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Re: If n denotes a number to the left of 0 on the number line
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09 Jan 2018, 05:59
dave13 wrote: AKProdigy87 wrote: The answer is A. We are given two pieces of information: 1) \(n^2 \frac{1}{10}\) To determine the conditions on the reciprocal of n: \(\frac{1}{n} for example if [m]\sqrt{x}\) = 4 then we need to squae both sides of equation so \(\sqrt{(x)}\) = \((4)^2\) > x= 16 now when it comes to the solution above from this equation \(n^2 < \frac{1}{100}\) we get this \(n < \frac{1}{10}\)  why ? should not we square both sides as I did in my example ? Why are we applying this formula \(\sqrt{x^2}\) = \(x\) if this doesnt look like \(n^2 < \frac{1}{100}\) ? < (here we dont have radical sign) why 100 in denominator is reduced by 10 ? shouldn't 100 be multiplied by itself as in my example ? in my example the number 4 turns into 16 and here it get reduced...so I am confused Also ss there a difference between \(\sqrt{x^2}\) and \(\sqrt{x}\) ? many thanks ! perhaps you friends can help chetan2u , niks18Always remember the rule  \(\sqrt{x}=5\) wll have only one solution as x=25 that is \(\sqrt{25}\) will always be 5 because square root cannot be negative But \(x^2=25\) means x can be 5 or 5
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If n denotes a number to the left of 0 on the number line
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09 Jan 2018, 08:09
hi dave13Quote: for example if \(\sqrt{x}\) = 4 then we need to squae both sides of equation so \(\sqrt{(x)}\) = \((4)^2\) > x= 16 now when it comes to the solution above from this equation \(n^2 < \frac{1}{100}\) we get this \(n < \frac{1}{10}\)  why ? should not we square both sides as I did in my example ? Note: \(\sqrt{n^2}=n\), because here \(n\) is a variable and you don't know the value. for eg. \((2)^2=4\) & \((2)^2=4\) so if we say \(n^2=4\), then on taking square root of both sides we will have \(n=2=2\) or \(2\) Hence here for \(n^2 < \frac{1}{100}\) we get \(n < \frac{1}{10}\) on taking square root of \(n^2\), because \(n\) is a variable here Quote: Why are we applying this formula \(\sqrt{x^2}\) = \(x\) if this doesnt look like \(n^2 < \frac{1}{100}\) ? < (here we dont have radical sign) why 100 in denominator is reduced by 10 ? shouldn't 100 be multiplied by itself as in my example ? in my example the number 4 turns into 16 and here it get reduced...so I am confused we are taking square root here and not squaring. as we have \(n^2\) so by taking square root we will get to \(n\); \(100=10^2\) and \(\sqrt{10^2}=10\) Quote: Also ss there a difference between \(\sqrt{x^2}\) and \(\sqrt{x}\) ? many thanks ! There is a lot of difference between \(\sqrt{x^2}\) and \(\sqrt{x}\) let's assume \(x=2\), then \(x^2=4\) and \(\sqrt{4}\) is different from \(\sqrt{2}\)



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Re: If n denotes a number to the left of 0 on the number line
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21 Feb 2018, 10:06
Please suggest where I have gone wrong.
n^2 < 1/100
So, 100 < 1/n^2 So, 1/n^2 > 100
So, I am getting C, while right answer is A.



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If n denotes a number to the left of 0 on the number line
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21 Feb 2018, 10:48
Nived wrote: Please suggest where I have gone wrong.
n^2 100
So, I am getting C, while right answer is A. Hi Nivedkindly read the question correctly. the question asks you to find the reciprocal of \(n\) and not of \(n^2\) what you have got here is the reciprocal of \(n^2\) which is incorrect. so you have \(\frac{1}{n^2}>100 =>\frac{1}{n^2}10^2>0\) \(=>(\frac{1}{n}10)(\frac{1}{n}+10)>0\) so you have either \(\frac{1}{n}>10\) or \(\frac{1}{n}<10\). Now since \(n\) is towards the left of \(0\), i.e. negative so \(\frac{1}{n}>10\) is not possible Hence \(\frac{1}{n}<10\)



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Re: If n denotes a number to the left of 0 on the number line
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22 Feb 2018, 17:46
topmbaseeker wrote: If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be
A. Less than 10 B. Between 1 and 1/10 C. Between 1/10 and 0 D. Between 0 and 1/10 E. Greater than 10 We are given that n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100. This means n is negative, and it is between 0 and 1/10 since (1/10)^2 = 1/100. Thus, n could be equal to values such as 1/11, 1/12, 1/13, etc. Notice that when we square these values, they are all less than 1/100. Let’s take the reciprocal of any of these values listed. The reciprocal of 1/11 is 11. Similarly, the reciprocal of 1/12 is 12 and the reciprocal of 1/13 is 13. Since these reciprocals are all less than 10, answer choice A is correct. Answer: A
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Re: If n denotes a number to the left of 0 on the number line
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21 Oct 2018, 20:20
Given n2<100 and n < 0 n2< 100 => 1/n2 > 100 => 1/n2  100>0 => (1/n+10)(1/n10) >0 solution for 1/n is either 1/n less than 10 or greater than 10 . But n is a negative number so 1/n is less than 10



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If n denotes a number to the left of 0 on the number line
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24 Nov 2018, 15:05
A video explanation can be found here: https://www.youtube.com/watch?v=lG5iq9xcswsFirst note that if n^2 < 1/100, the range of values of n would be 1/10 < n < 1/10 But that range is further restricted – since we’re told n is to the left of 0, then 1/10 < n < 0 (Note that C is a trap answer) Thinking about reciprocals, we move from negative fractions to negative whole numbers. (The correct answer may become easier to visualize if you draw out the number line.) Answer A
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Re: If n denotes a number to the left of 0 on the number line
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22 Jul 2019, 03:52
Sorry, but I am kind of confused about the sign. Please help me with the following.
When we have negative signs on a variable we're trying to find, we flip the equality sign right? So, first we have this: 1/10 < n we divide both side by n : 1/10n < 1 then, we multiply both side by 10 : 1/n < 10 why we don't flip the equality sign like this : 1/n > 10 instead of 1/n < 10?



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If n denotes a number to the left of 0 on the number line
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03 Aug 2019, 08:04
Gladiator59 chetan2u Bunuel VeritasKarishmaHello could you provide your assistance regarding my question? It has to do with inequalities. lets say we have 1<10n (n<0) when we divide by n I know that it should be like this 1/n>10 and then 1/n < 10 But what I want to ask is when we divide by n, which we know is a negative number, why can't we proceed like this, 1<10n (n<0) 1/n>10 since 1/(a negative number) = positive number



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Re: If n denotes a number to the left of 0 on the number line
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05 Aug 2019, 04:18
UNSTOPPABLE12 wrote: Gladiator59 chetan2u Bunuel VeritasKarishmaHello could you provide your assistance regarding my question? It has to do with inequalities. lets say we have 1<10n (n<0) when we divide by n I know that it should be like this 1/n>10 and then 1/n < 10 But what I want to ask is when we divide by n, which we know is a negative number, why can't we proceed like this, 1<10n (n<0) 1/n>10 since 1/(a negative number) = positive number If we know 1 < 10n (n is a negative number so the right hand side is negative too. n could take values such as 1/20, 1/50 etc) To process it easily, we can just divide both sides by 10 (n gets separated out) 1/10 < n Since n < 0, we get 1/10 < n < 0 If instead, we divide both sides by n, we get 1/n > 10 How did you get 1/n > 10?
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Re: If n denotes a number to the left of 0 on the number line
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05 Aug 2019, 06:44
VeritasKarishma wrote: UNSTOPPABLE12 wrote: Gladiator59 chetan2u Bunuel VeritasKarishmaHello could you provide your assistance regarding my question? It has to do with inequalities. lets say we have 1<10n (n<0) when we divide by n I know that it should be like this 1/n>10 and then 1/n < 10 But what I want to ask is when we divide by n, which we know is a negative number, why can't we proceed like this, 1<10n (n<0) 1/n>10 since 1/(a negative number) = positive number If we know 1 < 10n (n is a negative number so the right hand side is negative too. n could take values such as 1/20, 1/50 etc) To process it easily, we can just divide both sides by 10 (n gets separated out) 1/10 < n Since n < 0, we get 1/10 < n < 0 If instead, we divide both sides by n, we get 1/n > 10 How did you get 1/n > 10? Well, to be frank with you I was really confused between handling inequalities when there is a variable and when we have a specific number what I did was to consider n<0 but then imagined in my head that n is eg.2 so i both changed the sign of inequality and the sign of the fraction to positive, which is wrong so instead of just dividing 1<10n by n(n<0) and getting 1/n>10 I would divide by n and simultaneously think that n is a number like eg.2 so I would also change the sign of 1/n to 1/n which is wrong . thank you VeritasKarishma for your reply.



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Re: If n denotes a number to the left of 0 on the number line
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05 Aug 2019, 23:06
UNSTOPPABLE12 wrote: VeritasKarishma wrote: UNSTOPPABLE12 wrote: Gladiator59 chetan2u Bunuel VeritasKarishmaHello could you provide your assistance regarding my question? It has to do with inequalities. lets say we have 1<10n (n<0) when we divide by n I know that it should be like this 1/n>10 and then 1/n < 10 But what I want to ask is when we divide by n, which we know is a negative number, why can't we proceed like this, 1<10n (n<0) 1/n>10 since 1/(a negative number) = positive number If we know 1 < 10n (n is a negative number so the right hand side is negative too. n could take values such as 1/20, 1/50 etc) To process it easily, we can just divide both sides by 10 (n gets separated out) 1/10 < n Since n < 0, we get 1/10 < n < 0 If instead, we divide both sides by n, we get 1/n > 10 How did you get 1/n > 10? Well, to be frank with you I was really confused between handling inequalities when there is a variable and when we have a specific number what I did was to consider n<0 but then imagined in my head that n is eg.2 so i both changed the sign of inequality and the sign of the fraction to positive, which is wrong so instead of just dividing 1<10n by n(n<0) and getting 1/n>10 I would divide by n and simultaneously think that n is a number like eg.2 so I would also change the sign of 1/n to 1/n which is wrong . thank you VeritasKarishma for your reply. Yes, you don't have to change the sign of the fraction. Note that 1/n is a positive number because n is negative. When you make it 1/n, you are making it negative again.
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Re: If n denotes a number to the left of 0 on the number line
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