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Q. 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!
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
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 âº) The bug on teh larger tire travels the furthest.
HTH
Doug
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 âº) The bug on teh larger tire travels the furthest.
HTH
Doug
Weekly rate Chicago motels?
sassybluec
Does anyone know of any cheap motels in Chicago NOT the suburbs that are in a safe neighborhood?
Answer
There's a place called The Lodge Motel on Foster Ave. near Sheridan. It's pretty reasonably prices, in a mixed but nice neighborhood, only about a block from the lakefront and the running/bike path. It received three and a half stars (out of five) which seems pretty good for a motel. One room with a kingsized bed is only $87 a night! I pass by it all the time on my way to and from work and it seems pretty nice.
There's another place called The Heart of Chicago Motel on Clark street near Peterson. It's an old school motel and when I pass by it occasional it always seems busy. I've never stayed there, of course, but I had a bunch of friends stay there when they all came to town and they partied hearty there (a little too hearty, but that's another story). The website doesn't show the rates, but I'm assuming it's not too expensive. It's also in a safe area. Granted no area is totally safe, but this area is surrounded by quiet residential street and the booming Andersonville neighborhood.
Both motels are very close to public transportation. In fact, if you walk across the street from the Lodge Motel, you can catch an express bus that will take you downtown to Michigan Ave. where all the action is in minutes.
There's a place called The Lodge Motel on Foster Ave. near Sheridan. It's pretty reasonably prices, in a mixed but nice neighborhood, only about a block from the lakefront and the running/bike path. It received three and a half stars (out of five) which seems pretty good for a motel. One room with a kingsized bed is only $87 a night! I pass by it all the time on my way to and from work and it seems pretty nice.
There's another place called The Heart of Chicago Motel on Clark street near Peterson. It's an old school motel and when I pass by it occasional it always seems busy. I've never stayed there, of course, but I had a bunch of friends stay there when they all came to town and they partied hearty there (a little too hearty, but that's another story). The website doesn't show the rates, but I'm assuming it's not too expensive. It's also in a safe area. Granted no area is totally safe, but this area is surrounded by quiet residential street and the booming Andersonville neighborhood.
Both motels are very close to public transportation. In fact, if you walk across the street from the Lodge Motel, you can catch an express bus that will take you downtown to Michigan Ave. where all the action is in minutes.
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