Let $a$, $b$, and $c$ be positive real numbers. prove that \[\sqrt{a^2 - ab + b^2} + \sqrt{a^2 - ac + c^2} \ge \sqrt{b^2 + bc + c^2}.\]under what conditions does equality occur? that is, for what values of $a$, $b$, and $c$ are the two sides equal? hint(s):

Amarket is said to be equilibrium when quantity demanded is equal to quantity supplied. critically analyse the above statement by giving different types of market

According to this excerpt, a key part of our national security strategy is

After graduation, you plan to work for dynamo corporation for 12 years and then start your own business. you expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6) and $15,000 annually for the following 6 years (t = 7 through t = 12). the first deposit will be made a year from today. in addition, your grandfather just gave you a $32,500 graduation gift which you will deposit immediately (t = 0). if the account earns 9% compounded annually, how much will you have when you start your business 12 years from now?