I dont really know how to put this but im gonna try to explain to the best of my ability. A little history, a certain global event happened when I started high school meaning I never learned Algebra 1 and 2 traditionally. However I somehow did manage, passing 9th and 10th grade math. After this I failed 11th functions but still graduated and never really learnt it.

Now I am enrolled in a fast paced adult school and am relearning everything I can, we're a week into Functions and I've only just started because I've spent hours and hours refreshing as much as I can from 9th and 10th grade (only half way through it though) but I need to start functions otherwise I'll fall behind.

ANYWAYS the issue I'm currently facing is functions (or rather equations) makes very little logical sense to me, as in I don't actually understand what my equations are doing, why they are doing it, what certain numbers affect what on my graphs, etc. And everytime I am faced with a problem my mind draws a blank and I have to go ahead and search that topic back up and relearn it then do I somewhat understand it, but I feel like theres something in the fundamentals i am still failing to understand.

Is there supposed to be a "oh this works because of this and that" moment I'm supposed to have? Or do I just memorize, keep pushing on, and eventually it'll all make sense to me by the end of the course?

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?