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Chapter: 13 -Problem: 19 >> In Problems 19–24, an inequality is given. Write the inequality obtained by: (a) Adding 3 to each side of the given inequality. (b) Subtracting 5 from each side of the given inequality. (c) Multiplying each side of the given inequality by 3. (d) Multiplying each side of the given inequality by ?2.3 < 5
Answer Preview: The given inequality is 3 5 a Adding 3 to each side of the given inequalit…

, Chapter: 7 -Problem: 73 >> Problems 71–80 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the exact value of Transcribed Image Text: 7 ? [cos-¹ (-3) ]
Answer Preview: To find the exact value of tan arccos 7 8 we ll use the concept of trigonometric identities an…

, Chapter: 13 -Problem: 38 >> In Problems 37 – 54, perform the indicated operation and simplify the result. Leave your answer in factored form. Transcribed Image Text: x * la
Answer Preview: To perform the indicated operation and simplify we first ne…

, Chapter: 5 -Problem: 6 >> In Problems 5–15, find the exact value of each expression. Do not use a calculator. Transcribed Image Text: ? 3 sin 45° 4 tan. - 6
Answer Preview: To find the exact value of the given expression we will evaluate ea…

, Chapter: 4 -Problem: 8 >> In Problems 5 – 44, solve each logarithmic equation. Express irrational solutions in exact form. Transcribed Image Text: log, (3x1) = 2
Answer Preview: To solve the logarithmic equation log 3 3x 1 2 we can use the definition of logarithm…

, Chapter: 9 -Problem: 7 >> In Problems 7–26, graph the plane curve whose parametric equations are given, and show its orientation. Find the rectangular equation of each curve. Transcribed Image Text: x(t) = 3t+2, y(t) = t + 1; 0? t ? 4
Answer Preview: The graph of the plane curve whose parametric equations …

, Chapter: 13 -Problem: 4 >> In Problems 1 – 11, find the limit. Transcribed Image Text: lim ?1 - x² x-1-
Answer Preview: To find the limit of the expression lim x 1 1 x 2 we need to consider both the left hand l…

, Chapter: 12 -Problem: 43 >> True/False Test How many arrangements of answers are possible for a true/false test with 10 questions?
Answer Preview: For a true false test with 10 questions each question can have 2 possible answers true …

, Chapter: 13 -Problem: 102 >> In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. Transcribed Image Text: x4 - 1
Answer Preview: To factor the polynomial x 4 1 completely we can use the difference of squares formula whi…

, Chapter: 3 -Problem: 45 >> The complex zeros of f (x) = x4 + 1 For the function f (x) = x4 + 1:(a) Factor f into the product of two irreducible quadratics.(b) Find the zeros of f by finding the zeros of each irreducible quadratic.
Answer Preview: To find the complex zeros of the function f x x 4 1 we can factor it into the product of tw…

, Chapter: 8 -Problem: 43 >> In Problems 39–62, identify and graph each polar equation. Transcribed Image Text: r = 2 + sin 0
Answer Preview: plot r …

, Chapter: 1 -Problem: 21 >> In Problems 11–22, match each graph to one of the following functions: Transcribed Image Text: A. y = x² + 2 B. y = C. y = x² + 2 x + 2 D. y = x + 2 E. y = (x - 2)² F y = (x + 2)² G. y = |x - 21 H. y = x + 21 1. y = 2x² J. y = -2x² K. y = 21x| L. y = -2|x|
Answer Preview: A The graph of y x 2 2 is Which does not matches with the given graph B The graph of y x …

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, Chapter: 1 -Problem: 62 >> Wind Chill Redo Problem 61(a)–(d) for an air temperature of ? 10°C. Data from in problem 61(a)–(d) The wind chill factor represents the air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is Transcribe
Answer Preview: To redo Problem 61 a d for an air temperature of 10C we will use the formula for wind chill factor W …

, Chapter: 13 -Problem: 48 >> In Problems 43 – 54, factor each polynomial.x2 + 11x + 10
Answer Preview: To factor the given polynomial x 2 11x 10 we need to find two binomials whose product results i…

, Chapter: 6 -Problem: 77 >> In Problems 61–84, solve each equation on the interval 0 ? ? < 2?. Transcribed Image Text: 2 sin²0 5 sin0 + 3 = 0
Answer Preview: To solve the equation 2sin 5sin 3 0 on the interval 0 2 we c…

, Chapter: 13 -Problem: 125 >> In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. Transcribed Image Text: I- x + ?x - DX
Answer Preview: To factor the polynomial x^4 - x^3 + x - 1 completely, let's first check if there are any common fac…

, Chapter: 13 -Problem: 22 >> In Problems 17–22, use the graph shown to investigate the indicated limit. Transcribed Image Text: lim f(x) x-4 YA 8 6 69 4 2 4 8 X
Answer Preview: From the graph of f When we approach x 4 from …

, Chapter: 1 -Problem: 123 >> Find the domain of Transcribed Image Text: f(x) = x² +1 7-13x-11
Answer Preview: To determine the domain of the function f x sqrt x 2 1 7 3x 1 we need to identify any restrictions o…

, Chapter: 7 -Problem: 77 >> Problems 69–78. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.If h(x) is a function with range [?5, 8 ], what is the range of h(2x + 3)?
Answer Preview: To find the range of the function h 2x 3 when the original function h x has a range o…

, Chapter: 13 -Problem: 41 >> In Problems 37 – 54, perform the indicated operation and simplify the result. Leave your answer in factored form. Transcribed Image Text: x + 1 x - 3 + 2x x - 3 3
Answer Preview: To perform the indicated operation we need to add the two …

, Chapter: 5 -Problem: 4 >> In Problems 4–6, convert each angle in radians to degrees. Transcribed Image Text: ? 8
Answer Preview: To convert the angle 8 from radians to degrees we can use t…

, Chapter: 4 -Problem: 145 >> Problems 145–154. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the real zeros of g(x) = 4x4 ? 37x2 + 9. What are the x-intercepts of the graph of g?
Answer Preview: We have to find the real zeroes of the equation g x 4…

, Chapter: 9 -Problem: 11 >> For the ellipsethe vertices are the points ______and _________. Transcribed Image Text: + 4 25 1,
Answer Preview: For the ellipse with the equation …

, Chapter: 13 -Problem: 10 >> In Problems 9 – 18, factor each polynomial by removing the common monomial factor.7x ? 14
Answer Preview: To factor the polynomial 7x 14 by removing the common monomial factor we first ident…

, Chapter: 13 -Problem: 11 >> In Problems 9–42, find each limit algebraically. Transcribed Image Text: lim x x-4
Answer Preview: To find the limit algebraically as x approaches 4 we use the given ex…

, Chapter: 13 -Problem: 91 >> In Problems 77–92, simplify each expression. Transcribed Image Text: 64-2/3 125,
Answer Preview: To simplify the expression 64 125 2 3 we need to find the reciprocal of the given fract…

, Chapter: 3 -Problem: 44 >> Let f be the polynomial function of degree 4 with real coefficients, leading coefficient 1, and zeros x = 3 + i, 2, ?2. Let g be the polynomial function of degree 4 with intercept (0, ?4) and zeros x = i, 2i. Find ( f + g )(1).†
Answer Preview: To find f g 1 we need to evaluate the sum of the functions f x and g x at x 1 Let s start by fin…

, Chapter: 8 -Problem: 32 >> In Problems 25 – 36, write each complex number in rectangular form. Transcribed Image Text: 3ei ?/2
Answer Preview: To write the complex number 3e i 2 in rectangular form we ll use Euler s formul…

, Chapter: 1 -Problem: 52 >> In Problems 41–64, graph each function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x2) and show all the steps. Be sure to show at least three key points. Find the domain and the range of each function. Transcribed Image Text:
Answer Preview: To graph the function f x x we will start with the graph of the basic function y x and apply the nec…

, Chapter: 2 -Problem: 56 >> In Problems 45–60,(a) Find the vertex and the axis of symmetry of each quadratic function, and determine whether the graph is concave up or concave down.(b) Find the y-intercept and the x-intercepts, if any.(c) Use parts (a) and (b) to graph the function.(d) Find the domain and the range of the quadratic function.(e) Determine where the quadratic function is increasing and where it is decreasing.(
Answer Preview: Let s analyze the quadratic function f x 3x 2 3x 2 and address each part of the question a To find the vertex and the axis of symmetry we can use the …

, Chapter: 1 -Problem: 106 >> Express the area A of an isosceles right triangle as a function of the length x of one of the two equal sides.
Answer Preview: To express the area A of an isosceles right triangle as a function of the length x of one of the two …

, Chapter: 13 -Problem: 67 >> In Problems 11 – 68, solve each equation. Transcribed Image Text: x² - 1 x + 3 x2 x² - x -3 x² + x
Answer Preview: To solve the equation x x 2 1 x 3 x 2 x 3 x 2 x we need to find the values of x that satisfy this eq…

, Chapter: 6 -Problem: 89 >> Problems 89 and 90 require the following discussion: The shortest distance between two points on Earth’s surface can be determined from the latitude and longitude of the two locations. For example, if location 1 has (lat, lon) = (?1, ?1) and location 2 has (lat, lon) = (?2, ?2), the shortest distance between the two locations is approximately d = r cos?1 [(cos?1 cos?1 cos?2 cos?2) + (cos?1 sin?1 c
Answer Preview: To find the shortest distance between two locations on Earth s surface using the given formula …

, Chapter: 13 -Problem: 135 >> In Problems 127–136, expressions that occur in calculus are given. Factor each expression completely. Transcribed Image Text: 2(3x - 5) 3(2x + 1)³ + (3x - 5)² - 3(2x + 1)².2
Answer Preview: To factor each expression completely, let's take them one by one: Factor 2(3x - 5…

, Chapter: 13 -Problem: 14 >> In Problems 9 – 18, tell whether the expression is a monomial. If it is, name the variable(s) and the coefficient, and give the degree of the monomial. If it is not a monomial, state why not.5x2 y3
Answer Preview: Yes the expression 5x 2 y 3 is a monomial Variable s T…

, Chapter: 8 -Problem: 8 >> In Problems 8 and 9, test the polar equation for symmetry with respect to the pole, the polar axis, and the line ?= ?/2. Transcribed Image Text: 2 r² cos0 = 5
Answer Preview: It seems there is a slight mistake in your analysis The polar equation you provided is r 2cos 5 To c…

, Chapter: 13 -Problem: 44 >> In Problems 43 – 54, factor each polynomial.x2 + 6x + 8
Answer Preview: To factor the polynomial x 2 6x 8 we are looking for two binomials in the form ax b cx d that …

, Chapter: 5 -Problem: 19 >> In Problems 16–23, find the exact value of each of the remaining trigonometric functions. Transcribed Image Text: sin 12 13' 0 in quadrant II
Answer Preview: Given that sin 12 13 and is in the second quadrant we can find the exact values of the re…

, Chapter: 4 -Problem: 2 >> In Problems 1 – 3, for each pair of functions f and g, find: (a) (f º g)(2) (b) (g º f )(?2) (c) (f º f)(4) (d) (g º g)(?1) Transcribed Image Text: f(x) = ???x + 2; g(x) = 2x² + 1
Answer Preview: To find the values for a f g 2 b g f 2 c f f 4 and d g g 1 we need to evaluate the compositions of t…

, Chapter: 9 -Problem: 19 >> In Problems 19–28, analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it. Transcribed Image Text: X y + 25 4 1
Answer Preview: To analyze the given ellipse equation we need to rewrite it in standard form which is x h 2 a 2 y k 2 b 2 1 where h k is the center of the ellipse a i…

, Chapter: 13 -Problem: 3 >> For x2 + Bx + C = ( x + a)( x + b), which of the following must be true? (a) ab = B and a + b = C (b) a + b = C and a ? b = B (c) ab = C and a + b = B (d) ab = B and a ? b = C
Answer Preview: To find the values of a and b such that the expression x 2 Bx C ca…

, Chapter: 6 -Problem: 95 >> Problems 93–102. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.The exponential function f (x) = 1 + 2x is one-to-one. Find f?1.
Answer Preview: To find the inverse of the function f x 1 2x we can follow these ste…

, Chapter: 12 -Problem: 8 >> In Problems 7 – 14, find the value of each permutation.P(7, 2)
Answer Preview: To find the value of the permutation P 7 2 we use the …

, Chapter: 13 -Problem: 138 >> Show that x2 + x + 1 is prime.
Answer Preview: the statement x 2 x 1 is prime is not true In fact x 2 x 1 is not a prime expression …

, Chapter: 6 -Problem: 9 >> True or False Transcribed Image Text: cos ( 1/2 - 0) = cos
Answer Preview: The statement cos pi 2 theta cos theta is false The correct identity is cos pi 2 theta sin theta …

, Chapter: 3 -Problem: 50 >> In Problems 7 – 50, follow Steps 1 through 7 shown below to graph each function. Transcribed Image Text: Steps for Graphing a Rational Function R STEP 1: Factor the numerator and denominator of R. Find the domain of the rational function. STEP 2: Write R in lowest terms. STEP 3: Find and plot the in
Answer Preview: We are given the function as f x 2x 9 x 3 and for this we are required to find the asked details ans…

, Chapter: 8 -Problem: 16 >> In Problems 13 – 20, match each point in polar coordinates with either A, B, C, or D on the graph. Transcribed Image Text: -4- B -+----+ C D 1/60 -+-
Answer Preview: here polar coordinates of given point is given …

, Chapter: 1 -Problem: 32 >> In Problems 31–42:(a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. Transcribed Image Text: f(x): = 3x 4 if x if x = 0 = 0
Answer Preview: a To find the domain of the function f x we need to determine the set of all possible values for x t…

, Chapter: 2 -Problem: 15 >> If b2 ? 4ac > 0, which conclusion can be made about the graph of f (x) = ax2 + bx + c, a ? 0?(a) The graph has two distinct x -intercepts.(b) The graph has no x -intercepts.(c) The graph has three distinct x -intercepts.(d) The graph has one x -intercept.
Answer Preview: we have the Function f X aX 2 bX c where a is not equal to zero Using …

, Chapter: 5 -Problem: 19 >> In Problems 11–22, draw each angle in standard position. Transcribed Image Text: ? 6
Answer Preview: As we have the a…

, Chapter: 1 -Problem: 53 >> Explain why the vertical-line test works.
Answer Preview: The vertical line test is a method used to determine whether a graph represents a function or not It states that if any vertical line intersects a gra…

, Chapter: 13 -Problem: 51 >> In Problems 11 – 68, solve each equation. Transcribed Image Text: 3/12x3 = 0
Answer Preview: To solve the equation 1 2x 3 0 follow these steps 1 Add 3 to both sides of the equation to …

, Chapter: 6 -Problem: 86 >> Find the exact value: Transcribed Image Text: cot[sec-¹(sin+tan)]
Answer Preview: To find the exact value of cot arcsec sin pi 3 tan pi 6 let s break it down step by step Start wi…

, Chapter: 13 -Problem: 134 >> In Problems 127–136, expressions that occur in calculus are given. Factor each expression completely. Transcribed Image Text: 3x²(3x + 4)2 + x3 . 2(3x + 4). 3
Answer Preview: To factor the given expression completely, we need to find the common facto…

, Chapter: 13 -Problem: 20 >> In Problems 9–42, find each limit algebraically. Transcribed Image Text: lim (8x5 x-1 - 7x3 +8x2 + x -4)
Answer Preview: To find the limit algebraically we substitute the giv…

, Chapter: 7 -Problem: 74 >> Problems 66 – 75. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Solve: x( x ? 7) = 18
Answer Preview: To solve the equation x x 7 18 we need to find the values of x that satisfy this equation T…

, Chapter: 3 -Problem: 1 >> Graph f (x) = (x ? 3)4 ? 2 using transformations.
Answer Preview: To graph the function f x x 3 4 2 using transformations we can follow these steps Step 1 Start with …

, Chapter: 1 -Problem: 13 >> Determine if the function f (x) = ?x2 ? 7 is even, odd, or neither.
Answer Preview: To determine if the function f x x 2 7 is even odd or neither we need to examin…

, Chapter: 4 -Problem: 2 >> Answers are given at the end of these exercises. Transcribed Image Text: Solve the inequality: x - 1 x + 4 > 0
Answer Preview: To solve the inequality x 1 x 4 0 we can start by finding the critical points where the expression …

, Chapter: 9 -Problem: 3 >> The parametric equations x(t) = 2 sin t y(t) = 3 cos t define a(n) ____________.(a) Circle(b) Ellipse(c) Hyperbola(d) Parabola
Answer Preview: The parametric equations x t 2 sin t and y t 3 cos t define an b Ellipse An ellipse is a cl…

, Chapter: 6 -Problem: 122 >> A light beam passes through a thick slab of material whose index of refraction is n2. Show that the emerging beam is parallel to the incident beam.
Answer Preview: To show that the emerging beam is parallel to the incident beam when a light beam passes through a thick slab of material we can make use of the princ…

, Chapter: 12 -Problem: 6 >> Solve the each equation  Transcribed Image Text: C(n,r) =
Answer Preview: The notation C n r represents the binomial coefficient als…

, Chapter: 13 -Problem: 95 >> In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. Transcribed Image Text: y4 + 11y3 + 30y²
Answer Preview: To factor the polynomial y 4 11y 3 30y 2 completely we first look for common factors a…

, Chapter: 6 -Problem: 11 >> In Problems 11–20, simplify each trigonometric expression by following the indicated direction. Rewrite in terms of sine and cosine functions: Transcribed Image Text: tan csc 0
Answer Preview: To simplify the expression tan csc and rewrite it in terms of sine and cosine f…

, Chapter: 3 -Problem: 126 >> Problems 126 – 135 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Write f (x) = ?3x2 + 30x ? 4 in the form f (x) = a(x ? h)2 + k
Answer Preview: To write the quadratic function f x 3x 2 30x 4 in the form f x a x h 2 k we need t…

, Chapter: 8 -Problem: 49 >> In Problems 43–58, polar coordinates of a point are given. Find the rectangular coordinates of each point. Transcribed Image Text: ?? -2, El 4
Answer Preview: To convert the given polar coordinates 2 3 4 into rectangular coordi…

, Chapter: 1 -Problem: 43 >> The kinetic energy K of a moving object varies jointly with its mass m and the square of its velocity v. If an object weighing 25 kilograms and moving with a velocity of 10 meters per second has a kinetic energy of 1250 joules, find its kinetic energy when the velocity is 15 meters per second.
Answer Preview: To solve this problem we ll use the formula for kinetic energy K k m v …

, Chapter: 2 -Problem: 114 >> Problems 113–122 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Solve the inequality 27 ? x ? 5x + 3. Write the solution in both set notation and interval notation.
Answer Preview: To solve the inequality 27 x 5x 3 we can follow these st…

, Chapter: 6 -Problem: 59 >> In Problems 33–60, find the exact value of each expression. Transcribed Image Text: sin-¹(cos 37) 4
Answer Preview: To find the exact value of the expression arcsin cos 3 4 we …

, Chapter: 1 -Problem: 43 >> In Problems 37–48, determine algebraically whether each function is even, odd, or neither. Transcribed Image Text: f(x) = x + |x|
Answer Preview: To determine whether the function f x x x is even odd or neither we need to consider the behavior of …

, Chapter: 13 -Problem: 66 >> In Problems 55–68, rationalize the denominator of each expression. Assume that all variables are positive when they appear. Transcribed Image Text: ????
Answer Preview: To rationalize the denominator of the expression 2 3 you can …

, Chapter: 6 -Problem: 90 >> Problems 89 and 90 require the following discussion: The shortest distance between two points on Earth’s surface can be determined from the latitude and longitude of the two locations. For example, if location 1 has (lat, lon) = (?1, ?1) and location 2 has (lat, lon) = (?2, ?2), the shortest distance between the two locations is approximately d = r cos?1 [(cos?1 cos?1 cos?2 cos?2) + (cos?1 sin?1 c
Answer Preview: To find the shortest distance between Honolulu HI and Melbourne Australia we can use th…

, Chapter: 13 -Problem: 130 >> In Problems 125–132, use a calculator to approximate each radical. Round your answer to two decimal places. Transcribed Image Text: ?5-2 ?2 + 4
Answer Preview: let's approximate the expression (sqrt(5) - 2)/(sqrt…

, Chapter: 13 -Problem: 12 >> In Problems 11 – 16, select a setting so that each of the given points will lie within the viewing rectangle.(5, 0), (6, 8), (?2, ?3)
Answer Preview: To ensure that all three points 5 0 6 8 and 2 3 lie within the viewing rectangle we need to fi…

, Chapter: 8 -Problem: 19 >> In Problems 19–22, v1 = 4i + 6j, v2 = ?3i ? 6j, v3 = ?8i + 4j, and v4 = 10i + 15j.Find the vector v1 + 2v2 ? v3.
Answer Preview: To find the vector v1 2v2 v3 we need to add the corresponding components of th…

, Chapter: 3 -Problem: 2 >> Solve x2 + 2x + 2 = 0 in the complex number system.
Answer Preview: To solve the quadratic equation x 2 2x 2 0 in the complex number system we can use the qua…

, Chapter: 5 -Problem: 5 >> In Problems 4–6, convert each angle in radians to degrees. Transcribed Image Text: 9? 2
Answer Preview: To convert an angle from radians to degrees we can use the formula Angle in degre…

, Chapter: 4 -Problem: 11 >> In Problems 11–14, each function is one-to-one. Find the inverse of each function and check your answer. Find the domain and range of f and f ?1. Transcribed Image Text: f(x)= = 2x + 3 5x ? 2
Answer Preview: To find the inverse of the function f x 2x 3 5x 2 we can follow these steps Replace f x with y y 2x …

, Chapter: 9 -Problem: 8 >> For the parabola y2 = 4ax, the line segment joining the two points (a, 2a) and (a, ?2a) is called the ___________ ____________ .
Answer Preview: The line segment joining the two points a 2a and a 2a on the parabola y 2 4ax is called …

, Chapter: 6 -Problem: 118 >> Problems 115–124. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the average rate of change of f (x) = cos x from 0 to ?/2.
Answer Preview: To find the average rate of change of the function f x …

, Chapter: 12 -Problem: 10 >> Determine whether the following is a probability model. Transcribed Image Text: Outcome Kwamie Joanne Laura Donna Angela Probability 0.3 0.2 0.1 0.5 -0.1
Answer Preview: To determine whether the given data is a probability model we need to check i…

, Chapter: 13 -Problem: 96 >> In Problems 85–96, simplify each expression. Transcribed Image Text: (-3)²
Answer Preview: To simplify the expression sqrt 3 2 you f…

, Chapter: 5 -Problem: 148 >> Problems 143–152. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.If the real zeros of g(x) are ?2 and 3, what are the real zeros of g(x + 6)?
Answer Preview: To find the real zeros of g x 6 given the real zeros of g x we …

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, Chapter: 8 -Problem: 49 >> In Problems 49–52, find the area of the parallelogram with vertices P1, P2, P3, and P4.P1 = (1, 1, 2), P2 = (1, 2, 3), P3 = (?2, 3, 0), P4 = (?2, 4, 1)
Answer Preview: To find the area of the parallelogram formed by the vectors defined by the points P1 P2 P3 and P4 we …

, Chapter: 1 -Problem: 12 >> In Problems 9 – 14, find the domain of each function. Transcribed Image Text: f(x): X x² + 2x + 2x - 3 2
Answer Preview: In this case the function is defined except when the denomina…

, Chapter: 2 -Problem: 19 >> In Problems 17–24, match each graph to one the following functions. f (x) = x2 ? 2x + 1 Transcribed Image Text: A. E. -2 (-1,0) -2 YA 3 Y? 1 -3 2 X 2 X (0, -1) B. F. (-1, -1) y+ -2- y 2 -2 (1, 0) 2 x 3 x C. G. -2 2 -2 Jr. 2 x (0, -1) (1, 1) 3 x D. H. (-1, 1) 2 2 x (1, -1) -2-- X
Answer Preview: To match each graph to the function f x x 2 2x 1 we need to analyze the characteristics of the funct…

, Chapter: 6 -Problem: 56 >> In Problems 21–100, establish each identity. Transcribed Image Text: 1 cose 1 + cose (csc0 cot 0) 2 0)²
Answer Preview: To establish the identity 1 cos 1 cos csc cot 2 We ll work on the left side and simplify it step by …

, Chapter: 1 -Problem: 80 >> Suppose that the function y = f ( x) is decreasing on the interval [?2, 7 ].(a) Over what interval is the graph of y = f (x + 2) decreasing?(b) Over what interval is the graph of y = f (x ? 5) decreasing?(c) Is the graph of y = ?f ( x) increasing, decreasing, or neither on the interval [?2, 7]?(d) Is the graph of y = f (?x) increasing, decreasing, or neither on the interval [?7, 2]?
Answer Preview: To analyze how the given transformations affect the decreasing behavior of the function we ll need t…

, Chapter: 13 -Problem: 79 >> In Problems 77 – 82, determine where each rational function R is undefined. Determine whether an asymptote or a hole appears in the graph of R at such numbers. Transcribed Image Text: R(x) - x³ 2x² + 4x - 8 x²+x-6 -
Answer Preview: To find where the rational function R x x 3 2x 2 4x 8 x 2 x 6 is undefined we need to identify the v…

, Chapter: 6 -Problem: 93 >> Problems 90–99. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the length of the arc subtended by a central angle of 75° on a circle of radius 6 inches. Give both the exact length and an approximation rounded to two decimal places.
Answer Preview: To find the length of the arc subtended by a central angle of 75 on a circle yo…

, Chapter: 13 -Problem: 105 >> In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. Transcribed Image Text: x7 - x5
Answer Preview: To factor the polynomial x^7 - x^5, we can factor out the co…

, Chapter: 13 -Problem: 18 >> In Problems 9 – 18, factor each polynomial by removing the common monomial factor.60x2 y ? 48xy2 + 72x3y
Answer Preview: To factor the polynomial 60x 2y 48xy 2 72x 3y we can first look …

, Chapter: 8 -Problem: 5 >> If P = (x, y) is a point on the terminal side of the angle ? at a distance r from the origin, then tan?= _____.
Answer Preview: If P x y is a point on the terminal side of the angle at a distance r from the …

, Chapter: 3 -Problem: 1 >> Solve the inequality 3 ? 4x > 5. Graph the solution set.
Answer Preview: We have to solve t…

, Chapter: 5 -Problem: 6 >> In Problems 4–6, convert each angle in radians to degrees. Transcribed Image Text: ?? 4
Answer Preview: To convert an angle from radians to degrees we can use the formula Angle in degre…

, Chapter: 5 -Problem: 45 >> In Problems 35–46, convert each angle in radians to degrees. Transcribed Image Text: 17? 15
Answer Preview: To convert 17 15 radians to degrees you can use the convers…

, Chapter: 8 -Problem: 95 >> Problems 94–103. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Use Descartes’ Rule of Signs to determine the possible number of positive or negative real zeros for the function f (x) = ?2x3 + 6x2 ? 7x ? 8
Answer Preview: To use Descartes Rule of Signs we need to examine the signs of the coefficients in the polynomial fu…

, Chapter: 6 -Problem: 83 >> In Problems 75–86, find the exact value of each expression. Transcribed Image Text: tan (sin-13- +)
Answer Preview: To find the exact value of the expression tan sin 1 3 5 6 we ll use the properties of trigonometric …

, Chapter: 12 -Problem: 68 >> Problems 68 – 77. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the area of the sector of a circle of radius 4 feet and central angle ? if the arc length subtended by ? is 5 feet.
Answer Preview: To find the area of the sector of a circle you need to use the formula Area o…

, Chapter: 13 -Problem: 82 >> In Problems 77 – 82, determine where each rational function R is undefined. Determine whether an asymptote or a hole appears in the graph of R at such numbers. Transcribed Image Text: R(x) = x³ x4 3x² + 4x - 12 3x³ + x - 3
Answer Preview: To determine where the rational function R x is undefined we need to find the values of x for which …

, Chapter: 6 -Problem: 16 >> In Problems 11 – 26, find the exact value of each expression. Transcribed Image Text: tan-¹ (-1)
Answer Preview: The expression arctan 1 represents the inverse tangent function of 1 The invers…

, Chapter: 6 -Problem: 25 >> In Problems 13–36, solve each equation on the interval 0 ? ? < 2?. Transcribed Image Text: 2 sin ²0 1 = 0
Answer Preview: To solve the equation 2sin 2 1 0 on the interval 0 2 we can follow these steps Move the con…

, Chapter: 8 -Problem: 45 >> Given vectors u = i + 5j and v = 4i + yj, find y so that the angle between the vectors is 60°.
Answer Preview: To find the value of y such that the angle between vectors u and v is 60 we can use the dot product …

, Chapter: 1 -Problem: 87 >> (a) Graph f (x) = x ? 3 ? 3 using transformations. (b) Find the area of the region that is bounded by f and the x-axis and lies below the x-axis.
Answer Preview: a Graph f x x 3 3 using transformations To graph the function f x x 3 3 we can identify the transfor…

, Chapter: 2 -Problem: 118 >> Problems 113–122 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.State the domain and range of the relation given below. Is the relation a function? {(5, ?3), (4, ?4), (3, ?5), (2, ?6), (1, ?7)}
Answer Preview: The given relation is a set of ordered pairs 5 3 4 4 3 5 2 …

, Chapter: 6 -Problem: 55 >> In Problems 49–60, use a calculator to solve each equation on the interval 0 ? ? < 2?. Round answers to two decimal places. Transcribed Image Text: sec 0 -4
Answer Preview: To solve the equation sec 4 on the interval 0 2 we need to fin…

, Chapter: 1 -Problem: 76 >> In Problems 71–80, for the given functions f and g, find the following. For parts (a)–(d), also find the domain. f (x) = |x| ; g(x) = x Transcribed Image Text: (a) (f + g)(x) (e) (f + g)(3) (b) (f- g)(x) (f) (f - g)(4) (c) (f.g)(x) (g) (f.g)(2) (d) (x) (h) (2) (1)
Answer Preview: Let s step by step evaluate the expressions to get the values and domains for the provided functions …

, Chapter: 13 -Problem: 50 >> In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. Transcribed Image Text: 4/32x + ??/2x5
Answer Preview: To simplify the expression you can use the p…

, Chapter: 6 -Problem: 74 >> In Problems 61–84, solve each equation on the interval 0 ? ? < 2?. Transcribed Image Text: tan0 = cot
Answer Preview: To solve the equation tan cot on the interval 0 2 we c…

, Chapter: 13 -Problem: 119 >> How would you explain to a fellow student the underlying reason for the multiplication properties for inequalities ? That is, the sense (direction) of an inequality remains the same if each side is multiplied by a positive real number, whereas the direction is reversed if each side is multiplied by a negative real number.
Answer Preview: Understanding the multiplication properties for inequalities is crucial when working with mathemati…

, Chapter: 13 -Problem: 16 >> In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. Transcribed Image Text: ?75
Answer Preview: To simplify the expression sqrt 75 you can find the sq…

, Chapter: 7 -Problem: 76 >> Problems 69–78. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus. Transcribed Image Text: 1 - Inx. 2x x².1 x2 Solve:- 2 (x²)² 2 = 0
Answer Preview: To solve the equation x 2 1 x ln x 2x x 2 2 0 we ll follow these steps Simplify the expression Se…

, Chapter: 3 -Problem: 4 >> Given z = 5 + 2i, find the product z · z?.
Answer Preview: To find the product of a complex number z and its conjugate z you can use the formula z z a bi a bi …

, Chapter: 5 -Problem: 8 >> True or False The graphs of y = sin x and y = cos x are identical except for a horizontal shift.
Answer Preview: False T he graphs of y sin x and y cos x are not identical even afte…

, Chapter: 4 -Problem: 152 >> Problems 145–154. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.The relationship between the height H of an adult female and the length x of her tibia, in centimeters, is estimated by the linear model H(x) = 2.90x + 61.53. If incomplete skeletal remains of an adult fe
Answer Preview: To estimate the height of the female using the given linear model H x 2 90x 61 …

, Chapter: 9 -Problem: 18 >> In Problems 13 – 24, analyze each equation and graph it. Transcribed Image Text: r = 12 4 + 8 sin 0
Answer Preview: To analyze the equation r 12 4 8sin we ll explore its characteristics and then graph it The given equation represents a polar equation where r represe…

, Chapter: 6 -Problem: 97 >> Problems 90–99. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the equation of a sine function with amplitude 4, period ?/3, and phase shift 1.
Answer Preview: To find the equation of a sine function with the given amplitude period and ph…

, Chapter: 13 -Problem: 9 >> In Problems 1 – 11, find the limit. Transcribed Image Text: -: 1 x2 lim x--1x3 - 1
Answer Preview: x 1 Given …

, Chapter: 13 -Problem: 84 >> In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. Transcribed Image Text: 10x³ + 50x² + 40x
Answer Preview: To factor the polynomial 10x 3 50x 2 40x we can first look for the gr…

, Chapter: 5 -Problem: 64 >> In Problems 63–76, find an equation for each graph. Transcribed Image Text: Af 2TT 6TT 10TT X -4TT-2TT -4 I
Answer Preview: We have a graph with the below characteristics Amplitude A 4 When x 0 y 0 and the funct…

, Chapter: 6 -Problem: 13 >> In Problems 11 – 26, find the exact value of each expression. Transcribed Image Text: sin-¹ (-1)
Answer Preview: To find the exact value of the expression arcsin 1 we need to determine the angle whose …

, Chapter: 6 -Problem: 16 >> In Problems 13–24, find the exact value of each expression.tan 195°
Answer Preview: To find the exact value of tan 195 we can use the periodicity of the tangent function The t…

, Chapter: 8 -Problem: 53 >> Problems 52 – 61 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Find the exact value of 5 cos 60° + 2 tan?/4. Do not use a calculator.
Answer Preview: To find the exact value of 5 cos 60 2 tan 4 we need to recall …

, Chapter: 2 -Problem: 3 >> Find the average rate of change of f (x) = ?4x + 3, from 2 to 4.
Answer Preview: To find the average rate of change of a function f x over an …

, Chapter: 2 -Problem: 7 >> Open the “Quadratic Functions” interactive figure, which is available in the Video & Resource Library of MyLab Math (under Sullivan Guided Visualizations) or at bit.ly/3raFUGB.(a) Set the values of a , h , and k as follows: a = 2, h = 3, k = ?4. What is the equation of the quadratic function?(b) Set the values of a , h , and k as follows: a = 2, h = 1, k = ?3. What is the vertex of the graph of th
Answer Preview: a The equation of the quadratic function with a 2 h 3 and k 4 is …

, Chapter: 6 -Problem: 42 >> In Problems 39 – 62, find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator. Transcribed Image Text: 3? sin-¹ [sin(-37)
Answer Preview: To find the value of the composite function sin 1 sin 3 7 we need to evaluate it step by step The si…

, Chapter: 1 -Problem: 63 >> In Problems 51–70, find the domain of each function. Transcribed Image Text: f(x) = ?x - 4
Answer Preview: To determine the domain of the function f x x sqrt x 4 we need to identify the v…

, Chapter: 13 -Problem: 78 >> In Problems 77–92, simplify each expression. Transcribed Image Text: 43/2
Answer Preview: To simplify the expression 4 3 2 we can rewrite the exponent 3 2 as a fractional expon…

, Chapter: 6 -Problem: 68 >> In Problems 63–70, find the inverse function f?1 of each function f. Find the range of f and the domain and range of f?1. Transcribed Image Text: f(x) = cos(x + 2) + 1;-2 ? x ? ?-2
Answer Preview: To find the inverse function f 1 of the given function f x cos x 2 1 we ll follow these steps Replac…

, Chapter: 13 -Problem: 105 >> In Problems 91 – 106, find the quotient and the remainder. Check your work by verifying that (Quotient )(Divisor ) + Remainder = Dividendx3 ? a3 divided by x ? a
Answer Preview: To find the quotient and the remainder when (x^3 - a^3) is divided by (x - a), we can use polynomial …

, Chapter: 13 -Problem: 14 >> In Problems 9 – 18, factor each polynomial by removing the common monomial factor.x3 ? x2 + x
Answer Preview: To factor out the common monomial factor from the given polynomia…

, Chapter: 4 -Problem: 134 >> Pierre de Fermat (1601–1665) conjectured that the function f (x) = 2(2x) + 1 for x = 1, 2, 3, . . . , would always have a value equal to a prime number. But Leonhard Euler (1707–1783) showed that this formula fails for x = 5. Use a calculator to determine the prime numbers produced by f for x = 1, 2, 3, 4. Then show that f (5) = 641 × 6, 700,417, which is not prime.
Answer Preview: To evaluate the function f x 2 2x 1 for x 1 2 3 4 we can simply su…

, Chapter: 5 -Problem: 10 >> True or False Transcribed Image Text: sec 0 = 1 sin 0
Answer Preview: False The correct relationship …

, Chapter: 4 -Problem: 3 >> Approximate the solution(s) to x3 = x2 ? 5 using a graphing utility.
Answer Preview: We have to approximate the solution for this equation x 3 x 2 5 …

, Chapter: 9 -Problem: 17 >> In Problems 7 – 26, graph the plane curve whose parametric equations are given, and show its orientation. Find the rectangular equation of each curve. Transcribed Image Text: x(t) = ?t, y(t) = t³/²; t > 0
Answer Preview: The graph of the plane curve whose parametric equations are …

, Chapter: 6 -Problem: 131 >> Problems 127 – 136. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus. Transcribed Image Text: If f(x) = ex-1 +3, find the domain of f-1 (x).
Answer Preview: To find the domain of the inverse function f 1 x we need to determine the values of x for …

, Chapter: 12 -Problem: 4 >> In Problems 4 – 9, use the information supplied in the figure.How many are in A ? Transcribed Image Text: 20 A 1 2 6 4 ? 0 B 5 20 U
Answer Preview: To find the total number of elements in set A f…

, Chapter: 13 -Problem: 94 >> In Problems 79–126, factor each polynomial completely. If the polynomial cannot be factored, say it is prime. Transcribed Image Text: x38x² 20x
Answer Preview: To factor the polynomial completely we first look for common factors among its te…

, Chapter: 5 -Problem: 113 >> Problems 107–116. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus. Transcribed Image Text: Find the oblique asymptote of g(x)= = 4x3 + 6x² - 3x + 1 2x² - 4x + 3
Answer Preview: To find the oblique asymptote of the function g x 4x 3 6x 2 3x 1 2x 2 4x 3 we need to check if the d…

, Chapter: 6 -Problem: 1 >> Find the exact value of sec2 ?/15 ? tan2 ?/15.
Answer Preview: To find the exact value of sec 2 15 tan 2 15 we can use trigonometric identities and properties Firs…

, Chapter: 6 -Problem: 20 >> In Problems 13–36, solve each equation on the interval 0 ? ? < 2?. Transcribed Image Text: 5 csc 0 - 3 = 2
Answer Preview: To solve the equation 5csc 3 2 on the interval 0 2 we ll need to follow these steps Rewrit…

, Chapter: 8 -Problem: 34 >> In Problems 21 – 34, plot each point given in polar coordinates. Transcribed Image Text: (-3, ? 2
Answer Preview: The graph of t…

, Chapter: 2 -Problem: 24 >> In Problems 21 – 26,(a) Find the zero of each linear function(b) Graph each function using the zero and y -intercept.f (x) = ?6x + 12
Answer Preview: a To find the zero of the linear function f x 6x 12 we set the function equal to zero and solve f…

, Chapter: 2 -Problem: 10 >> The vertical line passing through the vertex of a parabola is called the_________________.
Answer Preview: The axis of symmetry is a vertical line that passes through the vertex and divides the …

, Chapter: 6 -Problem: 53 >> In Problems 39 – 62, find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator. Transcribed Image Text: tan-¹[tan()]
Answer Preview: To find the exact value of the composite function tan 1 tan pi 2 we need to understan…

, Chapter: 1 -Problem: 61 >> In Problems 51–70, find the domain of each function. Transcribed Image Text: p(x) = X |2x + 3 1
Answer Preview: To find the domain of the function p x x 2x 3 1 we need to consider the values of x for which …

, Chapter: 13 -Problem: 76 >> In Problems 69–76, rationalize the numerator of each expression. Assume that all variables are positive when they appear. Transcribed Image Text: 4-??x-9 x - 25 x = 25
Answer Preview: To rationalize the numerator of the expression we need to eliminate the s…

, Chapter: 6 -Problem: 76 >> In Problems 61–84, solve each equation on the interval 0 ? ? < 2?. Transcribed Image Text: sin² = 2 cos 0 + 2
Answer Preview: To solve the equation sin 2cos 2 on the interval 0 2 we can us…

, Chapter: 13 -Problem: 124 >> In Problems 115–124, expressions that occur in calculus are given. Factor each expression. Express your answer so that only positive exponents occur. Transcribed Image Text: 8x¹/3 - 4x-2/3 0 x
Answer Preview: To factor the expression 8x^(1/3) - 4x^(-2/3), let's first look for the common factors: …

, Chapter: 13 -Problem: 26 >> In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. Transcribed Image Text: x 10. ?y5
Answer Preview: To simplify the expression fifth root x 10y 5 you can …

, Chapter: 4 -Problem: 114 >> Problems 113 – 122. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Determine whether the function is one-to-one: {(0, ?4), (2, ?2), (4, 0), (6, 2)}
Answer Preview: To determine whether the given function is one to one we need t…

, Chapter: 5 -Problem: 33 >> In Problems 27 – 34, name the quadrant in which the angle ? lies. Transcribed Image Text: sec 0 0, sin > 0
Answer Preview: To determine the quadrant in which the angle lies given that sec 0 an…

, Chapter: 4 -Problem: 11 >> In Problems 5 – 44, solve each logarithmic equation. Express irrational solutions in exact form. Transcribed Image Text: log4|x| 3
Answer Preview: To solve the logarithmic equation log 4 x 3 we need to eliminat…

, Chapter: 9 -Problem: 24 >> In Problems 13 – 24, analyze each equation and graph it. Transcribed Image Text: r = 3 csc 0 csc 0 - 1
Answer Preview: The graph of the polar equation r 3…

, Chapter: 6 -Problem: 121 >> Problems 115–124. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Ben paddled his kayak 8 miles upstream against a 1 mile per hour current and back again in 6 hours. How far could Ben have paddled in that time if there had been no current?
Answer Preview: To determine how far Ben could have paddled if there had been no current we can use the concept of r…

, Chapter: 12 -Problem: 6 >> In Problems 5–7, compute the value of the given expression.P(10, 6)
Answer Preview: To compute the value of the expression P 10 6 we need to u…

, Chapter: 13 -Problem: 83 >> In Problems 77–92, simplify each expression. Transcribed Image Text: 9-3/2
Answer Preview: To simplify the expression 9 3 2 we can use the rule of …

, Chapter: 5 -Problem: 101 >> If A ? 0, find the intercepts of the graph of Transcribed Image Text: y = A cos [B(x - C)] + A
Answer Preview: To find the intercepts of the graph of the equation y A cos B x C A where A 0 we …

, Chapter: 6 -Problem: 6 >> If is a point on the unit circle that corresponds to a real number t, then sin t = ______, cost = ______, and t ant = _______. Transcribed Image Text: 1 2?2 3 P = (-1/31
Answer Preview: To find the values of sine cosine and the angle t we can use the coord…

, Chapter: 6 -Problem: 18 >> In Problems 13–36, solve each equation on the interval 0 ? ? < 2?. Transcribed Image Text: ?3 cot 0 + 1 = 0
Answer Preview: To solve the equation 3 cot 1 0 on the interval 0 2 we ll follow these steps Simplify the equation S…

, Chapter: 8 -Problem: 47 >> In Problems 43–58, polar coordinates of a point are given. Find the rectangular coordinates of each point. Transcribed Image Text: (6, 5? 6
Answer Preview: To convert the given polar coordinates …

, Chapter: 1 -Problem: 9 >> In Problems 9 – 14, find the domain of each function. Transcribed Image Text: f(x) = x x² - 9
Answer Preview: In this case the function is defined except when the denomi…

, Chapter: 2 -Problem: 13 >> In Problems 13 – 26, find the zeros of each quadratic function by factoring. What are the x-intercepts of the graph of the function?f (x) = x2 ? 9x
Answer Preview: To find the zeros of the quadratic function f x x 2 9x by factoring we need to s…

, Chapter: 6 -Problem: 58 >> In Problems 33–60, find the exact value of each expression. Transcribed Image Text: csc(tan-11)
Answer Preview: To find the exact value of csc arctan 1 2 we can use the definitions of the …

, Chapter: 1 -Problem: 26 >> In Problems 25–32, the graph of a function is given. Use the graph to find:(a) The intercepts, if any(b) The domain and range(c) The intervals on which the function is increasing, decreasing, or constant(d) Whether the function is even, odd, or neither Transcribed I

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9 Reviews for Precalculus Concepts Through Functions A Unit Circle Approach To Trigonometry Textbook Questions And Answers