Carlos and his friends are thinking about taking a cab home. The Cost for the cab ride is $1.50 per mile
2 answers:
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Answer:
New line =3*ZX
Step-by-step explanation:
It is given that the isosceles trapezoid is dilated using a scale factor of 1/3
and a line is drawn through the center of the new dilated figure, so
let us suppose that line is EF which is drawn and it will also pass through
the center in similar way the line ZX passes through so after considering this situation, we can come to this point
so new line will be 3 times longer than ZX.
Check the picture below.
so the chord is the one in red there, making the segment, in green there, with a central angle of 45°, and the minor segment will be that green one.
![\bf \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 =angle~in\\ \qquad degrees\\ ------\\ r=3\\ \theta =45 \end{cases} \\\\\\ A=\cfrac{3^2}{2}\left[ \cfrac{\pi(45) }{180} - sin(45^o) \right]\implies A=\cfrac{9}{2}\left[ \cfrac{\pi }{4}-\cfrac{\sqrt{2}}{2} \right] \\\\\\ A=\cfrac{9}{2}\left( \cfrac{\pi -2\sqrt{2}}{4} \right)\implies A\approx 0.3523112199491](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20segment%20of%20a%20circle%7D%5C%5C%5C%5C%0AA%3D%5Ccfrac%7Br%5E2%7D%7B2%7D%5Cleft%5B%20%5Ccfrac%7B%5Cpi%20%5Ctheta%20%7D%7B180%7D%20-%20sin%28%5Ctheta%29%20%5Cright%5D~~%0A%5Cbegin%7Bcases%7D%0Ar%3Dradius%5C%5C%0A%5Ctheta%20%3Dangle~in%5C%5C%0A%5Cqquad%20degrees%5C%5C%0A------%5C%5C%0Ar%3D3%5C%5C%0A%5Ctheta%20%3D45%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0AA%3D%5Ccfrac%7B3%5E2%7D%7B2%7D%5Cleft%5B%20%5Ccfrac%7B%5Cpi%2845%29%20%7D%7B180%7D%20-%20sin%2845%5Eo%29%20%5Cright%5D%5Cimplies%20A%3D%5Ccfrac%7B9%7D%7B2%7D%5Cleft%5B%20%5Ccfrac%7B%5Cpi%20%7D%7B4%7D-%5Ccfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%5Cright%5D%0A%5C%5C%5C%5C%5C%5C%0AA%3D%5Ccfrac%7B9%7D%7B2%7D%5Cleft%28%20%5Ccfrac%7B%5Cpi%20-2%5Csqrt%7B2%7D%7D%7B4%7D%20%5Cright%29%5Cimplies%20A%5Capprox%200.3523112199491)
so the chord is the one in red there, making the segment, in green there, with a central angle of 45°, and the minor segment will be that green one.