B3%7D~~%20-%20~~4%5Csqrt%7B3%7D%5Cimplies%20A%5Capprox%201.45)
Answer:
I am not sure about this question sry but u can try asking a tutor u don't need to use any points
The summation of the considered expression in terms of n from n = 1 to 14 is given by: Option D: 343
<h3>How to find the sum of consecutive integers?</h3>

<h3>
What are the properties of summation?</h3>
![\sum_{i=r}^s (a \times f(i) + b) = a \times [\: \sum_{i=r}^s f(i)] + (s-r)b](https://tex.z-dn.net/?f=%5Csum_%7Bi%3Dr%7D%5Es%20%20%28a%20%5Ctimes%20f%28i%29%20%2B%20b%29%20%3D%20a%20%5Ctimes%20%5B%5C%3A%20%5Csum_%7Bi%3Dr%7D%5Es%20f%28i%29%5D%20%2B%20%28s-r%29b)
where a, b, r, and s are constants, f(i) is function of i, i ranging from r to s (integral assuming).
For the given case, the considered summation can be written symbolically as:

It is evaluated as;
![\sum_{n=1}^{14} (3n + 2) = 3 \times [ \: \sum_{n=1}^{14} n ] + \sum_{n=1}^{14} 2\\\\\sum_{n=1}^{14} (3n + 2) = 3 \times \dfrac{(14)(14 + 1)}{2} + (2 + 2 + .. + 2(\text{14 times}))\\\\\sum_{n=1}^{14} (3n + 2) = 3 \times 105 + 28 = 343\\](https://tex.z-dn.net/?f=%5Csum_%7Bn%3D1%7D%5E%7B14%7D%20%20%283n%20%2B%202%29%20%3D%203%20%5Ctimes%20%5B%20%5C%3A%20%5Csum_%7Bn%3D1%7D%5E%7B14%7D%20n%20%5D%20%2B%20%5Csum_%7Bn%3D1%7D%5E%7B14%7D%202%5C%5C%5C%5C%5Csum_%7Bn%3D1%7D%5E%7B14%7D%20%20%283n%20%2B%202%29%20%3D%203%20%5Ctimes%20%5Cdfrac%7B%2814%29%2814%20%2B%201%29%7D%7B2%7D%20%2B%20%282%20%2B%202%20%2B%20..%20%2B%202%28%5Ctext%7B14%20times%7D%29%29%5C%5C%5C%5C%5Csum_%7Bn%3D1%7D%5E%7B14%7D%20%20%283n%20%2B%202%29%20%3D%203%20%5Ctimes%20105%20%2B%2028%20%3D%20343%5C%5C)
Thus, the summation of the considered expression in terms of n from n = 1 to 14 is given by: Option D: 343
Learn more about summation here:
brainly.com/question/14322177
Answer:
2 19/28 or 75/28
Step-by-step explanation:
Find common denominators then add, simplify if needed.
9514 1404 393
Answer:
6 = 6/1 = 12/2 = 18/3
Step-by-step explanation:
The simplest ratio of integers with a value of 6 is ...
6 = 6/1
We can multiply numerator and denominator by any non-zero integer value to obtain an equivalent:
6 = 12/2 = 18/3 = -54/-9