I need help with problem 2-1. I don\'t know how to approach it and I need to be

Question

I need help with problem 2-1. I don't know how to approach it and I need to be able to explain the steps. Can you please help? 2-1. Th e pizza numbers tell us how many pieces we can cut a pizza into, for a given number of cuts. For any n, let p(n) denote the maximum number of pieces into which we can cut a pizza using n straight cuts. Assume that the pizza is circular, and that the pieces are not moved inbetween cuts. The cuts are made so as to maximize the total number of pieces, not so that everybody gets a fair share. Determine p(0), p(1), p(2), p(3), and p(4). It turns out that p(n) is a quadratic function. Find it, and then calculate p(100).1 2-2. Suppose f(x) 2-5+12r+5. f(x) is defined for all real numbers. Give a piecewise definition (on all of its domain) of f(x) without using absolute value. The graph may help to answer this question, but justify your answer algebraically with a case-by-case argument from the equation for f(x). Your justification could begin with a statement such as, "When 2 3, then f(x) is given by the formula because ...". Then graph alz) =If(z)-201. and describe how the graphs of f and g are related.

Explanation / Answer

Hai,good morning, hoping my explanation helps you in understanding, as,we don't need fair shaped peices,we need not to cut the pizza through a same point.this is important, so we can get maximum peice.if no cuts we get 1full price I.e full pizza. And with a single cut ,we get two maximum prices ,and from 3 cuts we can get 7 prices (draw 3 lines through different points in a circle ,you get 7 pieces), and from 4 cuts we can get a maximum 11 prices (draw in the above manner).thus we can get the number if prices ,p(n) from 'n' cuts from the quadratic equation p(n)=(n^2+n+2)/2 .we can check it for above p(0)=(0^2+0+2)/2=1,,,p(1)={1^2+1+2}/2=2 and for 3 cuts p(3)=(3^2+3+2)/2=7, similarly p(4)=(4^2+4+2)/2=11 then p(100)=(100^2+100+2).2=10102/2=5051,hoping my explanation useful to you. If any more explanation needed I will give .

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