A few days ago
MATH-HELP-PRIME Factorization?
you are putting up a 90 foot fence in your back yard. According to the manufacturers instructions the fence posts should be equally spaced. List all the possible spacing options if the amount of space between the posts is a whole number or feet. If the posts should be spaced between 8 feet and 14 feet apart how far apart should your posts be?
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A few days ago
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Assuming the there is going to be a post at the very beginning and one at the very end of the fence
90 can be written as 1 * 2 * 3 * 3 * 5
So the spacing between the posts can be any subset of that
{1, 2, 3, 5, 2*3, 2*5, 3*3, 3*5, 2*3*3, 2*3*5, 3*3*5, 2*3*3*5}
= {1, 2, 3, 5, 6, 10, 9, 15, 18, 30, 45, 90}
To put the numbers in order
= {1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90}
For the second part, assuming that we still need the posts to be equally spaced, as you can see from the above set, if you want the posts to be spaced between 8 and 14 feet, you can put them at 9 feet apart or at 10 feet apart.
I hope this helped
Kia
1
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