Homework Statement
I would like to send a packet of size 1500 kilobytes from point A to
point B. There are a total of 3 links that it has to cross, of length 1000,
2000, 3000m respectively. The bandwidth on those links is 100, 1000,
and 500 kilobytes/second. Assume that there is no...
Homework Statement
A, B, I-Y^-1, X, Y are n x n invertible matrices
(A(I-Y^-1))^-1 = YB
Solve for Y
Homework Equations
The Attempt at a Solution
(I - Y^-1)^-1A^-1 = YB
(I - Y^-1)^-1A^-1B^-1 = Y
A^-1B^-1 = (I - Y^-1)Y
A^-1B^-1 = Y - I
A^-1B^-1*(A^-1B^-1)^-1 = Y - I(A^-1B^-1)^-1
I = Y -...
Homework Statement
Show that if a = (b mod m) and c = d(mod m) and m => 2, then a - c = (b - d)(mod m)
Homework Equations
c = d(mod m) <=> m|(c - d)
d = c + xm
The Attempt at a Solution
I don't know how any equivalences for a = (b mod m), is there a way to get b from a = (b mod...
Uh ok... what's wrong with what I did? I did c|ac = a, before and that apparently that's wrong so I used bc/c = b, this time. How else do I cancel out the c?
Should it be c|bc = c|acy => b = ay ?
Is my solution correct or wrong?
For a|b <=> ac|bc
a|b = x
ac|bc = y
b = ax
bc = acy
bc/c = acy/c => b = ay
If b = ax and b = ay then x = y
a|b = x <=> a|b = y therefore a|b <=> ac|bc
Is this correct?
<=> is equivalence, not <->.
Is Epistemology a science?
Seems kinda similar... took an Intro Philosophy course before and a lot of it is about AIs, Turing Test, etc. and whether they can think or not. Lots of mentions of Computer Scientists, Cognitive Scientists, Neurologists, Behaviourists/Psychologists.
Homework Statement
If a, b < c, and d are positive integers, prove the following inferences.
1. a|b \wedge c|d \rightarrow ac|bd
2. a|b <=> ac|bc
Homework Equations
The Attempt at a Solution
1.
a|b = x, then b = ax
c|d = y, then d = cy
bd = axcy
thus ac|bd =...
Homework Statement
1. Prove the following subset relationships:
a. Constant \subseteq Logarithmic
b. Logarithmic \subseteq Linear
c. n log n \subseteq Polynomial
Homework Equations
O(1) Constant
O(log n) Logarithmic
O(n) Linear
O(n log n) n log n
O(n^m), m > 1 Polynomial of order m
The...
1. Let f, g: R -> R where f(x) = ax + b and g(x) = x^2 - x + 1. If (g o f)(x) = 9x^2 - 9x + 3, determine the values of a and b.
So I got g(ax + b) = (ax + b)^2 - (ax + b) + 1
(a^2*x^2 + 2(a * b)x + b^2) - (ax + b) + 1 = 9x^2 - 9x + 3
(9x^2 + 2(3 * b)x + b^2) - (3x + b) + 1
(9x^2 + 2(3 *...
Homework Statement
Let h: Z -> Z be defined as follows:
h(n) = 0 if n is even and 1 if n is odd
Determine h^2, h^3, and h^500
Homework Equations
The Attempt at a Solution
If n is even, h(n) = 0 then h(h(n)) = h(0) = 0
If n is odd, h(n) = 1 then h(h(n)) = h(1) = 1
If n is even h(n) = 0...