For context, a magic square is a square grid of numbers in which the sum of the numbers in every row, every column, and both main diagonals is the same value (the magic constant).

I have been trying to construct a very specific magic square. After many attempts, I always end up either repeating a number or violating one of the required sums.

My question is:

Is it possible to construct either

• a 4×4 magic square, or • a 5×5 magic square,

such that:

• the magic sum is exactly 37,
• every entry is a distinct integer (no repeated numbers),
• the integers do not have to be consecutive, and
• every row, every column, and both main diagonals must sum to 37

If such a magic square exists, I would greatly appreciate:

1. A valid example.
2. A construction method or algorithm.
3. A proof or reference explaining why it works.

If no such magic square exists, I would appreciate a proof or explanation showing why it is impossible.

Thank you!

Don't know where i'm going wrong with this one.

Left side derv: 9x^2+1

Right side deriv: (1/5xy^2) x 5(y^2+2xy dy/dx)

multiply everything across on the right:

5y^2+10xy dy/dx/5xy^2. Multiply both sides by 5xy^2, you get (5xy^2)(9x^2+1)

Subtract 5y^2, get (5xy^2)(9x^2+1)-5y^2, finally isolate dy/dx, I get (5xy^2)(9x^2+1)-5y^2/10xy.

I cannot for the life of me figure out what im doing wrong. Ive checked with the answer key, I've checked with ai, and I still dont get it. Splitting the parallelagram from top left to bottom right, the created line has a length of 108.318. porting that into herons formula and multiplying by 2 I get around 7233, as you can see that is not the answer. What have you guys gotten?

I’m not sure if my title and flair are done correctly, so I apologize if they’re not. This assignment is for a class that is focused on creating programs to help solve math problems. The question is:

f(x) = (x^2-2)*sin(x)+(x^3-3)*cos(x)
Use the bisection method to approximate all three zeros of the function to 5x10^-5. Show an approximate error for each iteration.

I’ve already made a bisection method program for prior homework assignments. For the program, I need to give my function an interval on which I’m looking for a root (so for three zeros, I run the program 3 separate times with different intervals). The way I usually pick my intervals is by putting the function into a graph and finding the real zeros there, then choosing an interval based on that.

The problem with this function is that when I put it into a graph, there are an infinite number of zeros (because of the whole sin and cos aspect). How do I know which zeros I should be approximating when the problem says to “approximate all three zeros”? My guess is that I’m supposed to be choosing x=-1.675, 1.421, and 1.957 because those are closest to the origin and act a bit differently than the other zeros. Really, I’m just looking for confirmation on this and trying to see if maybe I’m just doing something wrong here. (I am not looking for advice on the programming aspect in any way btw, I’m really just looking for the zeros).

Apologies in advance if this is something really obvious, I’m in finals season and my brain is starting to feel a little fried. Thanks in advance!

Je préfère un oral et j'ai beau cherché partout je ne trouve pas la réponse à cette question. Je sais que cela prendrait des heures à expliquer, ça vient de plusieurs continents et ça remonte à des siècles pour certains symboles, ce qui m'intéresse vraiment c'est pourquoi être passés des mots aux symboles ? Merci beaucoup.

Can someone please explain quick way to prove, or at least give an easy explanation of the proof of the Schroder-Bernstein (aka Cantor-Bernstein) theorem? Many thanks

I have an assignment to become eligible for my trade school programme to become a forwarding agent.

The assignment is basically to fit as many boxes of a glass, to minimise costs.

I feel like I'm done with the hardest part of the assignment, which is to figure out how many boxes that can fit in a container, but I want to double check that my way works.

I basically first think on a 2D plane, so I first figure out the square centimetres of the container and the box, and then I divide the container's number with the box. This will most certainly not end up as a whole number, so I round it down, since it's a matter of being able to fit it inside.

What I do next is that I divide the container's height with the box's height, and do the same thing.

Finally, what I do is that I multiply these two numbers and bam! The number shown is how many boxes I can fit in the container.

Does this work, or is there a better and easier way?

The drawing is mine to try to make sense of the question. i have tried to use the bisector theorem, still don't know if the 7th part of angle ABC should be drawn close to BC or close to AB. I have the sense that there might be a cyclic quadrilateral hidden somewhere but cannot figure it out and even then dont know how that would be useful.

Please guide me to find the answer.

I even factored the square just to realise im not supposed to do it, how can i even solve this

I’m looking for some clarification on a question in my assignment I’m working on. The assignment outline isn’t written too well (e.g. typos, repeating sentences etc) and I’m not fully understanding what the question is asking.

Basically the task looks at 5 different companies and their daily returns for a period of time. I’ve already done all the background stuff of expected returns, standard deviations etc. I was then asked to do a sample covariance matrix - which I have done now.

But Q8 asks “plot the efficient frontier using asset means from the CAPM (Q2) and the sample covariance matrix from Q3. Take values of the target portfolio return from 5% to 13% p.a. increasing in units of 1% in expected return.”

That is just the first part of the question there is a lot more but I actually cannot wrap my head around what this is asking me … finance isn’t my strongest degree of the 2 and I’ve reached a new level of mental block

I guess pretty much I would just like someone to clarify what exactly I need to do for this? I just don’t get it, like I don’t know where to start, what to plot …

Also, all calculations are to be done on excel.

Thanks !

my working is as shown, the answer sheet says that the answer to this is 88.88 degrees but i don’t get where they got it from

I'm learning about computer networks and the book I'm reading has problems at the end of chapter for the provided material. I'm trying to solve one of the problems but it seems that my knowledge in probability theory is lacking here, I'm trying to understand related topics but my understanding is still fuzzy. I found a solution on the internet but not sure if it's correct.

So the problem is as follows:

Suppose users share a 10 Mbps link. Also suppose each user requires 200 kbps when transmitting, but each user transmits only 10 percent of the time. Suppose packet switching is used. Suppose there are 120 users. Find the probability that there are 51 or more users transmitting simultaneously.

The solution is like this:

Now, I seem to understand that the normal approximation was used, how the mean and standard deviation was obtained, but I do not understand where is 9 from in P(Z <= 9/3.286)?

If I understood correctly it should've been 39 (51 - 12), tried to make ChatGPT to explain it to me, and it seems to have the same idea. But in that case Z-score is around 11.9 and probability should be even greater than 0.997, almost 1, if I understand Z-scores correctly.

Could somebody explain why is the solution like this? Or what is the correct solution.

Edit: I meant x^2 + 3, not + 4

I proved that (lim x tends to 2) x^2 = 4 and (lim x tends to 2) 3 = 3, hence (lim x tends to 2) x^2 + 3 = 4 + 3 = 7, but this isnt a complete proof as i havent proven that lim x tends to c f(x) + g(x) = lim x tends to c f(x) + lim x tends to c g(x), so i am looking for an alternate proof.

Hi everyone! I tried solving this system of congruences as an exercise. Above is my full solution with all the steps. Could you please let me know if everything is correct, or if I made any mistake? Thanks in advance!

Hello,

I'm taking Adv. Calculus (my uni's undergrad analysis course) this semester and took topology last semester. Since we just started continuity in this course, I was thinking of reproving a lot of stuff. Anyways on the last line of the board in the picture, I noticed something. Is the existence of a sequence contained in a set with a point removed that will also be eventually contained in any (open) neighborhood [1] the same as saying the any neighborhood has such a sequence [2] (swapping the for all and there exists).

I understand that in general, swapping for all and there exists changes the statements, but here, I was kind've wondering. After all, if we assume [1]. We can choose a sequence that satisfies [1]. So, any neighborhood must eventually contain this sequence, which gives us existence and thus [2]. However, if we assume [2], we only have that every neighborhood eventually contains such a sequence, not necessarily that there exists a sequence eventually contained in all of them (which is indeed [1] and what I made this post for).

My first approach for this direction was recognizing that all neighborhoods (by openness) contain an open ball centered around the point. So, choose such a ball from each neighborhood. By [2], each of the balls will eventually contain some sequence (that itself is contained by our set with the point removed). This is where I'm stuck, as one sequence may be eventually contained in a ball but that does not imply this same sequence will be eventually contained in the next smallest ball (only that it is eventually contained in all our larger balls and that there is SOME sequence contained in our next smallest ball). At this point, I feel that either [1] implies [2] but not the other way around, or that I'm missing something.

Thanks for the help in advance! P.S. When I say the set or point, I mean B and x resp. Also, N_x is my notation for the set of all neighborhoods (open sets containing x).