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Tutors Answer Your Questions about real-numbers (FREE)
Question 235390: trains a and b are traveling in the same direction on parallel tracks. train a is traveling at 80 miles per hour and train b is traveling at 100 miles per hour. train a passes a station at 3:10 pm. If train B passes the same station at 3:22 pm at what time will train b catch up to a.
Click here to see answer by Alan3354(6053)  |
Question 235115: I understand that the irrationals are not closed under addition, mult, div, subtr, etc. However,
Is it possible to construct a line segment on a cartesian coordinate system such that all points on the line have irrational values for the y coordinate when x is rational (i'm using the relationship y = mx + b)? It's okay if there are restrictions, like, the segment length must be transcendental or something.
I'm looking for non-zero-length line-segments that avoid all points with rational coordinate pairs.
I also don't expect this to be true for ALL line segments with, say, irrational coordinates for the endpoints. I'm just interested in constructing a line segment of non-zero length that has only irrational values for y when x is rational. If x is irrational i won't care about y - as long as x and y are never rational together.
I don't know how constraints are explored in mathematics, nor how one looks for solutions to a problem like this, nor how one goes about testing for the existence of such a construction, let alone constructing one. if this problem is in a well-known class of problems i can research that myself if somebody can help me identify the class.
Click here to see answer by jim_thompson5910(13785)  |
Question 222567: between them, terry and shelly have 50 cassettes. if shelly has more than two thirds as many cassettes as terry, at least how many cassettes does shelly have? at most how much does terry have
Click here to see answer by drj(1380)  |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305
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