I have been stuck on a question for a bit now and I’m wondering if anybody here can help out. The question is this: “Two containers A and B contain the same amount of liquid, V liters. At time t=0, B contains pure water while A contains a paint mixture of F liters of paint and V-F liters of water. At time t=0, A begins to be supplied with clean water from a container C, and is simultaneously emptied of liquid into container B, which in turn is drained of liquid. All this with the same inflow rate, R=10 liters per second. In other words, the volume of liquid in containers A and B is constant ..read more

So, the value I've gotten for the number of classes is 6 (rounded up) but in the FDT, I got up to 7 classes because the highest number in the given data set is 1 number higher than the upper limit of the 6th class. I have no idea if skipping a number between classes is allowed or if the upper limit of a class is always 1 number below the lower limit of the next class, my math teacher didn't really give us a hint or said anything on what to do in this current situation. Based on what I've been taught, my procedure is that I would 1st get the range which is Highest number - Lower number = 36 ..read more

I'm working on Exercise 5.32 in The Knot Book by Colin Adams, which asks to prove that an algebraic link that has exactly one negative sign in its Conway notation has an almost alternating projection. In Adams et al.'s paper, they provide a proof for this (in the proof for Theorem 3.1), but I'm confused by the reasoning. They say, "Using Conway’s rules we can move a negative sign through the notation to the end of a parenthetical or to a period." What rules allow for this? I'm using just The Knot Book right now, and it doesn't seem to answer this. "If the last integer in the string after thi ..read more

obviously can't be done analytically, the phrase my question better. are there any numerical approaches that will always converge on every root eventually? I've been trying to figure this out for a while(I'm a bit of an amateur) but I can't seen to find out if its even possible. I've tried just about every root finding alg mentioned on Wikipedia with mixed success. I'm guessing there's a step I'm missing, do I need to first utilize the information in the coefficients and perhaps derivates to "tune" my methods? Usually 95% confidence would be enough be my project runs on a shader, meaning ever ..read more

https://quickshare.samsungcloud.com/kb1cgShVHt6f Hello mathematicians! Please do not give me the answer. I just need help putting together the equation. I went with this X=2X+15 but the answer did not make any sense. Please and thank you submitted by /u/Kratz17 [visit reddit] [comments ..read more

Hi! I’m practicing calculating the determinant of matrices because its been like 4 years since i last did it. And like. My answer to the following question is wrong according to both the answer key and a random calculator and i dont get it! | -5 -5| |-3 5| So i did (-5x5)-(-5x3)=-10. The answer key says its -40. Just what? EDIT: i realized i used 3 instead of -3 submitted by /u/JaysStar987 [visit reddit] [comments ..read more

This is the part of the proof I don't understand, https://imgur.com/a/snnmgmX . I understand that each row has linearity since each column has linearity and the determinant of the matrix is the determinant of the transpose, but how does that imply what it says that it implies? submitted by /u/CPDrunk [visit reddit] [comments ..read more

Can a 6 sided polygon NOT have exactly 6 interior angles? I'm creating definitions of shapes for myself to memorize, but the source I'm learning math from gives some pretty long definitions. For example, it said that a hexagon is a straight sided polygon with 6 sides and 6 interior angles. But a polygon is already straight sided, so they just made the definition longer without needing to. So I'd also like to know if anyone knows of a website with the shortest possible definitions for people learning math. Or if you know how I could find a website like that. Thank you! submitted by /u/Profess ..read more

Ok this might be dumb but I am doing some trig questions and I need to show exact form. Is there a way to get -cos(5pi/6) to show exact form on calculator. I know the answer is sqrt3/2 but my calculator only shows 0.8..... I have tried changing to radians and maths10 and all that but idk. (calculator model is casiofx-82AU) submitted by /u/PotatoSacks-com [visit reddit] [comments ..read more

why does multiplication mean "and" when dealing with probabilities? I understand that the probability of multiple events all occuring should be less than the probability of any single event of those, which makes sense, but why does that decrease in the ptobability be assosiated with multiplication, and if so, why is it different for dependent events. regarding the last point of dependent/independent events, I could actually be mixing things up, so another potential scenario would be that the probability of multiple events occurring at once doesn't generally have a rule but it's specific for i ..read more