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 . An ant climbs up the mound starting from ground level (y = 0). At what height y does the ant begin to see the tower?

Question

zzr0ck3r · Answer

are we walking from the left or the right?

zzr0ck3r · Answer

nm I guess it does not matter

zzr0ck3r · Answer

well think of how we can relate the things
we have that the slope of the line will be given by m = -2x
and we know the line should touch the curve at some point (a,b) and at (0,1100), the slope of this line is m = (1100-y)\(0-x)
so we have m = -2x and m = (1100-y)/(0-x)
we have two equations with 3 unknowns...that is no good, so we sub in y = -x^2+1000
and get
$$-2x=\frac{1100-(-x^2+1000)}{-x}$$
solve for x

zzr0ck3r · Answer

$$-2x=\frac{1100-(-x^2+1000)}{-x}$$solve for x