Evaluate each determinant. 3 -1 -5 3 -3 4 7) 0 0 -6 8) -6 5 -5 1 -2 -5 -3 -6 1 0 -2 6 6 -5 3 9) 5 5 -3 10) -5 -6 3

-5 dt 1+4t? 5.

2). EX+I 3t1 13 What is the value of EX+I for scores 46,3?

Consider the family of functions of the form y = x lnx-x+ (Ink)x, where x>0 and k is a positive constant. Each function in this family has a stationary point at A, as shown in Figure 7. k (b) Complete the table below by finding the y-coordinates of A for y=xlnx-x+(Ink) x where k = 1, 2, 3, and 4. 1 2 3 4 A Figure 7 Function x ln x - x x ln x-x+(In 2)x x lnx-x+ (In 3) x x lnx-x+ (In 4)x y-coordinate of A (c) Hence, make a conjecture for the y-coordinate of A, for any value of k.

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