Recent content by Kizaru

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...

Err yes, it should be x,y,z > 0. I haven't touched it since last night, so I'll see where I can get with the simpler problem today.

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...

What does f''(x) indicate about f(x)? When you see this, you will realize how the f'(c)=0 comes into play.

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.

Er yes, I got them mixed up. He probably caught it though.

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)...

Try to model a diff eq for the volume of the tank at all times. You will figure out the volume from there, and then you can use that in dQ/dt

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...

boboYO, that is a very interesting solution. Thank you!

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...

YES! Thank you. That's exactly what the result should simplify to (it's very similar to that of a toroid, after all a toroid is roughly just N of those). Thank you. You were right, I didn't make the assumptions in Mathematica, but I'm still quite a novice and don't know how to do that yet...