Poll

8 votes (47.05%)
6 votes (35.29%)
3 votes (17.64%)
2 votes (11.76%)
6 votes (35.29%)
2 votes (11.76%)
3 votes (17.64%)
2 votes (11.76%)
8 votes (47.05%)
6 votes (35.29%)

17 members have voted

Gialmere
Gialmere
Joined: Nov 26, 2018
  • Threads: 37
  • Posts: 1659
September 24th, 2020 at 10:03:09 AM permalink


In this age of covid, a small group of worshippers don masks and form a prayer circle on the lawn beside their church.



If 8 people stand in a circle with six feet of required social distance between them (along a chord):

1) What is the circumference of the circle?

2) What is the diameter of the circle?

3) How far in a straight line (chord) is Person A from Person C?

4) The prayer circle is formed on a square lawn measuring 25x25 feet. What is the maximum number of people who could stand in the circle and still be 6 feet apart?
Have you tried 22 tonight? I said 22.
IAchance5
IAchance5
Joined: May 28, 2010
  • Threads: 41
  • Posts: 167
Thanks for this post from:
Gialmere
September 24th, 2020 at 12:41:04 PM permalink
Quote: Gialmere



In this age of covid, a small group of worshippers don masks and form a prayer circle on the lawn beside their church.



If 8 people stand in a circle with six feet of required social distance between them (along a chord):

1) What is the circumference of the circle?

2) What is the diameter of the circle?

3) How far in a straight line (chord) is Person A from Person C?

4) The prayer circle is formed on a square lawn measuring 25x25 feet. What is the maximum number of people who could stand in the circle and still be 6 feet apart?



Been a while, so hopefully I'm thinking on the right lines.....

Since the chord between 2 people is 6, then the radius of circle will be 7.89ft (6/(2 sin(.39 radians))
1) C = 49.57ft
2) d = 15.78ft
3) AC cord = 11.15ft (2*7.89) sin(.785 radians)
4) 12 people at most.....if we went to 13 people then we would go slightly over the radius of 12.5.....12.62 would be the radius for 13 people
Wizard
Administrator
Wizard
Joined: Oct 14, 2009
  • Threads: 1338
  • Posts: 22085
Thanks for this post from:
Gialmere
September 24th, 2020 at 6:30:29 PM permalink

radius = 3/sin(22.5) = 7.839377789
1. 2*pi*radius = 6*pi/sin(22.5) = 49.2563
2. 2*radius = 6/sin(22.5) = 15.6788
3. sqrt(2)*radius = 3*sqrt(2)/sin(22.5) = 11.0866


If this are right, I'll think about #4.
It's not whether you win or lose; it's whether or not you had a good bet.
ssho88
ssho88
Joined: Oct 16, 2011
  • Threads: 41
  • Posts: 453
Thanks for this post from:
Gialmere
September 24th, 2020 at 7:08:34 PM permalink
Quote: Gialmere



In this age of covid, a small group of worshippers don masks and form a prayer circle on the lawn beside their church.



If 8 people stand in a circle with six feet of required social distance between them (along a chord):

1) What is the circumference of the circle?

2) What is the diameter of the circle?

3) How far in a straight line (chord) is Person A from Person C?

4) The prayer circle is formed on a square lawn measuring 25x25 feet. What is the maximum number of people who could stand in the circle and still be 6 feet apart?




No 4



sinθ > 3/12.5
θ >13.8865
2θ > 27.773

Max people < 360/27.773
Max people < 12.962

Max people = 12


Again, I don't really understand what is "stand in the circle" .... I assumed stand along the circle circumference.

Gialmere
Gialmere
Joined: Nov 26, 2018
  • Threads: 37
  • Posts: 1659
September 24th, 2020 at 7:31:47 PM permalink
Quote: IAchance5

Been a while, so hopefully I'm thinking on the right lines.....

Since the chord between 2 people is 6, then the radius of circle will be 7.89ft (6/(2 sin(.39 radians))
1) C = 49.57ft
2) d = 15.78ft
3) AC cord = 11.15ft (2*7.89) sin(.785 radians)
4) 12 people at most.....if we went to 13 people then we would go slightly over the radius of 12.5.....12.62 would be the radius for 13 people


1) Very close
2) Very close
3) Very close
4) Correct!


Quote: Wizard


radius = 3/sin(22.5) = 7.839377789
1. 2*pi*radius = 6*pi/sin(22.5) = 49.2563
2. 2*radius = 6/sin(22.5) = 15.6788
3. sqrt(2)*radius = 3*sqrt(2)/sin(22.5) = 11.0866

If this are right, I'll think about #4.


1) Correct!
2) Correct!
3) Correct!


Quote: ssho88

No 4



sinθ > 3/12.5
θ >13.8865
2θ > 27.773

Max people < 360/27.773
Max people < 12.962

Max people = 12


Again, I don't really understand what is "stand in the circle" .... I assumed stand along the circle circumference.


4) Correct!
---------------------------------


<Insert your own prayer circle punchline here>
Have you tried 22 tonight? I said 22.
chevy
chevy
Joined: Apr 15, 2011
  • Threads: 2
  • Posts: 27
September 24th, 2020 at 8:29:05 PM permalink
I "think" the answer to the 4th question might in be fact 13.
Call the worshipers A - M
With an odd number, there is nobody directly opposite A. Which means the people on the far side (#7=G & #8=H) are set in some from the opposite of the circle. i.e.

Assume the square is from y=+12.5 ft to -12.5 ft
Assume A is at the top border of the square (0,12.5)
With N=13, radius is r = 3/sin(.5*360/13) = 12.53574441 ft.

So center of circle would be at (0,-0.0357441)

The (horizontal) cord between the 7th person (G) and 8th person (H) is a distance of r * cos(.5*360/13) = 12.17147846 below the center of the circle at y=-12.20722256 ft. ...(from x = +3ft to -3ft for G & H respectively)

Thus G & H are still on the square lawn, even though the imaginary circle they are standing on (diameter = 2*12.5357441 = 25.07148882) extends out of the square.

If they hold hands along the cord (which seems likely), I think 13 fit entirely on the lawn.
If their arms curve along the circle, they are all standing on the lawn, but their arms would extend to an area above the boundary.....which I might argue the prayer "circle" is still standing in the square lawn.

Only if you need to paint the entire circle on the lawn so they know where to stand do you get limited to 12

14 still doesn't seem to work
Joeman
Joeman
Joined: Feb 21, 2014
  • Threads: 34
  • Posts: 1799
September 25th, 2020 at 5:13:34 AM permalink


***Waiting for the marbles to come out!***


(Except for the one in the lower left who is checking out that sexy b**ch next to him!)
"Dealer has 'rock'... Pay 'paper!'"
Wizard
Administrator
Wizard
Joined: Oct 14, 2009
  • Threads: 1338
  • Posts: 22085
September 25th, 2020 at 6:09:22 AM permalink
Quote: Gialmere

4) The prayer circle is formed on a square lawn measuring 25x25 feet. What is the maximum number of people who could stand in the circle and still be 6 feet apart?



I'm also confused by what is being asked of #4. Must the worshippers stand on the circumference of a circle? May they stand inside of it? Why mention a square, can't you just say the diameter of the circle is 25 feet?
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard
Administrator
Wizard
Joined: Oct 14, 2009
  • Threads: 1338
  • Posts: 22085
September 25th, 2020 at 9:25:22 AM permalink
You put $1 in a bank account at a fixed interest rate of 10%, compounded monthly. Over an infinite period of time, what ratio of the time will the balance start with a 1?
It's not whether you win or lose; it's whether or not you had a good bet.
Ace2
Ace2
Joined: Oct 2, 2017
  • Threads: 22
  • Posts: 726
September 25th, 2020 at 10:03:24 AM permalink
Quote: Wizard

You put $1 in a bank account at a fixed interest rate of 10%, compounded monthly. Over an infinite period of time, what ratio of the time will the balance start with a 1?

I guess log(2) =~ 30.1%
Itís all about making that GTA

  • Jump to: