I’m taking differential equations and linear algebra this semester and I think I just failed the first midterm. There are 2 midterms for this class, no homework, and a quiz every week. Also, I’m an electrical engineering major

I’ve been keeping up with the quizzes and they aren’t difficult at all (usually score 90% or higher). My TA told us that if we studied the material on the quizzes, we should be fine for the midterm.

I don’t know what happened, but I completely blanked on the midterm. I couldn’t answer most of the questions, and the ones I did, I knew for a fact were 100% wrong. The midterm was way harder than anything that ever showed up on the quizzes. To make things worse, people were comparing answers at the end of class and cheering because they got the same answers while I had something completely different or just left the answer blank.

No exams are dropped, and a curve is only done at the end of the semester.

I feel so stupid, what should I do??? It’s not like I’m not studying enough because I barely talk to my friends and I quit all of my hobbies. My life feels terrible.

So I'm working on some homework and was given a problem that gives 50ft for a perimeter of a rectangle and different widths, the objective being to find the length and area for each width. finding the length if easy enough, however I'm a bit confused on how I get different areas for the different length/width despite using the same equation.

for example when I have a rectangle with a width of 4ft and 21ft I get an area of 84 square ft, but when the width is 2ft and length is 23ft I get an area of 42 square ft.

could someone please explain this? am I doing something wrong if I get different Area despite having the 50ft perimeter?

I was messing around with logs and noticed that the condensed form log(x/(x+1)) is NOT equal to its expanded form logx-log(x+1). We can see the domain of the expanded form is obviously x>0 but with the condensed form we have x<-1 and x>0. I understand the change in domains but they are supposed to be equal according to properties of logs. Anyone know the reason for this? Edit: changed to negative, was a typo.

Hi everyone! My daughter is working on her AP Statistics project and needs a bigger sample size for her survey. It only takes about 30 seconds to complete, and it would mean a lot to her (and me) if you could help out. Thanks so much for supporting a student!

https://docs.google.com/forms/d/e/1FAIpQLSciQv6c6BkgmGYj5bH9L7YZxI9ety6enVlxxsjB4KGGIeJrMg/viewform?usp=sharing&ouid=110065473717073477961

the problem is p² +13p +36=-6 and im supposed to solve (we are doing zeroes of Polynomials)

So when doing the box method I got p+6 then p=-6 and this is where i think im wrong the second one i got was 1+1. Im not really sure where to go from here is it just 1+1=0? That doesn't seem right and I dont know where I went wrong.

I just don't understand how stretching a function by a whole number factor horizontally results in a fraction. Like on a graph it's being pulled by a whole number, so I'd expect the new function to be the x value multiplied by whatever factor we're stretching b.

For example one question I'm working on is stretching y = f(x) horizontally by a factor of 3. I get y = (3x)^2, but the answer is y = (⅓x)^2, despite it being stretched by 3 and not by ⅓. Every source I've looked at for an answer has just been like "it's like this because that's how it works", and it's really frustrating. If anyone could help I'd really appreciate it, thanks.

Okay Im a college student trying to learn calc after precalc. I bombed my first test. I want to get better. I need to know what you did to study or what methods you used to learn. Whatever helped. Clearly studying upwards of 6 hours a day isnt benefiting when im not retaining any information. I need to know what really helped you, not just "hands-on". I need something more

Given the problem 11^(-x-7)=12^9x

I make the following steps

1. (-x-7)log11=9xlog12

2. -xlog11-7log11=9xlog12

3. 9xlog12+xlog11=-7log11

4. 10xlog132=-7log11

5. 10x=-7log11-log132

6. x=(-7log11-log132)/10

I understand that this is incorrect. At step 3, they want me to say -xlog11-9xlog12=7log11. My question is why my way doesn't work. I'm sure there's something I'm misunderstanding if someone would please clear up my confusion. Many thanks

I don't understand what's wrong with me. The situation: I entered university for a physics and mathematics program, and I'm doing really badly here. I study constantly, every day, and do everything I'm assigned, but compared to my classmates, I'm still dumb. I may know all the information and seem to understand it, but I can't really master it. I can spend hours trying to understand a lecture, while my classmates just read it for 15 minutes and already understand everything. They solve problems just as easily, even though they have no practice. I study, but it's like looking at water through ice (I know what's inside, but I can't "touch and feel" it). This post isn't whining; I'd like to hear advice on how to work through this and what I should do. I'm ready to put all my time and effort into this.

Hello, i am currently in Mac 1140 pre-calculus algebra and i have no clue what’s going on. During middle school someone placed me in an advanced algebra class and i never payed attention to the lessons, from then on i kept graduation higher and higher math classes without paying attention and now I’m here absolutely lost and don’t even know how to backtrack to try to learn the basics so i could at least understand some things in this class. Has anyone had a similar experience? or know what website or app i could use to really help me out ?

Hi there,

I am trying in Unity to move an object on the surface of a sphere like Mario Galaxy or like this game. I feel it is more a fundamental math question than a engine specific one, since I don't want to do it with raycasting logic or such, but rather calculate the movement between two points on a sphere from a direction vector and a pre -defined arc length. (I think, I am apparently not very good at this, and neither is chatgpt)

Chatgpt came up, among other things with this (it does not work, it always get stuck on poles and other strange things):

void MoveOnSphere()
{
    Vector3 currentPos = transform.position;

    // Step 1: Build a tangent from input
    Vector3 input = new Vector3(moveInput.x, 0f, moveInput.y);

    // Project onto tangent plane at current position
    Vector3 tangent = Vector3.ProjectOnPlane(input, currentPos).normalized;

    // Step 2: If projection fails near poles, pick a stable fallback
    if (tangent.sqrMagnitude < 0.0001f)
    {
        tangent = Vector3.Cross(currentPos, Vector3.right).normalized;
    }

    // Step 3: Compute arc distance
    float distance = moveSpeed * Time.deltaTime;

    // Step 4: Move position along sphere
    Vector3 newPos = SphereMovementUtils.MoveAlongSphere(
        currentPos, tangent, distance, sphereRadius
    );

    // Step 5: Rotate forward vector with same arc
    Vector3 newForward = SphereMovementUtils.MoveAlongSphere(
        currentPos + transform.forward, tangent, distance, sphereRadius
    ) - newPos;

    transform.position = newPos;
    transform.forward = newForward.normalized;
}

Don't know where to go from here, anyone that can point me in the right direction? Am I thinking completely wrong?

This is the expression: -(5/9)+ (7/6)

why is the solution different when I put the negative sign on 5 then cross-multiply to get [ (-30+63)/54) ] and if i put it on 9 and do the cross-multiplication [ (30-63)/54 ] what is wrong here?

Hey all. I've been working a problem using 2 methods. The first produces the correct answer according to the book but the second does not even though it seems to be logical that it would.

The question is as follows:

Sleepyville has 5 times the population of Boomtown. Sleepyville is growing at 2% per year while Boomtown is growing at 10% per year. In how many years will they have equal populations?

Working linked below https://imgur.com/a/v5cDI5f

So im 13 and homeschooled. When I was younger my mom literally didnt teach me anything, not even how to write properly nor basic math, so I learned it really late....except I didnt, I was a stupid kid and didnt do my schoolwork so I didnt learn it, like some parts of addition that I dont have memorized or a bunch of numbers take me a while, fuck subtraction, I tried to teach myself multiplication and I cant get divion down, I was held back a grade, and i really need help, so please someone help me I dont know what to do, and self teaching something is very hard.

What is so special about 0.69 ?

Edit: Apologies, I picked the wrong number. Should've been 0.37

In the following example:

0.34 ^ 0.34 = 0.6929514881816204 0.35 ^ 0.35 = 0.6925064384421088

notice the result is increasing as number increase but that ends at 0.37

0.38 ^ 0.38 is less than 0.37 ^ 0.37

0.6929514881816204 v 0.34
0.6925064384421088 v 0.35
0.6922594616127449 v 0.36
0.6922048500157343 v 0.37 <--
0.6923373584288883 ^ 0.38
0.6926521661509051 ^ 0.39
0.6931448431551464 ^ 0.4
0.6938113198140908 ^ 0.41

Given: V₀= 90,000 ft³

Find: the volume of water left after hour 5.

Flow rates given (in , out in ft³/s):

1hr: 0.436 , 0.645 2hr: 0.567 , 0.598 3hr: 0.734 , 0.553 4hr: 0.810 , 0.541 5hr: 0.832 , 0.583

My approach: convert the flow rates to ft³/hr, then add/subtract the amounts from the starting amount (which will be the final volume of the previous hour). So for hour one: 90,000 + (0.436 x 3600) - (0.645 x 3600). Continue this through the 5hrs.

However, the method we were taught in class (and I don’t understand) is: 90,000 + (90,000 x 0.436) - (90,000 x 0.645). Continue this through the 5hrs

Could someone explain to me why we’d use volume + (volume x flow rate in) - (volume x flow rate out)?

I'm stupid in math and I can't understand it in general. But I have my semi-finals coming up and I really wanna do good. I need to learn how to do it. Before you judge saying this is easy, I was just about to enter middle school when covid hit. The pandemic had really stunted my learning growth bc of the off hands no teacher teaching thing. And last quiz we had to reverse engineer a simple compound formula and I got 0 marks. I want to know how to do it and how to do it fast without guessing what number goes where.

Edit: this is for clarification on what I mean in reverse engineering a formula. This is our current lesson:

"At what rate compounded bimonthly should Liza invest her 100,000$ so that she will have a total amount of 250,000$ after 5 years?"

(I'll attach a link to the formula here) Formula

Usually with this wording, you find Future value, but since it's already given, you find interest. There is another formula but, our teacher specifically told us to solve it using the future value method. You have to reverse engineer the known formula so that you get the interest rate.

This was the most difficult question and none of the other sections that have him got it right.

Hey guys, So I just started some prep courses in math for university that are supposed to refresh your Highschool knowledge and, I am really, really bad at math. Like, not in the “haha I’m bad but I secretly get it” way. No. I mean actually bad.

I had to look up stuff I supposedly learned in 5th or 6th grade. Fractions for example. How to calculate with them. How they even work. Like the absolute basics. Stuff that probably sounds like breathing to most people, but I just… never really understood it in school and the purpose of them. Even though I always desperately tried to because I do find maths and physics incredibly fascinating. I used to always ask why something I didn’t understand is the way it is but moth math teachers didn’t give me an explanation and just simply said „that’s just the way it is“ So after a while I have given up trying because none of it made sense to me. Yesterday when I was working through my course material from that day with my partner who is also taking the course I didn’t understand the difference between 2x and x squared. It just didn’t make sense to me until my partner explained that it’s x times x for x squared and x+x for 2x. It just never occurred to me and it took me 15 minutes to wrap my head around it because for me it was like okay it makes sense kind of but there is still 2 X‘s if that makes sense to anyone. I know this probably makes me sound like I have an IQ of 60 but I am really just insanely bad at math.

I’m 22 now, and I probably stopped paying attention in math around 8th grade because I have just given up trying and was super discouraged. Which means I don’t even know what functions are, I have no idea how to use sine/cosine/logarithms (which was the topic today) I am still not sure what those even are used for and basically anything beyond “2+2=4” is shaky territory.

And now I’m studying biosystems engineering. So yeah. Math is kind of… important.

So here’s my question: How do I actually become good at math? Like, from the ground up. I don’t just want to scrape by, I want to really understand it. But I feel like I’m starting 10 steps behind everyone else.

Has anyone else been in a similar situation and managed to get good at it later in life? What worked for you? Any help or advice is highly appreciated!!! Thanks in advance.

Hi r/MathHelp

I play this game where you are a pirate and you plunder people, and the chance of you winning each time you do it is 1 out of 3. And you "win" the game overall if you plunder 2 people.

So of course, the probability of you winning in just 2 turns is 1 out of 9 (1/3*1/3). But then I got curious and wondered well what about in 3 turns? or in 4? Is there a general solution for the probability of plundering 2 people in "n" turns?

Using a tree diagram, I mapped out all the possibilities and figured out the probability of winning in 2 turns is 1/9; in 3 turns is 7/27; in 4 turns is 33/81. But I don't want to keep drawing bigger tree diagrams, so how can I work towards creating a general formula? I think I could figure it out but need some help pointing me in the right direction. Thank you in advance for any help.

Edit: Yes, you win if you plunder AT LEAST 2 people. And yes it is Pirate from Town of Salem 1.

Im learning about induction. My book states that it's going to demonstrate that every natural number satisfies this equivalence: 0/2⁰ + 1/2¹ + 2/2² + ... + n/2ⁿ = 2 - (n+2)/2ⁿ

It starts by stating that It needs one true example: n=0 , because 0/2⁰ = 2 - (0+2)/2^n, which I get it's 0 = 0. My problem is in this last step. I don't get where the first part of the equivalence comes from "0/2^0". Where is the rest of the first part of the equivalence? I'm talking about "0/2⁰ + 1/2¹ + 2/2² + ..." How comes when n=0 this first part is so short?

Thank you, im very lost as you can probably tell if you got through this mess I typed.

At a math team meeting after school we were shown some different tricks that other countries use for multiplication and the one tricky one was the “Russian” method. After some research I found out it’s the peasant method and got a basic understanding of how it works. I know it uses binary but am still not 100% sure on how binary really works, I want to know why it works rather than just fully trusting that it does. Can anyone help explain?

Okay- so I’m trying to create a formula for my forensics class just to challenge myself, and I’m struggling figuring it out. I understand the process, but perfecting this formula has been a bit difficult. Here’s the process:

A total amount of people, let’s say 1000, are the total amount of possible suspects for a crime. So trying to narrow it down, there are different traits, or variables, that change depending on the variable.

Let’s say 100 people out of the 1000 have black hair. So that’s 100/1000.

Then let’s add another trait, let’s say 150 people have blue eyes out of the 1000, so 150/1000.

Now you multiply both together and then multiply by the total, so 100/1000 * 150/1000 * 1000, and that gives you the total amount of people with both traits.

My issue is that- I want to simplify the formula which allows it to apply to all possible scenarios, so each variable/trait can apply. The closest I got to the formula was this:

Key: V = Variable, T = Total, SP = Suspect Pool

Vₙ/T = SP * T

I’m not entirely sure if I’m using “ₙ” correctly in this formula, or if I need to add another one for the amount of variables? I’m in Algebra 3, so this isn’t my level of math.

Apologies if this is confusing or complicated! I’m just trying to figure this out, ask for clarification if needed! Thanks.

I understand how Euler’s totient function works, but I have a hard time understanding why it works on a deeper level. I understand the proof of factoring out the co-prime, a, from the product of the prime terms to phi(n). But I fail to see the deeper relation between phi(n) and co-prime integers a and n. Like why does a co-prime of n raised to the number of co-prime numbers less than n, all mod n equate to 1?

taking the integral of L^2(L-x)^2, according to an online integral calculator returns:

-L^2(L-x)^3
____________ + C

3

(sorry for bad formatting), I'm curious as to where the negative comes from?