So, I'm teaching myself calculus using the Open Course Ware at MIT and a few other online resources. I'm new to this forum and am hoping that if I get stuck anywhere I can bounce questions off someone here.
I think have most of this problem figure out, but I'm running into a dead-end. This shows up in the Problem Set 1, for course 18.01 'Single Variable Calculus'. Anyway here's the problem:
On the planet Quirk, a cell phone tower is a 100-foot pole on top of a green mound 1000 feet tall whose outline is described by the parabolic equation y = 1000 − x^2 (1000 minus x squared). An ant climbs up the mound starting from ground level (y = 0). At what height y does the ant begin to see the tower?Now, I can derive the equation of the tangent line that meets at point (0, 1100) from the equation y = 1000 - x^2 as y = 1100 - 2x. Since there is only one point where these two equations meet I thought I should be able to use the quadradic equation to solve 0 = x^2 - 2x + 100 but I get an imaginary number ( +- sqrt( -396 )). Can anyone tell me where I'm off track? Thanks