Solve for x. Geometry
2 answers:
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1/4 = 3/12, and 5/4 = 15/12, so it looks like there's a common difference between terms of 4/12 = 1/3. The the -th term in the sequence is given recursively by
By substitution, we get
and doing this again and again until we stop with an expression containing , we find that
Then the 12th term in the sequence is
If he could walk directly from the back door to the barn door, he would walk 10.2 yards less.
First, let's define our coordinate axis, I will use north as the y-axis and east as the x-axis.
So let's assume that Loto begins at the point (0, 0).
Then:
- He moves 8 yards east, to: (8yd, 0)
- He moves 6 yards north, to: (8yd, 6yd)
- He moves 12 yards east, to: (20yd, 6yd)
- He moves 5 yards north, to: (20yd, 11yd)
So he walked a total of 8yd + 6yd + 12yd + 5yd = 33yd
So he just moves from (0, 0) to (20yd, 11yd), thus the displacement is:
So, if he could walk directly he would only walk 22.8 ft
The difference is:
33yd - 22.8yd = 10.2 yd.
He would walk 10.2 yards less if he could walk directly from the back door to the barn door.
If you want to learn more about displacements, you can read: