Horusmaster Wrote:just wondering what's right circular cylinder?

edit: nvm just a fancy name for cylinder >.>
working on it now

HooKarez Wrote:The answer in the back of the book doesn't have any thetas whatsoever. And we haven't done differentiation of trigonometric functions yet. This is the fail Calculus course that people take if they couldn't take AP Calculus yet I can't solve it.

The answer says (4πr^3)/(3sqrt3) :\

Oh my, there's a figure that goes along with it.

It shows a Sphere with an inscribed Cylinder; two radii endpoints for the top and bottom bases are: (x, sqrt(r^2-x^2)) and (x, -sqrt(r^2-x^2)).

KajitiSouls Wrote:Now this one is considerably trickier.

To determine the new dimensions of the circumscribed rectangle based on the original rectangle's dimensions L and W, and the variable θ, we'll apply geometry and trigonometry.

Code:

sin(θ) = o/h
cos(θ) = a/h
For both cases, h will either be L or W.

X = sin(θ)*W + cos(θ)*L; new rectangle's length
Y = sin(θ)*L + cos(θ)*W; new rectangle's width

V = X*Y
  = sin(θ)^2*L*W + cos(θ)^2*L*W + sin(θ)*cos(θ)*(W^2 + L^2)
  = L*W + sin(θ)*cos(θ)*(W^2 + L^2)

We'll do the same trick as with the cone problem: find the derivative of the volume function based off of θ.

Code:

V' = (-sin(θ)^2 + cos(θ)^2)*(W^2 + L^2)

If θ = Π/4 = 45°, V' = 0.

[color=Red]V = L*W + 1/2(W^2 + L^2)[/color]

HooKarez Wrote:So, this is an annoying stat problem we were given. It's so frustrating. e.e

Sixteen passengers on a liner discover that they are an exceptionally representative body. Four are Englishmen, four are Scots, four are Irish and four are Welsh. There are also four of each of four different ages, 35,45,55,65 and no two of the same age are of the same nationality. By profession, four are lawyers, four are soldiers, four are clergymen and four doctors, and no two of the same profession are of the same age or of the same nationality.

It appears, also, that four are bachelors, four are married, four are widowed, and four are divorced and that no two of the same marital status are of the same profession, or of the same age, or of the same nationality. Finally, four are conservatives, four are liberals, four are socialists, and four are fascists, and no two of the same political sympathies are of the same marital status, or of the same profession, or of the same age or of the same nationality.

Three of the fascists are known to be a divorced English lawyer of 65, a married Scots soldier of 55 and a widowed Irish doctor of 45. It is then easy to specify the remaining fascist.

It is further given that the Irish socialist if 35, the conservative of 45 is a Scotsman and the Englishman of 55 is a clergyman. What do you know of the Welsh lawyer?

e.e

KajitiSouls Wrote:Matt, have you tried expanding your answer instead of keeping it as factored form? They should be the same answer.

srry for such a late response xD

Lozmaster Wrote:Ugh, I'm having a really dumb moment. Got all the way through a semi long question, and now i'm having a moron moment on what should be the easiest part of the question.

How does one integrate -1/(1-x+x^2) with respect to x? I have the anwser, but can't for the life of me work out which method was used for it.
(The anwser should be

)

xLeviathan Wrote:The integral of the interval (-1, 1) = 0, then you can try different Riemann Sums or (I think) add the area of the trapezoids? (1/x forms trapezoids when delta x = 1).