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Precalculus Concepts Through Functions A Unit Circle Approach To Trigonometry 5th Edition Michael Sullivan - Solutions

In Problem 51–58, use the division algorithm to rewrite each improper rational expression as the sum of a polynomial and a proper rational expression. Find the partial fraction decomposition of the proper rational expression. Finally, express the improper rational expression as the sum of a
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. x = y + z = -2y + z = 1 -2x - 3y = -4 4
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2х Зу 2x-3y - z = 0 3x + 2y + 2z = 2 x +5y +3z = 2
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. x + 4y - 3z = -8 3x у + 3z = 12 1 x + y + 6z
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2x - 2y + 3z = 6 4x - 3y + 2z = 0 -2x + 3y - 7z = 1
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 3x-2y 7x-3y 2x-3y + 2z 6 = + 2z = –1 + 4z = 0 =
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. x + 2z = 6 -x + 2y + 3z = -5 x - y = 6
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x + y z = 6 3x - 2y + z = -5 x + 3y - 2z = 14
The formula from Problem 59 can be used to find the area of a polygon. To do so, divide the polygon into non-overlapping triangular regions and find the sum of the areas. Use this approach to find the area of the given polygon.Data from problem 59A triangle has vertices (x1, y1), (x2 , y2), and
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x = y + z = -4 2x - 3y + 4z = -15 5x + y 2z = 12
Another approach for finding the area of a polygon by using determinants is to use the formulawhere (x1, y1), (x2 , y2), . . . , (xn, yn) are the n corner points in counterclockwise order. Use this formula to compute the area of the polygon from Problem 60 again. Which method do you prefer?
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. x + 2z: -x + 2y + 3z 2 y = 2322
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. z = -3 2x - 4y + z = -7 -2x + 2y3z = 4 x + 2y
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. z = 9 3x + 2y z = 8 3x + y + 2z = 1 x + y +
A tetrahedron (triangular pyramid) has vertices (x1, y1, z1), (x2 , y2 , z2), (x3, y3, z3), and (x4 , y4 , z4). The volume of the tetrahedron is given by the absolute value of D, whereUse this formula to find the volume of the tetrahedron with vertices (0, 0, 8), (2, 8, 0), (10, 4, 4), and (4, 10,
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x +4y - 3z = -8 - 3x - x + x у + 3z = 12 y + 6z =1 у 67
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. 3x + 3y + z = 8 x + 2y + z = 5 2xy +z = 4
A movie theater charges $15.00 for adults and $13.00 for senior citizens. On a day when 325 people paid for admission, the total receipts were $4445. How many who paid were adults? How many were seniors?
Problems 61–70. 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.Nick has a credit card balance of $4200. If the credit card company charges 18% interest compound
Problems 61–70. 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 f (x) = x + 4 and g(x) = x2 − 3x, find (g º f)(−3).
Graph the system of inequalities. [[x]+[y] ≤ 4 ||y[ < |x? - 3 |
An equation of the circle containing the distinct points (x1, y1), (x2 , y2), and (x3, y3) can be found using the following equation.Find the standard equation of the circle containing the points (7, −5), (3, 3), and (6, 2). 1 x1 y У1 x² + y² x² + y² 1 X 1 x2 Y2 x² + y² 1 Y3 x² + y² = 0 =
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 3x + y = 2x = y + -y+ 4x + z = 2/31 7 = 1 z 2y 8 00 | دی 3
Show that x2 X y2 y 1 = (y z)(x - y)(x − z). 1 N -
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x + y = 1 2xy + z = 1 x + 2y + z = 1813
Problems 61–70. 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.Plot the point given by the polar coordinatesand find its rectangular coordinates. 5п (-1, , 5 ) 4
Problems 63–72. 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 equation 2 cos²0 cose - 1 = 0 for 0 ≤ 0 < 2TT.
Problems 61–70. 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 whetheris even, odd, or neither. f(x) 3x x2 - 10
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x + 2y + z = 1 2xy + 2z = 2 3x + y + 3z = 3
In Problems 65–70 show that each matrix has no inverse. -3 6-1
Problems 61–70. 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 sec 52° cos 308°.
Problems 63–72. 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 2(x + 1)2 + 8 = 0 in the complex number system.
In Problems 65–70 show that each matrix has no inverse. 15 3 10 2
Problems 63–72. 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: x2 - 4x + 3 ≤ x + 18
Problems 61–70. 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-1≥ x + x-12 2 4
Problems 63–72. 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 the polar equation 3r = sinθ as an equation in rectangular coordinates. Identify the equation
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x = y + y 3x + 2y + z = 5 2z = 0
Problems 63–72. 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 the Intermediate Value Theorem to show that f (x) = 6x2 + 5x − 6 has a real zero on the interval
Problems 61–70. 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 function f (x) = 8x−3 − 4 is one-to-one. Find f−1.
In Problems 71–74, use a graphing utility to find the inverse, if it exists, of each matrix. Round answers to two decimal places. 25 18 -12 3 4 61 - 12 7 -1
In Problems 65–70, graph each equation and find the point(s) of intersection, if any. y 4 and the circle x2 + 4x + y² -4 = 0 x + 2
Problems 61–70. 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 an equation for the hyperbola with vertices (0, −5) and (0, 5), and a focus at (0, 13).
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 4x + y + z w = 4 x = y + 2z + 3w = 3
Problems 63–72. 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. Given f(x) = 2 and g(x)=√√x + 2, find the domain of (fog)(x) - 5
Problems 63–72. 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 $7500 is invested in an account paying 3.25% interest compounded daily, how much money will be in
Problems 61–70. 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 for D: 2x − 4xD − 4y + 2yD = D
Problems 63–72. 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 horsepower P needed to propel a boat through water is directly proportional to the cube of the
Problems 70–79. 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.For the points P = (−4, 3) and Q = (5, −1) write the vector v represented by the directed line
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. - 4x 2xy + z + y = 5 w = 5 z + w = 4
In Problems 75–78, use the inverse matrix found in Problem 71 to solve the following systems of equations. Round answers to two decimal places. 25x + 61y - 18x - 12y + 3x + 4y - + 12z = 15 72 = -3 2 = 12 2
Problems 61–70. 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 normal line is the line that is perpendicular to the tangent line at the point of tangency. If y =
Problems 63–72. 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.Change y = log5 x to an equivalent statement involving an exponent.
Problems 70–79. 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.List the potential rational zeros of the polynomial function P(x) = 2x3 − 5x2 + x − 10.
Problems 70–79. 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.Graph f (x) = (x + 1)2 − 4 using transformations (shifting, compressing, stretching, and/or
Consider the functions f (x) = x3 − 7x2 − 5x + 4 and f'(x) = 3x2 − 14x − 5. Given that f is increasing where f'(x) > 0 and f is decreasing where f'(x) < 0, find where f is increasing and where f is decreasing. Because polynomials are continuous over their domain, all endpoints are
In Problems 75–78, use the inverse matrix found in Problem 71 to solve the following systems of equations. Round answers to two decimal places. 25x + 61y 18x12y + 3x + 4y - 12z = 21 7z = 7 Z=-2
Problems 70–79. 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 tan 42° − cot 48° without using a calculator.
In Problems 75–78, use the inverse matrix found in Problem 71 to solve the following systems of equations. Round answers to two decimal places. 25x + 61y - 18x 12y + 3x + 4y - 12z = 25 7z = 10 z = -4
Problems 70–79. 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.Rationalize the numerator: √x + 7-10
Find real numbers a, b, and c so that the graph of the function y = ax2 + bx + c contains the points (−1, −2), (1, −4), and (2, 4).
Problems 70–79. 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.Express −5 + 5i in polar form and in exponential form.
In Problems 79–86, solve each system of equations using any method you wish. 2x + 3y = 11 5x + 7y = 24
Solve for x, y, and z, assuming a ≠ 0, b ≠ 0, and c ≠ 0. ax+by+cz = a + b + c a²x + b²y + c²z = ac + ab + bc abx + bcy = bc + ac
In Problems 90–96, use Descartes’ method from Problem 89 to find an equation of the tangent line to each graph at the given point.y = x2 + 2; at (1, 3)Data from problem 89Descartes’ method for finding tangent lines depends on the idea that, for many graphs, the tangent line at a given point
Problems 70–79. 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 function f (x) = 3 + log5 (x − 1) is one-to-one. Find f−1.
Problems 70–79. 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 distance between the vertices of f (x) = 2x2 − 12x + 20 and g(x) = −3x2 − 30x − 77.
Find the function y = ax2 + bx + c whose graph contains the points (1, −1), (3, −1), and (−2, 14).
Nikki and Joe take classes at a community college, LCCC, and a local university, SIUE. The number of credit hours taken and the cost per credit hour (2021–2022 academic year, tuition and approximate fees) are as follows:(a) Write a matrix A for the credit hours taken by each student and a matrix
In Problems 90–96, use Descartes’ method from Problem 89 to find an equation of the tangent line to each graph at the given point.2x2 + 3y2 = 14; at (1, 2)Data from problem 89Descartes’ method for finding tangent lines depends on the idea that, for many graphs, the tangent line at a given
In Problems 79–86, solve each system of equations using any method you wish. 5x - y + 4z = 2 = 3 -x+ 5y4z 7x + 13y4z = 17
Problems 70–79. 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.Expand: (2x − 5)3
Three painters (Beth, Solana, and Edie), working together, can paint the exterior of a home in 10 hours (h). Solana and Edie together have painted a similar house in 15 h. One day, all three worked on this same kind of house for 4 h, after which Edie left. Beth and Solana required 8 more hours to
Find the function f (x) = ax3 + bx2 + cx + d for which f (−3) = −112, f (−1) = −2, f (1) = 4, and f (2) = 13.
In Problems 90–96, use Descartes’ method from Problem 89 to find an equation of the tangent line to each graph at the given point.x2 + y = 5; at (−2, 1)Data from problem 89Descartes’ method for finding tangent lines depends on the idea that, for many graphs, the tangent line at a given
Solve for x and y, assuming a ≠ 0 and b ≠ 0. ax + by + by = a + b abxb²y = b² - ab
Find the function f (x) = ax3 + bx2 + cx + d for which f (−2) = −10, f (−1) = 3, f (1) = 5, and f (3) = 15.
Problems 70–79. 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 an equation of the line perpendicular to f (x) = −2/5 x + 7 where x = 10.
In Problems 90–96, use Descartes’ method from Problem 89 to find an equation of the tangent line to each graph at the given point.3x2 + y2 = 7; at (−1, 2)Data from problem 89Descartes’ method for finding tangent lines depends on the idea that, for many graphs, the tangent line at a given
Solve for matrix X:Use the following discussion for Problems 94 and 95. In graph theory, an adjacency matrix, A, is a way of representing which nodes (or vertices) are connected. For a simple directed graph, each entry, aij , is either 1 (if a direct path exists from node i to node j) or 0 (if no
Problems 91 – 100. 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.Factor each of the following: (a) 4(2x - 3)³.2 (x³ + 5)² + 2(x³ + 5).3x².(2x - 3)² b) ½ (3x
Asako has $20,000 to invest. As her financial planner, you recommend that she diversify into three investments: Treasury bills that yield 5% simple interest, Treasury bonds that yield 7% simple interest, and corporate bonds that yield 10% simple interest. Asako wishes to earn $1390 per year in
Problems 91 – 100. 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 n-¹ [ sin(-10)]. -1 9 sin
An unofficial, and often contested, guideline for website design is to make all website content available to a user within three clicks. The webpage adjacency matrix for a certain website is given by(a) Find B3. Does this website satisfy the Three-Click Rule?(b) Which page can be reached the most
Problems 91 – 100. 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.Graph f (x) = −31−x + 2.
Three retired couples each require an additional annual income of $2000 per year. As their financial consultant, you recommend that they invest some money in Treasury bills that yield 7%, some money in corporate bonds that yield 9%, and some money in “junk bonds” that yield 11%. Prepare a table
A young couple has $25,000 to invest. As their financial consultant, you recommend that they invest some money in Treasury bills that yield 7%, some money in corporate bonds that yield 9%, and some money in junk bonds that yield 11%. Prepare a table showing the various ways that this couple can
Write a brief paragraph outlining your strategy for solving a system of two linear equations containing two variables.
Problems 91 – 100. 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 −√3 + i in polar form and in exponential form.
In Problems 90–96, use Descartes’ method from Problem 89 to find an equation of the tangent line to each graph at the given point.x2 − y2 = 3; at (2, 1)Data from problem 89Descartes’ method for finding tangent lines depends on the idea that, for many graphs, the tangent line at a given
In Problems 90–96, use Descartes’ method from Problem 89 to find an equation of the tangent line to each graph at the given point.2y2 − x2 = 14; at (2, 3)Data from problem 89Descartes’ method for finding tangent lines depends on the idea that, for many graphs, the tangent line at a given
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.Solve: x2 − 3x < 6 + 2x
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. Graph: f(x) = 2x²x1 x² + 2x + 1 2
An important aspect of computer graphics is the ability to transform the coordinates of points within a graphic. For transformation purposes, a point (x, y) is represented as the column matrixTo translate a point (x, y) horizontally h units and vertically k units, we use the translation matrixand
Problems 91 – 100. 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 A = {2, 4, 6, . . . , 30} and B = {3, 6, 9, . . . , 30}, find A ∩ B.
Problems 91 – 100. 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 an equation of an ellipse if the center is at the origin, the length of the major axis is 20
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.State the domain of f (x) = −e x+5 − 6.
Besides translating a point, it is also important in computer graphics to be able to rotate a point. This is achieved by multiplying a point’s column matrix by an appropriate rotation matrix R to form the matrix product RX. For example, to rotate a point 60°, the rotation matrix is(a) Write the
Problems 91 – 100. 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.Iffind zw and z/w. Write the answers in polar form and in exponential form. z 6e 7/4 and w = =
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 a calculator to approximate cos−1 (−0.75) in radians, rounded to two decimal places.
Iffind a, b, c, d so that AB = BA. a b -=[ @ $ ] ₁ C d A and B = 1 1 -1 1

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