In submarine location problems, it is often necessary to find the submarine's closest point of approach to a sonobuoy in the water. Suppose that the submarine travels on a parabolic path y=x^2 and that the buoy is located at the point (2, -1/2).
Show that the value of x that minimizes the square of the distance, and hence the distance, between the points (x, x^2) and (2, -1/2) is a solution of the equation x=1/(x2+1)
2006-12-12 11:46:19 · 2 answers · asked by Anna 2 in Science & Mathematics ➔ Mathematics
*is a solution of the equation x=(x^2+1)
2006-12-12 12:10:59 · update #1
sorry thats wrong again....
*is the solution of the equation x=1/(x^2+1)
2006-12-12 12:15:29 · update #2
i believe the solution of this is a solution of the equation x = 1/(2(x^2+1))
i found d^2 = (x-2)^2 + (x^2 + 1/2)^2
i took the derivative
2(x-2) + 4x(x^2+1/2)
then i set it equal to 0 and simplified
i got 2x^3 + 2x - 1 = 0
that reduces to x = 1/(2(x^2+1))
2006-12-12 11:57:08 · answer #1 · answered by socialistmath 2 · 0⤊ 0⤋
ahh blank too many words!!
2006-12-12 11:48:02 · answer #2 · answered by Anonymous · 0⤊ 0⤋