Choosing randomly integers from $1$ to $10$
From Question 5 the practice book of the GRE math subject test: Sofia and Tess will each randomly choose one of the $10$ integers from $1$ to $10$. What i...
Category: General
Integral: $\int_{-\infty}^{\infty} x^2 e^{-x^2}\mathrm dx$
I don't know how to evaluate it. I know there is one method using the gamma function. BUT I want to know the solution using a calculus method like po...
Limacon/cardioid orientation confusion
I'm learning about polar equations and am trying to graph the curve r = 3 + 3 sin(theta), with theta between 0 and 2pi. Based on what I've learn...
Why is the eccentricity of a parabola 1?
What I know: The standard form for a parabola is $(x-h)^2=4a(y-k)$, if the axis of symmetry of the parabola is vertical, or $(y-k)^2=4a(x-h)$, if the axis...
Simplify Boolean Product of Sums Function
I've got a product of sums expression: F=(A'+B+C')&(A+D')(C+D') I need to show it as a sum of products and then simplify it. ...
Composition of function with itself
For the set of all functions $f:\{0,1, \dots,2014\} \to \{0,1,\dots, 2014\}$ such that $f\left(f\left(i\right)\right)=i$, for all $0 \leq i \leq 2014$. Co...
Express solution in simplest radical form: $(4x-1)(3x+7) = (5x-1)(2x+3)$
I need help with the problem. I'm in grade 11 math. $(4x-1)(3x+7)=(5x-1)(2x+3)$ So far I think I have to factor it and I got $(12x^2+25x-7)=(10x^2-13...
A 4-Regular graph with 7 vertices is non planar
A Graph with 7 vertices each having degree 4 cannot be planar. Any hints on the proof?
Eigenvectors of similar matrices
If $A$ and $B$ are similar matrices then every eigenvector of $A$ is an eigenvector of $B$. Is the above statement is true? I know that similar matrices h...
Proving $x^n - y^n = (x-y)(x^{n-1} + x^{n-2} y + ... + x y^{n-2} + y^{n-1})$
In Spivak's Calculus 3rd Edition, there is an exercise to prove the following: $$x^n - y^n = (x-y)(x^{n-1} + x^{n-2} y + ... + x y^{n-2} + y^{n-1})$$...
