helperid1839321

A short cylinder made of a piece of paper will hold more than a tall one. You are taking the square of the longer side versus the shorter one.

\(11\pi(\frac{8.5}{2\pi})^{2}=\frac{794.75}{4\pi}\ \textrm{vs.}\ 8.5\pi(\frac{11}{2\pi})=\frac{1028.5}{4\pi}\)

Is a definition given for how tall one story is?

Could you please repost this question? We can't see your numbers for the problem.

John has a 100% chance of being there if he arrives at 2:20 or earlier. Add 1/3.

At 3:00, he has a 1/3 chance. We can take this and take the average from 2:20 and 3:00 to get 2/3 for this 40 minute period. Multiply this by the portion of time. Add 4/9 to the probability.
Result: He has a 7/9 chance of catching the train.

Sorry, could you please edit it so we could see what you are talking about?

Sorry if I didn't clarify. I wasn't looking for the area of the triangle, I was looking for the area of the part of the section of the circle that wasn't a part of the triangle, but was ont the other side of the chord with the sector.

Thanks though! 

I will call the distance from B to C x.

Since all of the points are equal distance from eachother, \(FG = 3x \operatorname{and} HI = 4x\).

Area of a trapezoid = \(^{1}\!\!/\!_{2}(b_1+b_2)\times h\), where h = height, b₁ = length of bottom, and b₂ = length of top.

Area of FGIH = \(7x(\tfrac{\sqrt{3}}{2}x)=\tfrac{7\sqrt{3}}{2}x^{2}\)

Area of ABC = \(x(\tfrac{\sqrt{3}}{2}x)=\tfrac{\sqrt{3}}{2}x^{2}\)

Area ratio of FGIH to ABC = \(\tfrac{7\sqrt{3}}{2}x^{2}:\tfrac{\sqrt{3}}{2}x^{2}\) --> \(7:1\)

Your post just reminded me of something - 

When writing a number in base 3, all numbers that are multiples of 2, when taking the sum of their digits in base 3, were even.

I tried this out with 4 and 3, and it worked there as well.

I then figured out a pattern that I forgot to ask about - 

When writing a number in base x, do all numbers that are multiples of \(x-1\), when taking the sum of their digits, make another multiple of \(x-1\)?

This all started because of the trick that I used to figure out if a number was a multiple of 9 - sum up the digits until they are one. If it is 9, then it is a multiple of 9.

Deja vu...

I once did that, then realized what happened when I gave a thumbs down. I hope I got everyone I put down and gave them a thumbs up instead! 

That's a really cool drawing! Why didn't you tell us you were an artist or post about it?