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April 29, 2024, 01:51:15 pm
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andrewloppol

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« on: January 19, 2010, 04:57:34 pm »
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« Last Edit: September 04, 2015, 04:16:58 am by andrewloppol »
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andy456

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Re: Some basic questions
« Reply #1 on: January 19, 2010, 05:04:42 pm »
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I think it would be cause


I hope this is right :(

it would be for the second one
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brightsky

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Re: Some basic questions
« Reply #2 on: January 19, 2010, 05:06:35 pm »
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1. It becomes

2. It becomes

You need to be careful when you square both sides. Sometimes it may not be legit.

3.





This is as far as I could go.
« Last Edit: January 19, 2010, 05:09:56 pm by brightsky »
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cipherpol

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Re: Some basic questions
« Reply #3 on: January 19, 2010, 05:07:00 pm »
0








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Ilovemathsmeth

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Re: Some basic questions
« Reply #4 on: January 20, 2010, 12:07:05 am »
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Technically for part 1, it becomes which gives you

For part 2, you are right.

Part 3 is the equation for a circle graph. You need to always complete the square for such graphs to get the midpoint section and radius. In this case, from above is your radius.

To complete square, take the middle term (or power one term). Consider coefficient. Divide by two. Square. Add to the first two parts (power 2 and 1 sections) and then subtract from the bracket. Practice will get you this perfectly.
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cipherpol

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Re: Some basic questions
« Reply #5 on: January 26, 2010, 09:27:23 pm »
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Your book is wrong I think :P
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cipherpol

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Re: Some basic questions
« Reply #6 on: January 26, 2010, 09:33:31 pm »
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>.>, how the hell is that possible? I sketched the graph when m=1, and there are clearly no x-intercepts.

What page is this question?
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kyzoo

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Re: Some basic questions
« Reply #7 on: January 26, 2010, 09:35:06 pm »
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I'm going to start from

So either or
So either or

Edit: Totally wrong, you can't find the solution through pure algebra
« Last Edit: January 26, 2010, 10:55:13 pm by kyzoo »
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cipherpol

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Re: Some basic questions
« Reply #8 on: January 26, 2010, 09:39:05 pm »
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Ok then, if we sketch , we can see that the graph is greater than 0 when m>3 or m<0.

I think the book's answer is mistaken >>
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brightsky

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Re: Some basic questions
« Reply #9 on: January 26, 2010, 09:44:15 pm »
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Quote from: kyzoo on January 26, 2010, 09:35:06 pm
I'm going to start from

So either or
So either or

How can you be sure for every inequality question that you've got all the solutions? Is there a way to check besides drawing the graph?


Is the key factorising it? :)
« Last Edit: January 26, 2010, 09:49:57 pm by brightsky »
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m@tty

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Re: Some basic questions
« Reply #10 on: January 26, 2010, 09:44:56 pm »
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I think it should be or
Because for to be greater than , either both parts are or both parts .
You should always sketch graph of inequalities of degree other than 1.
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kyzoo

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Re: Some basic questions
« Reply #11 on: January 26, 2010, 09:50:27 pm »
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Quote from: brightsky on January 26, 2010, 09:44:15 pm
Quote from: kyzoo on January 26, 2010, 09:35:06 pm
I'm going to start from

So either or
So either or

How can you be sure for every inequality question that you've got all the solutions? Is there a way to check besides drawing the graph?

No. Like matty said, always use the graph with inequations.
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m@tty

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Re: Some basic questions
« Reply #12 on: January 26, 2010, 09:55:04 pm »
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Quote from: brightsky on January 26, 2010, 09:44:15 pm
Quote from: kyzoo on January 26, 2010, 09:35:06 pm
I'm going to start from

So either or
So either or

How can you be sure for every inequality question that you've got all the solutions? Is there a way to check besides drawing the graph?


Is the key factorising it? :)
No, it is way, way too easy to get confused when visualising inequalities.
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Ilovemathsmeth

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Re: Some basic questions
« Reply #13 on: January 30, 2010, 06:39:56 pm »
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Quote from: kyzoo on January 26, 2010, 09:35:06 pm
I'm going to start from

So either or
So either or

Edit: Totally wrong, you can't find the solution through pure algebra

True. Very common mistake - must always sketch a quadratic (and other higher powers) to determine inequalites. This is due to the shape of the graph being different between different points.
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TrueTears

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Re: Some basic questions
« Reply #14 on: January 30, 2010, 06:42:55 pm »
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Quote from: kyzoo on January 26, 2010, 09:35:06 pm
I'm going to start from

So either or
So either or

Edit: Totally wrong, you can't find the solution through pure algebra
You can, you just forgot the other half :P
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