I think it is B I hope I am right and helped
Answer:
![b = \sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}}](https://tex.z-dn.net/?f=b%20%3D%20%5Csqrt%7B%5Cfrac%7BC%5E%7B2%7D%20%7D%7B2%28%5Cpi%20%29%5E%7B2%7D%20%7D%20%20-%20%20a%5E%7B2%7D%7D)
Step-by-step explanation:
Given - The circumference of the ellipse approximated by
where 2a and 2b are the lengths of 2 the axes of the ellipse.
To find - Which equation is the result of solving the formula of the circumference for b ?
Solution -
![C = 2\pi \sqrt{\frac{a^{2} + b^{2} }{2} }\\\frac{C}{2\pi } = \sqrt{\frac{a^{2} + b^{2} }{2} }](https://tex.z-dn.net/?f=C%20%3D%202%5Cpi%20%5Csqrt%7B%5Cfrac%7Ba%5E%7B2%7D%20%2B%20b%5E%7B2%7D%20%7D%7B2%7D%20%7D%5C%5C%5Cfrac%7BC%7D%7B2%5Cpi%20%7D%20%20%3D%20%20%5Csqrt%7B%5Cfrac%7Ba%5E%7B2%7D%20%2B%20b%5E%7B2%7D%20%7D%7B2%7D%20%7D)
Squaring Both sides, we get
![[\frac{C}{2\pi }]^{2} = [\sqrt{\frac{a^{2} + b^{2} }{2} }]^{2} \\\frac{C^{2} }{(2\pi)^{2} } = {\frac{a^{2} + b^{2} }{2} }\\2\frac{C^{2} }{4(\pi)^{2} } = {{a^{2} + b^{2} }](https://tex.z-dn.net/?f=%5B%5Cfrac%7BC%7D%7B2%5Cpi%20%7D%5D%5E%7B2%7D%20%20%20%3D%20%20%5B%5Csqrt%7B%5Cfrac%7Ba%5E%7B2%7D%20%2B%20b%5E%7B2%7D%20%7D%7B2%7D%20%7D%5D%5E%7B2%7D%20%5C%5C%5Cfrac%7BC%5E%7B2%7D%20%7D%7B%282%5Cpi%29%5E%7B2%7D%20%20%7D%20%20%20%3D%20%20%7B%5Cfrac%7Ba%5E%7B2%7D%20%2B%20b%5E%7B2%7D%20%7D%7B2%7D%20%7D%5C%5C2%5Cfrac%7BC%5E%7B2%7D%20%7D%7B4%28%5Cpi%29%5E%7B2%7D%20%20%7D%20%20%20%3D%20%20%7B%7Ba%5E%7B2%7D%20%2B%20b%5E%7B2%7D%20%7D)
![\frac{C^{2} }{2(\pi )^{2} } = a^{2} + b^{2} \\\frac{C^{2} }{2(\pi )^{2} } - a^{2} = b^{2} \\\sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}} = b](https://tex.z-dn.net/?f=%5Cfrac%7BC%5E%7B2%7D%20%7D%7B2%28%5Cpi%20%29%5E%7B2%7D%20%7D%20%20%3D%20a%5E%7B2%7D%20%2B%20b%5E%7B2%7D%20%5C%5C%5Cfrac%7BC%5E%7B2%7D%20%7D%7B2%28%5Cpi%20%29%5E%7B2%7D%20%7D%20%20-%20%20a%5E%7B2%7D%20%3D%20b%5E%7B2%7D%20%5C%5C%5Csqrt%7B%5Cfrac%7BC%5E%7B2%7D%20%7D%7B2%28%5Cpi%20%29%5E%7B2%7D%20%7D%20%20-%20%20a%5E%7B2%7D%7D%20%20%3D%20b)
∴ we get
![b = \sqrt{\frac{C^{2} }{2(\pi )^{2} } - a^{2}}](https://tex.z-dn.net/?f=b%20%3D%20%5Csqrt%7B%5Cfrac%7BC%5E%7B2%7D%20%7D%7B2%28%5Cpi%20%29%5E%7B2%7D%20%7D%20%20-%20%20a%5E%7B2%7D%7D)
Okie doke. So, we are rounding this number to the nearest thousandths place, which is three digits behind the decimal. The rules for rounding are if the number is 5 or more in the digit behind it, the number goes up. If it is 4 or less, the number goes back. In other words, we depend on the digit right of the digit we are rounding to in order to see what we do. The number we are rounding is 1.49882. The 8 is in the thousandths place and the 8 is to the right of that, which is the ten thousandths place. Because 8 is greater than 5, the number rounds up. So the number rounded to the nearest thousandth is 1.500.
Is point B.
Because √3≈1.7.
So it should be B.
A unit is a measurement. for example, a unit could be an inch, or it could be a foot. to convert you need the exact measurement so if a line is 12 inches it's 1 foot. if it is 13 then it stays in inches. You convert units to the easiest variable to calculate and then you solve your equation from there.
Hope I helped! :)