The two problems are taken from this derivation of the inclusion-exclusion principle:
They are added in the document. Let me know if the documents does not work
Theory of Numbers (XVI)
Principle of Mathematical Induction
Prove that if n is an odd positive integer, then x + y is a factor of x^n + y^n.
(For example, if n = 3, then x^n + y^n = ( x + y )( x^2 - xy + y^2 ) )
See the attached file.
How does it work?
How does it apply or use magnetism?
Which basic equation(s) govern itsoperation?
Does this device have historical significance? If so, what is it?
What do you envision as the future of this device?
Can you imagine any other applications of the device?
1) Prove that in the equation x^2 - 3xy +2y^2 - 2x - 3y - 35 = 0, for every real value of y there is a real value of x, and for every real value of x there is a real value of y.
2) Use the Principle of Mathematical Induction to prove:
a) For every positive integer n, 4^(2n + 1) + 3^(n+2) is a multiple of 13.
b) 3^n > n^2 fo
A 3 phase, 50 Hz, 6 pole wound rotor induction machine has the following per phase parameters:
Rs = Negligible
Ls = 0.003 H
Rr = 0.3 Ohm
Lr = 0.002 H
Lm = 0.1 H
Rc = Infinity
Ns/Nr = 1.2
The voltage applied to each phase is 240 Vrms.
Find: the starting torque,
the maximum torque, andthe speed at max
A 12 pole, 60 Hz synchronous machine has an internal rms voltage of 10 kV.
Its internal synchronous reactance is 10 ohms. The machine is connected to a network
with a terminal voltage of 11 kV rms. The phase angle difference between the internal
and external voltages is 30 degrees (internal minus external).
(a) Is this machi