Homework Statement
Implement F(w, x, y, z) with an 8-to-1 multiplexer which is constructed from two 4-to-1 multiplexers. The control signals must be w, y, and z.Homework Equations
F(w, x, y, z) = \sum m(0, 3, 6, 8, 10, 13)
The Attempt at a Solution
I believe x is used for the strobes to...
Algebraically.
But I just got the answer. I used a K-Map to see the answer and then made a simplification (removing the ABD' term by showing it is irrelevant using perfect induction). It was cake after that. I still appreciate the response though.
Homework Statement
Given F = (A'+B')[ABD' + A'C + A'BD], simplify into a simplest product of sums.Homework Equations
The Attempt at a Solution
Multiplying through gives me A'BD + A'C. I have tried expanding, adding consensus terms, but I'm not sure how to take it from there. Additionally, I...
Homework Statement
Suppose that a, b, c are real numbers and x, y, z >= 0. Prove that
\frac{a^2}{x} + \frac{b^2}{y} + \frac{c^2}{z} \geq \frac{ (a+b+c)^2}{x+y+z}Homework Equations
Cauchy-Schwarz and Arithmetic Geometric Mean inequalities.The Attempt at a Solution
I wasn't really sure how to...
Look at your ODE. It's missing something. The population _DOUBLES_ every 40 minutes. You seem to have forgotten about this fact.
A suggestion: convert to hours at the very end.
It's clear the rate of salt entering the tank is 0, correct?
The rate leaving depends on the concentration and the rate of solution leaving, correct?
The concentration depends on the amount of salt and the amount of solution.
What is the amount of solution (aka the volume of the tank)...
Q = amount of salt in tank.
dQ/dt has units of mass/time right?
So the "rate in" and "rate out" must also have these same units.
Now, pure water enters the tank at the rate of 12L/min. That rate in contains no salt, therefore rate in = 0.
The rate out is tricky. The rate of salt leaving is...
OH, I see my mistake. I had
a^2 = -\left(\frac{bd}{c}\right)^2
Which is why I had the 2 inside the parentheses.
And from there we get a^2 = d^2 as well, and since one must be negative to satisfy ac+bd= 0 blah blah ab+cd = 0.
Thank you very much!
I tried that approach earlier and obtained
c^{2}(2-\frac{1}{b^{2}}) = 1
I was unable to manipulate it any further into something meaningful.
It feels like I am missing something from this approach as well.
Homework Statement
Suppose that a, b, c, d are real numbers such that a^2 + b^2 = c^2 + d^2 = 1 and ac + bd = 0. What is ab + cd? Homework Equations
a^{2} + b^{2} = c^{2} + d^{2} = 1
ac + bd = 0
The Attempt at a Solution
Clearly, ac = -bd. I know the solution is 0, but I am having trouble...