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#4 Re: Help Me ! » Express 30^(30^30) as a^(b^c) » 2015-08-27 19:46:48

Sorry, I thought I had a solution but it was wrong.

#9 Re: Euler Avenue » What had you learned today that you found interesting? » 2015-07-26 09:56:42

Today I learn that the golden ratio has the following interesting property:

http://mathhelpforum.com/algebra/246829-expression.html#post864349

#15 Re: Help Me ! » Solve this differential equation » 2014-07-31 03:41:26

Write the equation as

and use the substitution

#16 Re: Help Me ! » Challenging Applied maths question projectiles » 2014-07-27 00:47:32

Just solved it! big_smile


In solving algebraically for
you need to take the minus sign in front of the square root:



This value of
will work. In other words the bullet hits the plane on the way up rather than on the way down.

The computation is straightforward but tricky. You just need to take extra care not to make any careless mistake. smile

#17 Re: Help Me ! » Challenging Applied maths question projectiles » 2014-07-27 00:25:43

When the shot is fired, the plane has travelled a horizontal distance
. (You can picture this by drawing a diagram.)

The time taken for the bullet to rise to height
is given by



I think the idea is to solve for
algebraically and show that
(horizontal distance travelled by bullet)
(distance travelled by plane after passing gun).

#18 Re: Help Me ! » Unit circle / Geometry » 2014-07-25 22:07:49

It’s a unit circle so its radius is 1.

#19 Re: Puzzles and Games » problem on trains » 2014-07-25 21:48:12

Let the length of the train (in km) be
.

Let the speed (in kph) of the train relative to the first person be
; then its speed relative to the second person is
.

Therefore:

Hence:

So the train’s length is 0.05 km – i.e. 50 m.

#21 Re: Dark Discussions at Cafe Infinity » Brazil 1-7 Germany » 2014-07-14 01:38:34

Germany 1-0 Argentina after extra time. Well done Germany! cool

#22 Dark Discussions at Cafe Infinity » Brazil 1-7 Germany » 2014-07-08 22:43:37

Nehushtan
Replies: 14

Germany – out of this world!

Brazil – out of this World Cup …

20140708Brazil1-7Germany.jpg

#23 Re: Help Me ! » Factoring x^3-3x^2+x=0 » 2014-06-30 00:03:16

That’s all you can do. The quadratic polynomial



is irreducible over
and
.

In a way you could write

but this is probably not what you want.

#24 Re: Help Me ! » Sequences » 2014-06-08 00:44:07

Agnishom wrote:

The series is undefined as the first term is
.

#25 Re: Help Me ! » Inequality? » 2014-06-03 10:28:27

Agnishom wrote:

If a,b,c > 0
and abc=1

Prove that a^2 + b^2 + c^2 ≥ a+b+c


Jensen’s inequality states that if
is a convex function then



The function
is convex; therefore



But
by AM–GM.

Hence

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