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1. Question about the use of Leibniz notations …

Double check what the text book actually wrote if it wrote (d/dx)*y to mean dy/dx then throw it away. More likely you have misinterpreted the text. Is it possible to scan the page and include it in your next post?
2. Humidifier physics homework

3. acos(h/r) is theta, ie half the angle of the sector at the centre. Need to double your result. 2 is submerged area + wet area above water 5 is submerged area for 6 you are working out wet area above water
3. Question about the use of Leibniz notations …

The article states that u*dy/dx + y*du/dx = d(y*u)/dx its the product rule
4. Question 21 - Final question on higher paper

thomas49th is taking what is called General Secondary Certficate Examination (GCSE) in Maths in England. It includes number, algebra, statistics and geometry and is taken at the age of 16. The examination is graded A,B,C,D,E,F, U (unclassified). Students achieving grades A or B will be allowed...
5. Question 21 - Final question on higher paper

Follow the instructions in my post #18 and do the drawing. You do know Pythagoras' Theorem don't you?
6. Question 21 - Final question on higher paper

NO ABSOLUTELY NOT. Just as Hallsof Ivy said. The webpage above is for vector displacement not distance between points. Lots of people have been pointing you in the right direction including me. Sometimes to follow advice you have to let go of the idea of what you were attempting was right...
7. Question 21 - Final question on higher paper

The question show in from an examination paper for GCSE. Thomas49th will have been given past examination papers for practice. The examination will take place in May. Thomas49th you will not have been shown the distance formula for GCSE but you will have covered pythagoras and should be able...
8. Another trigonometry problem

Depends on the wording of the question verify that x=180 is a solution of ..... use the first method show that x=180 is a solution of...... use the second method.
9. Another trigonometry problem

To verify x=180 is a solution LHS is sin(360)=0 RHS is 2 -2cos(360)=2-2=0 LHS=RHS so x=180 is a solution to obtain x=180 as a solution (1-cos2x)=(tanx)(sin2x) sin2x=2(1-cos2x) sin2x=2(tanx)(sin2x) sin2x-2tan(x)(sin2x)=0 sin2x(1-2tanx)=0 sin2x=0 or 1-2tanx=0
10. Expected Net Winning

The problem as stated by OP is the expected net winnings for the winner . I was querying whether this was what was actually asked.
11. Expected Net Winning

This gives that a player on average will lose $24.90 on a$100 dollar bet. Your questions asks for the expected net winnings for the winner so this is not the same thing. I was assuming this question was really about expected values and as you had had difficulty in finding anything about...
12. Trig Functions question

Not until you do some multiplying. Do you understand what I mean by the difference of two squares?
13. Expected Net Winning

This should help http://en.wikipedia.org/wiki/Expected_value
14. Trig Functions question

Do you know what the value of sec^2x-tan^2x is? The difference of two squares helps too.
15. Some Discreet Math stuff

try http://www.artofproblemsolving.com/Forum/viewtopic.php?t=130011&sid=30947c30f2e1b1fe60d2082b59b7fe3c
16. : Limits

\lim_{\theta\rightarrow 0} \frac{\sin^24\theta}{\theta}=\lim_{\theta\rightarrow 0} \frac{16\theta^2}{\theta}=\lim_{\theta\rightarrow 0}16\theta=0
17. Mathematica Mathematical Induction simplification

rearrange - put the -1 at the end and then look closely at the two terms now together. If you require more help please show what you have tried.
18. Rational points on a circle

Techno - I agree with Matt Grime Gonzo never changed his mind about what he wanted proof of. However there was a lack of clarity (for me) about the statement. I took this to mean For any positive integer k, you can find k points on any circle such that each point is a rational distance...
19. : Limits

Is it not possible to use small angles {\sin \theta }\approx\theta so \frac{{\sin ^2 4\theta }}{\theta }\approx16\theta as \theta \rightarrow 0
20. Sum of a polygon's interior angles

Below is a link to an image showing what I mean by transforming a complex polygon to a simple one. I belive that sufficient repeations of this process on even a very overlapping complex polygon would result in a simple polygon. http://img101.imageshack.us/img101/5027/comptosimpps4.png [Broken]
21. Sum of a polygon's interior angles

I'll return to my idea in post #23 Let n_1, n_2, .....n_k be a set of k "angles" such that their sum is 180(k-2) Let m_1, m_2, .....m_k, be defined by m_i = 180 - n_i for 1<=i<=k ( some m_i may be negative) the sum of all m_i is 360 rotations when m_i>0 will be clockwise...
22. Sum of a polygon's interior angles

Giving it more thought this arranging causes problems with the induction still restricting to the case when all angles <180 for n>3 from the set of n angles choose 3, a_{1}, a_{2}, a_{3} such that a_1 + a_2 + a_3 = 180 + d_1 + d_2 so that a_1-d_1 + a_2 -d_2+ a_3 = 180 take the set of...
23. Vectors/ lines

This may help http://mathforum.org/library/drmath/view/62814.html
24. Sum of a polygon's interior angles

Ok Doodle Bob, I see the flaw in my method, halving the angles does not work as you have to take exactly 180 from the n angles so that ther n-1 form a polygon. Mea Culpa
25. Sum of a polygon's interior angles

When all the angles are <180 you do not need them in a certain order. For n>3 take the angles a_1, a_2, a_n form the n-1 polygon with angles a_{2}/2, a_{n}/2 and the angles a_3,...... a_{n-1} form the triangle with angles a_1, a_{2}/2, a_{n}/2 and add to the n-1 polygon placing the...
26. Sum of a polygon's interior angles

I was thinking convex polygons and so thought that n_1, n_2, .....n_k were all <180. Reading your posts again I now realise you are thinking concave or convex polygon and so some n_i >180. and in this case m_i = 180 - n_i is not true. But when n_1, n_2, .....n_k are all <180 then it...
27. How to solve

I think he did. From OP
28. Sum of a polygon's interior angles

Another approach Instead of the interior angle n_1, n_2, .....n_k Consider the exterior angles m_1, m_2, .....m_k,instead where m_i = 180 - n_i for 1<=i<=k and sum of all m_i is 360 Start with a line segment A_0 to A_1 at A_1 rotate clockwise through m_1 and draw a line...
29. Rational points on a circle

Gonzo - At first I was not entrirely sure what it was you wanted to prove (or find a counter example for). Following our discussions I am now clear on that. Like you however I am not clear how Techno's statements help. Techno - Thank you for answering my question re: unit circles and...
30. Rational points on a circle

k=4 is possible draw a rectangle with sides 3 and 4, hence diagonals 5. All vertices lie on circle radius 2.5. Do not see how this helps in general though.