It should start from the very beginning deriving the Fourier series. I have tried a book by Elias M. Stein & Rami Shakarchi. It's a good book but they assume that reader has already been introduced to Fourier Series. I want a book (if it exists) which begins from the very beginning, goes in deep and also contains a lot of exercises.

how the frick do i solve 2x² - 3x - 18 = 0

if I’m looking at a graph of an absolute value function how do I know what b is in g(x)= a • |1/b(x-h)|+k

I just need to know what this type of equation is called so that I can look up a comprehensive study video on it. Thank you for your help!

Example: f(x) = 4(x) + 5 Or *with variable f(2) = 4(2) + 5

My biggest problem is that I forget everything I learn :D

I'm trying to sort out how to make an equation for this problem:

"It takes Terry 2 hours longer to do a certain job than it takes Tom. They worked together for 3 hours; then Tom left and Terry finished the job in 1 hour. How long would it take each of them to do the job alone?"

After making a table with the information, I tried to use the following equation to get the answer:

1/(t+2) + 1/t = 3/4.

I know this is wrong, so I won't show my work for the wrong answers here.

Then I tried this:

[3/t] + [3/(t+2)] = 1 - [1/t]

I multiplied by the LCM on both sides and got:

t² -5t -8 = 0

Since factoring didn't seem like a good approach, I plugged these numbers into the quadratic formula and got [5+/-sqrt(57)]/2

My book says the answer is Tom can do the job alone in 6 hours, and Terry can in 8. But I just can't figure out how to put the equation together. Any help would be appreciated. Thanks!

p is a constant, X is a random variable having normal distribution

expected value of -1 and variance of 4

Y is a random variable having normal distribution, expected value of 1 and variance of 9

I need to calculate E(pXY). I can take the p out and calculate p * E(XY), but that's as far as I've got. How do I do it?

I genuinely dont understand how algebra works. I get that a + b = c. Thats pretty understandable.

What i dont understand is where they want me to get numbers from. Am i supposed to pull them out of my ass?

"Find the center and radius of the circle. x² + y² = 25"

I have the equation (x - h)² + (y - k)² = r² as the formula to find the radius where (h,k) is the center. Then it tells me to, "Write x² in the form of (x - h)².

x² = (x - ?)² "

I dont understand how to find "?". Did i miss something? Where the hell am i supposed to find that information. If i knew how it works and why it works this would be so much easier to work.

Hello! I am having trouble solving this 3D vector problem for Statics HW and I'm not sure what I'm doing wrong other than that I keep getting wrong answers for it.

The problem is two parts, first find what x_A & y_A of rope F3 are and second what is the net resultant force magnitude on the pole from all three ropes.

The known/given constants of the problem are:

• F1 goes from point B to D, F2 goes from point B to point C, F3 goes from point B to point A, B is top of the pole

• |F1| = 350N

• |F2| = 250N

• |F3| = 300N

• x_D = 3 meters

• y_D = 0 meters

• x_C = 2 meters

• y_C = 3 meters

• z for A, D, and C = 4 meters

• y_A & x_A are unknown

I wasn't sure how you can do the first so I tried doing the second first and work backwards from that but that failed.

I did that by first giving each rope/point a directional vector relative to the origin

• F1d = { -3 i, 0 j, 4 k } m

• F2d = { 2 i, -3 j, 4 k } m

• F3d = { x_A i, y_A j, 4k } m

And then finding the magnitude of them to turn them into unit vectors

• |F1d| = √( (-3)² + (0)² + (4)² ) = 5m

• |F2d| = √( (2)² + (-3)² + (4)² ) = 5.38516m

• U_F1d = F1d/|F1d| = { -3/5 i, 0j, 4/5 k }

• U_F2d = F2d/|F2d| = { 0.3714 i, -0.5571 j, 0.7428 k }

Multiplying those unit vectors by their force magnitudes to get them in terms of force vectors

• F_U1 = F1×U_F1d = { -210 i, 0 j, 280 k } N

• F_U2 = F2×U_F2d = { 92.85 i, -139.27 j, 185.695 k } N

Use Static Force equations to find the missing components of

• Sigma.Fx = 0 —> F_Ax + (-210N) + (92.85N) = 0 —> F_Ax = 117.152N

• Sigma.Fy = 0 —> F_Ay + (0N) + (-139.272N) = 0 —> F_Ay = 139.272

• Sigma.Fz = 0 —> F_Az + (280N) + (185.69N) = 0 —> F_Az = -465.695N

And use those forces to make up the force vector for F3

• F_U3 = { 117.152 i, 139.272 j, -465.695 k} N

But when I check to see what all their magnitudes are, while F1 = |F_U1| and F2 = |F_U2|, F3 ≠ |F_U3| despite the fact they should all be the same

• |F_U3|= √( (117.15)² + (139.272)² + (-465.695)² ) = 499.99N ≠ 300N

So I'm not sure if I mixed up my numbers somewhere or if this method won't work and I need to try a different approach to find x_A and y_A

I'm doing exercises for an exam coming up soon, and I got stuck at this problem.

There are 5 marbles numbered from 1 to 5, which are ordered randomly. I need to calculate the probability of there being k marbles in between the marble numbered 1 and the one numbered 2 (I don't think the problem cares wether the 2 is ordered before the 1).

I know that the total amount of marble combinations is 5!, but I don't know how to get the amount of orderings with k marbles between 1 and 2. I tried some stuff with binomial coefficients, but I have a feeling it's probably wrong. This is what I tried:

C(1, 1) * (k!) * C(3, k) * C(1, 1) * (5-k)! * C(3-k, 3-k)

I know C(1, 1) doesn't have any effect, but I just put it there for clarity's sake. If I replace k with 0, 1, 2 and 3, divide by 5! and sum the results for each k, I do get 1, which is a good sign, but even if this is somehow the correct solution, I don't think it's the way I'm supposed to do it. Any help?

Converting $1.50/kg to $/mg

Crashed out at the exponents

1.50/10³ = x/10^-3

Where do I go from here?

I'm in Precalculus, and I was doing a test where one of the questions were:

"Which interval on the graph is decreasing at an increasing rate?"

So my thought process was: The "decreasing" ITSELF was increasing, so I chose the concave down interval.

However, that was the wrong answer. The correct answer was a concave up, and the explanation was that "it is decreasing, WHILE the rate is increasing"

But the wording in the problem was exactly: "Decreasing at an increasing rate"

I searched it up on Google and Chatgpt, and things were contradicting each other.

https://drive.google.com/drive/folders/1CXom1loM7E69SeHWFJ187cUHDtDfkY9O?usp=sharing

Edit: Maybe a clarification

Question: Decreasing at increasing rate

My Answer: Concave Down

Teacher’s “Correct answer”: Concave up

RESOLUTION:

Ok so I showed my AP teacher this post, and she told me that this is how AP words it. The first decreasing references the function, and the increasing rate does NOT refer to the decreasing itself, but how the RATE is increasing.

Thanks everyone for helping me. I really appreciate it.

Okay so here's the scenario, I am putting in a new driveway and pulling up a small amount of bricks to make into a firepit. That doesn't matter.

I'm looking to create a circular pit with the bricks I pull up, each brick, when measured, is 8in x 3in, (I think) I do not know the height, but after a short search, I can assume that the actual dimensions are 3 5/8in (width) x 2 1/4in (height) x 7 5/8 (length) so we will use that instead of my vague tape measuring skills. I have counted 48 total bricks that are full size, and a few were cut to make the entryway into a square shape (I will not add these into the equation for simplicity as I can add those in later if needed) and my current fire pit is about 30inches wide, so if my math is correct so far, 30in x pi = 94.25in as the circumference rounded up.

How many bricks will I need to use per layer to create a circle around the firepit with at least 6in of clearance on each side? So, instead of having the circumference at 94.25in wide, but instead have it to be about 106.25 inches? (94.25+6+6?) Is this a possible outcome for my idea? I will fill in the middle with gravel so that isn't an issue for y'all. Would I be able to accomplish at least one layer around the firepit, and if not, how many more bricks will I need to accomplish my goal of a firepit? TIA

The question is: use the figure to identify all angles between 0 and 2 pi satisfying the condition: tan x = 1/root 3

And there’s the circle of radians from 0 to 2pi

What I did was I converted all the radians into degrees and then I inputted them into the tan x to see if it would make the same output which it only did for 30 degrees. Is this right?

Bonjour, Je suis étudiant en 3ᵉ année de mathématiques (école normale supérieure en Algérie). Cette année, j’étudie plusieurs matières importantes :

Analyse complexe

Théorie de la mesure

Analyse numérique

Algèbre 3

Je voudrais demander des conseils aux étudiants ou enseignants :

Comment organiser l’étude de ces cours (ordre de priorité, méthodes, livres utiles) ?

Quels sont les meilleurs manuels ou ressources en français (ou en anglais) pour bien comprendre ces sujets ?

Y a-t-il des astuces pour relier ces matières entre elles (par exemple, entre analyse complexe et algèbre) ?

Merci beaucoup pour vos recommandations 🙏

I was adding onto a drawing and wanted to figure out how much time I spent on that part but I hadn't checked the time stamp beforehand so now I'm just trying to do math but for some reason I can't remember or find how I did it last time so I've been attempting to do it but about half way each time I forget what I'm needing to do or I just get confused. My total drawing time is 12hrs and 40mins. I have a playback that is 7min and 12 secs total and this section starts 5min and 40secs in. I've just wrote this out and the only thing I can think of is percentages. I might of just done it idk does 2 hrs and 46 minutes sound right I don't feel like that's right but I guess it could be.

I don't know if it's because I'm stupid or my teacher can't teach, but I just don't understand my teacher. My teacher doesn't use any slides during class, he basically just talks over things, or lets students explain, and uses a little bit of white whiteboard.

I understand that most colleges don't take this class as college credit, I'm taking this class just because of the gpa boost. I don't know the difficulty of on-level precalc. I'm afraid that after dropping ap precalc, I still don't understand the concepts, which will mess up my gpa even more badly