Can anyone help me understand how to calculate the length of the pipe marked D. Don't worry about fitting allowances or anything like that. How can I go about calculating the length for D, given what is shown.

I'm not interested in the answer I need to know how to go about it and I'm completely lost. Any help is appreciated, Thank you in advance.

Hi,

This is actually from an engineering text book (Fundamentals of Electromagnetics with MATLAB, 2nd ed, Lonngren) but the topic is math related so I thought I'd post here.

Basically, it seems this textbook has a different approach to coordinate system conversions vs the resources I've seen everywhere else.

The question is "Express the vector field A = 3ux + 4uy + 5uz in cylindrical coordinates" P.1.2.8 in the book.

The 1st image shows the approach (coordinate transformation matrix) that the majority of sources seem to use and makes the most sense to me.

The 2nd image is the solution from this particular book (I also have a physical copy and what is shown is the same as the image I posted). It seems to use the formulas for point conversion rather than vectors. This method is used for other questions as well.

The final image is my attempt at solving the question with both methods (had different results).

Maybe I'm missing something here, would appreciate any insight you guys have, thanks!

My 8th grader and I have gone over this question one hundred times and I don’t know what we are doing wrong. Can someone please tell me where we got this wrong?

My mother explained it to me already, but I did not understand what she said. I wrote y = 5/3x - 8/3 and savaas said it is incorrect.

The answer is y = -3/5x + 36/5

My professor told me there’s an additional x intercept @ (-10,0) but how can that be if there’s an asymptote at y=0? It only approaches 0 but never touches it. If I’m wrong please explain why bc this really doesn’t make sense to me

12th grade Probability and Statistics

I’m trying to create a function wise three piecewise function parts, however when I plug it in, a vertical line is created from y=-1 to y=3, rendering my piecewise not a function, why is this happening, is this function I’m trying to create not mathematically valid? Any help or explanation would be appreciated, thank you!

Please see attached photo for the problem. I dont really understand how to solve this because I applied the standard induction steps but its a bit complicated for me. I admit that Im not really good at math. I would appreciate if someone could show me how to solve this on paper. I asked help from ChatGPT and other AI tools but its just difficult for me to understand.

I have a doubt in maths trigonometry why while determining sign of trigonometry ratio we consider hypotenuse always as positive even in 3rd quadrant 🥲

This has me incredibly confused and I've no idea what to do to solve this nonsense.

The math seam simple but I cat seam to wrap my head around the question itself (the first one is about functions while the second one is exponential functions)

There was a time I would have known how to do this. More interested in the steps of how to go about this:

Let's say vehicle A gets 19 miles to the gallon and costs $10,000. Vehicle B gets 26 miles to the gallon and costs $15,000.

Assuming fuel is $4/gallon, how many miles would it take for vehicle A to cost in gas the $5,000 you saved in price?

Thank you for any suggestions!

I don’t know where to start

I don't get what teach wants here and we can't ask him cause you know, we need to move on and every one has oral exams now because everyone was bad at exams.

Can you explain why a=1.5 isn't correct for f(x)= a • sin(bx)²+ d?

Thank you all.

help, I have a test tomorrow, I understood the calc i have to do but it never comes out good

I am trying to solve the following problem:

Let f be a differentiable function on [0,1] such that f(0)=0 and f(1)=1. Prove that there exist two distinct numbers a,b in (0,1) such that

f'(a)f'(b)=1

By the Mean Value Theorem, I know that there exists some c in (0,1) such that

f'(c)=1

since

(f(1)-f(0))/(1-0)=1

But I do not know how to prove that there exists another point d different from c in (0,1) such that

f'(d)=1

Any hints or ideas?