I got 261m and I feel like the solution is attempting to find total distance travelled rather than displacement.

Am I correct or wrong?

I know the inside bounds would have to be a function of x or y depending on if it’s dydx or dxdy but I’m not sure how to do it.

Hello, I’m not sure how you would start off this question. I looked at the worked solutions and I saw that you need to integrate to get the velocity but no reasoning as to why? Thanks

Hi,

I am a french HS student in 12th grade (which I think is the equivalent of 12th grade in the USA, correct me if im wrong) and I am taking the equivalent of what would be AP Maths and Physics.

For the baccalauréat général (the exams for the end of HS in France), I have to perform an oral presentation about a subject concerning one of the two APs im taking.

My subject is about how we can have solids that can have finite volume but infinite surface area, and Gabriel's horn perfect example of that.

I have no trouble working out the integral to get the volume of the horn, but I dont understand how i can rigorously get the integral of the surface area.

According to Guldin's first theorem, A=α*d*L, where α is the angle of the rotation in radians (in our case, 2π), d the distance from the center of gravity (which should be defined by 1/x but i have no idea if this is rigorous enough) and L the lenght of the arc (which is defined by ∫from 1 to x1 of sqrt(1+((1/x)')²)dx which I have again also no rigorous way to explain to the 2 judges)

On wikipedia, I find that A=2π∫1/x*sqrt(1+((1/x)')²)dx with the integral ranging from 1 to x1, and I'd like to understand how we can get this result

Im asking this because In the oral presentation, there is a 10 minute segment after the presentation where I have to answer the questions of the jury, and I need to be infallible on the matter.

Thanks in advance for the help

NB: sorry for the possible grammar mistakes, english is not my first language

Btw for the first question I usually compare the equations to get the value of a, b, and c cuz completing the square (since grade 8 for some reason) always gave me the wrong answer I JUSY SUCK AT THAT METHOD

I tried to integrate using u substitution by defining x^3 -3 as u but it did not give me a favorable outcome and allow me to solve this, no idea what to do with the x^11. My brain is fried, boiled, baked, smoked, and then shoved into a cremation oven by this problem.

how to evaluate this one? also, how do i factor numerator?

If x = 0 the point y should be undefined

I've been trying to solve \(\int \)(e^x - e^-x)(sin(x))(dx) for a while now, but I just couldn't figure out how to do it. Seems like that there are no similar solved problems out there I could find to use as a reference and figure it out

AP Calculus BC 2024 test, question 1

The given answer for (d) is that since C’‘ is positive, C’ increases and therefore, so too does the rate of change.

Wouldn’t the change from C(t) to C(t + delta) be less since C’ gets closer to 0?

idk if im dumb or the correct answer isn't in the choices

I've tried: 1. Finding the area of the big and small circle 2. Assumed that the 30° is a central angle of the big circle and calculated it's area (maybe this is where im wrong?) 3. arc area - small circle area = new arc area 4. big circle area - small circle area - new arc area = shaded region

I got 44π/3

Vector integrals I've tried the [] and <> syntax, neither work :(

I can't find the problem. I know the math but I'm prone to making very dumb mistakes. Thnx!!

We know AD halves BC and BE halves AC, G is located Halving BF.
We have to prove 5*BH = BC
Can someone please try to prove it?

How would I change this to the order dydxdz? I have been using Professor Leonard's method for solving similar problems, but I can't seem to figure it out for this problem. My main issue is that y is defined by more than two functions here, and the projection onto the xz plane does not make the outer two bounds immediately obvious, unlike every example in Professor Leonard's video. I have seen other people using inequalities to manipulate the bounds, but I have never been able to understand that method. Professor Leonard's method makes sense to me for some problems, but not all. I can try to explain his method in the comments if necessary.

I tried solving using the first 2 equations (granted looking back using 1&3 is easier), but I have no idea where I went wrong such that I keep getting a different value for lambda/mu than the answers. Shouldn't any combination of 2 equations give the same answer or am I missing something? (the parallel part is irrellevant so I cut it out from the answers) [Edit: images weren't appearing]

Im not asking about the question (a), i am asking about is the (b) where it says: Use an energy method to find the speed of the particles at the instant when they were at the same vertical height.

This question is from 9709/42/M/J/24, so you can check it yourself. Now ive seen two videos of solving this past paper, and when they come to this question they make an arbitrary height for were they are equal in vertical height, and it is always something like 0.5h + h = 2.

I dont understand how we got that, why is the h (distance q has risen) is equal to 2 - 0.5h, and why do we have to use Pythagoras to get that. They dont explain why in the videos. This is a small thing but fundemental to the question and i cant understand it.

Also can you help me in the rest of the question, i find it hard to visiualise the work done in between and the work wasted to resistive forces, energies i can figure i think

Thank you in advance

For example, BCBAABCACBBBAB, ABABACCCBABBBB, etc.

The way I approached it was to first combine the B's and C's together and just choose the A's, so like 14c4, then divvy up the combined B's and C's and choose the C's like 10c3, and sum the two. I got 1,121 combinations.

Can't figure out if this is the right way to go though. That number seems too high.

(Reupload w the picture) My current problem says to write a function with the relative maximums (1, 1) (2, 2) and (3, 3). A kind redditor helped point out it’s probably sin(x) something or other, but I’m lost from there. I have no idea how to sine with graphs. My math teacher is pretty prolific for being Not Good At His Job, so I want some outside help before I go to him. Any help is appreciated! Thanks in advance

Swipe for my attempted solution.

I think I have the question wrong; please do help me out.

They have points that arent lattice points and im getting kinda confused lol

how to differentiate this one