Answer:
Step-by-step explanation:
step 1
Find the radius of the circle
Remember that AB is a tangent to the circle at point B
so
AB is perpendicular to OA
The radius of the circle is equal to the segment OA
In the right triangle OAB
![sin(30\°)=\frac{OA}{OB}](https://tex.z-dn.net/?f=sin%2830%5C%C2%B0%29%3D%5Cfrac%7BOA%7D%7BOB%7D)
![OA=(OB)sin(30\°)](https://tex.z-dn.net/?f=OA%3D%28OB%29sin%2830%5C%C2%B0%29)
substitute the values
![OA=(16)0.5=8\ units](https://tex.z-dn.net/?f=OA%3D%2816%290.5%3D8%5C%20units)
step 2
Find the value of p
In the right triangle OPQ
see the attached figure to better understand the problem
Applying the Pythagoras Theorem
![OP^2=OQ^2+PQ^2](https://tex.z-dn.net/?f=OP%5E2%3DOQ%5E2%2BPQ%5E2)
substitute the values
Remember that OP is the radius
![8^2=p^2+(3p)^2](https://tex.z-dn.net/?f=8%5E2%3Dp%5E2%2B%283p%29%5E2)
![64=p^2+9p^2](https://tex.z-dn.net/?f=64%3Dp%5E2%2B9p%5E2)
![64=10p^2](https://tex.z-dn.net/?f=64%3D10p%5E2)
![p^2=\frac{64}{10}](https://tex.z-dn.net/?f=p%5E2%3D%5Cfrac%7B64%7D%7B10%7D)
![p=\frac{8}{\sqrt{10}}](https://tex.z-dn.net/?f=p%3D%5Cfrac%7B8%7D%7B%5Csqrt%7B10%7D%7D)
simplify
Answer:
1 9/141
Step-by-step explanation:
6 divided by 5.64 is 6/5.64
6-5.64 is 0.36. 0.36/5.64 is 36/564=18/282=9/141
the answer is 1 9/141
Steps to solve:
3 < x + 3 < 6
~Subtract 3 to everything
0 < x < 3
Best of Luck!
Answer: Children = 108
Adult = 52
Step-by-step explanation:
Let x = number of children
Let y = number of adult
Based on the information given, we can form an equation which will be:
x + y = 160 ........ i
2x + 5y = 476 ........ ii
Multiply equation i by 2
Multiply equation ii by 1
2x + 2y = 320 ....... iii
2x + 5y = 476 ........ iv
Subtract iii from iv
3y = 156
y = 52
Number of adults = 52
Since x + y = 160
x + 52 =160
x = 160 - 52
x = 108
Number of children = 108