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    Music and mathematics: how are they related?

    my main question: is there some mathematical formula that leads to a great song? be it a beat, melody, etc. what is the mathematical difference between dissonance and connosance? we know that listening to classical music at a young age results in high math scores. but why? i have listened to...
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    How would i go about breaking an isopeptide bond?

    Hi. i dont know alot about chemistry so bear with me. the bond is between a member of the carboxyl group and the amino acid lysine. as i understand i need an enzyme. what readily available enzyme would suffice? would protease work?
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    How do i generalize this result to higher dimensions? (arc length, surface area)

    a derivation of the formula for arc length is simple enough: given a function f[x], find the length of the arc from x0 to x1. lim(x1-x0)/n=dx n->inf x1 S=^{i=n-1}_{i=0}\sum\sqrt{(x+(i+1)dx-(x+idx))^2+f(x+(i+1)dx)-f(x+dx))^2} xo...
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    A righteous atheist is morally superior to a righteous theist

    "a righteous atheist is morally superior to a righteous theist" what do you think of this statement? suppose there are two people, person A and person B. person A believes that there is no afterlife, no god, nothing once you die. any good actions you do will not be rewarded. any bad...
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    Something interesting i realized. (more than one set of limits, change of variables)

    suppose i want to find the following integral: 7 \intx dx 3 now suppose for some demented reason i decided not to do it straightforward and get (49-9)/2=20 instead i use the substitution x=u2+4u+5 giving u1 \int(u2+4u+5)(2u+4)du u0 u1 \int2u3+12u2+26u+20 du u0 the indefinite integral is...
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    What should i do with my life?

    im 21 years old and i have done absolutely nothing in my life. i havent taken the sat,act, or any type of college entrance exams. i am stuck in a rut and i dont see a way to get my life moving. i have made so many mistakes in my life. there are so many regrets i have. i remember not having...
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    An algorithm for numerical double integration over non-rectangular regions.

    is there one that is stable and accurate?
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    Why is simpsons rule exact for 3rd degree polynomials?

    this is really perplexing. how can it be exact? simpsons rule uses quadratics to approximate the curve. how can it be exact if im approximating a cubic with a quadratic?
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    How do i find the arc length of an implicit curve given by f[x,y]=0?

    ? i used the implicit function theorem to find dy/dx, then applied that to the arc length formula, but i have to integrate with respect to x and there is the implicit function y[x] inside the radical. also, if it matters, the curve is assumed to be closed.
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    C/++/# How do i declare a function in the command promp window (c++ question)

    Hi. i wrote a script that finds the definite integral of a function using simpsons rule. right now the function to be integrated is defined as 2*pow(9-pow(x,2),.5). but this is very inconvenient to me because i must edit the program each time i want to find a new integral. my question is how...
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    How do i maximize the line integral?

    suppose i have a nonconservative vector field. and there is a path going from point A to point B. How do i determine the path taken from A to B such that the line integral is maximized? edit: actually after thinkin about it, this might be an undefined problem unless there is some constraint on...
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    Is my proof of greens theorem correct?

    here it is. [Broken]
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    Roots of unity of matrices

    hi. i have recently become very interested in the idea of the nth roots of unity. i have discovered how to calculate them (using eigenvalues), and i find it very fascinating that there are not n many nth roots of unity(unlike scalars). aparently in the case where the matrix is 2x2, there are...
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    Trapezoidal, simpsons rule, and higher order approximations

    hi. i was able to prove the trapezoidal rule and simpsons rule. (basically i used matrices to determine the coefficients m and b for mx+b when proving the trapezoidal rule and a,b,c for ax^2+bx+c such that the points coincide, then i integrated the approximating polynomial) the amount of...
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    How do i make a function return an array?

    in the c++ programming language, how do i make a function return an array?
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    Need the parametric equation of a circle perpendicular to a vector.

    i need a parametric equation of a circle in 3d space that is perpendicular to a vector <a,b,c>. (as t goes up the circle is traced counterclockwise, as viewed from the head of the vector.) in the form x[t],y[t],z[t] i know that x^2+y^2+z^2=constant and that ax+by+cz=0 But i cannot figure...
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    Functions and arrays.

    How do i create an array such that there is more than one index? the array declared here float array[i]; is like a vector but how do i create an array that is declared such as float array[i,j] which would be a matrix And how do i create a c function whose input is an array and the...
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    Nonconservative gradients (not an oxymoron)

    fx,fy=-y,x curl(fx,fy)=2 its counterclockwise so the gradient is pointing ccw. the gradient is the direction of max increase, so then the surface z=f[x,y] whose gradient is -y,x is a spiral/screw whose z position goes up forever as x and y are traced out counterclockwise so, a...
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    Double integral bounded by closed parametric curve

    question: how do i find the area under f[x,y] bounded by a closed parametric curve x[t],y[t]? it doesnt look like i can use a change of variables. it seems as though double integrals only with functions where the curve is given explicitly such as y[x] or x[y].
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    Runge kutta script

    Hi. im working on a runge kutta/integral finder. my goal is to make it "exact to the dx", so to speak. im a beginner at c++, so bear with me. the compiler im using is dev cpp, incase it matters. my main problem was that apparently i cant have a long double array of size greater than...
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    Determining a function by the properties it posesses

    Question about functions and defining new functions. im thinking about a kind of problem where you are given some property of a function, and the solution is to find what functions satisfy that property. for example: f[x+n*2pi]=f[x] for all integer n the solution is the trig functions...
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    Sliding down a hill with no friction, non-constant incline

    How do i solve this? heres how far i've gotten suppose i have x[q], y[q]=S, the surface of a hill dy/dx=(dy/dt)/(dx/dt) atan(dy/dx)= the angle of incline at a location on the hill -GM*cos(pi/2-atan(dy/dx))=the tangeantal component of acceleration im ignoring the perpendicular...
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    Quadratics of quadratics

    Question about quadratics of quadratics can any 4th degree polynomial be expressed as a quadratic of a quadratic function? or in the more general case, can any polynomial of degree 2^n be expressed as n-many quadratic functions of quadratic functions? and given a polynomial of degree...
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    Factorizing taylor polynomials of infinite degree

    an idea i had: factorizing taylor polynomials Can any taylor polynomial be factorized into an infinite product representation? I think so. I was able to do this(kinda) with sin(x), i did it this way. because sin(0)=0, there must be an x in the factorization. because every x of...
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    Lagrangian multipliers

    How does lagrange multipliers work? i was able to work out this proof of the idea, but its only true for a function with two independent variables and one dependent variable. Rn=the space that is the independent variables. x[Rn]=x C[Rn]=C=constant. dx/d[Rn]=grad(x)*v; v is a unit...
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    Euler lagrange equation, mechanics, need help

    Could somebody explain to me how lagrange multipliers works in finding extrema of constrained functions? also, what is calculus of variations and lagrangian mechanics, and can somebody explain to me what the lagrangian function is and the euler-lagrange equation. And, i read something about...
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    Is e^ix multivalued, roots of unity, etc

    questions: why is the sum of all the roots of unity equal to zero? z^(1/n)=z1,z2,...zn z1+z2+...+zn=0 It's obviously true when there's an even number of roots, (because each root has a partner that is pi radians away and therefore the negative of the other root). but i cant figure out...
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    Gravity where acceleration is changing

    I have a question about gravity: How do i formulate an equation that incorporates the change in distance between two objects- in other words, where the acceleration due to gravity is changing as the distance changes, instead of simply where the acceleration is held constant. Here's how far...
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    Cubic formula and vietes formulas

    First, Is there a way to convert a complex number to polar form without using boolean commands? And now, my real question: Do all of viete's formulas hold true when the coefficients of a cubic formula are complex? I wrote a script that finds the roots of a cubic formula with complex...
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    Questions about matrices and vectors:Why does the dot product of

    Questions about matrices and vectors: Why does the dot product of a and b equal |a||b|cos(angle between a and b) are the vectors of a matrix the columns or the rows, or can it be either? I know a 0 determinant of a matrix means the vectors lie on top of eachother, and the absolute...