3ab Math
NAME:
Energy and persistence conquer all things.
Benjamin Franklin
Energy and persistence conquer all things.
Benjamin Franklin
1. | The profit P, in thousands of dollars, made by a company t months after its beginning is given by
P(t) = 2t 3 – 15t 2 + 24t + 2 where 0 t 12 (a) Find (b) For which values of t is the profit decreasing? | 2. | A travel agent charters an aircraft and offers cheap flights to Hong Kong. The advertised price for the trip is $600 per person if 120 people or less sign up. For every person above 120 the price for each person will be reduced by $2. [For example if 123 people sign up then each person on the flight pays $594]. (a) If n is the number of persons above 120 signing up show that the total revenue,R (in dollars), received by the agent is given by R(n) = 72 000 + 360n – 2n 2 (b) How many passengers will provide the agent with the maximum possible revenue? (c) What is the maximum revenue the agent can obtain? (d) What restrictions, if any, need to be placed on the domain of n? | | |
3. | The graphs shown are graphs of: I : y = f(x)II : y = f /(x)III : y = f //(x)By studying the graphs, answerthe following questions.
(a) Describe the behaviour ofy = f(x) for x where (i) x < 0 (ii) 0 < x < 6 (iii) x > 6 (b) Find the values of thex – intercepts of y = f(x). (c) Determine the expression forthe function fi.e. y =
(d) What are the x-coordinates ofpoints A and B in Graph II? (e) Locate these x values on Graph Iand state their significance. (f) What is the x-coordinate of point C on Graph III and what isits significance on Graph I? | 4. | Determine the value of the variables a, b, c, d, e, f, g and h in the following diagrams. The variables appear either in the graph or in the respective function. (a) y = (x – 2) 2 + 3 (b) y = 2 2 x
(c) y = (x + f)(x + g)(x + h) |
Energy and persistence conquer all things.
Benjamin Franklin
Energy and persistence conquer all things.
Benjamin Franklin
1. | The profit P, in thousands of dollars, made by a company t months after its beginning is given by
P(t) = 2t 3 – 15t 2 + 24t + 2 where 0 t 12 (a) Find (b) For which values of t is the profit decreasing? | 2. | A travel agent charters an aircraft and offers cheap flights to Hong Kong. The advertised price for the trip is $600 per person if 120 people or less sign up. For every person above 120 the price for each person will be reduced by $2. [For example if 123 people sign up then each person on the flight pays $594]. (a) If n is the number of persons above 120 signing up show that the total revenue,R (in dollars), received by the agent is given by R(n) = 72 000 + 360n – 2n 2 (b) How many passengers will provide the agent with the maximum possible revenue? (c) What is the maximum revenue the agent can obtain? (d) What restrictions, if any, need to be placed on the domain of n? | | |
3. | The graphs shown are graphs of: I : y = f(x)II : y = f /(x)III : y = f //(x)By studying the graphs, answerthe following questions.
(a) Describe the behaviour ofy = f(x) for x where (i) x < 0 (ii) 0 < x < 6 (iii) x > 6 (b) Find the values of thex – intercepts of y = f(x). (c) Determine the expression forthe function fi.e. y =
(d) What are the x-coordinates ofpoints A and B in Graph II? (e) Locate these x values on Graph Iand state their significance. (f) What is the x-coordinate of point C on Graph III and what isits significance on Graph I? | 4. | Determine the value of the variables a, b, c, d, e, f, g and h in the following diagrams. The variables appear either in the graph or in the respective function. (a) y = (x – 2) 2 + 3 (b) y = 2 2 x
(c) y = (x + f)(x + g)(x + h) |