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#251 Help Me ! » Lemmas » 2011-04-17 11:12:47
- Au101
- Replies: 3
Just a really quick question. I understand what lemmas are, but I am trying to explain them in a fairly simple way to people in their last year of pre-university maths education - so they have a good knowledge of basic mathematical principles and methods, but probably haven't considered mathematical reasoning in much depth. My question is would it be correct to think of some of the trig identities, such as something as simple as:
In a proof of a trigonometry relation, as a lemma. I know lemmas are usually thought of as being perhaps a little more difficult and a little more interesting - but unless I've woefully misunderstood, this certainly serves the purpose of a lemma, since it is a relation which has already been proven and is used as a 'stepping stone' to a more complicated relation.
Thanks 
P.S. If this is not suitable, I wonder if anybody could suggest an alternative. I was thinking of using Bézout's identity:
Now Bézout's lemma states that such coefficients exist for every pair of nonzero integers (a,b), with in addition d > 0. It's just that something like a trig identity suggested itself to me as something really easy that A-level mathematicians have used before and would therefore see how lemmas work and what they are.
#252 Re: Help Me ! » Coordinate Systems (parabolas) » 2011-04-07 10:23:04
Well, I suppose, this is what one gets if one teaches oneself a topic several months before attempting relevant exercises. As has now been pointed out to me by a friend of mine, the point P is a general point on the parabola, and hence that equation of the tangent to C at P is that of a general tangent. Thank you so much to both of you for your trouble :)
#253 Re: Help Me ! » Coordinate Systems (parabolas) » 2011-04-07 09:27:57
Okay, well, if we begin with the first line,
Have I, then, misunderstood.
Is the equation of the tangent to the parabola at P. Why, then, can I substitute in the point of intersection of the other two tangents, I don't understand.
Thanks
#254 Re: Help Me ! » Coordinate Systems (parabolas) » 2011-04-07 09:20:55
Oh no not at all bobbym. Well, the way I see it is we have a parabola and I've found the equation of some tangent to that parabola at a point P with the coordinates given in the question. I also have the coordinates of the point of intersection of two separate tangents to the parabola, at the points A and B. Now, it seems to me that gAr's answer rests on the assumption that this point of intersection also lies on the tangent to the parabola at P. But I don't see why that is implied.
#255 Re: Help Me ! » Coordinate Systems (parabolas) » 2011-04-07 06:28:40
Oh okay, thanks gAr. This is what confused me, because that is, of course, the equation of the tangent to C at P. What I don't understand is why that passes through the point of intersection of the tangents to C at A and B.
#256 Help Me ! » Coordinate Systems (parabolas) » 2011-04-07 05:30:59
- Au101
- Replies: 9
Hi guys,
I'm a bit stuck on this question on coordinate systems:
I don't know where to go for part (b).
Any ideas?
Thanks
#257 Re: Help Me ! » Integration (Volume of the Solid of Revolution) » 2011-04-06 02:57:57
Ooooh, thank you very much, that's perfect
#258 Re: Help Me ! » Integration (Volume of the Solid of Revolution) » 2011-04-06 01:59:43
Thank you, gAr, that's absolutely right. Although, I don't quite see where you get the cone from, I don't suppose you could point that out for me please ?
#259 Help Me ! » Integration (Volume of the Solid of Revolution) » 2011-04-05 21:27:32
- Au101
- Replies: 6
Hi guys, I have a question on my integration work, regarding the volume of the solid of revolution.
Does anybody have any ideas? A worked solution can be found online here:
http://mytcl.net/edexcel/c4/c4.html (Go to Chapter 6 (Integration), Exercise L, Question 17) but I can't really follow it properly. Any help would be much appreciated .
Thanks.
#260 Re: Help Me ! » Dynamics » 2011-03-22 04:19:41
Aha, got it. Thanks Sameer
#261 Help Me ! » Dynamics » 2011-03-18 14:15:05
- Au101
- Replies: 2
Hi guys, I have a mechanics question on what I think is dynamics.
A particle P of mass 2 kg is acted on by two forces
And
(a) Show that the acceleration of P is
Which we do with
At time t = 0 P is at the point with position vector
Relative to a fixed origin O and has velocity
Calculate at time t = 3 seconds
(b) The velocity of P
Which is:
(c) The position vector of P
Here is where I am stuck. Does anybody have any suggestions? Thanks.
#262 Re: Help Me ! » Moments » 2011-03-16 06:34:30
Aha, thank you very much yet again Bob. Also, I like your new quote
#263 Help Me ! » Moments » 2011-03-15 09:17:42
- Au101
- Replies: 3
Hi guys, I'm really stuck on this tricky moments question:
Figure 2 is attached.
Thanks very much .
#264 Re: Help Me ! » A quick one on complex numbers » 2011-02-27 04:21:26
Of course, thanks a lot, it was just a new style of question I saw whilst flicking through an exercise on complex numbers (which I did a few months ago) and I wanted to make sure that I hadn't forgotten everything!
Thanks
#265 Help Me ! » A quick one on complex numbers » 2011-02-27 02:14:29
- Au101
- Replies: 3
Hi guys:)
Just a quick one - I wasn't sure how to find the square roots of (3 - 4i), does anybody have any ideas. I would have tried the binomial expansion, but I believe that it has a nice solution.
Thanks
#266 Re: Help Me ! » Roots » 2011-02-27 02:13:09
Hello, bob, yes I did practise, but I just sketched the curves on paper.
#267 Re: Help Me ! » Roots » 2011-02-27 00:00:56
Thank you Bob, that was brilliant
For the first (1) I imagine that it's to do with the cubic function. i.e. an x-cubed graph can only have, at most, three roots, and you know that negative numbers cubed are negative and positive numbers cubed are positive, so the cubic curves must increase to the left, turn or inflect and then resume increasing (after a second turning point where appropriate). I probably haven't explained that very well, but I think - or at least hope - that I have the general idea. Obviously that wouldn't apply for
, though.#268 Re: Help Me ! » Roots » 2011-02-26 10:58:30
Oooh that's very good, thanks again Bob
In all honesty, graph sketching is probably one of my weakest areas, so that would be very nice, thanks .
#269 Re: Help Me ! » Roots » 2011-02-26 09:58:13
Hi
I have another, similar question:
Show that the equation
Has one positive and two negative roots.
Can I just sub in successive integers and show where the roots occur?
#270 Re: Help Me ! » Roots » 2011-02-25 11:06:02
Ah that's perfect. Thank you once again Bob!
#271 Help Me ! » Roots » 2011-02-25 08:36:25
- Au101
- Replies: 10
Hi guys
I have a question about the first part of one of my linear interpolation questions.
Show that the largest possible root of the equation:
Lies in the interval [2,3].
I know how to prove that the root lies in this interval - one can simply let x = 2 and then let x = 3 and show that there is a change of sign. What I'm not sure about is quite how to show that this is the largest possible root. It seems fairly intuitively so from the graph, but I'm not sure about a good proof 
.
Thanks .
#272 Re: Help Me ! » Differentiation » 2011-02-20 02:05:10
Hi Bob, it's good to hear from you too.
Okay, so
So do I then discard t=-1 and sub in t=1?
#273 Help Me ! » Differentiation » 2011-02-20 01:40:03
- Au101
- Replies: 2
Hi guys,
I have a question about differentiation, which I'm not quite sure how to set out:
---
The curve C has parametric equations
Find an equation of the tangent to C at A (1,1).
---
Now
And obviously I have a y-coordinate and an x-coordinate.
I'm not so sure about finding the gradient, do I have to let x and y equal 1 and find that t=1?
#274 Re: Help Me ! » Argument of a Complex Number » 2011-02-05 05:36:15
Ohhh okay, fair enough .
Thanks a lot!
#275 Re: Help Me ! » Argument of a Complex Number » 2011-02-05 05:16:06
Hmmm, I see, thanks a lot gAr. Although, I still don't know quite how I would set out a proof that there can be only one value of a, especially - as the question implies - without finding a first. Could you, or anybody else, advise?