13.Let x(1)(t)=(ettet),x(2)(t)=(1t).x1t=ettet,x2t=1t. Show that x(1)(t) and x(2)(t) are linearly dependent at each point in the interval 0 ≤ t ≤ 1. Nevertheless, show that x(1)(t) and x(2)(t) are linearly independent on 0 ≤ t ≤ 1.

3. Suppose that the temperature on a metal plate is given by the function T with T(x, y) = 100 - (x² +4y²) where the temperature is measured in degrees Fahrenheit and a and y are each measured in feet. Now suppose that an ant is walking on the metal plate in such a way that it walks in a straight line from the point (1, 4) to the point (5, 6). (a) Find parametric equations for the ant's a and y coordinates as it walks the line from (1,4) to (5,6) in one minute at a constant speed. (b) What can you say about dr dt and dy dt for every value of t? (c) Determine the instantaneous rate of change in temperature with respect to t that the ant is experi- encing at the moment it is halfway from (1, 4) to (5,6). Include units in your answer.