For all numbers x, [x] denotes the value of x3 rounded to the nearest multiple ... ...
For all numbers
x, [
x] denotes the value of
x3 rounded to the nearest multiple of ten.
| Column A | | Column B |
| [x + 1] | | [x] + 1 |
(A) Column A is larger
(B) ...
(C) ...
(D) ...
(E) ...
*This question is included in
Nova Math - Problem Set B: Substitution 2
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Posted: 03/09/2012 14:49
I do not understand what the question is asking. I reviewed the example, but I don't see the relationship to the question.
Admin
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Posted: 03/09/2012 16:58
Jessica, this is a medium difficult question, so don't feel bad. It is an operator problem, where we practice to transform a "thing" to another form using a mathematical operation. In this case, the operator is symbolized by [..], and can be expressed verbally as "raise to the power of 3 anything inside the square brackets".
So, in Column A, we have [x+1], which can now be mathematically expressed as (x+1) raised to the power of 3, or (x+1)^3. Similarly in Column B we have [x] +1, which can be mathematically expressed as x^3 +1.
The question is asking, how does (x+1)^3 compare to x^3 +1? Which one is larger? Or are they equal? Or is there not enough information to decide?
Now that you understand the question, I am sure you can follow the explanation in the Solution.
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Posted: 09/28/2014 19:22
I'm confused about when x=5 [x]=0 or [x]=10?
Contributor
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Posted: 09/28/2014 21:56
Reply: when x=5, [x]=5^3 rounded to to the nearest 10 = 75 rounded to the nearest 10, which is 80.
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Posted: 01/02/2013 15:06
In your solution, how is [1] = to 0, and how is [2] = 10.
Admin
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Posted: 01/03/2013 01:35
Hi William,
[1] denotes the value of 1^3 = 1 rounded to the nearest multiple of ten. Now, the multiples of 10 that are closest to 1 are 0 and 10, and clearly 0 is closer to 1 than is 10. So, [1] = 0.
Note: Zero is a multiple of 10 because 0 = 0(10).
[2] denotes the value of 2^3 = 8 rounded to the nearest multiple of ten. Now, the multiples of 10 that are closest to 8 are 0 and 10, and clearly 10 is closer to 8 than is 0. So, [2] = 10.
Nova Press
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For all numbers x, [x] denotes the value of x3 rounded to the nearest multiple ... ...
Posted: 09/03/2013 10:28
Just i wanna understand that when i faced problem like this i should follow the rule 0 and 10. I'll compare the result wether close to 0 or 10!!!!! Is it correct??????
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For all numbers x, [x] denotes the value of x3 rounded to the nearest multiple ... ...
Posted: 10/30/2013 14:03
Hello, I can understand the answer being D, but my argument is if you say round up to the nearest multiple of 10 are you allowed to go backwards in maths? From 2 to 0 as opposed to from 2 to 10. I thought it was the same principle with approximating decimals. Eg 2.4 is approximately 3 not going backwards to 2.
Contributor
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Posted: 10/30/2013 19:41
Jane, the problem says "rounded to", not "rounded up to".
To answer the other question, 2.4 is rounded to 2, not 3. 2.5 would be rounded to 3.
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For all numbers x, [x] denotes the value of x3 rounded to the nearest multiple ... ...
Posted: 09/22/2014 22:43
I don't really get the point of the question. Most of time, without a range for x, the comparison is always unknown. Then why bother setting up such a difficult operation...
Contributor
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Posted: 09/23/2014 08:49
T, there is a range for x, in this problem it is "all numbers"
