Answer:
Step-by-step explanation:
You could talk about how how or low it goes.
For instance: if the graph was going very high then suddenly low you could say that it was going very high until it suddenly dropped.
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Step-by-step explanation:
The mode is 7 because it is 5 times
"determine the location" or namely, is it inside the circle, outside the circle, or right ON the circle?
well, we know the center is at (1,-5) and it has a radius of 5, so the distance from the center to any point on the circle will just be 5, now if (4,-1) is less than that away, is inside, if more than that is outiside and if it's exactly 5 is right ON the circle.
well, we can check by simply getting the distance from the center to the point (4,-1).
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{center}{(\stackrel{x_1}{1}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d = \sqrt{[4-1]^2+[-1-(-5)]^2}\implies d=\sqrt{(4-1)^2+(-1+5)^2} \\\\\\ d = \sqrt{3^2+4^2}\implies d =\sqrt{9+16}\implies d=\sqrt{25}\implies \stackrel{\textit{right on the circle}}{d = 5}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20%5Cstackrel%7Bcenter%7D%7B%28%5Cstackrel%7Bx_1%7D%7B1%7D~%2C~%5Cstackrel%7By_1%7D%7B-5%7D%29%7D%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B4%7D~%2C~%5Cstackrel%7By_2%7D%7B-1%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20d%20%3D%20%5Csqrt%7B%5B4-1%5D%5E2%2B%5B-1-%28-5%29%5D%5E2%7D%5Cimplies%20d%3D%5Csqrt%7B%284-1%29%5E2%2B%28-1%2B5%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20d%20%3D%20%5Csqrt%7B3%5E2%2B4%5E2%7D%5Cimplies%20d%20%3D%5Csqrt%7B9%2B16%7D%5Cimplies%20d%3D%5Csqrt%7B25%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bright%20on%20the%20circle%7D%7D%7Bd%20%3D%205%7D)
First notice that the triangle with sides
![x,y,a](https://tex.z-dn.net/?f=x%2Cy%2Ca)
and the triangle with sides
![z,a+b,x](https://tex.z-dn.net/?f=z%2Ca%2Bb%2Cx)
are similar. This is true because the angle between sides
![x,y](https://tex.z-dn.net/?f=x%2Cy)
in the smaller triangle is clearly
![30^\circ](https://tex.z-dn.net/?f=30%5E%5Ccirc)
, while the angle between sides
![y,z](https://tex.z-dn.net/?f=y%2Cz)
in the larger triangle is clearly
![60^\circ](https://tex.z-dn.net/?f=60%5E%5Ccirc)
. So the triangles are similar with sides
![x,y,a](https://tex.z-dn.net/?f=x%2Cy%2Ca)
corresponding to
![a+b,z,x](https://tex.z-dn.net/?f=a%2Bb%2Cz%2Cx)
, respectively.
Now both triangles are
![30^\circ-60^\circ-90^\circ](https://tex.z-dn.net/?f=30%5E%5Ccirc-60%5E%5Ccirc-90%5E%5Ccirc)
, which means there's a convenient ratio between its sides. If the length of the shortest leg is
![\ell_1](https://tex.z-dn.net/?f=%5Cell_1)
, then the length of the longer leg is
![\ell_2=\sqrt3\ell_1](https://tex.z-dn.net/?f=%5Cell_2%3D%5Csqrt3%5Cell_1)
and the hypotenuse has length
![\ell_3=\sqrt{{\ell_1}^2+{\ell_2}^2}=2\ell_1](https://tex.z-dn.net/?f=%5Cell_3%3D%5Csqrt%7B%7B%5Cell_1%7D%5E2%2B%7B%5Cell_2%7D%5E2%7D%3D2%5Cell_1)
.
Since
![x](https://tex.z-dn.net/?f=x)
is the shortest leg in the larger triangle, it follows that
![a+b=2x](https://tex.z-dn.net/?f=a%2Bb%3D2x)
, so
Answer: 50 degrees
You cut the arc measure 100 degrees in half. This is using the inscribed angle theorem. The angle 'a' is the inscribed angle that cuts off this 100 degree arc.