Quakerbrat wrote:Question #4
Which of the following circles has the greatest number of points of intersection with the parabola x^2 = y + 4?
I thought about this intuitively, thinking that a circle with radius 4 would hit the parabola at its x intercept as well as crossing the parabola at 2 other points, but clearly I was wrong.
Is there a concise mathematical way to solve this?
A total of x feet of fencing is to form three sides of a level rectangular yard. What is the maximum possible area of the yard, in terms of x?
I thought about it this way:
Area = W x L, from the constraints I know that 2W + L = x or 2L + W = x. Unfortunately, that's about as far as I get.
For #4: Just draw the circles and count the number of "hits." Edit:
For the circle with radius 4 the trap is thinking that one hit is actually two. So, take a look at radius three, too.
For #13: You are really close and just need to write down the equation to take the derivative, set to zero, and then solve. Edit:
Set A= w*l, and x = 2w+l, as you have. Now l = x-2*w, so A = w*(x-2*w). So, dA/dw = wx-2*w^2.
Set dA/dw = 0 and solve for w, then l to get the optimal points. Plugging back into A will give you the solution.