Tuesday, September 2, 2014

Constructing equilateral triangle inscribed in circle

First construct a circle of equal radius. Make the centres sit on each other.

    Constructing equilateral triangle inscribed in circle:




Monday, September 1, 2014

Constructing circumscribing circle


Center the circle at the perpendicular bisectors of the sides.


    Constructing circumscribing circle:




Proof: Invertibility implies a unique solution to f(x)=y

In mathematics, an inverse function is a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa. i.e., f(x) = yif and only if g(y) = x. Referred from Wikipedia.



    Proof: Invertibility implies a unique solution to f(x)=y: Proof: Invertibility implies a unique solution to f(x)=y for all y in co-domain of f.




Graphs of absolute value functions

vertex is when absolute value=0, so x can be found.


    Graphs of absolute value functions:




Sunday, August 31, 2014

Extraneous solutions to radical equations


Extraneous solutions - a solution of a simplified  version of an equation that does not satisfy the original equation. Referred from  http://www.mathwords.com/e/extraneous_solution.htm


    Extraneous solutions to radical equations: Extraneous Solutions to Radical Equations




Friday, August 29, 2014

Dependent and independent variables

For p=5q

p is dependent on what happens to q so p is the dependent variable.


    Dependent and independent variables exercise: the basics: Here we have a problem that asks us to identify which variables are dependent and independent. Hint: independent variables are not influenced and remain unchanged by the other variable.




Wednesday, August 27, 2014

How many people can a blimp carry

Density = Mass /Volume so volume is proportional to mass.




    How many people can a blimp carry: