Pathways to Math Literacy (Loose Leaf)
1st Edition
ISBN: 9781259218859
Author: David Sobecki Professor, Brian A. Mercer
Publisher: McGraw-Hill Education
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Chapter 4.3, Problem 11G
To determine
The x intercepts and explain their meaning when the profit made by the recycling business for the quantity of material recycled (in tons) is shown in the following graph.
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4.
The revenue (in thousands of dollars) from producing x units of an item is R(x)=8x-0.015 x².
a) Find the average rate of change of revenue when the production is increased from 1000 to 1001 units.
MATH 122
WORKSHEET 3
February 5, 2025
. Solve the following problems on a separate sheet. Justify your answers to earn full credit.
1. Let f(x) = x² - 2x + 1.
(a) Find the slope of the graph of y = f (x) at the point P = (0,1) by directly
evaluating the limit:
f'(0) = lim (
f(Ax) - f(0)
Ax
Ax→0
(b) Find the equation of the tangent line 1 to the graph of ƒ at P.
What are the x and y intercepts of 1 ?
(c) Find the equation of the line, n, through P that is perpendicular to the tangent line l.
(Line n is called the normal line to the graph of f at P.)
(d) Sketch a careful graph that displays: the graph of y = f (x), its vertex point, its
tangent and normal lines at point P, and the x and y intercepts of these lines.
Bonus: Find the coordinates of the second point, Q, (QP), at which the normal
line n intersects the graph of f.
2. A rock is thrown vertically upward with an initial velocity of 20 m/s
from the edge of a bridge that is 25 meters above a river bed. Based
on Newton's Laws of…
1
If ye y = sin x, find dy/dx and dy/dx²
at (0, 0).
Chapter 4 Solutions
Pathways to Math Literacy (Loose Leaf)
Ch. 4.1 - After reading the opening paragraph, what do you...Ch. 4.1 - Prob. 1GCh. 4.1 - Prob. 2GCh. 4.1 - Prob. 3GCh. 4.1 - Prob. 4GCh. 4.1 - Prob. 5GCh. 4.1 - Prob. 6GCh. 4.1 - Prob. 1CCh. 4.1 - Prob. 2CCh. 4.1 - Prob. 3C
Ch. 4.1 - Prob. 4CCh. 4.1 - Prob. 5CCh. 4.1 - This phenomenon is so common, in fact, that data...Ch. 4.1 - Find the standard deviation for Ji-Mins golf...Ch. 4.1 - Discuss how comparing the two standard deviations...Ch. 4.1 - A standard package of Oreos is supposed to contain...Ch. 4.1 - A standard package of Oreos is supposed to contain...Ch. 4.1 - The probability of a package of Oreos containing...Ch. 4.1 - The probability of a package of Oreos containing...Ch. 4.1 - The probability of a package of Oreos containing...Ch. 4.1 - The probability of a package of Oreos containing...Ch. 4.1 - The probability of a package of Oreos containing...Ch. 4.1 - The probability of a package of Oreos containing...Ch. 4.1 - The probability of a package of Oreos containing...Ch. 4.1 - As our friend Mr. Twain pointed out over 100 years...Ch. 4.1 - As our friend Mr. Twain pointed out over 100 years...Ch. 4.1 - As our friend Mr. Twain pointed out over 100 years...Ch. 4.1 - Prob. 1RCh. 4.1 - Prob. 2RCh. 4.1 - Prob. 3RCh. 4.1 - Prob. 4RCh. 4.1 - Prob. 1ACh. 4.1 - Prob. 2ACh. 4.1 - Prob. 3ACh. 4.1 - In a group of 500 women, how many would you expect...Ch. 4.1 - Prob. 5ACh. 4.1 - Prob. 6ACh. 4.2 - Prob. 0LOCh. 4.2 - Prob. 1CCh. 4.2 - Prob. 2CCh. 4.2 - Prob. 3CCh. 4.2 - Prob. 4CCh. 4.2 - The process used to find the distance from the...Ch. 4.2 - The process used to find the distance from the...Ch. 4.2 - The process used to find the distance from the...Ch. 4.2 - The process used to find the distance from the...Ch. 4.2 - Prob. 5CACh. 4.2 - Suppose that we know that the distance between...Ch. 4.2 - How does the distance between points P and Q...Ch. 4.2 - The lower illustration also shows points P, Q, M,...Ch. 4.2 - Based on the scale provided on the two-dimensional...Ch. 4.2 - Illustrate the grade of each trail by drawing a...Ch. 4.2 - Use the Pythagorean theorem to estimate the true...Ch. 4.2 - Prob. 7GCh. 4.2 - How far would you actually drive in covering that...Ch. 4.2 - Prob. 9GCh. 4.2 - Prob. 11GCh. 4.2 - What does the Pythagorean theorem say? When can...Ch. 4.2 - Why cant you just find the distance between two...Ch. 4.2 - Prob. 3RCh. 4.2 - Estimate the elevation of point A.Ch. 4.2 - Prob. 2ACh. 4.2 - How far would you walk along the trail from point...Ch. 4.2 - Prob. 4ACh. 4.3 - Prob. 0LOCh. 4.3 - The amount of profit that a company makes when...Ch. 4.3 - If he decides to make the play area 5 feet wide,...Ch. 4.3 - Prob. 2GCh. 4.3 - Prob. 3GCh. 4.3 - Based on the graph, what width makes the area as...Ch. 4.3 - Prob. 5GCh. 4.3 - Prob. 6GCh. 4.3 - Prob. 7GCh. 4.3 - Prob. 8GCh. 4.3 - Prob. 9GCh. 4.3 - Prob. 10GCh. 4.3 - Prob. 11GCh. 4.3 - Prob. 12GCh. 4.3 - Prob. 13GCh. 4.3 - Prob. 14GCh. 4.3 - Prob. 15GCh. 4.3 - Prob. 1TCh. 4.3 - If youre looking at a graph, what are some key...Ch. 4.3 - Prob. 2RCh. 4.3 - Type a short answer to each question. Think of...Ch. 4.3 - Prob. 4RCh. 4.3 - About how high above the ground was the ball when...Ch. 4.3 - How far away from where it was kicked did the ball...Ch. 4.3 - How high did the punt go?Ch. 4.3 - The hang time of a punt is how long its in the air...Ch. 4.3 - After how many seconds was the ball 45 feet above...Ch. 4.3 - Prob. 7ACh. 4.3 - Prob. 8ACh. 4.4 - Prob. 0LOCh. 4.4 - Describe the differences between linear and...Ch. 4.4 - Prob. 2CCh. 4.4 - Prob. 3CCh. 4.4 - Prob. 4CCh. 4.4 - Prob. 5CCh. 4.4 - Prob. 6CCh. 4.4 - Prob. 7CCh. 4.4 - Prob. 8CCh. 4.4 - Prob. 9CCh. 4.4 - Prob. 10CCh. 4.4 - If youre the coffee drinker represented by the...Ch. 4.4 - Find the relative change in caffeine for each...Ch. 4.4 - Complete this important statement about...Ch. 4.4 - Looking at the graph of the caffeine remaining in...Ch. 4.4 - Whats the multiplication factor that youd need to...Ch. 4.4 - Prob. 6GCh. 4.4 - Prob. 7GCh. 4.4 - Prob. 8GCh. 4.4 - Prob. 9GCh. 4.4 - Use either TABLE or TRACE commands on your...Ch. 4.4 - Prob. 11GCh. 4.4 - Compare exponential growth and exponential decay....Ch. 4.4 - What did you learn in this lesson about the value...Ch. 4.4 - Prob. 3RCh. 4.4 - How much money is Joe earning when hes 30?Ch. 4.4 - How much money is he allowing himself to spend...Ch. 4.4 - How much is Joe earning when hes 35? Show a...Ch. 4.4 - How much money is Joe allowing himself to spend...Ch. 4.4 - Carefully explain the meaning of the crossover...Ch. 4.5 - Prob. 0LOCh. 4.5 - Prob. 1GCh. 4.5 - Prob. 2GCh. 4.5 - Prob. 3GCh. 4.5 - Prob. 4GCh. 4.5 - Prob. 5GCh. 4.5 - Prob. 6GCh. 4.5 - Prob. 7GCh. 4.5 - Prob. 8GCh. 4.5 - Prob. 9GCh. 4.5 - Prob. 10GCh. 4.5 - Prob. 11GCh. 4.5 - Prob. 1CCh. 4.5 - Prob. 2CCh. 4.5 - Prob. 3CCh. 4.5 - Prob. 4CCh. 4.5 - Prob. 5CCh. 4.5 - Prob. 6CCh. 4.5 - Prob. 7CCh. 4.5 - Prob. 8CCh. 4.5 - Prob. 9CCh. 4.5 - Prob. 10CCh. 4.5 - Prob. 11CCh. 4.5 - Prob. 12CCh. 4.5 - Prob. 13CCh. 4.5 - Prob. 14CCh. 4.5 - Prob. 15CCh. 4.5 - Prob. 16CCh. 4.5 - Prob. 1RCh. 4.5 - Prob. 2RCh. 4.5 - Prob. 3RCh. 4.5 - Prob. 4RCh. 4.5 - Prob. 1ACh. 4.5 - Prob. 2ACh. 4.5 - Prob. 3ACh. 4.5 - Prob. 4ACh. 4.6 - Prob. 0LOCh. 4.6 - Newtons law of universal gravitation describes the...Ch. 4.6 - Newtons law of universal gravitation describes the...Ch. 4.6 - Newtons law of universal gravitation describes the...Ch. 4.6 - Newtons law of universal gravitation describes the...Ch. 4.6 - Prob. 5CCh. 4.6 - Prob. 6CCh. 4.6 - Prob. 7CCh. 4.6 - Prob. 8CCh. 4.6 - Prob. 9CCh. 4.6 - Prob. 10CCh. 4.6 - Prob. 11CCh. 4.6 - Prob. 12CCh. 4.6 - Use Newtons law of universal gravitation to find...Ch. 4.6 - Prob. 14CCh. 4.6 - Prob. 1GCh. 4.6 - Prob. 2GCh. 4.6 - Prob. 3GCh. 4.6 - Prob. 5GCh. 4.6 - Prob. 6GCh. 4.6 - Prob. 7GCh. 4.6 - A fun fact: you can use a microwave oven and a bar...Ch. 4.6 - Prob. 1RCh. 4.6 - Prob. 2RCh. 4.6 - Prob. 3RCh. 4.6 - Prob. 4RCh. 4.6 - Prob. 1ACh. 4.6 - Prob. 2ACh. 4.6 - Prob. 3ACh. 4.6 - Prob. 4ACh. 4.6 - Prob. 5ACh. 4.6 - Prob. 6ACh. 4.6 - Prob. 7ACh. 4.7 - Prob. 0LOCh. 4.7 - Prob. 1GCh. 4.7 - Prob. 2GCh. 4.7 - Prob. 3GCh. 4.7 - Prob. 4GCh. 4.7 - Prob. 5GCh. 4.7 - Prob. 6GCh. 4.7 - Prob. 7GCh. 4.7 - Prob. 8GCh. 4.7 - Prob. 9GCh. 4.7 - Prob. 10GCh. 4.7 - Prob. 11GCh. 4.7 - From years of experience, the owner of a small...Ch. 4.7 - Prob. 13GCh. 4.7 - Prob. 14GCh. 4.7 - Prob. 15GCh. 4.7 - Prob. 16GCh. 4.7 - Prob. 17GCh. 4.7 - Prob. 18GCh. 4.7 - Prob. 19GCh. 4.7 - In Questions 14, simplify each expression. Aside...Ch. 4.7 - In Questions 14, simplify each expression. Aside...Ch. 4.7 - In Questions 14, simplify each expression. Aside...Ch. 4.7 - In Questions 14, simplify each expression. Aside...Ch. 4.7 - Prob. 5CCh. 4.7 - Prob. 6CCh. 4.7 - Prob. 7CCh. 4.7 - Our next goal is to multiply (x5)by(x2+3x+4). a....Ch. 4.7 - Prob. 9CCh. 4.7 - What is a polynomial? What is meant by the phrase...Ch. 4.7 - Prob. 2RCh. 4.7 - What questions do you have about this lesson?Ch. 4.7 - Prob. 1ACh. 4.7 - Prob. 2ACh. 4.7 - Prob. 3ACh. 4.7 - Prob. 4ACh. 4.7 - Prob. 5ACh. 4.7 - Prob. 6ACh. 4.7 - Prob. 7ACh. 4.7 - Prob. 8ACh. 4.7 - Prob. 9ACh. 4.7 - Prob. 10ACh. 4.8 - Prob. 0LOCh. 4.8 - Perform the multiplication: 57=Ch. 4.8 - Prob. 2GCh. 4.8 - If the volume in the YouTube window is set at half...Ch. 4.8 - If the volume in the YouTube window is set at half...Ch. 4.8 - If the volume in the YouTube window is set all the...Ch. 4.8 - To get the overall volume, we _______ the...Ch. 4.8 - Prob. 7GCh. 4.8 - Prob. 8GCh. 4.8 - Prob. 9GCh. 4.8 - Prob. 10GCh. 4.8 - Prob. 11GCh. 4.8 - Prob. 12GCh. 4.8 - Prob. 1CCh. 4.8 - For the polynomial P(x)=(x1)(x+5), find each...Ch. 4.8 - Use the table and graph provided for...Ch. 4.8 - Prob. 4CCh. 4.8 - Prob. 5CCh. 4.8 - y(x)=(x+5)(x+4)(x2) Zeros: x intercepts:Ch. 4.8 - Prob. 7CCh. 4.8 - Prob. 8CCh. 4.8 - Prob. 9CCh. 4.8 - Prob. 10CCh. 4.8 - Prob. 11CCh. 4.8 - Prob. 12CCh. 4.8 - Prob. 13CCh. 4.8 - Prob. 14CCh. 4.8 - Prob. 15CCh. 4.8 - Prob. 16CCh. 4.8 - Prob. 17CCh. 4.8 - Prob. 18CCh. 4.8 - Prob. 19CCh. 4.8 - If the current yield per tree is 800, and will go...Ch. 4.8 - If the current yield per tree is 800, and will go...Ch. 4.8 - Prob. 22CCh. 4.8 - Prob. 23CCh. 4.8 - Prob. 24CCh. 4.8 - Prob. 1RCh. 4.8 - Prob. 2RCh. 4.8 - Prob. 3RCh. 4.8 - Prob. 1ACh. 4.8 - Prob. 2ACh. 4.8 - Prob. 3ACh. 4.8 - Prob. 4ACh. 4.8 - Prob. 5ACh. 4.8 - Prob. 6ACh. 4.9 - Prob. 0LOCh. 4.9 - Prob. 1CCh. 4.9 - Use the quadratic formula to find the two...Ch. 4.9 - One of the solutions provides the length of the...Ch. 4.9 - What is the significance of the other solution in...Ch. 4.9 - Whats the connection between the solutions of the...Ch. 4.9 - Prob. 6CCh. 4.9 - Prob. 7CCh. 4.9 - Prob. 8CCh. 4.9 - Prob. 9CCh. 4.9 - Prob. 10CCh. 4.9 - Prob. 1GCh. 4.9 - Prob. 2GCh. 4.9 - Prob. 3GCh. 4.9 - Prob. 4GCh. 4.9 - Prob. 5GCh. 4.9 - Prob. 6GCh. 4.9 - Experiment: The Time Needed To Drain a Bottle...Ch. 4.9 - Prob. 8GCh. 4.9 - Experiment: The Time Needed To Drain a Bottle...Ch. 4.9 - What is the quadratic formula used for? Why is...Ch. 4.9 - What types of applied problems can be solved using...Ch. 4.9 - Prob. 3RCh. 4.9 - Use a calculator or spreadsheet to make a table of...Ch. 4.9 - Find the vertex of the parabola using the formula...Ch. 4.9 - Explain what each coordinate of the vertex means.Ch. 4.9 - Find the intercepts for the function.Ch. 4.9 - Explain what each intercept means.Ch. 4.9 - Describe when the ball is headed upward, and when...Ch. 4.9 - Prob. 7ACh. 4.9 - The distance for golf shots is traditionally...Ch. 4.9 - Prob. 9ACh. 4.9 - Prob. 10ACh. 4.9 - Prob. 11ACh. 4.9 - Prob. 12ACh. 4.10 - After reading the opening paragraph, what do you...Ch. 4.10 - Record the data from your experiment in the table....Ch. 4.10 - Use these data to create a scatter plot. Use the...Ch. 4.10 - Using your graphing calculator, find an...Ch. 4.10 - Use your function to approximate the height of the...Ch. 4.10 - Evaluate your equation for x=0. What does your...Ch. 4.10 - What does the variable x represent?Ch. 4.10 - In the equation y=abx that models your data, what...Ch. 4.10 - In the equation y=abx that models your data, what...Ch. 4.10 - Using data from your original table, fill in this...Ch. 4.10 - Use these data to create a second scatter plot.Ch. 4.10 - Based on the scatter plot, what kind of equation...Ch. 4.10 - Use your graphing calculator to find the equation...Ch. 4.10 - Your equation has a variable in it, but also has...Ch. 4.10 - If you were to drop the golf ball from your...Ch. 4.10 - Find the relative change in height from one bounce...Ch. 4.10 - (This one requires some thought, but is the key...Ch. 4.10 - Whats the bounce height as a percentage of the...Ch. 4.10 - Write an expression that calculates the bounce...Ch. 4.10 - Write an equation that describes the bounce height...Ch. 4.10 - Using your answer to Question 17, its possible to...Ch. 4.10 - What do you think would be some sources of error...Ch. 4.10 - Type a short answer to each question. Weve studied...Ch. 4.10 - How could you tell if neither of those types of...Ch. 4.10 - Type a short answer to each question. Take another...Ch. 4.10 - What questions do you have about this lesson?Ch. 4.10 - The equation y=10,000(1.06)x describes the growth...Ch. 4.10 - Prob. 2ACh. 4.10 - The equation y=10,000(1.06)x...Ch. 4.10 - The model in Questions 1-3 is an example of...Ch. 4.10 - The model in Questions 1-3 is an example of...Ch. 4.10 - When an initial amount of P dollars is invested at...Ch. 4.10 - Prob. 7ACh. 4.10 - When an initial amount of P dollars is invested at...Ch. 4.10 - When an initial amount of P dollars is invested at...Ch. 4.10 - One of the best reasons for understanding...Ch. 4.10 - One of the best reasons for understanding...Ch. 4.10 - One of the best reasons for understanding...Ch. 4.10 - One of the best reasons for understanding...
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