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Puzzles ARACHNOPHOBIA! Two spiders walk across the xy-plane. The x and y coordinates of the first spider at time t seconds are
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and 
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The x and y coordinates of the second spider at time t seconds are
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and 
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The paths of these two spiders touch at one point -- find that point! Be sure to explain your reasoning along with giving your answer.
Hint: The two spiders do not get to that point at the same time!
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Comments | cosmo145 |  12:54:31, 18 Dec 07 |  Newbie
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| I got (13,14) as well, solved in terms of t and set the x and y coordinate formulas equal to each other then graphed them and found the intersection point.
| | | | Danik | 17:04:50, 10 Oct 07 | Newbie
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| Since the x of the two spiders has to be equal, and the y, you get two equations:
2t = 10 + s
4t - 12 = s^2 - 4s + 17
(where s and t are the times when the spiders pass the point)
Solving for either and putting the result into the corresponding equations you get the point (13,14).
| | | | bubba | 17:18:01, 09 Oct 07 | Newbie
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| For both equations, i solved for t in terms of x. Then I plugged those into the y= equations and got y = x^2 -24x +157 and y = 2x -12. Then I set those equal to each other and solved for y. I got y = x^2 -26x + 169. Then I set that equal to zero and got x = 13 (I used the quadratic equation). Then I plugged 13 into the original y= equations and I got y = 14. Therefore the coordinate of the intersection between the spiders was (13,14).
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