Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**new college student****Member**- Registered: 2021-09-19
- Posts: 1

Question:

1. If f(x)=x^6+x^5+x^4+x^3+x^2+x

Please find the quotient and remainder, when f(x^7) is divided by f(x).

2. Please evaluate, and prove, the value of the expression 1^5+2^5+…………+x^5.

3. If 1^n+2^n+3^n+…………+n^n is divisible by A, evaluate the maximum value of A, and represent your answer in terms of n, given that n is a positive integer.

Use the following information to answer the next 3 parts.

A, B and C are rivals. Today they have decided to end their problems with a game of shooting. The aim chances of A, B and C are respectively 1/3, 2/3 and 1. A will shoot first, then B, then C. Only 1 may survive.

Part I: If the three will shoot randomly,

Find the survival rates of A, B and C.

Part II: If the three will shoot, with strategy, to maximize their survival rates,

find the survival rates of A, B and C.

Part III: It is known that A has a method to further maximize his survival rate.

a) What method is it?

b) Given A uses the method in (a), find the survival rates of A, B and C.

All answers must be provided with steps. You may use a calculator.

Offline

**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,278

hi new college student

Welcome to the forum.

I think I can help with all three but here we don't just provide model answers to homework questions. What I'll do is suggest how you can tackle number 1. When you post back your work on that I'll move on to number 2. Hope that suits you.

Q1. There is a method that resembles long division but it's hard to communicate how it works. Also you may not be any good at long division anyway in which case it won't help so I'll show you an alternative.

What this question is asking for is this:

where Q is some function of x and R is a number.

This identity has to be true for all x, so putting x=0 will enable you do determine R straight away.

Then you can re-arrange the equation to make Q(x) the subject.

Both f(x) and f(x^7) are GPs (geometric progression). This may help with the simplification.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

Offline

Pages: **1**