57. Corvette acceleration The time t, in seconds, t Corvette to accelerate to x mph can be described t = 0.001(0.732x + 15.417x + 607.738) (Source: Motor Trend). How fast is the Corvette g after 8.99 seconds? Give your answer to the neares 58. Consumer Price Index Using Social Security 130 CHAPTER 2 Quadratic and Other Special Functions 3 :4 %3D 45. 2х + 46. %3D In Problems 47 and 48, solve using quadratic methods. 47. (x + 8)² + 3(x + 8) + 2 = 0 for national health described by 48. (s – 2)² – 5(s – 2) – 24 = 0 Administration data for selected years from 2012 APPLICATIONS can be described by the equation C = 0.068ť + 1.8t + 96 where x is the na 49. Profit If the profit from the sale of x units of a product is P = 90x – 200 – x², what level(s) of production will yield a profit of $1200? 50. Profit If the profit from the sale of x units of a product is P = 16x – 0.1x² – 100, what level(s) of production will yield a profit of $180? 51. Profit Suppose the profit from the sale of x units of a product is P = 6400x – (a) What level(s) of production will yield a profit of $61,800? Centers for Med pattern indicate does the mode where t is the number of years past 2010. With 2012 the reference year, a year in which the CPI = 1205 means goods and services that cost $100.00 in 2012 expected to cost $120.56 in that year. Find the year which the CPI is predicted to reach 150.00 59. Marijuana use For the years since 2001, the perces of high school seniors who have tried marijuana ca $7071 billion? 64. Velocity of ble an artery, the is greatest at the distance 18x – 400. the blood in %3D where Ris (b) Can a profit of more than $61,800 be made? 52. Profit Suppose the profit from the sale of x units of a product is P = 50x – 300 - 0.01x. (a) What level(s) of production will yield a profit of $250? considered as a function of time t accordino that is det p = f(t) = 0.17F – 2.61t + 52.64 the blood where k where t is the number of years past 2000 (Source: National Institute on Drug Abuse). In what year afe 2000 is the percent predicted to reach 55% if v = 2(0. (a) WE (b) Can a profit of more than $250 be made? 53. Flight of a ball If a ball is thrown upward at 96 feet per second from the top of a building that is 100 feet high, the height of the ball is given by 0.0 (b) W tion remains valid? 0. 60. Projectile motion Two projectiles are shot into the over a lake. The paths of the projectiles are oiven (a) y = -0.0013x + x + 10 and 162 feet S = 100 + 96t %3D 4 + -x + where t is the number of seconds after the ball is throWn. How long after it is thrown is the height 100 feet? 54. Flight of a ball A tennis ball is thrown into the air from the top of a hotel that is 350 feet above the ground. The height of the ball from the ground is given by 10 (b) y = SECT 3 81 where y is the height and x is the horizontal distane traveled (both in feet). Determine which projectile travels farther by substituting y = 0 in each equaticr and finding x. 61. Percent profit Ace Jewelry Store sold a necklace fir $144. If the percent profit (based on cost) equals he cost of the necklace to the store, how much did the store pay for it? Use OBJE • To fr D(t) = – 16t + 10t + 350 feet where t is the time, in seconds, after the ball is thrown. How long after the ball is thrown does it hit the ground? 55. Wind and pollution The amount of airborne particulate pollution p from a power plant depends on the wind speed s, among other things, with the relationship between p and s approximated by P = %3D 100 p = 25 – 0.01s² %3D where P is profit and C is cost. 62. Tourism spending The global spending on trave tourism (in billions of dollars) can be described by equation Find the value(s) of s that will make p = 0. (a) (b) What value of s from part (a) makes sense in the context of this application? What does p = 0 mean in this application? y = 1.48x – 25.23x + 416.91 56. Drug sensitivity The sensitivity S to a drug is related to the dosage size by where x equals the number of years past 1990 (Source: World Tourism Organization). Find the yer after 1990 in which spending is projected to reach 63. National health care Using data from 2002 and with projections to 2024, total annual expenditures S = 100x – x² where x is the dosage size in milliliters. (a) What dosage(s) will yield 0 sensitivity? (b) Explain what your answer in part (a) might mean. $1968 billion. 46. Modeling Consider the data given in the table Section 2.5 In Problems 33–36, a graph is given. Use the graph to (a) locate the vertex, (a) Make a scatter plot. (c) Try other function types and find one tha (b) Fit a linear function to the data, Quadratic and Other Special Functions 172 CHAPTER 2 better than a linear function. (a) Find the x-value that (b) Find the maximum a 8. 12 4 16 147 20 140 128 151 (b) determine the zeros, and 153 A. y = 7x –x² B. y = x² – x – 4 C. y = 8 – 2x – x² D. y = 49 – x² (c) match the graph with one of A, B, C, or D. 47. Modeling Consider the data given in the table (c) Try other function types and find one that 115 Section 2.3 (a) Make a scatter plot. (b) Fit a linear function to the data. 52. Supply Graph the first 34. function 50 better than a linear function. 33. 40 6. 53. Demand Graph the f demand function 10 15 30 20 25 250 210 20 200 150 220 100 У 4. 10 -6 54. Market equilibrium. (a) Suppose the sur p = 0.1q + 1 p = 85 - 0.2o portion of the -4 2 468 -8-6-4-2 -6 † 36. APPLICATIONS 10 35. 8. Section 2.1 same set of ax 25 48. Physics A ball is thrown into the air from a he of 96 ft above the ground, and its height is g equilibrium p (b) Use algebraid price and qu 55. Market equilibri is given by p = p+q= 410. F 56. Market equilib- modity is giver supply functio equilibrium q 57. Break-even p 20 15 give 16t, where t is the time in s 10 S = 96 + 32t – 4 6 %3D (a) Find the values of t that make S = 0. (b) Do both of the values of t have meaning application? (c) When will the ball strike the ground? 49. Profit The profit for a product is given by PlGs 1600, where x is the numberi 15 -6 -4 + 10 -5/- Section 2.4 37. Sketch a graph of each of the following basic functions. 82x – 0.10x2 produced and sold. Break-even points will or values of x where P(x) = 0. How break-even point for the product? (c) f(x) = x'/4 (b) f(x) = 1/x (a) f(x) = x² by C(x) = 17 given by R(x quantities. 58. Break-even OCO %3D S-x² if x <0 find the following. 38. If f (x) = 1/x ifx>0 %3D (b) f(0.0001) (d) f(10) (a) f(0) (c) f(-5) are given by are given by Section 2.2 50. Manufacturing employment Using U.S. Ener Information Administration data from 2012 an quantities. 59. Maximizin Sx 39. If f(x) = 3x - 2 if x < 1 find the following. %3D ifx>1 projected to 2040, the total U.S. employmentin manufacturing, E in millions, can be modeladh revenue ar (a) f(-2) (b) f(0) (c) f(1) (d) f(2) described 60. Break-ev In Problems 40 and 41, graph each function. P(x) = 1 the break E(t) = –0.0052² + 0.080t + 12 if x < 1 40. f(x) = 61. Maximu where t is the number of years past 2010. %3D 3x - 2 ifx>1 and R(x (a) In what year does the model predict that manufacturing employment will be t is maximum, and what is that maximum? (b) When does the model predict that manua employment will be 11.5 million? 51. Maximum area A rectangular lot is to be fene then divided down the middle to create two ide fenced lots (see the figure). If 1200 ft of fence i used, the area of each lot is given by that giv 41. (a) f(x) = (x – 2)² (b) f(x) = (x + 1)³ %3D profit. In Problems 42 and 43, use a graphing utility to graph each function. Find any turning points. 62. Break- pany F able c 42. y = x + 3x – 9x 43. y = x – 9x x is th prod (a) In Problems 44 and 45, graph each function. Find and identify any asymptotes. 1 44. y= 2x - 1 %3D 45. y= 1200 3x A = x 4
57. Corvette acceleration The time t, in seconds, t Corvette to accelerate to x mph can be described t = 0.001(0.732x + 15.417x + 607.738) (Source: Motor Trend). How fast is the Corvette g after 8.99 seconds? Give your answer to the neares 58. Consumer Price Index Using Social Security 130 CHAPTER 2 Quadratic and Other Special Functions 3 :4 %3D 45. 2х + 46. %3D In Problems 47 and 48, solve using quadratic methods. 47. (x + 8)² + 3(x + 8) + 2 = 0 for national health described by 48. (s – 2)² – 5(s – 2) – 24 = 0 Administration data for selected years from 2012 APPLICATIONS can be described by the equation C = 0.068ť + 1.8t + 96 where x is the na 49. Profit If the profit from the sale of x units of a product is P = 90x – 200 – x², what level(s) of production will yield a profit of $1200? 50. Profit If the profit from the sale of x units of a product is P = 16x – 0.1x² – 100, what level(s) of production will yield a profit of $180? 51. Profit Suppose the profit from the sale of x units of a product is P = 6400x – (a) What level(s) of production will yield a profit of $61,800? Centers for Med pattern indicate does the mode where t is the number of years past 2010. With 2012 the reference year, a year in which the CPI = 1205 means goods and services that cost $100.00 in 2012 expected to cost $120.56 in that year. Find the year which the CPI is predicted to reach 150.00 59. Marijuana use For the years since 2001, the perces of high school seniors who have tried marijuana ca $7071 billion? 64. Velocity of ble an artery, the is greatest at the distance 18x – 400. the blood in %3D where Ris (b) Can a profit of more than $61,800 be made? 52. Profit Suppose the profit from the sale of x units of a product is P = 50x – 300 - 0.01x. (a) What level(s) of production will yield a profit of $250? considered as a function of time t accordino that is det p = f(t) = 0.17F – 2.61t + 52.64 the blood where k where t is the number of years past 2000 (Source: National Institute on Drug Abuse). In what year afe 2000 is the percent predicted to reach 55% if v = 2(0. (a) WE (b) Can a profit of more than $250 be made? 53. Flight of a ball If a ball is thrown upward at 96 feet per second from the top of a building that is 100 feet high, the height of the ball is given by 0.0 (b) W tion remains valid? 0. 60. Projectile motion Two projectiles are shot into the over a lake. The paths of the projectiles are oiven (a) y = -0.0013x + x + 10 and 162 feet S = 100 + 96t %3D 4 + -x + where t is the number of seconds after the ball is throWn. How long after it is thrown is the height 100 feet? 54. Flight of a ball A tennis ball is thrown into the air from the top of a hotel that is 350 feet above the ground. The height of the ball from the ground is given by 10 (b) y = SECT 3 81 where y is the height and x is the horizontal distane traveled (both in feet). Determine which projectile travels farther by substituting y = 0 in each equaticr and finding x. 61. Percent profit Ace Jewelry Store sold a necklace fir $144. If the percent profit (based on cost) equals he cost of the necklace to the store, how much did the store pay for it? Use OBJE • To fr D(t) = – 16t + 10t + 350 feet where t is the time, in seconds, after the ball is thrown. How long after the ball is thrown does it hit the ground? 55. Wind and pollution The amount of airborne particulate pollution p from a power plant depends on the wind speed s, among other things, with the relationship between p and s approximated by P = %3D 100 p = 25 – 0.01s² %3D where P is profit and C is cost. 62. Tourism spending The global spending on trave tourism (in billions of dollars) can be described by equation Find the value(s) of s that will make p = 0. (a) (b) What value of s from part (a) makes sense in the context of this application? What does p = 0 mean in this application? y = 1.48x – 25.23x + 416.91 56. Drug sensitivity The sensitivity S to a drug is related to the dosage size by where x equals the number of years past 1990 (Source: World Tourism Organization). Find the yer after 1990 in which spending is projected to reach 63. National health care Using data from 2002 and with projections to 2024, total annual expenditures S = 100x – x² where x is the dosage size in milliliters. (a) What dosage(s) will yield 0 sensitivity? (b) Explain what your answer in part (a) might mean. $1968 billion. 46. Modeling Consider the data given in the table Section 2.5 In Problems 33–36, a graph is given. Use the graph to (a) locate the vertex, (a) Make a scatter plot. (c) Try other function types and find one tha (b) Fit a linear function to the data, Quadratic and Other Special Functions 172 CHAPTER 2 better than a linear function. (a) Find the x-value that (b) Find the maximum a 8. 12 4 16 147 20 140 128 151 (b) determine the zeros, and 153 A. y = 7x –x² B. y = x² – x – 4 C. y = 8 – 2x – x² D. y = 49 – x² (c) match the graph with one of A, B, C, or D. 47. Modeling Consider the data given in the table (c) Try other function types and find one that 115 Section 2.3 (a) Make a scatter plot. (b) Fit a linear function to the data. 52. Supply Graph the first 34. function 50 better than a linear function. 33. 40 6. 53. Demand Graph the f demand function 10 15 30 20 25 250 210 20 200 150 220 100 У 4. 10 -6 54. Market equilibrium. (a) Suppose the sur p = 0.1q + 1 p = 85 - 0.2o portion of the -4 2 468 -8-6-4-2 -6 † 36. APPLICATIONS 10 35. 8. Section 2.1 same set of ax 25 48. Physics A ball is thrown into the air from a he of 96 ft above the ground, and its height is g equilibrium p (b) Use algebraid price and qu 55. Market equilibri is given by p = p+q= 410. F 56. Market equilib- modity is giver supply functio equilibrium q 57. Break-even p 20 15 give 16t, where t is the time in s 10 S = 96 + 32t – 4 6 %3D (a) Find the values of t that make S = 0. (b) Do both of the values of t have meaning application? (c) When will the ball strike the ground? 49. Profit The profit for a product is given by PlGs 1600, where x is the numberi 15 -6 -4 + 10 -5/- Section 2.4 37. Sketch a graph of each of the following basic functions. 82x – 0.10x2 produced and sold. Break-even points will or values of x where P(x) = 0. How break-even point for the product? (c) f(x) = x'/4 (b) f(x) = 1/x (a) f(x) = x² by C(x) = 17 given by R(x quantities. 58. Break-even OCO %3D S-x² if x <0 find the following. 38. If f (x) = 1/x ifx>0 %3D (b) f(0.0001) (d) f(10) (a) f(0) (c) f(-5) are given by are given by Section 2.2 50. Manufacturing employment Using U.S. Ener Information Administration data from 2012 an quantities. 59. Maximizin Sx 39. If f(x) = 3x - 2 if x < 1 find the following. %3D ifx>1 projected to 2040, the total U.S. employmentin manufacturing, E in millions, can be modeladh revenue ar (a) f(-2) (b) f(0) (c) f(1) (d) f(2) described 60. Break-ev In Problems 40 and 41, graph each function. P(x) = 1 the break E(t) = –0.0052² + 0.080t + 12 if x < 1 40. f(x) = 61. Maximu where t is the number of years past 2010. %3D 3x - 2 ifx>1 and R(x (a) In what year does the model predict that manufacturing employment will be t is maximum, and what is that maximum? (b) When does the model predict that manua employment will be 11.5 million? 51. Maximum area A rectangular lot is to be fene then divided down the middle to create two ide fenced lots (see the figure). If 1200 ft of fence i used, the area of each lot is given by that giv 41. (a) f(x) = (x – 2)² (b) f(x) = (x + 1)³ %3D profit. In Problems 42 and 43, use a graphing utility to graph each function. Find any turning points. 62. Break- pany F able c 42. y = x + 3x – 9x 43. y = x – 9x x is th prod (a) In Problems 44 and 45, graph each function. Find and identify any asymptotes. 1 44. y= 2x - 1 %3D 45. y= 1200 3x A = x 4
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
50,57,58,59,60,61,62
Transcribed Image Text:57. Corvette acceleration The time t, in seconds, t
Corvette to accelerate to x mph can be described
t = 0.001(0.732x + 15.417x + 607.738)
(Source: Motor Trend). How fast is the Corvette g
after 8.99 seconds? Give your answer to the neares
58. Consumer Price Index Using Social Security
130
CHAPTER 2
Quadratic and Other Special Functions
3
:4
%3D
45.
2х +
46.
%3D
In Problems 47 and 48, solve using quadratic methods.
47. (x + 8)² + 3(x + 8) + 2 = 0
for national health
described by
48. (s – 2)² – 5(s – 2) – 24 = 0
Administration data for selected years from 2012
APPLICATIONS
can be described by the equation
C = 0.068ť + 1.8t + 96
where x is the na
49. Profit If the profit from the sale of x units of a product
is P = 90x – 200 – x², what level(s) of production
will yield a profit of $1200?
50. Profit If the profit from the sale of x units of a product
is P = 16x – 0.1x² – 100, what level(s) of production
will yield a profit of $180?
51. Profit Suppose the profit from the sale of x units of a
product is P = 6400x –
(a) What level(s) of production will yield a profit of
$61,800?
Centers for Med
pattern indicate
does the mode
where t is the number of years past 2010. With 2012
the reference year, a year in which the CPI = 1205
means goods and services that cost $100.00 in 2012
expected to cost $120.56 in that year. Find the year
which the CPI is predicted to reach 150.00
59. Marijuana use For the years since 2001, the perces
of high school seniors who have tried marijuana ca
$7071 billion?
64. Velocity of ble
an artery, the
is greatest at
the distance
18x – 400.
the blood in
%3D
where Ris
(b) Can a profit of more than $61,800 be made?
52. Profit Suppose the profit from the sale of x units of a
product is P = 50x – 300 - 0.01x.
(a) What level(s) of production will yield a profit of
$250?
considered as a function of time t accordino
that is det
p = f(t) = 0.17F – 2.61t + 52.64
the blood
where k
where t is the number of years past 2000 (Source:
National Institute on Drug Abuse). In what year afe
2000 is the percent predicted to reach 55% if
v = 2(0.
(a) WE
(b) Can a profit of more than $250 be made?
53. Flight of a ball If a ball is thrown upward at 96 feet per
second from the top of a building that is 100 feet high,
the height of the ball is given by
0.0
(b) W
tion remains valid?
0.
60. Projectile motion Two projectiles are shot into the
over a lake. The paths of the projectiles are oiven
(a) y =
-0.0013x + x + 10 and
162 feet
S = 100 + 96t
%3D
4
+ -x +
where t is the number of seconds after the ball is throWn.
How long after it is thrown is the height 100 feet?
54. Flight of a ball A tennis ball is thrown into the air from
the top of a hotel that is 350 feet above the ground. The
height of the ball from the ground is given by
10
(b) y =
SECT
3
81
where y is the height and x is the horizontal distane
traveled (both in feet). Determine which projectile
travels farther by substituting y = 0 in each equaticr
and finding x.
61. Percent profit Ace Jewelry Store sold a necklace fir
$144. If the percent profit (based on cost) equals he
cost of the necklace to the store, how much did the
store pay for it? Use
OBJE
• To
fr
D(t) = – 16t + 10t + 350 feet
where t is the time, in seconds, after the ball is thrown.
How long after the ball is thrown does it hit the ground?
55. Wind and pollution The amount of airborne
particulate pollution p from a power plant depends
on the wind speed s, among other things, with the
relationship between p and s approximated by
P =
%3D
100
p = 25 – 0.01s²
%3D
where P is profit and C is cost.
62. Tourism spending The global spending on trave
tourism (in billions of dollars) can be described by
equation
Find the value(s) of s that will make p = 0.
(a)
(b) What value of s from part (a) makes sense in the
context of this application? What does p = 0 mean
in this application?
y = 1.48x – 25.23x + 416.91
56. Drug sensitivity The sensitivity S to a drug is related to
the dosage size by
where x equals the number of years past 1990
(Source: World Tourism Organization). Find the yer
after 1990 in which spending is projected to reach
63. National health care Using data from 2002 and
with projections to 2024, total annual expenditures
S = 100x – x²
where x is the dosage size in milliliters.
(a) What dosage(s) will yield 0 sensitivity?
(b) Explain what your answer in part (a) might mean.
$1968 billion.
Transcribed Image Text:46. Modeling Consider the data given in the table
Section 2.5
In Problems 33–36, a graph is given. Use the graph to
(a) locate the vertex,
(a) Make a scatter plot.
(c) Try other function types and find one tha
(b) Fit a linear function to the data,
Quadratic and Other Special Functions
172 CHAPTER 2
better than a linear function.
(a) Find the x-value that
(b) Find the maximum a
8.
12
4
16
147
20
140 128
151
(b) determine the zeros, and
153
A. y = 7x –x²
B. y = x² – x – 4
C. y = 8 – 2x – x²
D. y = 49 – x²
(c) match the graph with one of A, B, C, or D.
47. Modeling Consider the data given in the table
(c) Try other function types and find one that
115
Section 2.3
(a) Make a scatter plot.
(b) Fit a linear function to the data.
52. Supply Graph the first
34.
function
50
better than a linear function.
33.
40
6.
53. Demand Graph the f
demand function
10
15
30
20
25
250 210
20
200
150
220
100
У
4.
10
-6
54. Market equilibrium.
(a) Suppose the sur
p = 0.1q + 1
p = 85 - 0.2o
portion of the
-4
2 468
-8-6-4-2
-6 †
36.
APPLICATIONS
10
35.
8.
Section 2.1
same set of ax
25
48. Physics A ball is thrown into the air from a he
of 96 ft above the ground, and its height is g
equilibrium p
(b) Use algebraid
price and qu
55. Market equilibri
is given by p =
p+q= 410. F
56. Market equilib-
modity is giver
supply functio
equilibrium q
57. Break-even p
20
15
give
16t, where t is the time in s
10
S = 96 + 32t –
4 6
%3D
(a) Find the values of t that make S = 0.
(b) Do both of the values of t have meaning
application?
(c) When will the ball strike the ground?
49. Profit The profit for a product is given by PlGs
1600, where x is the numberi
15
-6
-4 +
10
-5/-
Section 2.4
37. Sketch a graph of each of the following basic
functions.
82x – 0.10x2
produced and sold. Break-even points will or
values of x where P(x) = 0. How
break-even point for the product?
(c) f(x) = x'/4
(b) f(x) = 1/x
(a) f(x) = x²
by C(x) = 17
given by R(x
quantities.
58. Break-even
OCO
%3D
S-x²
if x <0
find the following.
38. If f (x) = 1/x ifx>0
%3D
(b) f(0.0001)
(d) f(10)
(a) f(0)
(c) f(-5)
are given by
are given by
Section 2.2
50. Manufacturing employment Using U.S. Ener
Information Administration data from 2012 an
quantities.
59. Maximizin
Sx
39. If f(x) =
3x - 2
if x < 1
find the following.
%3D
ifx>1
projected to 2040, the total U.S. employmentin
manufacturing, E in millions, can be modeladh
revenue ar
(a) f(-2) (b) f(0) (c) f(1) (d) f(2)
described
60. Break-ev
In Problems 40 and 41, graph each function.
P(x) = 1
the break
E(t) = –0.0052² + 0.080t + 12
if x < 1
40. f(x) =
61. Maximu
where t is the number of years past 2010.
%3D
3x - 2
ifx>1
and R(x
(a) In what year does the model predict that
manufacturing employment will be t is
maximum, and what is that maximum?
(b) When does the model predict that manua
employment will be 11.5 million?
51. Maximum area A rectangular lot is to be fene
then divided down the middle to create two ide
fenced lots (see the figure). If 1200 ft of fence i
used, the area of each lot is given by
that giv
41. (a) f(x) = (x – 2)²
(b) f(x) = (x + 1)³
%3D
profit.
In Problems 42 and 43, use a graphing utility to graph
each function. Find any turning points.
62. Break-
pany F
able c
42. y = x + 3x – 9x
43. y = x – 9x
x is th
prod
(a)
In Problems 44 and 45, graph each function. Find and
identify any asymptotes.
1
44. y=
2x - 1
%3D
45. y=
1200 3x
A = x
4
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Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education