What is 50% of 500,000?
2 answers:
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Answer:
4. 8.8 years
5. 8.6 meters
Step-by-step explanation:
4. The process of solving the equation f(x) = g(x) gives rise to a 4th-degree equation. Those are best solved using some sort of machine solver. A graphing calculator is often a good place to start. If you're going to do that anyway, you may as well start with a graphical solution to the question.
A plot of the two curves finds they intersect at about x = 8.8. (See the first attachment.) This avoids the extraneous solutions introduced by the process of eliminating the radical.
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5. Analytical solution is simpler here, but the graphing calculator is faster yet. It shows the two rocks are at the same height at 8.6 meters (if they're launched at the same time).
... f(x) = g(x)
... -4.9x^2 +17 = -4.9x^2 +13x
... 17 = 13x . . . . . add 4.9x^2
... 17/13 = x . . . . time when rocks meet
... f(17/13) = -4.9(17/13)^2 +17 = -1416.1/169 +17 ≈ 8.62071
... f(17/13) ≈ 8.6 . . . . height at which rocks meet
