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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
Administrator
Registered: 2010-06-20
Posts: 8,056

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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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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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
Administrator
Registered: 2010-06-20
Posts: 8,056

Re: dilation problem

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

Bob


Children are not defined by school ...........The Fonz
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
Administrator
Registered: 2010-06-20
Posts: 8,056

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


Children are not defined by school ...........The Fonz
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
Administrator
Registered: 2010-06-20
Posts: 8,056

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


Children are not defined by school ...........The Fonz
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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#12 2017-02-22 10:12:57

ET ag
Member
Registered: 2017-02-22
Posts: 10

Re: dilation problem

Hello mathstudent2000,

Since you use AoPS, you should be familiar with the AoPS Honor Code. Specifically, you should know that you should try to look up answers but rather try them. Remember, the teachers of your course are happy to help you on the Page Feed.

Also, the answer 0 is correct given Bob's reason.


If a second was a minute, and a minute was an hour, how many hours would be in one day? (There are multiple answers and they are debatable)

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