11-17-2008, 09:13 PM | #1 |
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[High School - Precalculus] Skills Review
Alright, I got this paper with some selected problems on it, and a few of them are a little confusing to me.
#2: A regular hexagon is inscribed within a circle of radius 1 unit. Find the ratio of the area of the circle to the area of the hexagon. I got 2(pi)sqrt(3)/9 for the answer, but I'm just wondering if I did it right or if I'm completely off. #7: How many positive integers are factors of 5400? I got 47 for this one, but I did it "the long way." I was wondering if there was a shorter way of doing this than finding all of the factors and counting them up. And finally #10: Express 0.31245 (with the "45" at the end repeating) as the ratio of two positive integers. The decimal to fraction button on my calculator failed at this one.
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11-17-2008, 10:00 PM | #2 |
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Re: [High School - Precalculus] Skills Review
#2: I got the same answer as you. Good Job? (Assuming I didn't screw up either...)
#7: Start by prime factoring 5400. 5400 = 2^3 * 3^3 * 5^2 So, the factors of 5400 will be combinations of these numbers. How many combinations can you make? 2 can appear 4 ways [0,1,2, or 3 times], 3 can appear 4 ways, 5 can appear 3 ways. So, the number of combinations = 4*4*3 = 48. Perhaps you missed one? (You know 47 is wrong immediately because only square numbers have an odd number of factors, and 5400 is not a square number) #10: let n = 0.31245454545... then 100n = 31.24545454545... subtract one from the other, 99n = 30.933 n = 3437 / 11000 So, 0.312454545... = 3437 / 11000 |
11-17-2008, 10:06 PM | #3 |
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Re: [High School - Precalculus] Skills Review
Alright, #2 is right.
#7: The short way involves first getting a prime factorization; after you do so, you see that the prime factorization is 2^3 * 3^3 * 5^2. Now, think about how you would get all of the factors. You have a choice between choosing 2s, 3s, and 5s. You multiply the number of ways you can pick each one together, and you should get the right answer. Thus, the answer is 4 ways to pick 2s (pick zero 2s, one 2, two 2s, or 3 twos) * 4 ways for 3 * 3 ways for 5 (3 and five have the same logic as 2). So the final answer is 4*4*3 = 48. (ouch, you were one off!) #10: Suppose 0.31245 (45 repeat) = x. Thus, 312.45 (45 repeat) = 1000x. Thus 312 and 45/99 (I'm sure you know this) = 1000x. Convert to an improper fraction --> 30933/99 = 1000x. Thus, x, the fraction form of the decimal, is equal to 30933/99000 which is also, 3437/1100. Edit: Whoa, I didn't simplify, and used 100x instead of 1000x. Fixed. Also, damn you dag12 for posting before me.
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Last edited by sumzup; 11-17-2008 at 10:14 PM.. Reason: minor errors |
11-18-2008, 01:49 PM | #4 |
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Re: [High School - Precalculus] Skills Review
Ahhh, I started with the prime factorization for #7 but then had no clue what from there, heh. And I just had no clue at all with #10 but I understand now. Thanks!
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