math HW help. PLEASE!?

Question

show that the trinomial x(squared) + x + 31 will not give prime numbers for very many values of x.

this one is kinda of long, sorry.

2 bugs grow tired of walking and decide to hop onto a nearby racing bike. 1 bug sits within the tread of the smaller front wheel while the other bug sits within the tread of the larger back wheel. first, can u intuit the shape of the path that each bug will travel? second, can u intuit which bug, if either, travels a greater distance through space during any given bicycle ride?

thanks, help with either, or both, would be fantastic!

Answer 1

That 1'st one bothers me because I don't know what 'very many values of x' actually means.
x = 1 => x² + x + 31 = 33 composite
x = 2 => x² + x + 31 = 37 prime
x = 3 => x² + x + 31 = 43 prime
x = 4 => x² + x + 31 = 51 prime
x = 5 => x² + x + 31 = 61 prime
x = 6 => x² + x + 31 = 73 prime
x = 7 => x² + x + 31 = 87 composite
and it seems as if x² + x +31 has generated a lot more primes than non-primes (composites) thus far. And any proof that needs to get much further along than this, will need some -serious- number theory that you probably won't see until your Senior year or your 1'st year of Grad School.

The bugs travel along a path called a 'cycloid'. It looks like a bunch of 'half-circles' placed next to each other (Google on 'cycloid', there's gotta be a site out there with a picture ☺) The bug on teh larger tire travels the furthest.

HTH

Doug

Answer 2

I'll take a look at to provide an explanation for the pleasant I can: Firstly, every time you wish to clear up for a variable (on this case x), you have got to positioned the variable on one part and the opposite numbers at the different. So first positioned the x at the left part of the equation. To do that, you'll be able to realize that x is terrible (-x). Because of this, to stability the equation, you upload POSITIVE x to every part: five + x = eight - x + x Now, you realize that -x + x equals zero, so you'll now take that out of the equation: five + x = eight Now you have got to positioned the five at the proper part so x can also be on my own. You recognise that five is a POSITIVE quantity (+five), with the intention to stability the equation, you subtract five on every part: five - five + x = eight - five five - five equals zero, so you'll now take that out of the equation: x = eight - five Now you'll clear up x with no trouble. x = three So this implies the last reply is x = three If we plug in three to the equation, we will se that it's actual. five = eight - three five = five I desire this is helping =)

Answer 3

circle



idk i suck so dont put that i am trying