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mathematics
precalculus
Precalculus 9th edition Michael Sullivan - Solutions
Dan receives $375 per week for selling new and used cars at a car dealership in Oak Lawn, Illinois. In addition, he receives 5% of the profit on any sales that he generates. Write a linear equation that represents Dan’s weekly salary S when he has sales that generate a profit of x dollars.
Florida Power & Light Company supplies electricity to residential customers for a monthly customer charge of $5.69 plus 8.48 cents per kilowatt-hour for up to 1000 kilowatt-hours.(a) Write a linear equation that relates the monthly charge C, in dollars, to the number x of kilowatt-hours used in
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 100°C corresponds to 212°F. Use the equation to find the Celsius measure of 70°F.
The Kelvin (K) scale for measuring temperature is obtained by adding 273 to the Celsius temperature.(a) Write a linear equation relating K and °C.(b) Write a linear equation relating K and °F (see Problem 121).Data from problem 121The relationship between Celsius (°C) and Fahrenheit (°F)
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 25-inch run.(a) Write a linear equation that relates the height y of the ramp above the floor to the horizontal distance x from the platform.(b) Find and interpret the
A report in the Child Trends DataBase indicated that, in 1996, 22.2% of twelfth grade students reported daily use of cigarettes. In 2006, 12.2% of twelfth grade students reported daily use of cigarettes.(a) Write a linear equation that relates the percent y of twelfth grade students who smoke
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. If it spends $40,000 on advertising, then 100,000 boxes of cereal will be sold, and if it spends $60,000,
Show that the line containing the points (a, b) and (b, a), a ≠ b, is perpendicular to the line y = x. Also show that the midpoint of (a, b) and (b, a) lies on the line y = x.
The equation 2x – y = C defines a family of lines, one line for each value of C. On one set of coordinate axes, graph the members of the family when C = -4, C = 0, and C = 2.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. Refer to Figure 47 and use the converse of the PythagoreanTheorem.
Which of the following equations might have the graph shown? (More than one answer is possible.)(a) 2x + 3y = 6(b) 2x €“ 3y = 6(c) 3x + 4y = 12(d) x - y = 1(e) x - y = -1(f) y = -2x - 1(g) y = -1/2x + 10(h) y = x + 4 УА
Can the equation of every line be written in slope–intercept form? Why?
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 y-intercept, but different slopes, can they have the same x-intercept?
A student is asked to find the slope of the line joining (-3, 2) and (1, -4). He states that the slope is 3/2. Is he correct? If not, what went wrong?
Poverty thresholds are determined by the U.S. Census Bureau. A poverty threshold represents the minimum annual household income for a family not to be considered poor. In 1998, the poverty threshold for a family of four with two children under the age of 18 years was $16,530. In 2008, the poverty
In problem, list the intercepts and test for symmetry.y = x2 + 4
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer Perpendicular to the line y = 2x – 3; containing the point (1, -2)
The figure illustrates how net sales of Wal-Mart Stores, Inc., have grown from 2002 through 2008. Use the midpoint formula to estimate the net sales of Wal-Mart Stores, Inc., in 2005. How does your result compare to the reported value of $282 billion? Wal-Mart Stores, Inc. Net sales (in $ billions)
In problem, list the intercepts and test for symmetry.y = x2 - 3x - 4
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer Perpendicular to the line y = ½ x + 4; containing the point (1, -2)
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
In problem, list the intercepts and test for symmetry.y = x4 - 1
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer Parallel to the line y = 5; containing the point (4, 2)
A hot-air balloon, headed due east at an average speed of 15 miles per hour and at a constant altitude of 100 feet, passes over an intersection (see the figure).Find an expression for the distance d (measured in feet) from the balloon to the intersection t seconds later. East 15 mph 100 ft
In problem, list the intercepts and test for symmetry.y = x3 - 27
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer Parallel to the line x = 5; containing the point (4, 2)
A Dodge Neon and a Mack truck leave an intersection at the same time.The Neon 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.
Suppose that you have a rectangular field that requires watering.Your watering system consists of an arm of variable length that rotates so that the watering pattern is a circle. Decide where to position the arm and what length it should be so that the entire field is watered most efficiently.When
In problem, list the intercepts and test for symmetry.4x2 + y2 = 4
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer Parallel to the line x - 2y = -5; containing the point (0, 0)
Refer to Problem 60. 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.(a) What are the
What Went Wrong? A student stated that the center and radius of the graph whose equation is (x + 3)2 + (y - 2)2 = 16 are (3, -2) and 4, respectively. Why is this incorrect?
In problem, list the intercepts and test for symmetry.9x2 + 4y2 = 36
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer Parallel to the line 2x - y = -2; containing the point (0, 0)
Refer to Problem 59. Overlay a rectangular coordinate system on a major 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.(a) What are the
In problem, list the intercepts and test for symmetry.x2 - y - 4 = 0
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer Parallel to the line y = -3x; containing the point (-1, 2)
The layout of a Little League playing field is a square, 60 feet on a side. How far is it directly from home plate to second base (the diagonal of the square)?
Which of the following equations might have the graph shown?(a) (x - 2)2 + = 3(b) (x + 2) 2 + y2 = 3(c) x2 + (y - 2) 2 = 3(d) (x + 2) 2 + y2 = 4(e) x2 + y2 + 10x + 16 = 0f) x2 + y2 + 10x - 2y = 1(g) x2 + y2 + 9x + 10 = 0(h) x2 + y2 - 9x - 10 = 0 Уд
In problem, list the intercepts and test for symmetry.x2 + y - 9 = 0
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer Parallel to the line y = 2x; containing the point (-1, 2)
A major league baseball €œdiamond€ is actually a square, 90 feet on a side (see the figure).What is the distance directly from home plate to second base (the diagonal of the square)? 2nd base 90 ft Pitching rubber 3rd base 90 ft 1st base -Home plate
Which of the following equations might have the graph shown?(a) (x - 2)2 + (y + 3) 2 = 13(b) (x - 2) 2 + (y - 2) 2 = 8(c) (x - 2) 2 + (y - 3) 2 = 13(d) (x + 2) 2 (y - 2) 2 = 8(e) x2 + y2 - 4x - 9y = 0(f) x2 + y2 + 4x - 2y = 0(g) x2 + y2 - 9x - 4y = 0(h) x2 + y2 -
In problem, list the intercepts and test for symmetry.y = 5√x
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer Vertical; containing the point (4, -5)
In problem, find the length of each side of the triangle determined by the three points and . State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.)P1 = (7, 2); P2 =
If the circumference of a circle is 6p, what is its radius?
In problem, list the intercepts and test for symmetry.y = 3√x
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer Horizontal; containing the point (-3, 2)
In problem, find the length of each side of the triangle determined by the three points and . State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.)P1 = (-2, -1); P2 =
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?
In problem, list the intercepts and test for symmetry.y2 = x + 9
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer Slope undefined; containing the point (3, 8)
In problem, find the length of each side of the triangle determined by the three points and . State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.)P1 = (-1, 4); P2 =
Find an equation of the line containing the centers of the two circlesx2 + y2 – 4x + 6y + 4 = 0andx2 + y2 + 6x + 4y + 9 = 0
In problem, list the intercepts and test for symmetry.y2 = x + 4
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer Slope undefined; containing the point (2, 4)
In problem, find the length of each side of the triangle determined by the three points and . State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.)P1 = (2, 1); P2 =
Refer to Problem 52.The line x €“ 2y + 4 = 0 is tangent to a circle at (0, 2).The line y = 2x €“ 7 is tangent to the same circle at (3, -1). Find the center of the circle.Data from problem 52The tangent line to a circle may be defined as the line that intersects the circle in a
In problem, draw a complete graph so that it has the type of symmetry indicated.y-axis YA(0, 4) (2, 2) (0, 0) -3 -2
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer x-intercept = -4; y-intercept = 4
Geometry Verify that the points (0, 0), (a, 0), and (a/2, √3a/2) are the vertices of an equilateral triangle. Then show that the midpoints of the three sides are the vertices of a second equilateral triangle (refer to Problem 52).Data from problem 52An equilateral triangle is one in which all
Use the Greek method described in Problem 53 to find an equation of the tangent line to the circle x2 + y2 €“ 4x + 6y + 4 = 0 at the point (3, 2ˆš2 - 3).Data form problem 53The Greek method for finding the equation of the tangent line to a circle uses the fact that at any point
In problem, draw a complete graph so that it has the type of symmetry indicated.Origin Уд 4- E, 2) (п, 0) (0, 0), х -4
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer x-intercept = 2; y-intercept = -1
Geometry Find the midpoint of each diagonal of a square with side of length s. Draw the conclusion that the diagonals of a square intersect at their midpoints.Use (0, 0), (0, s), (s, 0), and (s, s) as the vertices of the square.
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 52). Use this method to find an equation of the tangent line to the circle x2+ y2= 9 at the point
In problem, draw a complete graph so that it has the type of symmetry indicated.x-axis Уд 5 (5, 3) (0, 2) (-4, 0), -5
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer Slope = -2; y-intercept = -2
Geometry An equilateral triangle is one in which all three sides are of equal length. If two vertices of an equilateral triangle (0, 4) are (0,0), and find the third vertex. How many of these triangles are possible?
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.If the equation of the circle is and the equation of the tangent line is, show that:If the equation of the circle is x2 + y2 = r2 and the equation of
In problem, draw a complete graph so that it has the type of symmetry indicated.y-axis -9 (2, –5) -9(0, –9)
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you preferSlope = -3; y-intercept = 3
Geometry The medians of a triangle are the line segments from each vertex to the midpoint of the opposite side (see the figure). Find the lengths of the medians of the triangle with vertices at A = (0, 0), B = (6, 0), and C = (4, 4). Median Midpoint B
The endpoints of the diameter of a circle are (-3, 2) and (5, -6). Find the center and radius of the circle. Write the standard equation of this circle.
Earth is represented on a map of a portion of the solar system so that its surface is the circle with equation x2+ y2+ 2x + 4y €“ 4091 = 0 .A weather satellite circles 0.6 unit above Earth with the center of its circular orbit at the center of Earth. Find the equation for the orbit of the
In 2008, the Singapore Flyer opened as the world€™s largest Ferris wheel. It has a maximum height of 165 meters and a diameter of 150 meters, with one full rotation taking approximately 30 minutes. Find an equation for the wheel if the center of the wheel is on the y-axis. க ப இ்
In problem, the graph of an equation is given.(a) Find the intercepts.(b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin. 4 -4 4 -4
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you preferContaining the points (-3, 4) and (2, 5)
The midpoint of the line segment from P1 to P2 is (5, -4). If, P1 = (7, -2) what is P2?
The original Ferris wheel was built in 1893 by Pittsburgh, Pennsylvania, bridge builder George W.Ferris. The Ferris wheel was originally built for the 1893 World’s Fair in Chicago, but was also later reconstructed for the 1904 World’s Fair in St. Louis. It had a maximum height of 264 feet and a
In problem, the graph of an equation is given.(a) Find the intercepts.(b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin. -2 -8 2.
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you preferContaining the points (1, 3) and (-1, 2)
The midpoint of the line segment from P1 to P2 is (-1, 4). If, P1 = (-3, 6) what is P2?
Show that the points , andare the vertices of a right triangle in two ways:(a) By using the converse of the Pythagorean Theorem(b) By using the slopes of the lines joining the vertices
Find the area of the blue shaded region in the figure, assuming the quadrilateral inside the circle is a square. Yt x2 + y2 = 36
In problem, the graph of an equation is given.(a) Find the intercepts.(b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin. Ул -3 3 X -3
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you preferSlope = 1/2 containing the point (3, 1)
Find all points on the y-axis that are 6 units from the point (4, -3).
Show that the points A = (3, 4), B = (1, 1), and C = (-2, 3) are the vertices of an isosceles triangle.
Find the area of the square in the figure. х2 + у2 %3D 9
In problem, the graph of an equation is given.(a) Find the intercepts.(b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin. Ул 3 3 x -3 -3
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you preferSlope = - 2/3; containing the point (1, -1)
Find all points on the x-axis that are 6 units from the point (4, -3).
Graph the line with slope 2/3 containing the point (1, 2).
In problem, the graph of an equation is given.(a) Find the intercepts.(b) Indicate whether the graph is symmetric with respect to the x-axis, the y-axis, or the origin. 40 -6 -40-
In problem, find an equation for the line with the given properties. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you preferSlope = 2; containing the point (4, -3)
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