Carlos is using the distributive property to evaluate the expression 14 (49) by using friendlier numbers. His work is shown below. Carlos’s Work 14 (49) Step 1 14 (40 + 9) Step 2 14 (40) + 9 Step 3 560 + 9 Step 4 569 What was the first error that Carlos made? Step 1 should have been 14(7 + 7). Step 2 should have been 14(40) + 14(9). Step 3 should have been 23(40). Step 4 should have been 5,040.

The weekly revenue for a company is r = 3p^2 + 60p + 1060, where p is the price of the company's product. what price will result in a revenue of $1200.

The table below represents the displacement of a fish from its reef as a function of time: time (hours) x displacement from reef (feet) y 0 4 1 64 2 124 3 184 4 244 part a: what is the y-intercept of the function, and what does this tell you about the fish? (4 points) part b: calculate the average rate of change of the function represented by the table between x = 1 to x = 3 hours, and tell what the average rate represents. (4 points) part c: what would be the domain of the function if the fish continued to swim at this rate until it traveled 724 feet from the reef? (2 points)

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .