Path To College Mathematics
1st Edition
ISBN: 9780134654409
Author: Martin-Gay, K. Elayn, 1955-
Publisher: Pearson,
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Chapter 7, Problem 10T
To determine
To determine the number of selections from a committee to travel to a national meeting.
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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 7 Solutions
Path To College Mathematics
Ch. 7.1 - Prob. 1ESCh. 7.1 - Prob. 2ESCh. 7.1 - Prob. 3ESCh. 7.1 - Prob. 4ESCh. 7.1 - Prob. 5ESCh. 7.1 - Prob. 6ESCh. 7.1 - Prob. 7ESCh. 7.1 - Prob. 8ESCh. 7.1 - Prob. 9ESCh. 7.1 - Prob. 10ES
Ch. 7.1 - Prob. 11ESCh. 7.1 - Prob. 12ESCh. 7.1 - Prob. 13ESCh. 7.1 - Prob. 14ESCh. 7.1 - Prob. 15ESCh. 7.1 - Prob. 16ESCh. 7.1 - Prob. 17ESCh. 7.1 - Prob. 18ESCh. 7.1 - Prob. 19ESCh. 7.1 - Suppose a 6-sided die is tossed twice. (This is a...Ch. 7.1 - Prob. 21ESCh. 7.1 - Prob. 22ESCh. 7.1 - Prob. 23ESCh. 7.1 - Prob. 24ESCh. 7.1 - Solve. Current license plates in California now...Ch. 7.1 - Prob. 26ESCh. 7.1 - Although there are exceptions, the call signs for...Ch. 7.1 - Prob. 28ESCh. 7.1 - Prob. 29ESCh. 7.1 - Prob. 30ESCh. 7.1 - Prob. 31ESCh. 7.1 - Prob. 32ESCh. 7.1 - Prob. 33ESCh. 7.1 - Prob. 34ESCh. 7.1 - Prob. 35ESCh. 7.1 - Prob. 36ESCh. 7.1 - Prob. 37ESCh. 7.1 - Prob. 38ESCh. 7.1 - Prob. 39ESCh. 7.1 - Prob. 40ESCh. 7.1 - Prob. 41ESCh. 7.1 - For security purpose, a company is starting to...Ch. 7.2 - Prob. 1ESCh. 7.2 - Prob. 2ESCh. 7.2 - Prob. 3ESCh. 7.2 - Prob. 4ESCh. 7.2 - Prob. 5ESCh. 7.2 - Prob. 6ESCh. 7.2 - Prob. 7ESCh. 7.2 - Prob. 8ESCh. 7.2 - Prob. 9ESCh. 7.2 - Prob. 10ESCh. 7.2 - Prob. 11ESCh. 7.2 - Prob. 12ESCh. 7.2 - Prob. 13ESCh. 7.2 - Prob. 14ESCh. 7.2 - Prob. 15ESCh. 7.2 - Prob. 16ESCh. 7.2 - Prob. 17ESCh. 7.2 - Prob. 18ESCh. 7.2 - Prob. 19ESCh. 7.2 - Prob. 20ESCh. 7.2 - Prob. 21ESCh. 7.2 - Prob. 22ESCh. 7.2 - Prob. 23ESCh. 7.2 - Prob. 24ESCh. 7.2 - Prob. 25ESCh. 7.2 - Prob. 26ESCh. 7.2 - Prob. 27ESCh. 7.2 - Prob. 28ESCh. 7.2 - Prob. 29ESCh. 7.2 - Prob. 30ESCh. 7.2 - Prob. 31ESCh. 7.2 - Prob. 32ESCh. 7.2 - Prob. 33ESCh. 7.2 - Prob. 34ESCh. 7.2 - Prob. 35ESCh. 7.2 - Prob. 36ESCh. 7.2 - Prob. 37ESCh. 7.2 - Prob. 38ESCh. 7.2 - Prob. 39ESCh. 7.2 - Prob. 40ESCh. 7.2 - Solve. Some of these exercises may be solved using...Ch. 7.2 - Prob. 42ESCh. 7.2 - Prob. 43ESCh. 7.2 - Prob. 44ESCh. 7.2 - Prob. 45ESCh. 7.2 - Prob. 46ESCh. 7.2 - Prob. 47ESCh. 7.2 - Prob. 48ESCh. 7.2 - Prob. 49ESCh. 7.2 - Prob. 50ESCh. 7.2 - Prob. 51ESCh. 7.2 - Prob. 52ESCh. 7.2 - Prob. 53ESCh. 7.2 - Prob. 54ESCh. 7.2 - Prob. 55ESCh. 7.2 - Prob. 56ESCh. 7.2 - Prob. 57ESCh. 7.2 - Prob. 58ESCh. 7.2 - Prob. 59ESCh. 7.2 - Prob. 60ESCh. 7.2 - Is it possible to evaluate P65 Explain why or why...Ch. 7.2 - Prob. 62ESCh. 7.2 - Prob. 63ESCh. 7.2 - Prob. 64ESCh. 7.2 - Explain why P55 can be calculated but is not...Ch. 7.2 - Prob. 66ESCh. 7.2 - Prob. 67ESCh. 7.2 - Prob. 68ESCh. 7.3 - Prob. 1ESCh. 7.3 - Evaluate each combination. See Examples 2 through...Ch. 7.3 - Prob. 3ESCh. 7.3 - Prob. 4ESCh. 7.3 - Prob. 5ESCh. 7.3 - Prob. 6ESCh. 7.3 - Prob. 7ESCh. 7.3 - Prob. 8ESCh. 7.3 - Prob. 9ESCh. 7.3 - Prob. 10ESCh. 7.3 - Prob. 11ESCh. 7.3 - Prob. 12ESCh. 7.3 - Prob. 13ESCh. 7.3 - Prob. 14ESCh. 7.3 - Prob. 15ESCh. 7.3 - Prob. 16ESCh. 7.3 - Prob. 17ESCh. 7.3 - Prob. 18ESCh. 7.3 - Prob. 19ESCh. 7.3 - Prob. 20ESCh. 7.3 - Prob. 21ESCh. 7.3 - Prob. 22ESCh. 7.3 - Prob. 23ESCh. 7.3 - Prob. 24ESCh. 7.3 - Prob. 25ESCh. 7.3 - Prob. 26ESCh. 7.3 - Prob. 27ESCh. 7.3 - Prob. 28ESCh. 7.3 - Prob. 29ESCh. 7.3 - Prob. 30ESCh. 7.3 - Prob. 31ESCh. 7.3 - Prob. 32ESCh. 7.3 - Prob. 33ESCh. 7.3 - Prob. 34ESCh. 7.3 - Prob. 35ESCh. 7.3 - Prob. 36ESCh. 7.3 - Prob. 37ESCh. 7.3 - Prob. 38ESCh. 7.3 - Prob. 39ESCh. 7.3 - Prob. 40ESCh. 7.3 - Prob. 41ESCh. 7.3 - Prob. 42ESCh. 7.3 - Prob. 43ESCh. 7.3 - Prob. 44ESCh. 7.3 - Prob. 45ESCh. 7.3 - Prob. 46ESCh. 7.3 - Prob. 47ESCh. 7.3 - Prob. 48ESCh. 7.3 - Prob. 49ESCh. 7.3 - Prob. 50ESCh. 7.3 - Prob. 51ESCh. 7.3 - Prob. 52ESCh. 7.3 - Prob. 53ESCh. 7.3 - Prob. 54ESCh. 7.3 - Prob. 55ESCh. 7.3 - Prob. 56ESCh. 7.3 - Prob. 57ESCh. 7.3 - Prob. 58ESCh. 7.3 - Prob. 59ESCh. 7.3 - Prob. 60ESCh. 7.3 - Prob. 61ESCh. 7.3 - Prob. 62ESCh. 7.3 - Prob. 63ESCh. 7.3 - Prob. 64ESCh. 7.3 - Prob. 65ESCh. 7.3 - Prob. 66ESCh. 7.3 - Prob. 67ESCh. 7.3 - Prob. 1IRCh. 7.3 - Prob. 2IRCh. 7.3 - Prob. 3IRCh. 7.3 - Prob. 4IRCh. 7.3 - Prob. 5IRCh. 7.3 - Prob. 6IRCh. 7.3 - Prob. 7IRCh. 7.3 - Prob. 8IRCh. 7.3 - Prob. 9IRCh. 7.3 - Prob. 10IRCh. 7.3 - Prob. 11IRCh. 7.3 - Prob. 12IRCh. 7.3 - Prob. 13IRCh. 7.3 - Prob. 14IRCh. 7.3 - Prob. 15IRCh. 7.4 - Prob. 1ESCh. 7.4 - Prob. 2ESCh. 7.4 - Prob. 3ESCh. 7.4 - Prob. 4ESCh. 7.4 - Prob. 5ESCh. 7.4 - Prob. 6ESCh. 7.4 - Prob. 7ESCh. 7.4 - Prob. 8ESCh. 7.4 - Prob. 9ESCh. 7.4 - Prob. 10ESCh. 7.4 - Prob. 11ESCh. 7.4 - Prob. 12ESCh. 7.4 - Prob. 13ESCh. 7.4 - Prob. 14ESCh. 7.4 - Prob. 15ESCh. 7.4 - Prob. 16ESCh. 7.4 - Prob. 17ESCh. 7.4 - Prob. 18ESCh. 7.4 - Prob. 19ESCh. 7.4 - Prob. 20ESCh. 7.4 - Prob. 21ESCh. 7.4 - Prob. 22ESCh. 7.4 - Prob. 23ESCh. 7.4 - Prob. 24ESCh. 7.4 - Prob. 25ESCh. 7.4 - Prob. 26ESCh. 7.4 - Prob. 27ESCh. 7.4 - Prob. 28ESCh. 7.4 - Prob. 29ESCh. 7.4 - Prob. 30ESCh. 7.4 - Prob. 31ESCh. 7.4 - Prob. 32ESCh. 7.4 - Prob. 33ESCh. 7.4 - Prob. 34ESCh. 7.4 - Prob. 35ESCh. 7.4 - Prob. 36ESCh. 7.4 - Prob. 37ESCh. 7.4 - Prob. 38ESCh. 7.4 - Prob. 39ESCh. 7.4 - Prob. 40ESCh. 7.4 - Prob. 41ESCh. 7.4 - Prob. 42ESCh. 7.4 - Prob. 43ESCh. 7.4 - Prob. 44ESCh. 7.4 - Prob. 45ESCh. 7.4 - Prob. 46ESCh. 7.4 - Prob. 47ESCh. 7.4 - Prob. 48ESCh. 7.4 - Prob. 49ESCh. 7.4 - Prob. 50ESCh. 7.4 - Prob. 51ESCh. 7.4 - Prob. 52ESCh. 7.4 - Prob. 53ESCh. 7.4 - Prob. 54ESCh. 7.4 - Prob. 55ESCh. 7.4 - Prob. 56ESCh. 7.4 - Prob. 57ESCh. 7.4 - Prob. 58ESCh. 7.4 - Prob. 59ESCh. 7.4 - Prob. 60ESCh. 7.4 - Prob. 61ESCh. 7.4 - Prob. 62ESCh. 7.4 - Prob. 63ESCh. 7.4 - Prob. 64ESCh. 7.4 - Prob. 65ESCh. 7.4 - Prob. 66ESCh. 7.4 - Prob. 67ESCh. 7.4 - Prob. 68ESCh. 7.4 - Prob. 69ESCh. 7.4 - Prob. 70ESCh. 7.4 - Prob. 71ESCh. 7.4 - Prob. 72ESCh. 7.4 - Prob. 73ESCh. 7 - Prob. 1VCCh. 7 - Prob. 2VCCh. 7 - Prob. 3VCCh. 7 - Prob. 4VCCh. 7 - Prob. 5VCCh. 7 - Prob. 6VCCh. 7 - Prob. 7VCCh. 7 - Prob. 8VCCh. 7 - Prob. 9VCCh. 7 - Prob. 10VCCh. 7 - Prob. 11VCCh. 7 - Prob. 12VCCh. 7 - Prob. 13VCCh. 7 - Prob. 14VCCh. 7 - Prob. 15VCCh. 7 - Prob. 16VCCh. 7 - Prob. 17VCCh. 7 - Prob. 18VCCh. 7 - Prob. 19VCCh. 7 - Prob. 20VCCh. 7 - Prob. 21VCCh. 7 - Prob. 1RCh. 7 - Draw a tree diagram for each experiment. Then use...Ch. 7 - Prob. 3RCh. 7 - Prob. 4RCh. 7 - Prob. 5RCh. 7 - Prob. 6RCh. 7 - Prob. 7RCh. 7 - Prob. 8RCh. 7 - Prob. 9RCh. 7 - Prob. 10RCh. 7 - Prob. 11RCh. 7 - Prob. 12RCh. 7 - Prob. 13RCh. 7 - Prob. 14RCh. 7 - Prob. 15RCh. 7 - Prob. 16RCh. 7 - Prob. 17RCh. 7 - Prob. 18RCh. 7 - Prob. 19RCh. 7 - Prob. 20RCh. 7 - Prob. 21RCh. 7 - Prob. 22RCh. 7 - Prob. 23RCh. 7 - Prob. 24RCh. 7 - Prob. 25RCh. 7 - Prob. 26RCh. 7 - Prob. 27RCh. 7 - Prob. 28RCh. 7 - Prob. 29RCh. 7 - Prob. 30RCh. 7 - Prob. 31RCh. 7 - Prob. 32RCh. 7 - Prob. 33RCh. 7 - Prob. 34RCh. 7 - Prob. 35RCh. 7 - Prob. 36RCh. 7 - Prob. 37RCh. 7 - Prob. 38RCh. 7 - Prob. 39RCh. 7 - Prob. 40RCh. 7 - Prob. 41RCh. 7 - Prob. 42RCh. 7 - Prob. 43RCh. 7 - Prob. 44RCh. 7 - Prob. 45RCh. 7 - Prob. 46RCh. 7 - Prob. 47RCh. 7 - Prob. 48RCh. 7 - Prob. 49RCh. 7 - Prob. 50RCh. 7 - Prob. 51RCh. 7 - Prob. 52RCh. 7 - Prob. 53RCh. 7 - Prob. 54RCh. 7 - Prob. 55RCh. 7 - Prob. 56RCh. 7 - Prob. 57RCh. 7 - Prob. 58RCh. 7 - Prob. 59RCh. 7 - Prob. 60RCh. 7 - Prob. 61RCh. 7 - Prob. 62RCh. 7 - Prob. 63RCh. 7 - Prob. 64RCh. 7 - Prob. 65RCh. 7 - Prob. 66RCh. 7 - Prob. 67RCh. 7 - Prob. 68RCh. 7 - Prob. 69RCh. 7 - Prob. 70RCh. 7 - Prob. 71RCh. 7 - Prob. 72RCh. 7 - Prob. 73RCh. 7 - Prob. 74RCh. 7 - Prob. 1GRFTCh. 7 - Prob. 2GRFTCh. 7 - Prob. 3GRFTCh. 7 - Prob. 4GRFTCh. 7 - Prob. 5GRFTCh. 7 - Prob. 6GRFTCh. 7 - Prob. 7GRFTCh. 7 - Prob. 8GRFTCh. 7 - Prob. 9GRFTCh. 7 - Prob. 10GRFTCh. 7 - Prob. 11GRFTCh. 7 - Prob. 12GRFTCh. 7 - Prob. 13GRFTCh. 7 - Prob. 14GRFTCh. 7 - Prob. 1TCh. 7 - Prob. 2TCh. 7 - Prob. 3TCh. 7 - Prob. 4TCh. 7 - Prob. 5TCh. 7 - Prob. 6TCh. 7 - Prob. 7TCh. 7 - Prob. 8TCh. 7 - Prob. 9TCh. 7 - Prob. 10TCh. 7 - Prob. 11TCh. 7 - Prob. 12TCh. 7 - Prob. 13TCh. 7 - Prob. 14TCh. 7 - Prob. 15TCh. 7 - Prob. 16TCh. 7 - Prob. 17TCh. 7 - Prob. 18TCh. 7 - Prob. 19TCh. 7 - Prob. 20TCh. 7 - Prob. 21TCh. 7 - Prob. 22TCh. 7 - Prob. 23TCh. 7 - Prob. 24TCh. 7 - Prob. 25TCh. 7 - Prob. 26TCh. 7 - Prob. 27TCh. 7 - Prob. 28TCh. 7 - Prob. 29TCh. 7 - Prob. 30TCh. 7 - Prob. 31TCh. 7 - Prob. 1CRCh. 7 - Prob. 2CRCh. 7 - Prob. 3CRCh. 7 - Prob. 4CRCh. 7 - Prob. 5CRCh. 7 - Prob. 6CRCh. 7 - Prob. 7CRCh. 7 - Prob. 8CRCh. 7 - Prob. 9CRCh. 7 - Prob. 10CRCh. 7 - Prob. 11CRCh. 7 - Prob. 12CRCh. 7 - Prob. 13CRCh. 7 - Prob. 14CRCh. 7 - Prob. 15CRCh. 7 - Prob. 16CRCh. 7 - Prob. 17CRCh. 7 - Prob. 18CRCh. 7 - The Swiss Re Building, in London, is a unique...Ch. 7 - Prob. 20CRCh. 7 - Prob. 21CRCh. 7 - Prob. 22CRCh. 7 - Prob. 23CRCh. 7 - Prob. 24CRCh. 7 - Prob. 25CRCh. 7 - Prob. 26CRCh. 7 - Prob. 27CRCh. 7 - Prob. 28CRCh. 7 - Prob. 29CRCh. 7 - Prob. 30CRCh. 7 - Prob. 31CRCh. 7 - Prob. 32CR
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- 3. Use the graph for problem #35, p175 to answer the questions. The average price (in cents) per gallon of unleaded gasoline in the United States for the years 2010 to 2019 is shown in this chart. Find the average rate of change per year in the average price per gallon for each time period. Source: U.S. Energy Information Administration. a) 2010 to 2013 b) 2012 to 2018 c) 2014 to 2019arrow_forward4. Researchers at Iowa State University and the University of Arkansas have developed a piecewise function that can be used to estimate the body weight (in grams) of a male broiler during the first 56 days of life according to W(t)=48+3.64t+0.6363²+0.00963 t³ if 1St≤28, -1004+65.8t if 28arrow_forward3. Given the function h(x)=(x²+x-12 if x≤1 3-x if x>1' a) Graph the function h(x). Make the graph big enough to be easily read using the space below. Be sure to label all important aspects of the graph. b) Find all values of x where the function is discontinuous. c) Find the limit from the left and from the right at any values of x found in part b.arrow_forward2. Find the instantaneous rate of change for each function f(x)=2x²-x+3 at x=0..arrow_forward4x-3 2. Determine the interval over which the function is continuous. x+4arrow_forward1. Find the average rate of change for the following functions over the given intervals. a) f(x)=4x-2x²+3x between x=-1 and x=4 b) y lnx between x=1 and x=4arrow_forward1. Find all values x=a where the function is discontinuous, determine if the discontinuity is removable or non- removable. For each value of x, give the limit of the function as x approaches a. Be sure to note when the limit doesn't exist and explain how you know. a) f(x)= 2-x x²(x+5) b) f(x)= x²-9x x²+3x c) p(x)=-3x²+2x²+5x-8arrow_forwardTask Description: Read the following case study and answer the questions that follow. Ella is a 9-year-old third-grade student in an inclusive classroom. She has been diagnosed with Emotional and Behavioural Disorder (EBD). She has been struggling academically and socially due to challenges related to self-regulation, impulsivity, and emotional outbursts. Ella's behaviour includes frequent tantrums, defiance toward authority figures, and difficulty forming positive relationships with peers. Despite her challenges, Ella shows an interest in art and creative activities and demonstrates strong verbal skills when calm. Describe 2 strategies that could be implemented that could help Ella regulate her emotions in class (4 marks) Explain 2 strategies that could improve Ella’s social skills (4 marks) Identify 2 accommodations that could be implemented to support Ella academic progress and provide a rationale for your recommendation.(6 marks) Provide a detailed explanation of 2 ways…arrow_forward1. Iodine-131 is tone of the most commonly used radioactive isotopes of iodine. It is used to treat hyper- thyroidism and some kinds of thyroid cancer. (a) Iodine-131 has a half-life of about 8 days. Find an expression for I(t), the mass of Iodine-131 remaining after t days, in terms of t and Io, the initial mass of Iodine-131 present at time t = 0. (b) If a dose of 0.9 mg of Iodine-131 is administered, how much is still present after 24 hours? (c) How much Iodine-131 is present after one week? Does your answer make sense?arrow_forwardQuestion 2: When John started his first job, his first end-of-year salary was $82,500. In the following years, he received salary raises as shown in the following table. Fill the Table: Fill the following table showing his end-of-year salary for each year. I have already provided the end-of-year salaries for the first three years. Calculate the end-of-year salaries for the remaining years using Excel. (If you Excel answer for the top 3 cells is not the same as the one in the following table, your formula / approach is incorrect) (2 points) Geometric Mean of Salary Raises: Calculate the geometric mean of the salary raises using the percentage figures provided in the second column named “% Raise”. (The geometric mean for this calculation should be nearly identical to the arithmetic mean. If your answer deviates significantly from the mean, it's likely incorrect. 2 points) Starting salary % Raise Raise Salary after raise 75000 10% 7500 82500 82500 4% 3300…arrow_forwardd₁ ≥ ≥ dn ≥ 0 with di even. di≤k(k − 1) + + min{k, di} vi=k+1 T2.5: Let d1, d2,...,d be integers such that n - 1 Prove the equivalence of the Erdos-Gallai conditions: for each k = 1, 2, ………, n and the Edge-Count Criterion: Σier di + Σjeл(n − 1 − d;) ≥ |I||J| for all I, JC [n] with In J = 0.arrow_forwardT2.4: Let d₁arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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