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#1 2013-08-10 06:51:50

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

dilation problem

When a square of area 4 is dilated by a scale factor of k, we obtain a square of area 9. Find the sum of all possible values of k.


Genius is one percent inspiration and ninety-nine percent perspiration

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#2 2013-08-10 07:15:44

bob bundy
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Registered: 2010-06-20
Posts: 6,539

Re: dilation problem

When all lengths are increased by a scale factor k, each side of the square is k times bigger so the area gets bigger by a factor of k squared.

I would expect a single answer here, but the wording suggests more than one.  It is possible to dilate 'the other way' to generate a backwards square.  I guess that's a second answer.

Bob

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#3 2013-08-10 07:29:05

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: dilation problem

i got one value for k (3/2) but i don't know how to get the other one


Genius is one percent inspiration and ninety-nine percent perspiration

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#4 2013-08-10 07:39:32

bob bundy
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Registered: 2010-06-20
Posts: 6,539

Re: dilation problem

That looks good to me.  Just say minus the same for the second one.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#5 2013-08-10 07:48:36

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: dilation problem

what do you mean by just say minus the same for the second one


Genius is one percent inspiration and ninety-nine percent perspiration

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#6 2013-08-10 07:50:05

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: dilation problem

i got 0 since 3/2+-3/2 is 0


Genius is one percent inspiration and ninety-nine percent perspiration

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#7 2013-08-10 08:01:20

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,539

Re: dilation problem

I suppose that is correct.  Bit strange though.  If you got the first k wrong, but knew to make it minus, you'd still get 0.  Wrong working but right answer.  Hhhmmm.  Worrying.  If I was testing a student, I'd ask for both answers, just to be certain.  Is this work computer marked by any chance?

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#8 2013-08-10 08:05:03

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: dilation problem

what do you mean by computer marked?


Genius is one percent inspiration and ninety-nine percent perspiration

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#9 2013-08-10 08:15:57

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,539

Re: dilation problem

If a student hands in work on a sheet of paper I can view all the working and award marks for good maths.  Some on-line courses only want answers that can be checked by a computer.  So it is necessary to submit single letters (if multi-choice) or numbers so that the program can do an exact comparison.  It's easy for the course administrators but somewhat poor at detecting student misunderstandings.

eg.

Let's say you thought k was 9/4 and the second answer -9/4

A human marker could see you had misunderstood about area scale factors, but a computer would give you the mark because 9/4 -9/4 =0 and the computer is set to mark that correct.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#10 2013-08-10 08:22:37

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: dilation problem

yeah its for my hw on aops


Genius is one percent inspiration and ninety-nine percent perspiration

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#11 2013-08-10 08:26:09

mathstudent2000
Member
Registered: 2013-07-26
Posts: 79

Re: dilation problem

so i guess it is computer marked


Genius is one percent inspiration and ninety-nine percent perspiration

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