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

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.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,124

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

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

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

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,124

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

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

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

Genius is one percent inspiration and ninety-nine percent perspiration

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,124

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

what do you mean by computer marked?

Genius is one percent inspiration and ninety-nine percent perspiration

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,124

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

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

yeah its for my hw on aops

Genius is one percent inspiration and ninety-nine percent perspiration

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

so i guess it is computer marked

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