Answer:
X=11/2
Step-by-step explanation:
2x=8+3
2x=11
x=11/2
Answer:
![\approx 15.9](https://tex.z-dn.net/?f=%5Capprox%2015.9)
Step-by-step explanation:
The length of an arc with measure
and radius
is given by
. From the figure, we know that the radius of arc ADC is 4, but we don't know the measure of the arc. Since there are 360 degrees in a circle, the measure of arc ADC is equal to the measure of the arc formed by
subtracted from 360. The measure of the arc formed by
consists of two congruent angles,
and
. To find them, we can use basic trigonometry for a right triangle, since by definition, tangents intersect a circle at a right angle.
In any right triangle, the cosine of an angle is equal to its adjacent side divided by the hypotenuse, or longest side, of the triangle.
We have:
![\cos \angle AOB=\cos \angle COB=\frac{4}{10},\\\angle AOB=\arccos(\frac{4}{10})=66.42182152^{\circ}](https://tex.z-dn.net/?f=%5Ccos%20%5Cangle%20AOB%3D%5Ccos%20%5Cangle%20COB%3D%5Cfrac%7B4%7D%7B10%7D%2C%5C%5C%5Cangle%20AOB%3D%5Carccos%28%5Cfrac%7B4%7D%7B10%7D%29%3D66.42182152%5E%7B%5Ccirc%7D)
Therefore, ![\angle AOC=2\cdot 66.42182152=132.84364304^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20AOC%3D2%5Ccdot%2066.42182152%3D132.84364304%5E%7B%5Ccirc%7D)
The measure of the central angle of
must then be ![360-132.84364304=227.15635696^{\circ}](https://tex.z-dn.net/?f=360-132.84364304%3D227.15635696%5E%7B%5Ccirc%7D)
Thus, the length of
is equal to:
(three significant figures as requested by question).
Answer:
at the vertex x = 4.5
Step-by-step explanation:
hope this helps! :)
Answer:
Infinite decimals that do not repeat.
Step-by-step explanation:
Repeating decimals can be as fractions where the top and bottom are integers.
Examples: .3333333333333333333333333333333.... can be written as 1/3.
or .19191919191919191919..... can be written as 19/99.
Terminating decimals can also be written as fractions where the top and bottom are integers.
Examples: .11=11/100 or .161=161/1000
Any number that can be written as a fraction where the top and bottom are integers (bottom integer not 0)
is a rational number.
Repeating decimals are infinite. So what I think they mean by infinite here is numbers like
or
. There are not rational. They cannot be written as a fraction where the top and bottom are integers.