Theory of Numbers (XVI) Principle of Mathematical Induction Prove that if n is an odd positive integer, then x + y is a factor of xn + yn. (For example, if n = 3, then xn + yn = ( x + y )( x2 – xy + y2 ) ...continues
Rates and Unite Prices (Basic Mathematics)
Describe a simple process for using rates and unit prices that might help someone who is having difficulty understanding these concepts. Include an example of your own to explain the solution process.
If you had an unlimited amount of 2p and 5p coins. Consider the linear diophantine equation 2x + 5y = n Show that all amounts n>=N=4 are obtainable.
Show that if a = b (mod n) then (i) a^j = b^j (mod n) for any positive integer j (ii) ca =cb (mod n) for any integer c (iii) f(a) = f(b) (mod n) for any polynomial with integer coefficients
Show that each of the following holds: [1,1,1,1,1,1,....]^2 = [2,1,1,1,1,1,....] [1,2,2,2,2,2,....]^2 = [2] [1,1,1,1,1,1,....][0,1,1,1,1,1,....] = [1] In each case make a conjecture about a possible generalisation, and explore it (i.e. attempt to prove your conjectures true or false). Note:We can write down any ...continues
The Last Outpost is a tourist stop in a western resort community.
1. C-V-P Analysis The Last Outpost is a tourist stop in a western resort community. Kerry Yost, the owner of the shop, sells hand-woven blankets for an average price of $30 per blanket. Kerry buys the blankets from weavers at an average cost of $21. In addition, he has selling expenses of $3 per blanket. Kerry rents the buil ...continues
1. Mrs Bollo's second grade class of thirty student conducted a pet ownership survey . Results of the survey indicate that eight students own a cat, 15 students own a dog, and 5 students own both a cat and a dog, How many of the students surveyed own only a cat? 2. Please use a venn diagram to answer the questions? At east ...continues
