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May
14
comment How to find out what changes applied to integral?
Substituting $x=-8u+2u^2$ could get somewhat close to what you are expecting, but not exactly the expression you have.
May
14
comment Vertices required to construct a graph with at least $500$ edges
It should be $n \geq 33$ not $32$
May
14
comment Vertices required to construct a graph with at least $500$ edges
And $n\choose2$ $\geq$ $500$ will give you $n \geq 32$
May
14
comment Vertices required to construct a graph with at least $500$ edges
If there are $n$ vertices, pick a vertex and see how many vertices can be connected to that ? $n-1$? Each of the $n$ vertices are connected to $n-1$ in $n(n-1)$ ways, but you are counting each connection twice, therefore total connections should be $\frac{n(n-1)}{2}$ which is $n\choose2$
May
14
comment Why does $\binom{10}{7} = \frac{10!}{(10-7)!7!}$
@50ndr33 Watch these videos at artofproblemsolving.com/Videos/index.php?type=counting
May
14
revised Integral of $x^2\ln(x)$ using Simpson's rule
edited tags
May
14
revised Calculate the volume between two spheres
edited tags
May
14
comment solving Differential Equation
@Sean87 I like the writing on the cup (Feel the same way about changing the world)
May
14
comment solving Differential Equation
Yes, of course (Thanks)
May
14
comment solving Differential Equation
@Prasad, also mention that $\log()$ here is to the base $e$ otherwise one can use $\ln()$
May
14
comment solving Differential Equation
It should be $7 e^{arctan(t)}$ because $x(0)=3$ not $4$. You still have +1
May
14
answered solving Differential Equation
May
14
comment What is the geometrical representation of $1/R$?
@Patrick, I envy you (blackboard at home?) My +1
May
14
comment Mathmatical representation of recursion function
Your $foo(n)$ is a flat function with value $1$, unless you are going to change your question to something else later.
May
14
comment Mathmatical representation of recursion function
How is your answer helping this question?
May
14
comment Mathmatical representation of recursion function
$f(1) =f(0)+f(-2)-1 = 1+1-1 = 1, f(2)=f(1)+f(-1)-1=1. f(3)=f(2)+f(0)-1=1$
May
13
comment elementary inequality proof
Use $\frac{5a+b}{2} \geq \sqrt{5ab}$ and also the fact that $\sqrt{5} > 2$ to get the desired result.
May
13
comment Triangle-ish Number Series
$T$ is not the same in those two expressions, and if they are then $q=x-(n+1)y$
May
13
comment Multiplication convention rules
The fact that students have to face such a teacher year after year, I would give a warning (if I come across such grading) and the second such mistake would cause termination.
May
13
comment How to multiply two polynomials represented by values at distinct points?
Computationally if you store them as a vector, that is equivalent to what J.D. has answered. (If one has written a program in any language one would know)