Suppose temperature °F in a region of 3-space, measured in meters, is given by T= 100 1+ (x − 3)² + y² + (z + 2)² and a bug is a point (2, 1,-1). (a) What direction should the bug fly when attracted to heat? (b) Find the components of a vector that starts at (2,1,-1) and ends at (3, 0, -2). Is this in the same direction as the převious answer? Physically, why fly towards (3, 0, -2)? (c) What is the rate of change of temperature at (2, 1, -1) when flying towards the heat? (decimal answer and include units) (d) What direction is the most rapid decrease in temperature?

the space curve (t) = (2t, t², 2t)

16. Find both the vector equation and the parametric equations of the line through (-2,2,8) and (1, - 4,0), where t =0 corresponds to the first given point. The vector equation is (x,y,z) = + (1). Find the parametric equations of the line through (-2,2,8) in the direction from (-2,2,8) toward (1,-4,0). The parametric equations are x = (Use the answer from the previous step to find this answer.) y%3D (1) O t(3,-6,-8). O t(-6,3,-8). O t(-8,-6,3). O t(-8,3,-6). 17. If possible, find the absolute maximum and minimum values of the following function on the region R. f(x,y) = 5 e-X-Y; R={(x,y): x20, y2 0} Determine the absolute maximum value of f(x,y) on R. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The absolute maximum value of f on R is O B. The function f(x,y) has no absolute maximum value on R. Determine the absolute minimum value of f(x,y) on R. Select the correct choice below and, if necessary, fill in the answer box to…

Determine the vector equation for the line that is parallel to 7 = [1,5,-7]+t[2,-1,5] with the same x-intercept as [x, y, z]=[-1,8,6]+t[-2,4,3]. 3.