Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20130606 10:15:30
Rates of change (conical vessel)Okay, so, having hopefully got myself reacquainted with the very basics of differentiation, I now realise how much basic geometry I've forgotten (sigh  if only i still had my formula books ). Anyway, enough complaining, so I'm looking at the chain rule and rates of change and the first question I have is: So, does anyone know where I've gone wrong? Last edited by Au101 (20130606 10:16:11) #2 20130606 16:47:38
Re: Rates of change (conical vessel)hi Au101, You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #3 20130606 17:38:18
Re: Rates of change (conical vessel)I am confused,since (i) wants rate depending on depth.so we should calculate dv/dh at h=5(which is 25π).correct me if i'm wrong. Last edited by {7/3} (20130606 17:39:52) There are 10 kinds of people in the world,people who understand binary and people who don't. #4 20130606 20:14:56
Re: Rates of change (conical vessel)hi {7/3) Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #6 20130606 23:24:34
Re: Rates of change (conical vessel)Well, h is a function of t, so it comes down to the same thing. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #8 20130607 00:13:49
Re: Rates of change (conical vessel)No problem. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #9 20130607 00:57:19
Re: Rates of change (conical vessel)It's great to be back, bob bundy Thanks so much. I have a feeling you're right, I just didn't have enough confidence in my answer, but the book agrees with me that the answer to part (ii) is: {7/3} and anonimnystefy, you're absolutely right. We know that h varies with t, specifically, it varies at the uniform rate of: (As the question tells us.) And we know that V varies with h, specifically, it varies at a rate of: (According to my calculations) We know, then, that V also varies with t, since it varies with h, which varies with t. Specifically, by the chain rule, it varies at a rate of: #10 20130607 05:43:02
Re: Rates of change (conical vessel)Just a very very quick point of confusion I'd like to clear up, if I may: I have the question: And after some mathematics, I come up with the solution that the length l of NT is: Which agrees with the answer book, except the answer book does not have the modulus sign. I just wanted to clearup why I can simply get rid of the modulus signs in this case, since my rustiness even extends to calculations of distance #11 20130607 18:19:51
Re: Rates of change (conical vessel)hi Au101, You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #12 20130607 21:58:43
Re: Rates of change (conical vessel)So, surely, I should keep them? The answer book simply has I had thought that maybe the answer book was giving a simplified answer, it's an old Alevel book, but the syllabus was very different back then, so I'm never sure what I'm expected to know But looking at it, if I draw a graph, I don't think T can ever  on this graph  be above N on the yaxis, so  presumably  the distance can always be given by N  T, with no need to worry about what would happen if T were to occur above N, giving a negative distance? #13 20130607 22:34:51
Re: Rates of change (conical vessel)Maybe it depends on the way a question is worded. I've met some where the distance along the x axis of a particle from the origin is given as a function of t. For some t the distance comes out negative and you're supposed to interpret that as meaning the particle is to the left of (0,0) . You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #14 20130607 22:40:03
Re: Rates of change (conical vessel)Okay, thanks bob bundy I don't think I'll worry about it too much, I mean, I just want to get my calculus back to a good enough level to start looking at some new maths and physics &c., so it's just some general practice It's good for me to understand as much as possible though 