SOLUTION: Can someone please help me with this word problem? Looks like its dealing with Pythagorean Theorem?
The incline of a roller coaster is 2 times as long as its elevation, and the
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Pythagorean-theorem
-> SOLUTION: Can someone please help me with this word problem? Looks like its dealing with Pythagorean Theorem?
The incline of a roller coaster is 2 times as long as its elevation, and the
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Question 1041874: Can someone please help me with this word problem? Looks like its dealing with Pythagorean Theorem?
The incline of a roller coaster is 2 times as long as its elevation, and the horizontal length of the roller coaster is 11 m more than the elevation.
What is the length of the incline in meters? Round to the nearest meter:
Options are:
8
15
22
Does anyone know how I could reverse engineer this with my graphing calculator to try each solution and see which one is correct? Or tell me step by step how to come up with the equation to solve this?
I know that the important information is: incline = 2 times as long as elev
and horiz length - 11 meters more than elev
I'm just not sure what to do with the info.
Thanks so much in advance! Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! Let x be the elevation, then the elevation and horizontal length forms a right angle (90 degrees) and the incline is the hypotenuse. Therefore, we can use the Pythagorean Theorem to solve for the elevation.
:
x^2 +(x+11)^2 = (2x)^2
:
x^2 +x^2+22x+121 = 4x^2
:
-2x^2 +22x +121 = 0
:
2x^2 -22x -121 = 0
:
Use the quadratic formula
:
x = (-(-22) + square root( (-22)^2 - 4(2)(-121) ) ) / 2(2) = 15.0263
x = (-(-22) - square root( (-22)^2 - 4(2)(-121) ) ) / 2(2) = -4.0263
:
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We select the positive value for x (elevation) which is 15.0263
The length of the incline is 2 * elevation approx 30 meters
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