Sorry about that I missed the squares out on the trig functions. I've corrected them to the inequality I actually got!
Wouldn't \rho^2 = x^2 + y^2 + z^2 though? I tried rearranging the inequality to use that but couldn't get very far. When I sketched the shape it was x^2 + y^2 coming up and...
Hi guys,
I've been doing past paper questions for an exam and I've gotten stuck with the limits of an integral. We have to evaluate
\int\int\int _{\Omega} \frac{1}{(1+z)^2} dx dy dz
where \Omega = \left\{ (x, y, z) : x^2 + y^2 \leq z^2 \leq 1 - x^2 - y^2, z \geq 0 \right\}
using spherical...
Hi guys,
I've just started university this week and I've been given a mountain of assignments. One of them has a proof question in it. Since this is an assignment I want to make clear that I don't want help with the actual proof.
In the first part of the question I'm asked to, given a...
Hi,
I've been doing some additional maths papers and I've seen the use of the substitution u=tan(x/2) in order to calculate integrals. In the mark scheme it states that this particular substitution used to be fairly common, however is not on the modern A-level syllabus.
Would someone...
Hi Guys,
Having read the two latest posts I find that my understanding of the concept is a lot clearer now. I see why it is that we use them and the reasons for actually having the vector product itself which was one of my main concerns in the topic.
I'll take your recommendation, Studiot...
Hi guys,
Thank you for the replies. I apologise if my question has caused all the 'beyond A-level fuss', but I guess in a sense that is really what I'm wanting to be explained (all though granted I understand if it cannot be explained without me having high-level knowledge to back-up the...
Hi Guys,
I realize that this may seem like a really simple question but it's really driving me crazy. In my A-level maths we've just started looking at the cross product and I understand how to calculate it, it's application in calculating areas ect but I find myself not understanding what...
Hi,
I'm sorry about my lack of clarity I'll try to explain my problem in more detail. I have a ratio of this form:
R=BD/AC
Where R is a six digit decimal and B, D, A and C are integers between 20 and 81 inclusive.
What I'm trying to do is write an algorithm that will approximate values for...
Hey guys,
Very quick question. Can anyone recommend an algorithm for factorising a number (no more than 10,000,000) which will factorise a number into two smaller numbers both of which fall within predetermined limits? I'm trying to find a variety of solutions to the problem AC=R where R is a...
Hi guys,
I've been reading a chapter from a book and I've been attempting a question which uses the binomial theorem to prove Fermat's Little Theorem. The question goes as follows:
Let p be a prime number:
i) Show that if r, s are positive integers such that r divides s, p divides r and p does...
Thank you very much for your reply - apologies for not replying myself sooner.
I see exactly what you mean now, part of what helped was reading the next chapter about multinomial coefficients; it helps put things in perspective.
Thanks again,
Oscar
Hey guys,
I've been reading up on binomial coefficients and I have found a brief section on n choose r. I understand vaguely what it actually is, however in my textbook there is a step by step proof of how we show that:
( \stackrel{n}{r} ) = \frac{n!}{r!(n-r)!}
I can follow where...
Sorry if I'm being stupid here;
Could you please tell me how you got s=ln(cosh(t))? I evaluated the integral as C=ln(cosh(s)), so I am confused as to how you made this step. I'm okay as to how you solved the problem from there on though :)
Thank you for the help,
Oscar