I will first start with a scenario, I have to apply some adjustments to a particular value. These adjustments are either compound or non-compounded and they can either be added or subtracted to the value. They are executed in the order they are stored (they are stored in a database with a sequence number starting […]

For a National Board Exam Review: Find the equation of the perpendicular bisector of the line joining (4,0) and (-6, -3) Answer is 20x + 6y + 29 = 0 I dont know where I went wrong. This is supposed to be very easy: Find slope between two points: $${ m=\frac{y^2 – y^1}{ x^2 – […]

I have three equations of the form: $$i_1^3L_1+i_1K+V_1+(i_2+i_3+C)Z_n=0$$ $$i_2^3L_2+i_2K+V_2+(i_1+i_3+C)Z_n=0$$ $$i_3^3L_3+i_3K+V_3+(i_1+i_2+C)Z_n=0$$ where $L_1,L_2,L_3,K,V_1,V_2,V_3,C$ and $Z_n$ are all known constants. What methods can I use to obtain the values of $i_1,i_2$ and $i_3$ ?

Can you use noninteger powers Like is $x^{8.3} / x^{2.2} = x^{6.1}$?

Show that $\tan {\pi \over 8} = \sqrt 2 – 1$, using the identity $\tan 2\theta = {{2\tan \theta } \over {1 – {{\tan }^2}\theta }}$ Using $\tan 2\theta = {{2\tan \theta } \over {1 – {{\tan }^2}\theta }}$ with $\theta = {\pi \over {16}}$: $\eqalign{ & \tan {\pi \over 8} = {{2\tan {\pi \over […]

I have the function $$f(t)=\sin(t)+\sin(\sqrt2t)$$ I would like to calculate the fundamental period of $f(t)$. I know that the period of $\sin(t)$ is $2\pi$ and the period of $\sin(\sqrt2t)$ is $\sqrt2\pi$. I sense that I must work out the lcm of $2$ and and $\sqrt2$ but I’m unsure on how to do this.

I have been using simple inequalities of fractional powers on a positive interval and keep abusing the inequality for $x>1$. I was just wondering if there is a nice way to prove the inequality in a couple line: Let $x \in [1,\infty)$ and $r,s \in \mathbb{R}$ What is an easy way to prove the equality […]

I’ve had trouble on this one problem for a couple days. Complete the square on the X and Y terms to find the center and radius of the circle. $x^2+2x+y^2-4y=-4\:\:$

Say that $c_1 = -i$ and $c_2 = 3$. For this problem, let $z_0$ be an arbitrary complex number. We can rotate $z_0$ around $c_1$ by $\pi/4$ counterclockwise to get $z_1$. Next, we canrotate $z_1$ around $c_2$ by $\pi/4$ counter-clockwise to get $z_2$. There exists a complex number $c$ where we can get $z_2$ from […]

Let $0\leq x,y,z\leq 1$. What is the minimum of $$F(x,y,z)=\frac{1}{x+y}+\frac{1}{x+z}-\frac{1}{x+y+z}?$$ We have $F(1,1,1)=2/3$, $F(1,1,0)=F(1,0,1)=F(1,0,0)=1$, and $F(0,1,1)=3/2$. Is the minimum $2/3$?

Intereting Posts

Can I bring the variable of integration inside the integral?
Sum equals integral
Can one tell based on the moments of the random variable if it is continuos or not
Intuition behind variational principle
What would be the value of $\sum\limits_{n=0}^\infty \frac{1}{an^2+bn+c}$
How do I compute the following limit: $ \lim_{x \to \infty} \frac{x!}{\left( \frac{x}{e} \right)^{x}}$?
Unclear proof of a proposition on semisimple rings in Lang
Does there exist a real Hilbert space with countably infinite dimension as a vector space over $\mathbb{R}$?
How do I prove that $x^p-x+a$ is irreducible in a field with $p$ elements when $a\neq 0$?
In a complex vector space, $\langle Tx,x \rangle=0 \implies T = 0$
Prove that $x^{2} \equiv 1 \pmod{2^k}$ has exactly four incongruent solutions
Chameleons Riddle
Counting number of solutions with restrictions
What is linearity of Expectations?
Equality in the Schwarz-Pick theorem implies function is a linear fractional?