March 28, 2007 :: EMAT 6600 :: Problem Solving Class Notes
Are these parabolas “parallel” to teach other? What does it mean for two curves to be parallel? Does it mean that the tangent lines at each x value are parallel on both curves?
They will always be 10 units apart on the vertical sense of distance.
Adding a constant just moves the parabola up and down.
Problem, express ∆d in terms of k and d.
∆d = 5 (approx.), k=10 d=25
This is the model of a “real-life application.” On some of the driving ranges (for people who enjoy something like golf). At a driving range, you may be up on a platform when you drive the ball. Knowing this ∆d will help determine how far you actually drove the ball.
Express the “lower” curve as f(x) = -ax(x-d) + k and the “upper” curve as g(x) = -a[x-(d+∆d)] [x + ∆d]. If we equate f(x) and g(x), we’ll be able to solve for ∆d.
120 degree Triangle.
This is NOT going to be an isosceles right triangle. Claim: the ratio of BA/AC = AB’(B’C) – may be helpful in proving this problem. (Consider incircle as well.)