Post your math problems here

@e4e5f4exf4nicht said in #14:

But what is 2+2 mod 3...
Depends on which way you see it.
2 + (2 mod 3) = 2 + 2 = 4.
(2 + 2) mod 3 = 4 mod 3 = 1.

What is
The point P is inside a rectangle. The distance from P to one corner of the rectangle is 5 cm and its
distance from the opposite corner is 14 cm. The distance from P to a third corner is 10 cm. What is
the distance, in cm, from P to the fourth corner?

@ForumMathSolver said in #29:

Just to clarify, the lines joining X to the two sides are such that the angle formed between them is alpha, right? In other word, there are other such lines possible, right?
Yes, and you can rotate it.

@imminentloss-foryou said in #32:

The point P is inside a rectangle. The distance from P to one corner of the rectangle is 5 cm and its
distance from the opposite corner is 14 cm. The distance from P to a third corner is 10 cm. What is
the distance, in cm, from P to the fourth corner?

Let the corners be A, B, C and D. Let PA = 5 cm, PC = 14 cm, PB = 10 cm and we have to find PD.
PA^2 + PC^2 = PB^2 + PD^2 [British Flag theorem, where P is an internal point in rectangle ABCD]
Thus, 5^2 + 14^2 = 10^2 + PD^2
Thus, 100 + PD^2 = 25 + 196
Thus, PD^2 = 221 - 100
Thus, PD^2 = 121
Thus, PD = 11 (PD is positive)

Can you explain this Symbol :

Doppelpfeil (double up arrow)

stellt Tetration dar (stands for tetration)

In easy language please

@e4e5f4exf4nicht said in #35:

Can you explain this Symbol :
Doppelpfeil (double up arrow)
stellt Tetration dar (stands for tetration)
In easy language please

A simple way of understanding:
Addition: a + b = Well, I hope you know what it means. For example, 2 + 3 = 5.
Multiplication: a x b = a + a + a + ... + a (b times). For example, 2 x 3 = 6
Exponentiation: a^b = a x a x a ... x a (b times). For example, 2^3 = 2 x 2 x 2 = 8
Tetration: (^b)a or a <double arrow> b = a^a^a^a^...^a (b times). For example, (^3)2 = 2^2^2 = 2^4 = 16 (calculation always starts from the top)

Thank you for the british flag theorem. Until now I've never heard of this generalisation of the Pythagorean theorem.

@e4e5f4exf4nicht said in #37:

Thank you for the british flag theorem. Until now I've never heard of this.
No probs! It can be proved using the distance formula or the Pythagorean Theorem.

Them: Easy Peasy, Lemon Squeezy!
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