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...
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?
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...
"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...
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...
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...
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?
?
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.
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...
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...
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...
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...
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...
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...
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...
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].
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...