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Mathematics, 23.06.2019 06:40 21hendlill

$\text{i was eating cookies and had some thoughts. if i wanted to cut out exactly }$ $\frac{1}{3}$ of the cookie to share with someone, how far from one side would i have to make a straight cut to get that exact amount? how far would i have to cut if i wanted to cut off $\frac{1}{n}$ $\text{ of the cookie? }$ $\text{basically, the question is, find the value of }a\text{ given only n, and r}$ $\text{one way of finding this, is by finding the area of the shaded reigon, q in terms of}$ $\text{r, a, and b, and equating it to the area of the fraction of the cookie then solving for a.}$ $\text{in math, this means solving } \frac{1}{n}\pi r^2=q \text{ for }f(r, n)=a.$ $\text{from the diagram, we can see that }r=a+b$ $\text{eventually, by 2 different means, i found 2 equations that, if solved, would give the}$ $\text{ relationship between r, n, and a.}$ $\text{they are as follows: }$ $\text{1. }\frac{1}{n}\pi r=r\theta-bsin(\theta) \text{ where }\theta=cos^{-1}(\frac{b}{r})$ $\text{2. }\frac{1}{n}\pi=\theta-sin(2\theta) \text{ where }\theta=cos^{-1}(\frac{b}{r})$ $\text{these 2 equations are equivalent, but annoying to solve.}$ $\text{to claim these points, solve for a in terms of r and n, showing all work.}$ $\text{i would like an analytic solution if possible.}[\tex][tex]\text{all incorrect, spam, or no-work solutions will be reported.}$

$[tex]\text{i was eating cookies and had some thoughts. if i wanted to cut out exactly }[/tex][tex] \$

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