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mathematics
precalculus

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

In Problems 59–66, write an equation for each parabola. -2 У 2 (0, 1) -2 (1, 2) X
Billy hit a baseball with an initial speed of 125 feet per second at an angle of 40° to the horizontal. The ball was hit at a height of 3 feet above the ground.(a) Find parametric equations that model the position of the ball as a function of time.(b) How long was the ball in the air?(c) Determine
Problems 52–61. 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 cos2 x + cos x − 1 = 0, 0 ≤ x < 2π
Problems 52–61. 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 region bounded by the graph ofthe x-axis, and the vertical lines x = 0 and x = 8.
Problems 52–61. 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 v = 10i − 24j, find ||v||.
In Problems 59–66, write an equation for each parabola. -2 У 2 -2 L (2, 1) (1,0) X
Problems 52–61. 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 an arc length of 14 feet subtends a central angle of 105°, what is the radius of the circle?
Formulate a strategy for analyzing and graphing an equation of the form Ax² + Cy2 + Dx + Ey + F = 0
Problems 52–61. 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.A radioactive substance has a half-life of 15 years. How long until there is 40% of a sample remaining?
The hypocycloid is a plane curve defined by the parametric equations(a) Graph the hypocycloid using a graphing utility.(b) Find a rectangular equation of the hypocycloid. x(t) = cos³t y(t) = sin³t 0 ≤ t ≤ 2π
In Problems 59–66, write an equation for each parabola. -2 УА 2 -2 (2,0) (0, -1) 2 X
Problems 52–61. 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 k so that y = sin(kx) has a period of 5π/6.
Explain how your strategy presented in Problem 61 changes if the equation is of the formData from problem 61Formulate a strategy for analyzing and graphing an equation of the form Ax2 + Cy2 + Dx + Ey + F = 0 Ax² + Bxy + Cy2 + Dx + Ey + F = 0
Problems 52–61. 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 vertex form of the quadratic function whose graph has vertex (−3, 8) and y-intercept 5.
In Problems 57–66, find an equation for each ellipse. Graph the equation.Foci at (1, 2) and (−3, 2); vertex at (−4, 2)
In Problems 59–66, write an equation for each parabola. -2 YA 2 (0, 1) AL -2 (2, 2) 2 X
In Problems 51–64, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation.2y2 − x2 + 2x + 8y + 3 = 0
In Problems 69–76, analyze each equation. 2 (x - 3)² 4 y² 25 || 1
Problems 63 – 71. 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.Simplify: (4x²1)8 3(2x + 3)² · 2 − (2x + 3)³ · 8(4x² − 1)².8x [(4x - 1)³]²
Find parametric equations for the circle x2 + y2 = R2 , using as the parameter the slope m of the line through the point (−R, 0) and a general point P = (x, y) on the circle.
In Problems 57–66, find an equation for each ellipse. Graph the equation.Center at (1, 2); focus at (4, 2); contains the point (1, 3)
Problems 63 – 71. 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 graph ofhas an absolute minimum whenWhat is the minimum value rounded to two decimal places?
Problems 63 – 71. 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 horizontal asymptote for the graph of f(x) = 4ex+1 - 5
Problems 63 – 71. 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 triangle: a = 7, b = 9, and c = 11
Find parametric equations for the parabola y = x2, using as the parameter the slope m of the line joining the point (1, 1) to a general point P = (x, y) of the parabola.
Problems 63 – 71. 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 triangle: a = 14, b = 11, C = 30°
Problems 63 – 71. 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 g(x) = √x - 7+2, find g-¹ (3).
In Problems 69–76, analyze each equation. (y + 2)² 16 (x - 2)² 4 = 1
Problems 63 – 71. 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.Transform the equation xy = 1 from rectangular coordinates to polar coordinates.
The Gateway Arch in St. Louis is often mistaken to be parabolic in shape. In fact, it is a catenary, which has a more complicated formula than a parabola. The Arch is 630 feet high and 630 feet wide at its base.(a) Find the equation of a parabola with the same dimensions. Let x equal the horizontal
Research plane curves called hypocycloid and epicycloid. Write a report on what you find. Compare and contrast them to a cycloid.
Problems 67–75. 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.Find the oblique asymptote of R(x) = = 4x²9x + 7 2x + 1
Problems 63 – 71. 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 complex number 2 − 5i in polar form.
Problems 67–75. 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.Graph the equation 3x − 4y = 8 on the xy-plane.
Problems 67–75. 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.Find the difference quotient of f(x) = 1 x + 3 as h→0.
Problems 67–75. 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.Graph y = 2 cos(2x) + sin(x/2) on the xy-plane.
Problems 85 – 94. 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.Givenfind the exact value of each of the remaining trigonometric functions. tan || = من
Suppose that two people standing 2 miles apart both see the burst from a fireworks display. After a period of time the first person, standing at point A, hears the burst. One second later the second person, standing at point B, hears the burst. If the person at point B is due west of the person at
Problems 67–75. 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.The International Space Station (ISS) orbits Earth at a height of approximately 248 miles above the
Problems 63 – 71. 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 log5x + log5 (x − 4) = 1.
Problems 85 – 94. 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 distance between the pointsand (-3 -3, 7|2 2/
Problems 67–75. 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.The displacement d (in meters) of an object at time t (in seconds) is given by d(t) = 2 cos(4t).(a)
In Problems 81–85, use the fact that the orbit of a planet about the Sun is an ellipse, with the Sun at one focus. The aphelion of a planet is its greatest distance from the Sun, and the perihelion is its shortest distance. The mean distance of a planet from the Sun is the length of the semimajor
Problems 85 – 94. 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: 3 tan[cos-¹(-²)]
Extracorporeal shock wave lithotripsy is a procedure that uses shockwaves to fragment kidney stones without the need for surgery. Using an elliptical reflector, a shock wave generator is placed at one focus and the kidney stone is positioned at the other focus. Shock waves pass through a water
Problems 67–75. 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.Find the exact value of cos 285°.
Problems 67–75. 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 log5 (7 − x) + log5 (3x + 5) = log5 (24x).
Problems 91 – 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.Forfind the amplitude, period, phase shift, and vertical shift. = - 2sin(3x f(x) = sin(3x + ) + 5,
Problems 67–75. 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.If f (x) = 1/4 x3+ 1 and g(x) = 3/4 x2, find all numbers c in the interval [0, 2] where g(c) equals the
Show that the graph of an equation of the formwhere A and C are of the same sign, Ax² + Cy² + Dx + Ey + F = 0 A = 0, C = 0 #
Let A be either endpoint of the latus rectum of the parabola y2 − 2y − 8x + 1 = 0, and let V be the vertex. Find the exact distance from A to V.
Problems 85 – 94. 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 x = 9y2 − 36, list the intercepts and test for symmetry.
Problems 91 – 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 rectangular coordinates of the point with the polar coordinates (12, ㅠ 3.
Problems 85 – 94. 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.Expressas a single trigonometric function. 1 + cos 34° 2
A rectangle is inscribed in an ellipse with major axis of length 14 meters and minor axis of length 4 meters. Find the maximum area of a rectangle inscribed in the ellipse. Round your answer to two decimal places.
Problems 85 – 94. 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: 4x+1 = 8x−1
Consider the circle (x − 2)2 + y2 = 1 and the ellipse with vertices at (2, 0) and (6, 0) and one focus at (4 + 3, 0). Find the points of intersection of the circle and the ellipse.
Problems 91 – 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 area of the region enclosed by the graphs of y = √9 x² and y = x + 3.
Problems 85 – 94. 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 standard form of the equation of a circle with radius √6 and center (−12, 7).
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.Find the domain of the rational functionFind any horizontal, vertical, or oblique asymptotes.
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 the right triangle shown. B C 14 52° b
Problems 85 – 94. 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.In 1978, Congress created a gas guzzler tax on vehicles with a fuel economy of less than 22.5 miles
Problems 91 – 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.Solve the triangle described: a = 7, b = 10, and C = 100°
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 2√3 tan (5x) + 7 = 9 for 0 < x <
Problems 85 – 94. 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) = ln(x + 3), find the average rate of change of f from 1 to 5.
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.What value doesapproach as x → −4? R(x) = 3x² + 14x + 8 x² + x - 12
Problems 91 – 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.Transform the polar equation r = 6 sinθ to an equation in rectangular coordinates. Then identify and
Problems 91 – 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.Evaluate cos(sin-¹()).
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.Find the zeros of the quadratic function f (x) = (x − 5)2 − 12. What are the x-intercepts, if any,
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: log: (-1) = 4
Problems 85 – 94. 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 − 5x| − 2 = 4
Problems 91 – 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.What is the inverse function for f (x) = 3ex−1 + 4?
Show that D a C b d
In Problems 1–4, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, state that it is inconsistent. -2x + y = 4x + 3y = -7 9
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.Find the work done by a force of 80 pounds acting in the direction of 50° to the horizontal in moving
In Problems 1–6, solve each equation. √√3x + 1 = 4
Problems 91 – 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.Solve (2x + 3)2 + x2 = 5x(2 + x) + 1.
In Problems 1–4, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, state that it is inconsistent. 1 3* 2y = 1 - 2y 5x - 30y = 18
Problems 91 – 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 midpoint of the line segment connecting the points (3, −8) and (−2, 5).
In Problems 1 – 10, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, state that it is inconsistent. 3x-4y = 4 X x — 3y = - 2
Solve e−2x+1 = 8 rounded to four decimal places.
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.Find the difference quotient of f (x) = 2x2 − 7x as h → 0.
In Problems 1 – 10, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, state that it is inconsistent. X x - 2y - 4 = 0 3x + 2y - 4 = 0
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: (x + 3)2 = 20
Solve the inequality: 3x + 4 < 8 − x
In Problems 1–4, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, state that it is inconsistent. xy + 2z= y + 2z = 5 3x + 4y z = -2 5x + 2y + 3z = 8 -
Solve the equation: 3x + 4 = 8 − x
In Problems 1 – 10, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, state that it is inconsistent. y = 2x - 5 x = 3y + 4
Graph the equation: y + 4 = x2
In Problems 5 – 24, graph each equation of the system. Then solve the system to find the points of intersection. y = x² + 1 y = x + 1
Graph the equation: 3x − 2y = 6
In Problems 1–4, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, state that it is inconsistent. 3x + 2y - 82 8z = -3 2 -х - у + 6x-3y + 15z = 8 3 2 = 1 =
(a) Graph the line: 3x + 4y = 12(b) What is the slope of a line parallel to this line?
In Problems 5 – 16, determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression. 5x +2 x 3 - 1
In Problems 5 – 16, determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression. 2 x²1
Graph the equation: y2 = x2 − 1
In Problems 5 – 24, graph each equation of the system. Then solve the system to find the points of intersection. y = x² + 1 y = 4x + 1
Graph the equation: x2 + y2 = 9.
In Problems 5 – 24, graph each equation of the system. Then solve the system to find the points of intersection. y = y = √36x² 8 - x
In Problems 5 – 16, determine whether the given rational expression is proper or improper. If the expression is improper, rewrite it as the sum of a polynomial and a proper rational expression. x² + 5 2-4

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