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A slightly different question about tangential circles and the spaces in between.
Compare this question to the following, from the 2004 SAT Practice Test:
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Scenario 1: Which winning number group is more likely to occur?
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We've all seen this problem, but many of our students haven't. It's the related rate problem from calculus: the balloon being filled with air.
There are two questions being demonstrated here.
(1) "If the volume increases at a constant rate, what is happening to the radius?" and
(2) "If the radius increases at a constant rate, what is happening to the volume?"
The first question is to figure out which situation is modeled in red and which in blue.
Then we can ask:
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Which is true?
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Which one is the better question?
Which one is easier to solve?
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Which lock is more secure?
1.
2.
3. (three numbers needed)
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Which one is most secure?
Three numbers ...
This one with three extra wheels you can swap in ...
Or this one, with three letters?
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Is this the largest parabolic segment that can fit in a square?
... You sure this one isn't just a little bit larger?