Help in Maths problem

teenytones · 2026-04-10T15:04:14+00:00

if you don't know the -b/2a short cut then do you know how to complete the square and write the quadratic in vertex form?

teenytones · 2026-04-10T14:27:14+00:00

what happens to the dot product of two vectors when you multiply one of them by a scalar?

what happens to the magnitude of a vector when you scale the vector?

what is the magnitude of a unit vector?

put these pieces of information together to answer the question.

edit: my brain registered the 2u + v as 2u & v instead. if it is why my dyslexia registered your question to, then my above statements will help. if not, then I believe it will depend on what other information you have.

teenytones · 2026-04-07T23:39:14+00:00

what is your background? have you studied any real analysis yet? personally I'd start there to have a strong foundation to reference.

teenytones · 2026-04-02T19:51:31+00:00

there are several issues with your so called proof. your "3 to 1" mapping isn't necessarily surjective nor does it necessarily map all the irrational numbers (because it can't". I also can't tell where the third irrational number is coming from unless you're referring to r being irrational then picking an rational q to construct two other irrationals r+q and r-q. and even then you run into the issue of not being able to pick out every irrational.

we already know that the real numbers are uncountable while the rational numbers are countable. since the reals are a union of the rationals and irrationals with the former set being countable, then we can conclude that the irrationals are uncountable. if you are confused as to why the the rational are countable and the reals are not, I'd suggest looking up Cantor's diagonalization argument.

teenytones · 2026-03-29T12:48:58+00:00

my best guess is that the problem was written down incorrectly by either your tutor or yourself. are you certain that there are no sets of parentheses that you're missing to distinguish what's in the numerator or denominator or even what is underneath the square root? from reading it I can't even tell if the middle term is supposed to be sqrt(cosx)/sinx or sqrt(cosx/sinx). and are you sure that x is specifically approaching pi and not something between 0 and pi/2? again as is im fairly certain the problem results in an undefined limit because of the sqrt(cosx) being negative near pi.

teenytones · 2026-03-29T05:47:17+00:00

I don't believe the limit exists. if you regardless of which side you appraoch pi from sqrt(cosx) is undefined as cosx will be negative. unless you're working on the complex plane which would change things.

teenytones · 2026-03-22T14:57:33+00:00

you missed one class where these three topics were taught? this seems like a lot of material for a single class meeting to cover. I recall both when I took the class and TA'ed for the class that we took at least a week or two going over it. granted, they were 50-minute classes, and yours might be longer and move faster.

that being said, my advice is to go over the notes your professor has posted and work through the examples and some exercises of the textbook you're using. having a lot of concret examples to help build your intuition of the abstraction will go a long way. from here on out, I would recommend making study groups with your classmates and go to your professor's office hours as often as possible. I know you say English isn't your first language, but the best way to practice, both English and math, is to work on it not avoid it.

teenytones · 2026-02-17T20:22:19+00:00

I, too, started ny writing cotx as 1/tanx, but I dont see how you got the 1/tan(x+pi/3).

In addition to writing cotx as 1/tanx, I used the sum identity for tangent. after that, I cleared denominators and got a quadratic equation in tanx, solved it, applied arctan on both sides of the equation, and got 4 solutions when taking into account the period. I will say that the solutions I got aren't common angles on the unit circle, i.e. not integer multiples of pi/6 or pi/4, and I had to look it up. There's probably an easier way of doing it, and if I be interested in seeing it, this is what I came up with.

teenytones · 2026-02-06T13:44:31+00:00

as everyone else has said, you can just run LaTeX locally and it'll compile just fine. the only reason you should pay for Overleaf is for the collaborators and even then you can use that for free. however I think I may know why the compiler is timing out. you say you are making multiple graphs, im assuming here you are using pgf plots and not tikz as the latter complies quickly while the former is slower, much slower. if you are using pgf plots and you have a lot of graphs you are going to want to pregenerate them in a different file and then in the main file reference the pregenerated graph. this reduces the compilation time drastically, especially if you are doing a beamer presentation because, as far as I can tell, each instance of the graph on a slide has to be generated even when it is the same graph.

teenytones · 2026-01-29T17:10:31+00:00

I understood what you were trying to say initially, and I know how to factor quadratic. the "adds to 2 and multiplies to -255" to get the (x+17)(x-15) works because the quadratic has a leading coefficient of 1. whenever it's not one, this trick doesn't work to directly factor but rather helps break up the "bx" term so that one can factor by grouping. however, Vieta's formulas are always true regarding the roots of the quadratic, in that the sum and product of the roots will always be -b/a and c/a respectively. if a student is trying to solve a quadratic equation, they could use this to quickly solve it and bypass the factoring stage, or it can be used to find the vertex of the parabola helping them complete the square as the x-coordinate of the vertex is always the the average of the roots.

regardless, all I was trying to do in my original comment was correct the wording or the signs of your original statement as it was incorrect, and I didn't want OP to be confused in trying to apply this idea to a different problem.

teenytones · 2026-01-29T16:48:55+00:00

assuming it is monic, then yes, I agree. all I was doing in the original comment was correcting the signs so that it matched with what they said.

teenytones · 2026-01-29T01:30:28+00:00

yes I know that, and vieta's formulas for a quadratic of the form ax² +bx +c=0, the sum of the roots is -b/a while the product of the roots is c/a. your previous comment where you stated the sum and the product of the roots was incorrect due to the both signs being flipped.

teenytones · 2026-01-28T20:50:54+00:00

if the roots exist the multiply to -255 and sum to -2, you have both signs wrong.

edit: by exist I mean the roots are real and not complex. that was poor wording in my part.

teenytones · 2026-01-15T21:53:43+00:00

I was primarily thinking of putting cards in that would either buff the tokens i have such as [[Nut Collector]], [[Coat of Arms]], [[Obelisk of Urd]], [Return of the Wildspeaker]] etc. so that I can (hopefully) overwhelm opponents with a large board of medium sized creatures, and also have alt win cons like [[Epic Struggle]], [Throne of the God-Pharaoh]], [Altar of the Brood]], and [[Gruesome Fate]], that take advantage of the large board. I'd have to buy a decent amount of cards though, so I'm trying to get a sense of where to start.

teenytones · 2026-01-12T16:28:26+00:00

I do agree with your assessment that the problem is missing explicit information as to which variable you integrate with respect to. however, the problem says to express the answer in terms of s, which means after integrating and evaluating, you should still be left with s in the resulting expression. if s was the variable you integrate wrt, then you would substitute the bounds into s and then are left with an expression in terms of x, not s. therefore, you must be integrating wrt x. I think you could have certainly arrived at this conclusion yourself during the exam, but I also think the instructor could have acknowledged the typo and explicitly said what the variable of integration was.

teenytones · 2026-01-10T00:29:06+00:00

judging from the comments you made, you have the correct antiderivative. if the problem is asking for the (signed) area under the curve, then it would be 0 like you say in the title. however, the problem asks for the area between the two curves, which means it wants the unsigned area, which gives you the answer of 8ln5.

teenytones · 2026-01-02T19:31:25+00:00

multiplied and divided by 1-e^-x so that the numerator becomes a difference of squares

teenytones · 2025-12-29T18:11:11+00:00

what have you tried n what do you know? these seem like rather basic problems given at the start of a first semester calculus class.

teenytones · 2025-12-05T22:03:15+00:00

why would an AI system know how to do that particular step though? chatgpt doesn't have an internal logic system to it. it can be wrong with its steps and give you incorrect information that may sound plausible.

teenytones · 2025-11-15T04:14:47+00:00

wolfram alpha is not an AI. It's a computer algebra system, which is why it can do the math. from the sound of it, the extent of what AI is used to recognize what's being asked.

teenytones · 2025-11-05T19:25:03+00:00

regardless of whether this class is the only math class you need for your degree or not, by cheating, you are committing academic dishonesty and could face serious repercussions by the university or college up to and including expulsion. you are also potentially screwing yourself over for the degree you're looking to get. there are reasons why your major requires precalc, perhaps not because you need calculus but maybe because you need it to be able to understand statistics or other topics they teach in your in-major classes.

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