# Tutor profile: Jack P.

## Questions

### Subject: Pre-Calculus

(5.2 -5.4i) + (3.8 -4.2i)

(5.2 -5.4i) + (3.8 -4.2i) =(5.2 + 3.8)+(-5.4 - 4.2)i =9 -9.6i.

### Subject: Environmental Engineering

Polychlorinated-biphenyls (PCBs) and 2, 3, 7, 8-TCDD (dioxin) are both considered lethal in sufficient concentration. The ratio of the rates of the median lethal single dose of PCB and the median lethal single dose of dioxin that is expected to kill 50% of a group of test animals is most nearly:

LD50 PCB = 15,000 LD50 dioxin = 0.001 Ratio= 15,000/.001= 1.5*10^7

### Subject: Calculus

Find all intervals on which function f given by f(x) = sin x is concave up.

The first and second derivatives of function f are given by f '(x) = cos x f "(x) = - sinx We now study the sign of f "(x) by solving the inequality - sin x > 0 Multiply both sides by -1 to obtain sin x < 0 Let us study sin x < 0 over the interval [0, 2pi] which represents one period of sin x. sin x is negative for x in the interval [pi , 2 pi]. Hence sin x is concave up on the interval (pi , 2 pi). We now extend this result over the domain of f which is (-infinity , +infinity) and say that sin x is concave up on all intervals of the form (pi + 2Pi k , 2pi + 2pi k) where k is an integer taking the values 0, -1, +1, -2, +2,...

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