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chevy
chevy
Joined: Apr 15, 2011
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Thanks for this post from:
Gialmere
December 4th, 2020 at 8:46:28 AM permalink

ray from light from signal to top right corner of rear of truck's van continues on to your eye.

similar triangles give (in feet)

x/(8+8+24) =((12+2/3) - 4) / (18 - (12+2/3))

x= (40 ft) * (104 in) / (64 in) =

x= 65 ft


Though this assumes your eyes are located at the front of your car. If we assume a car length of maybe 12 ft and driver's seat is say 4 ft from the front bumper....

x = 61 ft


EDIT: i.e. the car's front bumper is at 61 ft from rear of truck....your eyes are still at 65ft
charliepatrick
charliepatrick
Joined: Jun 17, 2011
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December 4th, 2020 at 8:57:18 AM permalink
I had mnisread it as 12'6" rather than 12'8"! Nevertheless I agree that if you were doing 25mph and kept to the 2-second rule you would be able to see the lights. Therefore you wouldn't be too near to the truck! However that wouldn't apply further back - now that's a mathematical puzzle depending on both of your speeds.
Gialmere
Gialmere
Joined: Nov 26, 2018
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December 4th, 2020 at 5:47:16 PM permalink
Quote: ThatDonGuy


The top of the truck is 5 1/3 feet below the stoplight, and 40 feet to the right of the stoplight
Let X be the distance you are behind the truck
Your eyes are 14 feet below the stoplight, and (40 + X) feet to the right of the stoplight
The minimum distance where you can see the stoplight is where the two height/length ratios are equal
40 / (5 1/3) = (40 + X) / 14
15 / 2 = (40 + X) / 14
210 = 80 + 2X
X = 65 feet


Quote: chevy


ray from light from signal to top right corner of rear of truck's van continues on to your eye.

similar triangles give (in feet)

x/(8+8+24) =((12+2/3) - 4) / (18 - (12+2/3))

x= (40 ft) * (104 in) / (64 in) =

x= 65 ft


Though this assumes your eyes are located at the front of your car. If we assume a car length of maybe 12 ft and driver's seat is say 4 ft from the front bumper....

x = 61 ft


EDIT: i.e. the car's front bumper is at 61 ft from rear of truck....your eyes are still at 65ft


Correct!
-----------------------------------


A man was waiting at a red light when an alligator and a parrot approached his car window.

The man rolled down his window to see what they wanted.

The alligator said "Excuse me sir, we have reason to believe you've taken hallucinogenics."
Have you tried 22 tonight? I said 22.
Gialmere
Gialmere
Joined: Nov 26, 2018
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December 7th, 2020 at 8:00:33 AM permalink
It's easy Monday. Let's dance...



The ratio of boys to girls at a high school dance is 9:10.

An extra 17 boys arrive and the ratio changes to 8:7.

How many girls are there at the dance?
Have you tried 22 tonight? I said 22.
Wizard
Administrator
Wizard
Joined: Oct 14, 2009
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Thanks for this post from:
Gialmere
December 7th, 2020 at 8:16:35 AM permalink
Quote: Gialmere

How many girls are there at the dance?



70
It's not whether you win or lose; it's whether or not you had a good bet.
chevy
chevy
Joined: Apr 15, 2011
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Thanks for this post from:
Gialmere
December 7th, 2020 at 8:17:28 AM permalink


B=# of Boys, G=# of Girls)

Originally : B = (9/10) G

Later : B+17 = (8/7) G

Solving

(9/10) G +17 = (8/7) G

G=70 girls (and B= 63 boys)

Gialmere
Gialmere
Joined: Nov 26, 2018
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December 7th, 2020 at 4:22:07 PM permalink
Quote: Wizard

70


Quote: chevy



B=# of Boys, G=# of Girls)

Originally : B = (9/10) G

Later : B+17 = (8/7) G

Solving

(9/10) G +17 = (8/7) G

G=70 girls (and B= 63 boys)


Correct!
----------------------------

Trust me ... You can dance.

Love,

Alcohol
Have you tried 22 tonight? I said 22.
Wizard
Administrator
Wizard
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December 8th, 2020 at 8:01:18 AM permalink
It's Toughy Tuesday and I am ready!
It's not whether you win or lose; it's whether or not you had a good bet.
Gialmere
Gialmere
Joined: Nov 26, 2018
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December 8th, 2020 at 8:08:22 AM permalink
It's toughie Tuesday. You're hexed...



A hexagon with consecutive sides of lengths 2, 2, 7, 7, 11, and 11 is inscribed in a circle.

What is the radius of the circle?
Have you tried 22 tonight? I said 22.
ChesterDog
ChesterDog
Joined: Jul 26, 2010
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Thanks for this post from:
Gialmere
December 8th, 2020 at 9:15:09 AM permalink
Quote: Gialmere


......
What is the radius of the circle?




Let r = the radius of the circle.
Let A = the central angle subtending a side of length 2.
Let B = the central angle subtending a side of length 7.
Let C = the central angle subtending a side of length 11.

Apply the "law of cosines" for each angle:
cos A = ( r2 + r2 - 22 ) / (2 r2 ) = 1 - 22 / ( 2 r2 )
cos B = ( r2 + r2 - 72 ) / (2 r2 ) = 1 - 72 / ( 2 r2 )
cos C = ( r2 + r2 - 112 ) / (2 r2 ) = 1 - 112 / ( 2 r2 )

Using "trial and error" to find r such that 2A + 2B + 2C = 360 degrees yields r = 7.

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