If the temperature at a point (x, y, z ) is given by T (x, y, z) = 85 + (1 − z/100) e^ − ( x^2 + y^2 ) , find the direction from the point (2 , 0 , 99) in which the temperature decreases most rapidly. Provide a unit vector for your answer.

Find the volume of the described solid. the solid lies between planes perpendicular to the x-axis at x = 0 and x=7. the cross sectionsperpendicular to the x-axis between these planes are squares whose bases run from the parabolay=-31x to the parabola y = 30/x. a) 441b) 147c) 864d) 882

At the olympic games, many events have several rounds of competition. one of these events is the men's 100-meter backstroke. the upper dot plot shows the times (in seconds) of the top 8 finishers in the final round of the 2012 olympics. the lower dot plot shows the times of the same 8 swimmers, but in the semifinal round. which pieces of information can be gathered from these dot plots? (remember that lower swim times are faster.) choose all answers that apply: a: the swimmers had faster times on average in the final round. b: the times in the final round vary noticeably more than the times in the semifinal round. c: none of the above.

What are the solutions of the system? solve by graphing. y = x^2 + 3x + 2 y = 2x + 2