Precalculus enhanced with graphing utilities 6th edition pdf download

Precalculus enhanced with graphing utilities 6th edition pdf download

Precalculus : enhanced with graphing utilities,Solutions Manual for Precalculus Enhanced with Graphing Utilities 6th Edition by Sullivan.

About The Book Precalculus Enhanced With Graphing Utilities 6th Edition Online Textbook Pdf The Sullivan’s time-tested approach focuses students on the fundamental skills they need A) m B) m C) m D) m 19) If a rock falls from a height of 90 meters on Earth, the height H (in meters) after x seconds is approximately H(x) = 90 - x2 2 Edition 6th Utilities Graphing Enhanced Precalculus lus are suitable for other freshman and sophomore math courses such as College Algebra and Trigonometry; however, Download File PDF Ebook Edition 6th Utilities Graphing With Enhanced Precalculus As recognized, adventure as well as experience more or less lesson, amusement, as capably as Title: Solutions Manual for Precalculus Enhanced with Graphing Utilities 6th Edition by Sullivan: Author: Sullivan" Subject: Solutions Manual for Precalculus Enhanced with Graphi ... read more

Little League Baseball Refer to Problem Overlay a rectangular coordinate system on a Little League baseball diamond so that the origin is at home plate, the positive x-axis lies in the direction from home plate to first base, and the positive y-axis lies in the direction from home plate to third base. Distance between Moving Objects A Ford Focus and a Mack truck leave an intersection at the same time. The Focus heads east at an average speed of 30 miles per hour, while the truck heads south at an average speed of 40 miles per hour. Find an expression for their distance apart d in miles at the end of t hours. Graphs Distance of a Moving Object from a Fixed Point A hot-air balloon, headed due east at an average speed of 15 miles per hour at a constant altitude of feet, passes over an intersection see the figure.

Find an expression for its distance d measured in feet from the intersection t seconds later. Net Sales The figure illustrates how net sales of Wal-Mart Stores, Inc. Use the midpoint formula to estimate the net sales of Wal-Mart Stores, Inc. Source: Wal-Mart Stores, Inc. Drafting Error When a draftsman draws three lines that are to intersect at one point, the lines may not intersect as intended and subsequently will form an error triangle. If this error triangle is long and thin, one estimate for the location of the desired point is the midpoint of the shortest side. The figure shows one such error triangle. a Find an estimate for the desired intersection point. b Find the length of the median for the midpoint found in part a. See Problem Source: www. htm y 1.

Poverty Threshold Poverty thresholds are determined by the U. Census Bureau. A poverty threshold represents the minimum annual household income for a family not to be considered poor. Assuming poverty thresholds increase in a straight-line fashion, use the midpoint formula to estimate the poverty threshold of a family of four with two children under the age of 18 in Source: U. Census Bureau 2. If M is the midpoint of a line segment AB , find the coordinates of B. Make up an equation satisfied by the ordered pairs 12, 02, 14, 02, and 10, Comment on any similarities. Draw a graph that contains the points 1 - 2, - 12, 10, 12, 11, 32, and 13, Compare your graph with those of other students. Are most of the graphs almost straight lines?

Discuss the various ways that these points might be connected. Explain what is meant by a complete graph. Write a paragraph that describes a Cartesian plane. Then write a second paragraph that describes how to plot points in the Cartesian plane. Now we discuss how to find intercepts from an equation algebraically. To help understand the procedure, we present Figure From the graph, we can see that the intercepts are -4, 0 , -1, 0 , 4, 0 , and 0, The x-intercepts are -4, -1 , and 4. The y-intercept is Notice that x-intercepts have y-coordinates that equal 0; y-intercepts have x-coordinates that equal 0.

This leads to the following procedure for finding intercepts. The equation has two solutions, -2 and 2. The x-intercepts are -2 and 2. Symmetry often occurs in nature. Consider the picture of the butterfly. Do you see the symmetry? A graph is said to be symmetric with respect to the x-axis if, for every point x, y on the graph, the point x, -y is also on the graph. A graph is said to be symmetric with respect to the y-axis if, for every point x, y on the graph, the point -x, y is also on the graph. A graph is said to be symmetric with respect to the origin if, for every point x, y on the graph, the point -x, -y is also on the graph. Notice that, when a graph is symmetric with respect to the x-axis, the part of the graph above the x-axis is a reflection or mirror image of the part below it, and vice versa. When a graph is symmetric with respect to the y-axis, the part of the graph to the right of the y-axis is a reflection of the part to the left of it, and vice versa.

Symmetry with respect to the origin may be viewed in two ways: 1. As a reflection about the y-axis, followed by a reflection about the x-axis 2. As a projection along a line through the origin so that the distances from the origin are equal Figure 30 y y y —x1, y1 x2, y2 x1, y1 x3, y3 x1, —y1 x x3, —y3 —x2, y2 x2, y2 x2, —y2 Symmetry with respect to the x-axis E XAM PL E 2 x1, y1 x1, y1 x x2, y2 x —x2, —y2 —x1, —y1 Symmetry with respect to the y-axis Symmetry with respect to the origin Symmetric Points a If a graph is symmetric with respect to the x-axis and the point 4, 2 is on the graph, then the point 4, -2 is also on the graph.

b If a graph is symmetric with respect to the y-axis and the point 4, 2 is on the graph, then the point -4, 2 is also on the graph. c If a graph is symmetric with respect to the origin and the point 4, 2 is on the graph, then the point -4, -2 is also on the graph. Now Work PROBLEM 23 19 Graphs When the graph of an equation is symmetric with respect to the x-axis, the y-axis, or the origin, the number of points that you need to plot is reduced. For example, if the graph of an equation is symmetric with respect to the y-axis, then, once points to the right of the y-axis are plotted, an equal number of points on the graph can be obtained by reflecting them about the y-axis. Because of this, before we graph an equation, we first want to determine whether it has any symmetry. The following tests are used for this purpose.

Tests for Symmetry To test the graph of an equation for symmetry with respect to the x-Axis Replace y by -y in the equation. If an equivalent equation results, the graph of the equation is symmetric with respect to the x-axis. y-Axis Replace x by -x in the equation. If an equivalent equation results, the graph of the equation is symmetric with respect to the y-axis. Origin Replace x by -x and y by -y in the equation. If an equivalent equation results, the graph of the equation is symmetric with respect to the origin. b We now test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.

x-Axis: To test for symmetry with respect to the x-axis, replace y by - y. y-Axis: To test for symmetry with respect to the y-axis, replace x by - x. Origin: To test for symmetry with respect to the origin, replace x by -x and y by -y. Graphs Since the result is not equivalent to the original equation, the graph of the x2 - 4 is not symmetric with respect to the origin. Also, did you notice that the point 2, 0 is on the graph along with -2, 0? How could we have found the second x-intercept using symmetry? The next three examples use intercepts, symmetry, and point plotting to obtain the graphs of additional key equations. It is important to know the graphs of these key equations. Find any intercepts and check for symmetry first. Solution Figure 32 Replace y by -y. y-Axis: Replace x by -x. Origin: Replace x by -x and y by -y. The origin 0, 0 is the only intercept.

Because of the symmetry with respect to the origin, we only need to locate points on the graph for which x Ú 0. See Table 5. Points on the graph could also be obtained using the TABLE feature on a graphing utility. See Table 6. Do you see the symmetry with respect to the origin from the table? Figure 32 shows the graph. The graph is not symmetric with respect to the y-axis or the origin. Because the equation is solved for x, it is easier to assign values to y and use the equation to determine the corresponding values of x. Because of the symmetry, we can restrict ourselves to points whose y-coordinates are non-negative. Then use the symmetry to find additional points on the graph.

See Table 7. For example, since 1, 1 is on the graph, so is 1, Since 4, 2 is on the graph, so is 4, -2 , and so on. Plot these points and connect them with a smooth curve to obtain Figure We proceed to solve for y. Figure 34 shows the result. Notice that when x 6 0 we get an error. Can you explain why? x Check for intercepts first. We conclude that there is no y-intercept. We conclude that there is no x-intercept. x Next check for symmetry. The graph is symmetric only with respect to the origin. x Use the equation to form Table 9 and obtain some points on the graph. Because of symmetry, we only find points x, y for which x is positive. Armed with this information, we can graph x 1 the equation.

x Observe how the absence of intercepts and the existence of symmetry with respect to the origin were utilized. Figure 37 confirms our algebraic analysis using a TI Plus. True or False The y-coordinate of a point at which the graph crosses or touches the x-axis is an x-intercept. True or False If a graph is symmetric with respect to the x-axis, then it cannot be symmetric with respect to the y-axis. Be sure to label the intercepts. Then plot the point that is symmetric to it with respect to a the x-axis; b the y-axis; c the origin. a Find the intercepts. b Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin.

y-axis x-axis y Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. If the graph of an equation is symmetric with respect to the y-axis and 6 is an x-intercept of this graph, name another x-intercept. Solar Energy The solar electric generating systems at Kramer Junction, California, use parabolic troughs to heat a heat-transfer fluid to a high temperature. This fluid is used to generate steam that drives a power conversion system to produce electricity. For troughs 7. Department of Energy DOE Digital Photo Archive Given that the point 1, 2 is on the graph of an equation that is symmetric with respect to the origin, what other point is on the graph? If the graph of an equation is symmetric with respect to the origin and - 4 is an x-intercept of this graph, name another x-intercept.

If the graph of an equation is symmetric with respect to the x-axis and 2 is a y-intercept, name another y-intercept. Microphones In studios and on stages, cardioid microphones are often preferred for the richness they add to voices and for their ability to reduce the level of sound from the sides and rear of the microphone. a Find the intercepts of the graph of the equation. b Test for symmetry with respect to the x-axis, y-axis, and origin. com a Find the intercepts of the graph of the equation. Department of Energy Explaining Concepts: Discussion and Writing Draw a graph of an equation that contains two x-intercepts; at one the graph crosses the x-axis, and at the other the graph touches the x-axis.

Make up an equation with the intercepts 2, 0 , 4, 0 , and 0, 1. Draw a graph that contains the points 0, 1 , 1, 3 , and 3, 5 and is symmetric with respect to the x-axis. An equation is being tested for symmetry with respect to the x-axis, the y-axis, and the origin. Explain why, if two of these symmetries are present, the remaining one must also be present. Draw a graph that contains the points - 2, 5 , - 1, 3 , and 0, 2 that is symmetric with respect to the y-axis. Compare your graph with those of other students; comment on any similarities. Can a graph contain these points and be symmetric with respect to the x-axis? The origin? Why or why not? Interactive Exercises Ask your instructor if the applets below are of interest to you.

y-axis Symmetry Open the y-axis symmetry applet. Move point A around the Cartesian plane with your mouse. How are the coordinates of point A and the coordinates of point B related? x-axis Symmetry Open the x-axis symmetry applet. Origin Symmetry Open the origin symmetry applet. OBJECTIVE 1 Solve Equations Using a Graphing Utility In this text, we present two methods for solving equations: algebraic and graphical. Some equations can be solved using algebraic techniques that result in exact solutions. For other equations, however, there are no algebraic techniques that lead to an exact solution. For such equations, a graphing utility can often be used to investigate possible solutions. When a graphing utility is used to solve an equation, usually approximate solutions are obtained. One goal of this text is to determine when equations can be solved algebraically. If an algebraic method for solving an equation exists, we shall use it to obtain an exact solution.

A graphing utility can then be used to support the algebraic result. However, if no algebraic techniques are available to solve an equation, a graphing utility will be used to obtain approximate solutions. Unless otherwise stated, we shall follow the practice of giving approximate solutions as decimals rounded to two decimal places. The ZERO or ROOT feature of a graphing utility can be used to find the solutions of an equation when one side of the equation is 0. That is, solving an equation for x when one side of the equation is 0 is equivalent to finding where the graph of the corresponding equation in two variables crosses or touches the x-axis.

Round answers to two decimal places. Begin by graphing Y1. Figure 38 shows the graph. From the graph there appears to be one x-intercept solution to the equation between -2 and Graphs NOTE Graphing utilities use a process in which they search for a solution until the answer is found within a certain tolerance level such as within 0. Therefore, the y-coordinate may sometimes be a nonzero value such as [email protected] , which is 1. This feature is used most effectively when neither side of the equation is 0. At a point of intersection of the graphs, the value of the y-coordinate is the same for Y1 and Y2. Thus, the x-coordinate of the point of intersection represents a solution to the equation. Do you see why? The INTERSECT feature on a graphing utility determines a point of intersection of the graphs.

Using this feature, we find that the graphs intersect at 1 See Figure 41 a and b. STEP 3: Use ZERO or ROOT to determine each x-intercept of the graph. Using INTERSECT, we find the point of intersection to be 1 If the two expressions are equal, the solution checks. True or False In using a graphing utility to solve an equation, exact solutions are always obtained. Skill Building In Problems 5—16, use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. All solutions lie between - 10 and Verify your solution using a graphing utility. Each step contains exactly the same horizontal run and the same vertical rise. The ratio of the rise to the run, called the slope, is a numerical measure of the steepness of the staircase.

For example, if the run is increased and the rise remains the same, the staircase becomes less steep. If the run is kept the same, but the rise is increased, the staircase becomes more steep. This important characteristic of a line is best defined using rectangular coordinates. Figure 44 a on the next page provides an illustration of the slope of a nonvertical line; Figure 44 b illustrates a vertical line. Two comments about computing the slope of a nonvertical line may prove helpful: 1. Any two distinct points on the line can be used to compute the slope of the line.

See Figure 45 for justification. Figure 45 Triangles ABC and PQR are similar equal angles , so ratios of corresponding sides are equal. That is, if x increases by 4 units, then y will decrease by 5 units. The average rate of change of y with respect 5 to x is -. However, most graphing utilities have a rectangular screen. Because of this, using the same interval for both x and y will result in a distorted view. We need to adjust the selections for Xmin, Xmax, Ymin, and Ymax so that a square screen results. On most graphing utilities, this is accomplished by setting the ratio of x to y at 3 : 2.

Notice that the line now bisects the first and third quadrants. Compare this illustration to Figure When the slope of a line is positive, the line slants upward from left to right. When the slope of a line is negative, the line slants downward from left to right. When the slope is 0, the line is horizontal. Figures 48 and 49 also illustrate that the closer the line is to the vertical position, the greater the magnitude of the slope. So, a line with slope 6 is steeper than a line whose slope is 3. The fact that the slope is means that for every horizontal Run 4 movement run of 4 units to the right there will be a vertical movement rise of 3 units. If we start at the given point 3, 2 and move 4 units to the right and 3 units up, we reach the point 7, 5. By drawing the line through this point and the point 3, 2 , we have the graph. If we start at the given point 3, 2 and move 5 units to the right and then 4 units down, we arrive at the point 8, By drawing the line through these points, we have the graph.

This approach brings us to the point -2, 6 , which is also on the graph shown in Figure No matter what y-coordinate is used, the corresponding x-coordinate always equals 3. See Figure 52 a. Consult your manual to determine the methodology required to draw vertical lines. Figure 52 b shows the graph that you should obtain. Figure 53 4 Use the Point—Slope Form of a Line; Identify Horizontal Lines y L x, y y — y1 x 1, y1 Let L be a nonvertical line with slope m and containing the point x1, y1. See Figure 54 for the graph.

Now Work PROBLEM 45 33 Graphs E X A MP L E 5 Finding the Equation of a Horizontal Line Find an equation of the horizontal line containing the point 3, 2. Graph the line. Solution First compute the slope of the line. In the solution to Example 6, we could have used the other point, -4, 5 , instead of the point 2, 3. The equation that results, although it looks different, is equivalent to the equation obtained in the example. Try it for yourself. Now Work PROBLEM 37 6 Write the Equation of a Line in Slope—Intercept Form Another useful equation of a line is obtained when the slope m and y-intercept b are known. Graph the equation. Solution To obtain the slope and y-intercept, write the equation in slope—intercept form by solving for y. Graph the line using the 2 1 fact that the y-intercept is 2 and the slope is -. Then, starting at the point 0, 2 , go to 2 the right 2 units and then down 1 unit to the point 2, 1.

Now Work PROBLEM 77 8 Graph Lines Written in General Form Using Intercepts Refer to Example 7. Another approach to graphing equation 4 would be to find its intercepts. Remember, the intercepts of the graph of an equation are the points where the graph crosses or touches a coordinate axis. The x-intercept is 4 and the point 4, 0 is on the graph of the equation. Plot the points 4, 0 and 0, 2 and draw the line through the points. Graphs Every line has an equation that is equivalent to an equation written in general form. Figure 61 y 9 Find Equations of Parallel Lines Rise Run Rise Run x THEOREM When two lines in the plane do not intersect that is, they have no points in common , they are said to be parallel. Look at Figure There we have drawn two parallel lines and have constructed two right triangles by drawing sides parallel to the coordinate axes.

The right triangles are similar. Two angles are equal. Because the triangles are similar, the ratios of corresponding sides are equal. Criterion for Parallel Lines Two nonvertical lines are parallel if and only if their slopes are equal and they have different y-intercepts. If two nonvertical lines are parallel, then their slopes are equal and they have different y-intercepts. If two nonvertical lines have equal slopes and they have different y-intercepts, then they are parallel. Since the line that we seek also has slope -2 and contains the point 2, -3 , use the point—slope form to obtain its equation. Figure 64 Now Work y PROBLEM 59 10 Find Equations of Perpendicular Lines 90° x THEOREM When two lines intersect at a right angle 90° , they are said to be perpendicular.

The following result gives a condition, in terms of their slopes, for two lines to be perpendicular. Criterion for Perpendicular Lines Two nonvertical lines are perpendicular if and only if the product of their slopes is - 1. There is no loss in generality that is, neither the angle nor the slopes are affected if we situate the lines so that they meet at the origin. Do you see why this must be true? Suppose that the lines are perpendicular. Then triangle OAB is a right triangle. m2 m1 E X AM PL E 11 Finding the Slope of a Line Perpendicular to Another Line 3 2 If a line has slope , any line having slope - is perpendicular to it.

Graph the two lines. Solution First write the equation of the given line in slope—intercept form to find its slope. Any line perpendicular to this line will have slope 3. Otherwise, the angle between the two lines will appear distorted. Two nonvertical lines have slopes m1 and m 2, respectively. True or slope. False Vertical lines have an 9. undefined True or False Perpendicular lines have slopes that are reciprocals of one another. Skill Building In Problems 11—14, a find the slope of the line and b interpret the slope.

y —2, 2 2 1, 1 y —1, 1 2 2, 2 0, 0 2 x —2 —1 2 x —2 —1 2 x —2 —1 2 In Problems 15—22, plot each pair of points and determine the slope of the line containing them. Graph the line by hand. Use this information to locate three additional points on the line. Answers may vary. See Example 2. Slope 4; point 1, 2 Slope 2; point - 2, 3 3 Slope ; point - 3, 2 3 Slope - 2; point - 2, - 3 Slope - 1; point 4, 1 In Problems 37—44, find an equation of the line L. Express your answer using either the general form or the slope—intercept form of the equation of a line, whichever you prefer.

Containing the points 1, 3 and - 1, 2 Containing the points - 3, 4 and 2, 5 Slope undefined; containing the point 2, 4 Slope undefined; containing the point 3, 8 Horizontal; containing the point - 3, 2 Vertical; containing the point 4, - 5 Verify your graph using a graphing utility. Find an equation of the y-axis. Find an equation of the x-axis. In Problems —, the equations of two lines are given. Determine if the lines are parallel, perpendicular, or neither. Geometry Use slopes to show that the triangle whose vertices are - 2, 5 , 1, 3 , and - 1, 0 is a right triangle. Geometry Use slopes to show that the quadrilateral whose vertices are 1, - 1 , 4, 1 , 2, 2 , and 5, 4 is a parallelogram.

Geometry Use slopes to show that the quadrilateral whose vertices are - 1, 0 , 2, 3 , 1, - 2 , and 4, 1 is a rectangle. Geometry Use slopes and the distance formula to show that the quadrilateral whose vertices are 0, 0 , 1, 3 , 4, 2 , and 3, - 1 is a square. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number x of miles driven. What is the cost of renting the truck if the truck is driven miles? Cost Equation The fixed costs of operating a business are the costs incurred regardless of the level of production.

Fixed costs include rent, fixed salaries, and costs of leasing machinery. The variable costs of operating a business are the costs that change with the level of output. Variable costs include raw materials, hourly wages, 42 and electricity. Write a linear equation that relates the daily cost C, in dollars, of manufacturing the jeans to the number x of jeans manufactured. What is the cost of manufacturing pairs of jeans? Write a linear equation that relates the cost C and the number x of miles driven annually. com b Find and interpret the x-intercept of the graph of your equation. c Design requirements stipulate that the maximum run be 30 feet and that the maximum slope be a drop of 1 inch for each 12 inches of run. Will this ramp meet the requirements? d What slopes could be used to obtain the inch rise and still meet design requirements? php a Write a linear equation that relates the monthly charge C, in dollars, to the number x of kilowatt-hours used in a month, 0 … x … b Graph this equation.

c What is the monthly charge for using kilowatthours? d What is the monthly charge for using kilowatthours? e Interpret the slope of the line. Source: Commonwealth Edison Company, March, a Write a linear equation that relates the monthly charge C, in dollars, to the number x of kilowatt-hours used in a month, 0 … x … Measuring Temperature The relationship between Celsius °C and Fahrenheit °F degrees of measuring temperature is linear. Find a linear equation relating °C and °F if 0°C corresponds to 32°F and °C corresponds to °F. Use the equation to find the Celsius measure of 70°F. Measuring Temperature The Kelvin K scale for measuring temperature is obtained by adding to the Celsius temperature. a Write a linear equation relating K and °C. b Write a linear equation relating K and °F see Problem Access Ramp A wooden access ramp is being built to reach a platform that sits 30 inches above the floor.

The ramp drops 2 inches for every inch run. Cigarette Use A report in the Child Trends DataBase indicated that, in , In , a Write a linear equation that relates the percent y of twelfth grade students who smoke cigarettes daily to the number x of years after b Find the intercepts of the graph of your equation. c Do the intercepts have any meaningful interpretation? d Use your equation to predict the percent for the year Is this result reasonable? org Product Promotion A cereal company finds that the number of people who will buy one of its products in the first month that it is introduced is linearly related to the amount of money it spends on advertising. a Write a linear equation that relates the amount A spent on advertising to the number x of boxes the company aims to sell.

b How much advertising is needed to sell , boxes of cereal? c Interpret the slope. Can you draw a conclusion from the graph about each member of the family? Prove that if two nonvertical lines have slopes whose product is - 1 then the lines are perpendicular. Which of the following equations might have the graph shown? More than one answer is possible. m is for Slope The accepted symbol used to denote the slope of a line is the letter m. Investigate the origin of this symbolism. Begin by consulting a French dictionary and looking up the French word monter. Write a brief essay on your findings.

Grade of a Road The term grade is used to describe the inclination of a road. How does this term relate to the notion of slope of a line? Investigate the grades of some mountainous roads and determine their slopes. The figure shows the graph of two parallel lines. Which of the following pairs of equations might have such a graph? The figure shows the graph of two perpendicular lines. Carpentry Carpenters use the term pitch to describe the steepness of staircases and roofs. How does pitch relate to slope? Investigate typical pitches used for stairs and for roofs. Can the equation of every line be written in slope— intercept form? Does every line have exactly one x-intercept and one y-intercept?

Are there any lines that have no intercepts? What can you say about two lines that have equal slopes and equal y-intercepts? What can you say about two lines with the same x-intercept and the same y-intercept? Assume that the x-intercept is not 0. If two distinct lines have the same slope, but different x-intercepts, can they have the same y-intercept? If two distinct lines have the same y-intercept, but different slopes, can they have the same x-intercept? Which form of the equation of a line do you prefer to use? Justify your position with an example that shows that your choice is better than another. Have reasons. What Went Wrong? A student is asked to find the slope of the line joining - 3, 2 and 1, - 4. He states that the 3 slope is. Is he correct? If not, what went wrong? Slope Open the slope applet. Move point B around the Cartesian plane with your mouse. a Move B to the point whose coordinates are 2, 7. What is the slope of the line? b Move B to the point whose coordinates are 3, 6.

Move B to the point whose coordinates are 4, 4. Move B to the point whose coordinates are 4, 1. Move B to the point whose coordinates are 3, - 2. Slowly move B to a point whose x-coordinate is 1. What happens to the value of the slope as the x-coordinate approaches 1? What can be said about a line whose slope is positive? What can be said about a line whose slope is negative? What can be said about a line whose slope is 0? i Consider the results of parts a — c. What can be said about the steepness of a line with positive slope as its slope increases? j Move B to the point whose coordinates are 3, 5. Move B to the point whose coordinates are 5, 6. Move B to the point whose coordinates are - 1, 3.

Consider, for example, the following geometric statement that defines a circle. The fixed distance r is called the radius, and the fixed point h, k is called the center of the circle. Figure 67 shows the graph of a circle. To find the equation, let x, y represent the coordinates of any point on a circle with radius r and center h, k. Then the distance between the points x, y and h, k must always equal r. Notice that the graph of the unit circle is symmetric with respect to the x-axis, the y-axis, and the origin. To graph the equation by hand, compare the given equation to the standard form of the equation of a circle.

The comparison yields information about the circle. The circle has center 1 -3, 22 and a radius of 4 units. To graph this circle, first plot the center 1 -3, Since the radius is 4, locate four points on the circle by plotting points 4 units to the left, to the right, up, and down from the center. These four points can then be used as guides to obtain the graph. Otherwise, the circle will appear distorted. Figure 70 shows the graph on a TI Plus. Solution This is the equation discussed and graphed in Example 2. Subtract 4 from both sides. Apply the Square Root Method. Look back at Figure 69 to verify the approximate locations of the intercepts. If an equation of a circle is in the general form, we use the method of completing the square to put the equation in standard form so that we can identify its center and radius. Solution Group the expression involving x, group the expression involving y, and put the constant on the right side of the equation.

Remember that any number added on the left side of the equation must be added on the right. To graph the equation by hand, use the center 1 -2, 32 and the radius 1. See Figure 71 a. To graph the equation using a graphing utility, solve for y. Graphs Figure 71 b illustrates the graph on a TI Plus graphing calculator. Solution Figure 72 y 3 To find the equation of a circle, we need to know its center and its radius. Here, the center is 11, Since the point 14, is on the graph, the radius r will equal the distance from 14, to the center 11, Given an equation, classify it and graph it.

Given a graph, or information about a graph, find its equation. This text deals with both types of problems. You may study various equations, classify them, and graph them. The second type of problem is usually more difficult to solve than the first. In many instances a graphing utility can be used to solve problems when information about the problem such as data is given. True or False Every equation of the form 5. Skill Building In Problems 7—10, find the center and radius of each circle. Write the standard form of the equation. y 4, 2 2, 3 1, 2 0, 1 2, 1 0, 1 1, 2 x x x 1, 0 x In Problems 11—20, write the standard form of the equation and the general form of the equation of each circle of radius r and center 1h, k2. Graph each circle. Center at the origin and containing the point 1 - 2, 32 Center 11, 02 and containing the point 1 - 3, 22 Center 12, 32 and tangent to the x-axis Center 1 - 3, 12 and tangent to the y-axis With endpoints of a diameter at 11, 42 and 1 - 3, 22 With endpoints of a diameter at 14, 32 and 10, 12 Find the area of the square in the figure.

A weather satellite circles 0. Find the equation for the orbit of the satellite on this map. Find the area of the blue shaded region in the figure, assuming the quadrilateral inside the circle is a square. The tangent line to a circle may be defined as the line that intersects the circle in a single point, called the point of tangency. See the figure. Ferris Wheel The original Ferris wheel was built in by Pittsburgh, Pennsylvania, bridge builder George W. It had a maximum height of feet and a wheel diameter of feet. Find an equation for the wheel if the center of the wheel is on the y-axis. Source: inventors. It has a maximum height of meters and a diameter of meters, with one full rotation taking approximately 30 minutes.

b b c The tangent line is perpendicular to the line containing the center of the circle and the point of tangency. The Greek Method The Greek method for finding the equation of the tangent line to a circle uses the fact that at any point on a circle the lines containing the center and the tangent line are perpendicular see Problem Refer to Problem Find the center of the circle. If a circle of radius 2 is made to roll along the x-axis, what is an equation for the path of the center of the circle? If the circumference of a circle is 6p , what is its radius?

Explain how the center and radius of a circle can be used to graph the circle. Why is this incorrect? Place the cursor on the center of the circle and hold the mouse button. Drag the center around the Cartesian plane and note how the equation of the circle changes. a What is the radius of the circle? b Draw a circle whose center is at 11, What is the equation of the circle? c Draw a circle whose center is at 1 - 1, d Draw a circle whose center is at 1 - 1, - e Draw a circle whose center is at 11, - f Write a few sentences explaining the role the center of the circle plays in the equation of the circle. Place the cursor on point B, press and hold the mouse button. Drag B around the Cartesian plane. a What is the center of the circle? b Move B to a point in the Cartesian plane directly above the center such that the radius of the circle is 5.

c Move B to a point in the Cartesian plane such that the radius of the circle is 4. d Move B to a point in the Cartesian plane such that the radius of the circle is 3. e Find the coordinates of two points with integer coordinates in the fourth quadrant on the circle that result in a circle of radius 5 with center equal to that found in part a. f Use the concept of symmetry about the center, vertical line through the center of the circle, and horizontal line through the center of the circle to find three other points with integer coordinates in the other three quadrants that lie on the circle of radius 5 with center equal to that found in part a. add; 25 2. b The midpoint of the line segment connecting the points. c The slope of the line containing the points. d Then interpret the slope found in part c. Create a table of values to determine a good initial viewing window.

Use a graphing utility to approximate the intercepts. List the intercepts of the following graph. Label the intercepts on the graph. In Problems 16 and 17, use a graphing utility to approximate the solutions of each equation rounded to two decimal places. Slope undefined; containing the point 1 - 3, 42 Containing the points 13, - 42 and 12, 12 Graph each circle by hand. Determine the intercepts of the graph of each circle. Find two numbers y such that the distance from 1 - 3, 22 to 15, y2 is Graph the line with slope containing the point 11, Make up four problems that you might be asked to do given the two points 1 - 3, 42 and 16, Each problem should involve a different concept.

Be sure that your directions are clearly stated. Describe each of the following graphs in the xy-plane. Give justification. and What is the radius of this circle? The endpoints of the diameter of a circle are 1 - 3, 22 and 15, - Find the center and radius of the circle. Write the general equation of this circle. Suppose the points 1 - 2, - 32 and 14, 52 are the endpoints of a line segment. a Find the distance between the two points. b Find the midpoint of the line segment connecting the two points. a Find the slope of the line containing P1 and P2. b Interpret this slope. In Problems 2 and 3, graph each equation by hand by plotting points. Use a graphing utility to approximate the intercepts and label them on the graph. Write the slope—intercept form of the line with slope - 2 containing the point 13, - Write the general form of the circle with center 14, - 32 and radius 5. Graph this circle. Also find a line perpendicular to it containing the point 0, 3. From the graph, it appears that the data follow a linear relation.

Zestimate vs. Sale Price in Oak Park, IL Sale Price thousands of dollars Internet-based Project Determining the Selling Price of a Home Determining how much to pay for a home is one of the more difficult decisions that must be made when purchasing a home. Location, size, number of bedrooms, number of bathrooms, lot size, and building materials are just a few. Fortunately, the website Zillow. com has developed its own formula for predicting the selling price of a home. Examples: triangular matrices with zero diagonal. There are n! orders of 1, The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. Minimum cost at a comer! About us. Textbook Survival Guides. Elite Notetakers. Referral Program.

Campus Marketing Coordinators. Study Guides Homework Help Textbook Solutions Notetakers. Study Guides. Log in Sign Up. Get Full Access to Math - Textbook Survival Guide. Forgot password? Register Now. Join StudySoup for FREE. Already have an account? Login here. Full solutions for Precalculus Enhanced with Graphing Utilities 6th Edition ISBN: Get Full Solutions. Precalculus Enhanced with Graphing Utilities 6th Edition - Solutions by Chapter Get Full Solutions. Chapter 1: Graphs Chapter 1. On the screen you will see a slider. Pay particular attention to the key points matched by color on each graph. For convenience the graph of g1 Chapter 6. Author: Michael Sullivan ISBN:

I don't want to reset my password. Precalculus Enhanced with Graphing Utilities 6th Edition - Solutions by Chapter. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: Since problems from chapters in Precalculus Enhanced with Graphing Utilities have been answered, more than students have viewed full step-by-step answer. This expansive textbook survival guide covers the following chapters: Adjacency matrix of a graph.

Elimination on [A b] keeps equations correct. Constant diagonals wrap around as in cyclic shift S. Eigenvectors in F. Examples: triangular matrices with zero diagonal. There are n! orders of 1, The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. Minimum cost at a comer! About us. Textbook Survival Guides. Elite Notetakers. Referral Program. Campus Marketing Coordinators. Study Guides Homework Help Textbook Solutions Notetakers. Study Guides. Log in Sign Up. Get Full Access to Math - Textbook Survival Guide. Forgot password? Register Now. Join StudySoup for FREE. Already have an account? Login here. Full solutions for Precalculus Enhanced with Graphing Utilities 6th Edition ISBN: Get Full Solutions. Precalculus Enhanced with Graphing Utilities 6th Edition - Solutions by Chapter Get Full Solutions. Chapter 1: Graphs Chapter 1. On the screen you will see a slider. Pay particular attention to the key points matched by color on each graph.

For convenience the graph of g1 Chapter 6. Author: Michael Sullivan ISBN: Key Math Terms and definitions covered in this textbook Adjacency matrix of a graph. Augmented matrix [A b]. Circulant matrix C. Fast Fourier Transform FFT. Indefinite matrix. Minimal polynomial of A. A directed graph that has constants Cl, Nilpotent matrix N. Permutation matrix P. Those extremes are reached at the eigenvectors x for Amin A and Amax A. Schur complement S, D - C A -} B. Appears in block elimination on [~ g ]. Simplex method for linear programming. T- 1 has rank 1 above and below diagonal. Orthonormal columns complex analog of Q. Wavelets Wjk t. COMPANY About us Team Careers Blog STUDY MATERIALS Schools Subjects Textbook Survival Guides RESOURCES Elite Notetakers Referral Program Campus Marketing Coordinators Scholarships SUPPORT Contact FAQ Sitemap.

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Precalculus Enhanced with Graphing Utilities 6th Edition - Solutions by Chapter,Description

PRECALCULUS ENHANCED WITH GRAPHING UTILITIES 6TH EDITION. FISH DISKS 1 AMIGA STUFF MAIN Download the free trial version below to get started Double click the PRECALCULUS ENHANCED WITH GRAPHING UTILITIES 6TH EDITION. FISH DISKS 1 AMIGA STUFF MAIN Download the free trial version below to get started Double click the downloaded file to install the software' 'pearson education mymathlab Enhanced With Graphing Utilities 6th Edition Sullivan Author: blogger.com 6th edition" Precalculus Enhanced with Graphing Utilities. by Michael Sullivan III | Mar 2, out of 5 stars Hardcover $ $ Page 3/ Download Ebook Precalculus Sullivan 6th Edition 09 to rent $ to buy. Get it as soon as Thu, Oct FREE Page 13/89 precalculus-enhanced-with-sullivan-6th-edition-pdf-free Title: Solutions Manual for Precalculus Enhanced with Graphing Utilities 6th Edition by Sullivan: Author: Sullivan" Subject: Solutions Manual for Precalculus Enhanced with Graphi Chapter 1. Graphs -- Chapter 2. Functions and models -- Chapter 3. Polynomial and rational functions -- Chapter 4. Exponential and logarithmic functions -- Chapter 5. Trigonometric Precalculus: Enhanced with Graphing Utilities. Sullivan, Sullivan. 6. th. edition, © HS Binding: • For graphing-intensive courses • NEW! Teacher’s Edition ... read more

Interpret the slope of the line. Some equations can be solved using algebraic techniques that result in exact solutions. See Figure 20 on previous page. True or False The point 1 - 1, 42 lies in quadrant IV of the Cartesian plane. We shall see that functions, like numbers, can be added, subtracted, multiplied, and divided.

Figure 64 Now Work y PROBLEM 59 10 Find Equations of Perpendicular Lines 90° x THEOREM When precalculus enhanced with graphing utilities 6th edition pdf download lines intersect at a right angle 90°they are said to be perpendicular. Begin by graphing Y1. Skill Building In Problems 13 and 14, plot each point in the xy-plane. Table 3 Figure 24 The user can scroll within the table if it is created in AUTO mode. If the graph of an equation is symmetric with respect to the x-axis and 2 is a y-intercept, name another y-intercept. How many of these triangles are possible?