A symmetric 2×2 matrix (i. e. T= ) is negative semi- definite, i. e. T≤0 for all ∈ℝ2 , if and only if both of the following is true: tr()≤0 det()≥0 (This fact can be explained in terms the eigenvalues of . Let 1 and 2 be the eigenvalues of , then tr()=1+2 while det()=12 . The two conditions above ensure that 1,2≤0 . ) Use the fact given above to determine whether the following functions concave, convex, or neither. fs(theta 1, theta 2) = - theta1^4 - theta 2^4 - (theta 2 - theta 1)^3
a. concave
b. convex
c. not concave and not convex

Your friend uses c=50p to find the total cost, c, for the people, p, entering a local amusement park is the cost of admission proportional to the amount of people entering the amusement park? explain.

1) prove that 731^3−631^3 is divisible by 100 2) prove that 99^3−74^3 is divisible by 25

Write the equation of a line that is perpendicular to the given line and that passes through the given point. –3x – 6y = 17; (6, 3) y = x – 9 y = 2x – 9 y = –2x – 9 y = x + 0 3. is the relationship shown by the data linear? if so, model the data with an equation. x y 1 5 5 10 9 15 13 20 the relationship is linear; y – 5 = (x – 1). the relationship is not linear. the relationship is linear; y – 5 = (x – 1). the relationship is linear; y – 1 = (x – 5). write an equation in point-slope form for the line through the given point with the given slope. (–10, –1); m = y + 10 = (x + 1) y – 1 = (x – 10) y – 1 = (x + 10) y + 1 = (x + 10) 5. write an equation for each translation of . 6.5 units up y + 6.5 = | x | y = | 6.5 x | y = | x | + 6.5 y = | x | – 6.5 6. write an equation for each translation of . 5.5 units right y = | x | + 5.5 y = | x – 5.5 | y = | x | – 5.5 y = | x + 5.5 | 7. which equation translates y = | x | by 8 units to the left? y = | x | – 8 y = | x | + 8 y = | x – 8| y = | x + 8|