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Reciprocal

by ieeyorei » Wed Mar 11, 2009 7:23 pm
If n denotes a number to the left of 0 on the number line such that the sq of n is less than 1/100, then the reciprocal of n must be

a. less than -10
b. b/w -1 and -1/10
c. b/w -1/10 and 0
d. b/w 0 and 1/10
e. greater than 10

A
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by DanaJ » Wed Mar 11, 2009 9:28 pm
n^2 < 1/100 means that n is between -1/10 and 1/10. Since n is on the left of zero on the number line, this means that n is between -1/10 and 0:
-1/10 < n < 0. Finding the reciprocal means flipping the "<" into ">", but since n is negative, the ">" will be flipped again back to "<":

1/(-1/10) < 1/n < 0
-10 < n < 0.
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by scoobydooby » Wed Mar 11, 2009 11:32 pm
n<1/100
=>n<1/10 or n>-1/10

since n<0, n must lie between -1/10 and 0

reciprocal of n would be between -10 and infinity
=> less than -10


hence A
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by franciskyle » Thu Mar 12, 2009 2:02 am
n < 0 & n^2 < 1/100... n < - 1/10

Multiplying both sides by -10 while dividing by n

-10 > 1/n

Therefore A
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