Math Is Fun Forum

Correct, Mathsy!

Problem # n+10

Mathsyperson, Kylekatarn and wcy are a team for solving problems. The possibility of one solving a problem is 45%, the other is 50% and the third is 55%. What is the probability that a problem would be solved?

A quonset hut would be half of a right solid cylinder. Length is given as 205  feet. Width is given as 80 feet, and height 24 feet. But if the width is 80 feet, the height would have to be 25.46479 feet. That is obtained by dividing 80 by pi.
The volume would be pi*r²*h/2 = (3.141592 x 648.4556 x 205)/2
= 208,811.285 cubic feet

If the value of the current month is B and the previous month A,
[(B-A)/A]*100 is the right way of calculating the percentage increase, which you have done. Problem arises when the difference is 0 and both the values are 0. I don't think there is any mathematical solution, but if you could program in such a way that
the formula is applied only when the difference ≠ 0
and when the difference is zero, the percentage change is zero,
your problem could be solved!

Problem # n+8

Can you find two numbers composed of only ones which give the same result by addition and multiplication?

Welcome to the forum, Tahlia!
Keep visiting, new pages are being put on the website! You'd love them too!

Yes, I used logarithm to the base 10 for convenience.
The idea is to show that
Infinity + 1 = Infinity
Infinity + Infinity = Infinity
Infinity x Infinity = Infinity
Infinity ^ Infinity = Infinity
Infinity ^ Infinity ^ Infinity ^ Infinity ........Infinite times = Infinity
This is true because because we can never say for what value of n
log(n)infinity would be undefined.
And this is only the fourth stage of iteration (also referred to as 'tetration').
No wonder, Infinity is beyond comprehension for the human mind!

If we are talking of infinite number of zeros after the decimal, before the 1, in b,
the proof is correct!
Because, a²-b² would be equal to a-b.
This is because we have defined 0.0000000000.......1 as 1 ater an infinite number of zeros after the decimal followed by 1,
as kylekatarn denotes 0.(0)1.

However, if the number of zeros is finite, (Don't worry, it is not)
a²-b² would contain more 9s than a-b.

Oops, I made a mistake.

If, as I had said earlier, x∈ Real numbers,
my question would have no answer as
(-1 x 10^n) -1 would give a negative odd number for a
large value of n (n ∈ Natural Numbers).  And this number raised to itself would give a negative number which would be much lesser than zero!
Therefore, the smallest value would be -∞

I forgot while posting that one that a^-n = 1/a^n
Therefore, the minmum value of x^x is not -∞
I am sorry I wasn't concentrating 100%

0^0^0 is not defined.
But for 1, as you pointed out,  2^Mx > x^x^x.
For this problem, let us take value of x ≥ 2, x ∈ N

0.(0)1 is 1/(10^ ∞)
When I had to deal with numbers like 9.9999999999999999999....8,
I put a horizontal arrow pointing towards the right above the 9 after the decimal.Then I put the number 8. This meant that 9 keeps on recurring but the last digit is 8. But your method seems better, more convenient. Whether it would be accepted by Mathematicians worldover is another thing!

But the point I wanted to make is 0.999999999999...................... is a devilish number and would never be found in any mathematical problem or solution. It cannot be represented in a graph, It cannot be said to be irrational, yet it cannot be expressed as a rational number. It is not a transcendental number. As a rule, it should be possible to represent all decimals as a rational number. But this number defies the rule, although it is a recurring decimal. Sin 89.99999999999999999999999999999........ degrees can be said to be equal to this number. 

I give up..........

Problem # n+7

If x ∈ Real Numbers, What is the minimum value of x^x?

Reminded me of one of Murphy's Love Laws:-

Brains x Beauty x Availability = Constant