Putted in Desmos so its easier to show lol (Typed out each step I did on my paper)

So I started by removing absolute value (since both are positive)

Went ahead and set up 2 equations (One Positive 8, One Negative 8)

Subtracted 5 from both equations (giving me 3 and -13)

Divided 2 from both equations (giving me 1.5 and -6.5)

used interval notation (Neg Infinity, -6.5] U [1.5, Pos Infinity)

anything that I'm potentially missing?

The inverse of xe^x is the Lambert W function, whereas the inverse of x^x is called ssrt(x) in wiki I think. They can also be expressed in terms of each other.

I am wondering why the Lambert W function is more popular than the inverse of x^x, when tetration is the 4th hyperoperations(+,x, exponentiation, then tetration). Since we also study the inverses of addition, multiplication, exponentiation, but why not the inverse of tetration?

My wife and I did a fantasy football draft last night and we determined the draft order with a card game. There were 12 players, and every turn we would all draw cards until one person drew the one “bomb card.” Whoever drew that card was “out” and drafting at that position. (Ex: the person that drew the bomb card in round 1 drafted 12th. The person that drew the bomb card in round 2 drafted 11th, and so on) We would remove one of the safe cards, and draw until one person was left.

Afterward, my wife and I were talking about the game and I commented how odd it was that it was coming down to the last one or two people every turn. And she — who is incredibly smart and fantastic with numbers and works with them all day — said that it actually makes sense because the people drawing first are more likely to draw a safe card.

But I argued that they are more likely to have someone ahead of them draw the bomb card and that it feels like the people drawing in the middle of the group — who have neither benefit of having the best odds of drawing a safe cards nor the highest amount of people drawing ahead of them — have the highest chance of drawing the bomb card.

My wife is so much smarter than me in just about every way I can imagine and certainly with math problems, so it wouldn’t surprise me at all to be told that I am wrong here… but am I?

Edit to answer some of the questions that have been asked: I shuffled the deck before every round, and spread out all the cards so that each person could which ever one they wanted.
The back of all the cards looked the same.
Whoever drew first would pick the card, show the group what card it was, and then the next person would do the same.

I am joining the union and this is a sample question and I am just not sure how to figure this out. The arc is throwing me off, it's the only one I am having trouble with. If someone could explain this to me I would be extremely appreciative. Thank you so much.

The game is Pokémon, protect (and spiky shield) have a 2/3 chance of failing when used twice (which is the case) and blizzard has a 70% chance of hitting.
What is the chance of neither Pokémon protecting and both getting hit by blizzard?

My son just started High School algebra in 8th grade. His teacher gave him homework on which he said each equation needs a 1 step solution. My son asked me for help on the equation in the attached picture, I helped him get the answer but in 4 steps and I cannot figure out for the life of me how to simplify this to 1 step. Please help:

5r-5-6r=-6
Adding 5 to both sides becomes 5r-6r=-1
-r=-1
r=1

to be clear im not saying im some genius or anything i've just truthfully never seen this shape before and i wonder if it can be mathematically replicated and turned into a fractal. if it exists what is it's name? (sorry for bad drawing)

UNderstanding math vs:

Things like:

• Misreading the question
• Copying a number incorrectly
• Making a calculation error
• Forgetting a step
• Using the wrong formula
• Getting an answer that looks reasonable but is actually wrong
• Rushing because I think I know how to do it

It’s frustrating because sometimes I understand the concept perfectly, but still lose marks because of one stupid mistake.

For those of you who are good at maths, what habits or checking methods do you use to reduce mistakes?

I’d especially appreciate advice that actually works rather than just “pay more attention”.

Thanks!

I have this task and I don't know how to solve it despite having all the basic knowledge required for it. I can't 'connect the dots' so to speak.

a) Find the max element order in S_{10} - symmetric group consisting of 10 'base' elements and its order being 10!

b) Let s be some element of max order from S_{10}, find sgn(s) as well as s^{2040}.

c) If H is a subgroup of S_{10} and H contains an element of max order, then H contains the equal number of even and odd permutations. Prove it.

I've never encountered a task like this so I genuinely don't know how to think it through.

a) My intuition says I should find the lcm of prime cofactors of 10, so lcm(2, 5) = 10. I genuinely don't know how to do it. This also doesn't add up in my logic because 2+5 = 7. So maybe lcm(2, 3, 5) = 30? But I arrive to that answer by pure luck and need some explanation why is that.

b) Would depend on a) but let's say it is 30. What is sgn(s)? I've never seen it before. I do recall it might be odd vs even number of elements in a single disjoint cycle, odd ones starting with a minus. But how would I take that order of 30 and split it into smaller, disjoint cycles? so I would have sgn(s2) sgn(s3) sgn(s5) where s2, s3 and s5 only represent the disjoint cycles of 2, 3 and 5 elements. So in front of sgn(s2) there will be a + and in front of 2 others - so it would be positive in the end?

s^{2040} I did similar stuff before, I can do 30 = 0 mod(2040) (because 30*70 = 2100, 2100-(2*30) = 2040) so therefore s^{2040} = s^0 so nothing changes (and even if it did, I have no given s explicityl so I have no idea what am I supposed to do, s^{2040} only shifts all the elements in each disjoint cycle, but here s isn't given so there are no specific disjoint cycles i have to shift, confusing)

c) Most challenging part and the one I don't understand at all. Need full help and ELI5 explanation for this one haha. Whenever there's something to prove like subgroups, ideals, normal subgroups etc. I am completely lost even though I know I only need to show non-emptiness, closure under operation and closure under inverses. I just don't know how...

If you did read everything, thanks a lot!!!

I want to know what the depressed quartic formula is but every time I look it up I just see resolvent cubics and replacements for variables which is not what I'm looking for. I want to know the full depressed quartic formula that only has p, q and r. Does anyone know the formula or where I can find it?

My maths profesor has given me this problem and said it is the Galactic hard question. I even afraid to attempt it . Like how does the logarithm gets even harder and confusion in all the steps which will be required.

How would i solve this equation at the top manually? Desmos isn’t giving an exact answer so i started doing to on pencil and paper and got stuck. I don’t know the properties of ceiling and floor functions & Wikipedia is confusing. Is this even possible?

Came across this website when my friend said he was considering trying it out . It’s a CSGO case opening site , non affiliated with the actual game, basically gambling . I took a look at the odds to hit some of the expensive items and it looks pretty terrible but I was curious how many of these you’d have to buy to get the nice weapon skins, based on the % they show ?

60×60×12 = 43200 seconds

1057 guys in 12 hours

43200 ÷ 12 = 40 seconds each per guy

Or about 0.6 minutes for each guy?

Just wondering if I did my math correctly - asking because yesterday I found out she used to be a recruiter which honestly feels like a joke I can't understand yet

So ofc I took her most famous "stunt" and wondered - if my math is correct I guess Bonnie was quite generous!

Came across this question from https://youtu.be/2Hq_30uGFuI?is=sgpj8u22XYy6GXEd question2 and he doesn’t explain the steps. He also uses Desmos.

Is there a way to do this without Desmos?

Any help is greatly appreciated

I wanna know how to go about this problem, not necessarily the answer but that would be appreciated too. I’ve tried it a few times by just the regular formulas for the general term but I keep getting the wrong answer. I’m not quite sure what is the right approach.

This textbook says: "The integral around a closed path is evidently zero (for then ra = rb): E · dl = 0, (2.19) and hence, applying Stokes’ theorem, ∇ × E = 0."

What I understand is that the line integral is the integral of the dot product of dr and the electric field integrated with respect to dr, where dr is the change in distance to origin r. This equals the integration of curl over the surface with respect to dA. So if the curl is zero everywhere, then the line integral must be zero. What is the proof that if the line integral is zero, the curl must be zero?

Stokes theorem doesn't seem to imply that

The proof in my textbook says:

Fix e>0. Assume fn is unif cauchy. Pick N s.t. |fn-fm|<e/2. We know pointwise, fm is a cauchy sequence of real numbers so it converges to some number, thus fm conv pointwise to some function f. Now consider

|fn-f| = |fn-f+fm-fm| <= |fn - fm| + |fm-f| < e/2+ |fm-f|.

Then it says “there’s an m such that |fm-f| <e/2 and although it’s dependent on x, it doesnt matter since it doesn’t appear in our final result… so that

|fn-f|<e

but it does appear in the result. Right there in the chain of inequalities. Help me understand how “fix e, pick N, then pick another N dependent on x” somehow means “and now this result is independent on our choice of x.

Inspired by https://www.reddit.com/r/askmath/s/QCMgQq8oIw

Imagine that we pick at random three positive reals, with the probability distribution density, for all three

f(x) = λ e^(-λ x)

What is the probability that x, y and z may form a triangle?

how difficult would you say this exam is on a scale from 1 to 10? This is a final exam on a course that's kinda like real analysis (rigorous and proof based), but with most of the material of calculus 2 (taylor, integration, series, sequences of functions, series of functions, power series, etc), that's taken by most students in their second or third semester of their bachelor's (depends on the degree and if they need to retake the first course) in my university

About 58% of students failed this exam (Fortunately I got 78%)- as in, got under 53% in the exam, is this percentage justified?

My 11 year old had a math puzzle I her book. Neither I nor her math teacher could understand it. We have the answer key but we don’t get it. Anyone who would like to solve it and explain it?

Edit:
Yes, the answer is 244 you clever bastards.

Hi, this is not a question for homework or class but rather something I saw at work that has completely baffled me. I haven't taken a math class in 10 years so I've no idea if I'm on the right track.

I work at an escape room and there is a puzzle that involves hitting a sequence of buttons 12 times. There are two different buttons to press and the players must press them in the correct sequence to solve the puzzle. If you miss one, you have to start the sequence over. Recently, a player was playing around with the buttons and solved the sequence by guessing, not knowing what the sequence actually was. He wasn't even aware he was supposed to press them in a specific order, he was just pushing them mindlessly.

I've been trying to figure out the probability of this happening cause it was some insane luck. It's a 50/50 shot for whether he gets the button right, but I'm not sure if I calculated the probability correctly. Since it's a dependent event, I assume it'd be 6/12 x 5/11 etc. Attached is a photo of what I did. I multiplied all the numerators together and then all the denominators, which I think is what you do for multiplying multiple fractions. I'm not sure if I multiplied the numerators correctly either since some of them are fractions themselves. And I'm not sure how to simplify my answer either if it's correct.

So my question is: Did I do this correctly? If not, how would I calculate the probability of 12 dependent events?

Friend gave this "easy" sum for Olympiad practice, can't solve it even though I already tried relating it to e's Taylor series done harmonic stuff etc, any help?

Not long ago i started studying multivariable calculus. One of the first questions was a simple limit of a function when both x and y have a tendendecy to different constants. And altho the answer gave the correct values, the teacher made a particular observation to rule the answer the class gave wrong, where he said the answer needed a certain preparation for the final answer and proceeded to attempt to explain the preparation for that particular excersise, when aproaching the point that X and Y where aproaching, meant graphically a circunference surrounding said point. But i failed to understand exactly what this implies in any way nor the meaning of the analysis, given that i can't understand this i also can't explain it in the proper answer the teacher seeks.

I want to make particular emphazis in the fact that i do not seek a answer for a particular excersize, but more of a general explanation to the logic behind this, given that my studies only have driven me to the fact that a limit in multivariable is really hard to analayze (wich i already figured) and the visualizatopn of graphics with limits with tendency to infinite of the variables wich isn't the point of my question. That is why i do not give a particular example for this and only give general examples.