Suppose the Sunglasses Hut Company has a profit function given by P(q) = 0.01q2 + 3q 49, where q is the number of thousands of pairs of sunglasses sold and produced, and P(q) is the total profit, in thousands of dollars, from selling and producing q pairs of sunglasses. A) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your answer to three decimal places.) Answer: S thousand pairs of sunglasses need to be sold. B) What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your answer to three decimal places.) Answer: [: thousand dollars of maximum profits can be expected. The cost 0 (in dollars) for a company to produce and sell a: thousand gadgets is given by 1 2 0203 2z+5020 (a) What is the company's start-up cost? S :] (b) What is the minimum cost? 5 :J (c) How many gadgets must the company produce and sell in order to incur the least cost? (Be careful with your units!) Mark wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing. If Mark has 800 feet of fencing, what dimensions would maximize the area of the pen? a) Let w be the length of the pen perpendicular to the barn. Write an equation to model the area of the pen in terms of w b) What width w would maximize the area? A quadratic function has its vertex at the point ( 1, 1). The function passes through the point ( 9, 3). Find the quadratic and linear coefficients and the constant term of the function. The quadratic coefficient is [j The linear coefficient is [j The constant term is C] Jane has a pre-paid cell phone with Splint. She can't remember the exact costs, but her plan has a monthly fee and a charge for each minute of calling time. In June she used 350 minutes and the cost was $85.50. In July she used 570 minutes and the cost was $118.50. A) Express the monthly cost 0 as a function of a}, the number of minutes of calling time she used. Ross sells 130 shirts at a price of $20 each. They find that if they increase the shirt price by $1, the number of shirts sold drops by 4. Find an equation in the form 3; 2 ma: + b that models the shirt sales, where a: is the price of a shirt and y is the number of shirts sold. NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t) = 4.9t2 + 172t + 339. Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? The rocket splashes down after [j seconds. How high above sea-level does the rocket get at its peak? The rocket peaks at C] meters above sea-level. Find the equation of the line with slope = 3 and passing through (-10,-22). Write your equation in the form y 2 ma: + b. Find the equation for the line that passes through the points ( 9, 7) and ( 8, 10). Give your answer in point-slope form. You do not need to simplify. :] 10 Find the equation for the line that passes through ( 10, 5) that has slope ?. Give your answer in point-slope form. You do not need to simplify. : 5 If the slope of the line passing through the two points A(0, 10) and B(2, w) is equal to 5, then find the value of w. Sonny has entered a reading contest at the local library. After reading two books, he has read 392000 words of text. After five books, he has read 980000 words of text. Write a linear function in slope-intercept form to model his progress where a: is the number of books read ande y is the total number of words read. How many book will he need to read to reach a total of 10,000,000 words? :] Grain is pumped out of a full grain silo into a barge at a rate of 11 cubic meters per minute. The silo holds 6000 cubic meters of grain. Let y be the cubic meters remaining in the silo after 2 minutes. Write an equation in slope-intercept form that models the amount of grain in the silo. How many cubic meters of grain remain in the silo after 5 hours? :] A plumber charges a flat rate of $73 to make a house call and charges $52 for labor. Let y be the total cost of the house call plus labor and let a: be the number of hours worked. Write an equation in slope-intercept form that models the cost of the work performed. How much does it cost if the plumber works for 4 hours? 5:] Consider the line with the equation: 63/ + 3:1: = 6 Give the equation of the line parallel to Line 1 which passes through (4, 8) : [: Give the equation of the line perpendicular to Line 1 which passes through (4, 8) : l: Determine the slope and the y-intercept of the linear function given in the table: x 1 3 6 8 11 y 6.5 9.5 14 17 21.5 Given the points (-9, -8) and (5, 9), find the rate of change between the points. (Round to three [3] decimal places)