1. K

    Calculus Old Quiz Problems Help

    1. Let R be the region bounded by the graphs of y= sinx and y = 1 - sinx on (pi/6, 5pi/6) Use the washer or disk method to set up (but do not evaluate) an integral that will determine the volume of the solid obtained by revolving R about the line y=3 2. Use calculus determine volume of the...
  2. M

    Volume of Hexagonal Pyramid - Using Integration from (0-h)

    The Question: By using Riemann’s sum, synthesise a mathematical model for finding the exact volume of any ‘tepee’ tent of side s and height h. Here's what I have so far However, I am currently unsure if I am heading in the right direction, and am stuck at what comes next. Any help would be...
  3. O

    Combinatorics with several conditions

    Hello. I have a math problem that I need to solve, however Im really stuck and also kind of depressed now. We have 30 balls. 6 red, 7 white, 9 green and 8 blue. We want to seperate them to 4 different boxes. · First box can only contain 13 or less balls, which can be either red or...
  4. W

    How difficult is this problem?

    Two spheres of radius 10 and 5 are concentric with their centers both at the same point, the origin. What is the volume outside the sphere of radius 5 but inside radius 10?
  5. K

    difficult geometry

  6. Z

    A probability question about Bayes'Rule,that is a little difficult for me.

    80% of the murders committed in a certain town are committed by men. A dead body has been found.Two detectives examine the body.The first detective,who is right seven times out of ten,announces that the murderer was a male.But the other detective,who is right 3 times out of 4,says that the...
  7. S

    Wierd Area Problem (difficult)

    Hi all, I am a maths teacher from the UK. A week or so ago I found a problem that looked challenging so I set it to one of my genius pupils as a bit of a "try this in your own time" extension. He came to me a few days later and said "I have tried to solve this problem for 2 days now and I can't...
  8. P

    Difficult Proofs I Cannot Find

    Hi, I cannot solve the following, could you please help me ? It is very urgent ! 1) Prove that : ∛ 5 + √2 is an irrational number 2) Prove that : ∛(45+29√2) + ∛(45-29√2) is an integer. Thanks for any help :) !
  9. R

    Your Most Difficult Math Class

    What is the most difficult or challenging math course you have taken? What made it so hard?
  10. S

    Another difficult integration question

    I'm having hard time getting started on this question. I tried to use substitution to integrate 1/x^4sqrt(1+x) first but I feel like there should be another way to approach it.. trigonometric substitution and power series don't seem to work. Any ideas??
  11. S

    Difficult integration question?

    So far, I tried to represent this function as a power series by using 1/(1-x)=1+x+x^2+x^3... By doing that, I got the addition of four summations: sigma (-1)^n x^(6n+5)/64^(n+1) + sigma (-1)^n x^(6n+2)/64^(n+1) + sigma (-1)-^n 4x^(6n+1)/64^(n+1) + sigma (-1)^n (x^(6n) sinx)/64^(n+1) Then I don't...
  12. H

    Difficult to evaluate area of a spherical triangle than that of a plane tritangle

    Difficult to evaluate area of a spherical triangle than that of a plane triangle How to evaluate the area covered by a spherical triangle, having one of its interior angles 150 degree included by two adjacent sides (each as a great circle arc) of lengths 26 & 39 units, on the spherical...
  13. H

    Difficult to evaluate area of a spherical rectangle than that of a plane rectangle

    How to evaluate the area covered by a spherical rectangle, having length & width (each as a great circle arc) of 18 & 6 units respectively, on a spherical surface with a radius 50 units? any help is highly appreciated. thanks in advance.......(Flower)(Flower)
  14. C

    Need help with difficult calculus question

    The question is: Determine whether the integral \int_{1}^{\infty}\frac{6}{x^{4}}dx diverges or converges and evaluate it if it converges
  15. P

    difficult integral

    How can be proved that $$ \int_{0}^{\pi/4}\arctan\left(\frac{e^{3ix}+e^{-3ix}}{\sqrt{e^{2ix}+e^{-2ix}}\left(e^{2ix}+e^{-2ix}+3\right)}\right)dx=0? $$ I've no idea how to prove it. I only observe that the exponential can be rewrite as a cosine.
  16. A

    You want to be really difficult workers

    You want to be really difficult workers last year petition pay I'm using six pounds is all for both these them still feeling it so choose what you need to challenge yourself Alpha Shred okay many tearing up here's one her not to make funny faces you doing if you're doing the right thing usually...
  17. S

    Difficult limit problem

    I have this question: lim (x^3+x^2)^(1/3)-(x^3-X^2)^(1/3) x->infinity I know that I have to simplify this equation first into a fractional form before applying L'Hopital's rule since it is in indeterminate form (infinity - infinity). I tried to get rid of the cube roots by multiplying by...
  18. C

    Difficult indefinite integral

    My friend showed me an integral that we both had no idea how to solve: \int\frac{ln(cot(x))}{sin(2x)}dx We couldn't find any shortcut formulas in the books that fit this form, when we began integration by parts the \int vdu was more complicated than the original problem. I suspect that perhaps...
  19. N

    Simple problem or a difficult one ??

    Hello all, My boy asked me these days for an apparent simple math problem. Could you be so kind to help me find the solution, please ? I'm glad to get some hints, please. --------- Tom write 20 numbers, each with at least two digits, with all digits equal (like 22, 666, 7777, etc) . The total...
  20. L

    Maynard Smith and the Haystack Model

    Hello there! I'm trying to write an essay on the Haystack Model, but I can't seem to get these two formulas to match: The second concept offered by Maynard Smith is group selection. He introduces a what later became known as ‘the haystack model’; a simplified mathematical model that serves...