Math Is Fun Forum

I prefer (2)(3) = 6, typically reserving

Geeze I got a virus a while ago but with a trio of antivirus/antispyware programs I hope it's completely gone by now... hope this worm isn't lying dormant somehwere... :S

1. Sonic the Hedgehog
2. confinement
3. bread

The formula for the volume of a cone is

If the similar tank has the same ratio of dimensions, then we know

Therefore,

So when V is doubled, r is multiplied by the cube root of 2.

Therefore, the new tank will have a radius of

Thanks Jane. The solutions have

Also I tried to work this out using the difference in kinetic energy since

But I get a different answer! Isn't

thanks Jane I've got it now

Amazing ganesh, I don't think i have ever seen you use the same picture twice

A longer but geometrical (yay) proof

Let points BCE be collinear and let point A be such that triangle ABE is isosceles with AB = BE, and triangle ACE is isosceles with AC = AE. Let D be the point where the angle bisector of <CAE touches CE. AE = 1 and cos(<ABE) = pi/5

Then,
Since <AEC = 2pi/5 , then <ACE = 2pi/5, <BCA = pi - 2pi/5 = 3pi/5, <BAC = pi/5.
∴ ABC is isosceles. So BC = AC = AE = 1.
Now, <CAD = pi - pi/2 - 2pi/5 - pi/10, so sin(pi/10) = CD/AC = CD
∴ BD = BC + CD = 1 + sin(pi/10)

Since CD = CE (bisector), BE = AB = 1+2sin(pi/10),

So, from triangle ABD,

And solve for sin(pi/10)

You can then use formula to find cos(pi/10)

Nowhere near 10 seconds but at least I did them in my head

I would love to know the answer to 1038, but I'll let others have a go first (quick, someone answer it!)

1] kitten
2] loud
3] invisible