Word problem:
Lilian wants to construct a closed rectangular box with a square top and a volume of 96 cubic inches using two types of materials. The wooden material for the bottom and sides costs P5 per square inch while the glass material for the top costs twice as much per square inch as that for the wooden material. find the dimensions and cost of the least expensive box.

My answer:

https://imgur.com/a/nSuI6uY

if the sd is the mean didference from the mean, shouldn't it be smth like σ=E(|x-μ|)? how does taking the sqrt of the variance give the sd, well dqrt doesn't distribute over addition, and these 2 values are not actually thesame, so why pick the 2nd one?

title edit: variance, deviation*

I want to do linear algebra done right but before that i want to go through introductory book. Solutions also needed. Thanks

Problem:

A, B, C are three towns forming a triangle. A man has to walk from one to the next, ride thence to the next, and drive thence to his starting-point. He can walk, ride, and drive a mile in (a), (b), (c) minutes respectively.

If he starts from B, he takes (a + c - b) hours. If he starts from C, he takes (b + a - c) hours, and if he starts from A, he takes (c + b - a) hours. Find the length of the circuit.

My attempt:

Suppose x, y and z are the lengths of the sides, and (1/a), (1/b), and (1/c) are the speeds on each side. If I add all the equations, I get:

x/a + y/b + z/c = 20(a + b + c)

This is in the form of D/S = T. How can I write it in the form D = TS

y = sec⁻¹(2/(x + 1))

Solution

The inverse secant function sec⁻¹(x) is defined for |x| ≥ 1.

|2/(x + 1)| ≥ 1

x ≠ -1

This leads to two cases:

Case 1:

2/(x + 1) ≥ 1

2 ≥ x + 1 ⟹ x ≤ 1

Case 2:

2/(x + 1) ≤ -1

2 ≤ - (x + 1) ⟹ x ≤ -3

Thus,

x ≤ -3

The domain of the function is:

(-∞, -3]

How can you count the number of distinct n by n binary matrices up to rotation?

For n = 1 the answer is 2

For n = 2 it is 6 (corrected by testtest26)

As the title suggests, I've developed a profound passion for physics and programming since childhood. Currently, I'm in the 11th grade, where I have chosen to focus on mathematics. Despite my enthusiasm, I occasionally encounter challenging questions that I find difficult to solve, which makes me feel anxious during exams and waste all of my time.

I'd greatly appreciate any advice or suggestions you may have regarding effective study techniques for mathematics. Additionally, if you could recommend any materials, such as books, websites, or online resources that could assist me in strengthening my mathematical skills, I'd be very grateful. Thanks.

I will preface this by saying that I’m a chemist, so all I’ve learned regarding markov chains and hidden markov modeling has been self-taught.

I’ve been working on the implementation of hmm for uncovering patterns on an electrochemical signal (current response of a painted metal exposed to H2SO4).

The transition matrix is based on a segmentation i created using PELT algorithm and feel that it’s strongly correct. My biggest pain thus far has been the emission probabilities; the variance between the states defined is on the lower end, I calculated them based on means and std and then obtaining the probability density but my model has so far been unsuccessful hence I come begging, pleading for help. I’ve ran out of ideas. I’ve tried by doing some data augmentation to help the overlapping states, I’ve tried a Gaussian HMM, I’ve tried switching to kurtosis and skewness but to no avail. I believe my model to be wrong as it doesn’t exactly match the original states of the pelt segmentation. I’m also wondering that maybe it is right and I’m over killing it? My thoughts elude me at this point. Any sense of direction would be appreciated

Basically the title. I'm solving a question for my analysis course and I'm trying to make my proof rigorous so I have 0 < a_k for all k >>0 but I want to show that there exists some t such that 0 < t <= a_k for all k >> 0.

(a_n) is a sequence that converges to a non-zero positive number and all terms of a_n are greater than or equal to 0.

Thank you so much!!

If you take the antiderivative of x^k, you get (x^(k+1))/(k+1). Since 1/x = x^-1, taking the antiderivative of it should give you (x^(-1+1))/(-1+1) = (x^0)/0, but instead it gives ln(x). This means that ln(x) must equal (x^0)/0.

(A-B)' = A' union (A intersect B)

I cant seem to find a way to make them equal each other.

From the left hand side I have only concluded that (A-B)' = A' union B but I cant find a way to make it equal A' union (A intersect B).

Hi everyone,

I’m currently studying binomial and continuous option pricing theory. I used a few books and have a pretty good idea of the different parts involved but every source I used lacked comprehensive practice questions.

Does anyone know of a good place to practice with enough questions? The subjects are arbitrage and risk free measures, stochastic PDEs, Black-Scholes model, etc.

Thanks in advance!

Last night me and my friends went to a party and decided to buy candys before so 6 of us pay 16.500 each to buy them. Then we were 7 to go to the party and we spent 95.000 in water there. 75.000 my friend “Tincho” and 20.000 my other friend “Felipe”. “Felipe” was the one who didnt pay the candys so he is now contributing that 16.500, into the water cost. how can we pay each one the same for the waters, how much we have to give to Tincho? Felipe has to pay more? Tried all possibilities but my brain got fried and couldt resolve it.

I'm trying to find Pythagorean triples within a given range, i.e., all the numbers in the triple should be between the given lower and upper limits, both inclusive. The triples don't have to be primitive.

For example, given the range [11, 20], the program should generate (12,16,20). As mentioned above, this is not a primitive triple, but is a scaled version of the primitive triple (3,4,5) where k=4.

The Wikipedia article discusses generating the triples using Euclid's method, and links to many more. None of these consider an upper limit, but there's a StackOverflow question that does. Why can't I use one of those answers then? Because, it isn't as simple as changing the starting value of a loop. Many of the algorithms depend on the generated numbers being coprime, which wouldn't be true for 12 and 16. The "bases" for them, 3 and 4 are coprime, but that means the algorithm has to start outside the lower limit, and generate a lot of spurious triples before it produces anything in the given range. There are other conditions that fail too if we don't start from 1, like, the starting numbers should be of different parity, which again, hold for 3 and 4, but not for 12 and 16.

I've found no resource that solves the problem of generating triples no smaller than a given lower limit. One option would be generating all triples starting with (3,4,5) and filtering out the ones that don't fall in the given range, but that'd be very wasteful.

Can you suggest an efficient algorithm to solve this problem?

It looks like Patrick took down his website with all of his notes. It’s been gone since 2023 apparently. Did anyone back up his notes? I was looking to refresh my knowledge going into a tough semester.

He still has his YouTube, but I do better with written notes.

hi all,

i am self-studying precalculus (stewart) with hopes of moving on eventually to their calculus book. question--i am really struggling to work through cycloids, hypocycloids, etc. i feel like it shouldn't be this difficult to me. everything on paper is pretty straightforward but i find myself getting very confused and stuck once i start drawing diagrams or writing out equations.

how critical is this stuff in calculus? i have made the mistake of moving onto the next topic before i'd mastered the previous so i am trying my best to avoid that while also moving forward. it feels like my momentum is breaking

the functions are f(x) = 2x^2 - 3x + 4 and g(x) = x^2 + 5x - 3

hello, i’m a 10th grader in algebra 2 honors, and i’m currently stuck on this equation 🥲 my assignment says i can use any method to find the points of intersection but i just did what i knew which was setting both f(x) and g(x) equal to each other now im stuck when it comes to trying to get x on one side. idk if there’s an easier method for this bc it’s the only thing i know but i really need assistance 😭

I am having trouble understanding something seemingly simple.

Start with 1,000. Say I want to calculate a 7% increase.

1,000 * 1.07 = 1,070 (which I'd normally say is a 7% increase)

But, 1 - (1,000 / 1,070) = .0654 (which is only 6.54% increase)

Why?! My brain hurts.

Am I looking at this incorrectly?

∀{n:n∈ℕ}

My presumption is that it would be read as "for all n such that n is a natural number," but I would like some confirmation/correction of that statement if possible, please.

All help is greatly appreciated!

( i - sqrt3) to the power of 40.

Its been a long time since iv done this and i have nowhere to check as for some reason online calculators dont work. i just need simplification

I’m deciding between using Calculus for Dummies, CLEP Calculus by Gregory Hill, or Khan Academy. I plan to take the CLEP in December or January. I have learned precalc and have minimal experience in calculus 1, so I’m looking to self teach, and then take the CLEP in time to sign up for a Calculus 2 class for next spring at a CC. Which option is the best? I like Khan Academy so far , but worried there is not a wide enough range of problems to practice and they seem to be repetitive..

I'm looking especially at Ron Larson's Trigonometry 11e (ISBN13: 978-0357455210).

I've seen some of its exercises, and they look so varied and awesome, but the fact that it only has solutions for half of its many exercises just brings me down. I'm studying by myself, trying to learn math on the side, being a bit busy, and being unable to verify my work quickly just doesn't cut it for me. It's much faster than asking you smart folks. I'm fine struggling with a problem for days, but knowing I wouldn't be able to confirm my solution properly makes me reluctant to begin, as I have no chance of knowing I'm actually making progress.

Do you use Chegg or the like, for these sorts of things? I haven't found the above book there. Are there trigonometry books with "cute pix" and entertaining exercises that offer full solutions? I'm at that stage in my learning path where too much abstraction can be daunting, and I prefer silly bells and whistles to keep me going when I'm tired. For example, some of the trig books for India's JEE seem to go with FULL solutions most of the time, like "Trigonometry for JEE Main and Advanced", and they're awesome, but a bit dry.

PS: I'm not criticising why some publishers choose to offer half of the answers. But I prefer books that give solutions in full, myself.

this equation makes no sense for me. in my textbook there's only example sin(-pi/6)=-sin pi/6=1/2.but what if it's -11pi/6?there no way sin can be negative in the 1th quarter of circle. same accordingly cos(-t)= cos t. it seems ok only if t stretched across 0 and -p in the first instance, and if it's on the rigjt side y[1;-1]. i feel very retarded, maybe i haven't understood something, if so, please correct me and i will be glad for explaining to these.

Hi there!

I really would like to relearn most rules for basic mathematics (currently 9th Grade Gymnasium in Germany) because I always seem to mess up simple stuff because I just don‘t know what I am allowed to do and what I am not allowed to do.

So, if anyone knows a good website with these rules and could link it in the replies, I‘d appreciate it.

Thank you! :>

Hello, I am looking for some suggestions on how to solve non-linear PDEs. I am a beginner and mostly use python. Any referece material will be very helpful. Thanks

Kia has 10 coins in a bag. There are three £1 coins and seven 50p coins. Kia takes at random, 3 coins from this bag. Work out the probability she takes out exactly £2.50.

Really stuck on this question :,) due wednesday

Tried out the math academy diagnostic exam and according to it I’ve mastered 7% of mathematical foundations 1, I’m 28 😢

My brain is fryin, why is there so many. For example: 2sin^2(a)=1-cos2a or 1+cos2a=1+cos^2(a)- sin^2(a) and so on. Am I just not getting something here?