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

In Problems 13–32, use the accompanying graph of y = f(x). x = −6 (-4,2) -8 -6 -4 -2 y, 4 2 -2 -4 I 2 (2,3) 6 (6,2) X
In Problems 9–42, find each limit algebraically. x² 2 - 4 lim x=0x² + 4 X
In Problems 13–32, use the accompanying graph of y = f(x).Does exist? If it does, what is it? x = −6 (-4,2) -8 -6 -4 -2 y, 4 2 -2 -4 I 2 (2,3) 6 (6,2) X
In Problems 13–32, use the accompanying graph of y = f(x).Does exist? If it does, what is it? x-0 x = −6 (-4,2) -8 -6 -4 -2 y, 4 2 -2 -4 I 2 (2,3) 6 (6,2) X
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. x 10. ⁰y5
In Problems 19 – 26, factor the difference of two squares.36x2 − 9
In Problems 11 – 68, solve each equation. y 5 5 2у
In Problems 19 – 36, perform the indicated operation and simplify the result. Leave your answer in factored form. 6х x2 - 4 3x - 9 2x + 4
In Problems 19 – 28, tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 10z²+z 2
In Problems 9–42, find each limit algebraically. lim (3x - 2)5/2 x→2
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 4. x⁹y7 xy3
In Problems 19 – 36, perform the indicated operation and simplify the result. Leave your answer in factored form. 12x 5x + 20 4x² 2 x²16 2
In Problems 19 – 28, tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. x² + 5 2 x³ - 1 3
In Problems 11–48, write each expression in the standard form a + bi. 2-i -2i
In Problems 9–42, find each limit algebraically. lim (2x + 1) 5/3 x-1
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. X 3хуг 81x4y2
In Problems 23–42, graph each function. Use the graph to investigate the indicated limit. limf(x), f(x) = 3√x
In Problems 21–32, find the derivative of each function at the given number.f (x) = 2x3 − x2 at 2
In Problems 23–30, an integral is given.(a) What area does the integral represent?(b) Graph the function, and shade the region represented by the integral.(c) Use a graphing utility to approximate this area. π/4 S -T/4 cosx dx
In Problems 19 – 28, tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 3x3 + 2x - 1 x2 + x +1
In Problems 19 – 36, perform the indicated operation and simplify the result. Leave your answer in factored form. 8x x²-1 2 10x x + 1 X
In Problems 11–48, write each expression in the standard form a + bi. 6 - i 1 + i
In Problems 11 – 68, solve each equation.(x + 2)(x − 3) = (x − 3)2
In Problems 9–42, find each limit algebraically. x²4 2 lim x-2x² - 2x
In Problems 23–42, graph each function. Use the graph to investigate the indicated limit. lim f(x), f(x) = sinx x-π/2
In Problems 25–32, write each inequality using interval notation, and illustrate each inequality using the real number line. x ≥ 4
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. √36x
In Problems 23–30, an integral is given.(a) What area does the integral represent?(b) Graph the function, and shade the region represented by the integral.(c) Use a graphing utility to approximate this area. 2 S²ex dx
In Problems 19 – 36, perform the indicated operation and simplify the result. Leave your answer in factored form. x 2 4x x² - 4x + 4 2 X 12x
In Problems 11–48, write each expression in the standard form a + bi. 2 + 3i 1- i
In Problems 11 – 68, solve each equation.z(z2 + 1) = 3 + z3
In Problems 13–22, a function f is nonnegative and continuous on an interval [a, b].(a) Graph f, indicating the area A under f from a to b.(b) Approximate the area A by partitioning [a, b] into four subintervals of equal width and choosing u as the left endpoint of each subinterval.(c)
In Problems 16 – 27, use the accompanying graph of y = f (x). (-6, 2) | -6 م (-2,2) .(-4,1) -2 -4 ۷۸ 4 2 -O-2 -4 2 ا 4 ه X
In Problems 11 – 68, solve each equation. 1 2 X - 4 = 3 -X
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 3/192x5
In Problems 11–22, use U = universal set = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 3, 4, 5, 9}, B = {2, 4, 6, 7, 8}, and C = {1, 3, 4, 6} to find each set. Bnc C
In Problems 19–24, an inequality is given. Write the inequality obtained by:(a) Adding 3 to each side of the given inequality.(b) Subtracting 5 from each side of the given inequality.(c) Multiplying each side of the given inequality by 3.(d) Multiplying each side of the given inequality by
In Problems 19 – 26, factor the difference of two squares.9x2 − 1
In Problems 13–22, a function f is nonnegative and continuous on an interval [a, b].(a) Graph f, indicating the area A under f from a to b.(b) Approximate the area A by partitioning [a, b] into four subintervals of equal width and choosing u as the left endpoint of each subinterval.(c)
In Problems 19 – 28, use synthetic division to determine whether x − c is a factor of the given polynomial.4x4 − 15x2 − 4; x − 2
In Problems 11 – 68, solve each equation. 1-1/2 x x = 5
In Problems 16 – 27, use the accompanying graph of y = f (x). (-6, 2) | -6 م (-2,2) .(-4,1) -2 -4 ۷۸ 4 2 -O-2 -4 2 ا 4 ه X
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 4/243
In Problems 19–24, an inequality is given. Write the inequality obtained by:(a) Adding 3 to each side of the given inequality.(b) Subtracting 5 from each side of the given inequality.(c) Multiplying each side of the given inequality by 3.(d) Multiplying each side of the given inequality by
In Problems 19 – 26, factor the difference of two squares.x2 − 16
In Problems 16 – 27, use the accompanying graph of y = f (x). (-6, 2) | -6 م (-2,2) .(-4,1) -2 -4 ۷۸ 4 2 -O-2 -4 2 ا 4 ه X
In Problems 19 – 36, perform the indicated operation and simplify the result. Leave your answer in factored form. 4x - 8 -3x 12 12 - 6х
In Problems 11 – 68, solve each equation.0.9t = 0.4 + 0.1t
In Problems 21–32, find the derivative of each function at the given number.f (x) = 2x2 + 1 at −1
In Problems 19–24, an inequality is given. Write the inequality obtained by:(a) Adding 3 to each side of the given inequality.(b) Subtracting 5 from each side of the given inequality.(c) Multiplying each side of the given inequality by 3.(d) Multiplying each side of the given inequality by −2.1
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 4/48x5
Repeat Problem 23 for the coordinatesData from problem 23On the real number line, label the points with coordinates 0, -2, 2, -1.5, 2, and 23
In Problems 19 – 26, factor the difference of two squares.x2 − 25
In Problems 19 – 28, tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. X +2
In Problems 11 – 68, solve each equation.0.9t = 1 + t
In Problems 19 – 36, perform the indicated operation and simplify the result. Leave your answer in factored form. 6x - 27 5x 2 4x 18
In Problems 16 – 27, use the accompanying graph of y = f (x). (-6, 2) | -6 م (-2,2) .(-4,1) -2 -4 ۷۸ 4 2 -O-2 -4 2 ا 4 ه X
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. √√x12 y8
In Problems 25–34, replace the question mark by < ,> or =, whichever is correct. ? 0
In Problems 19 – 26, factor the difference of two squares.25x2 − 4
In Problems 11 – 68, solve each equation. 2 y + y = 3
In Problems 19 – 28, tell whether the expression is a polynomial. If it is, give its degree. If it is not, state why not. 2y³ -√2
In Problems 19 – 36, perform the indicated operation and simplify the result. Leave your answer in factored form. x2 – 3x – 10 x2 + 2x – 35 + 4x – 21 + x2 + 9x + 14 x2
In Problems 19 – 36, perform the indicated operation and simplify the result. Leave your answer in factored form. x2 x²+x-6 x² + 4x 5 - x² - 25 x² + 2x 15 -
In Problems 9–42, find each limit algebraically. 3x + 4 lim x=2x² + x
In Problems 23–42, graph each function. Use the graph to investigate the indicated limit. limf(x), f(x) = 1 x2
In Problems 33–44, find the one-sided limit. lim (4- 2x) x-2-
In Problems 27 – 36, factor the perfect squares.9x2 + 6x + 1
In Problems 11 – 68, solve each equation. 3 2x - 3 || 2 x + 5
In Problems 19 – 36, perform the indicated operation and simplify the result. Leave your answer in factored form. 2x² - x - 28 3x² - x - 2 - 4x2 + 16x +7 3x2 + 11x + 6
In Problems 9–42, find each limit algebraically. (x + 1)² lim x-1 x² - 1
In Problems 33–42, use a graphing utility to approximate the derivative of each function at the given number. f(x) = -x³ + 1 x2+5x +7 at 8
In Problems 29 – 48, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form.(10x5 − 8x2) + (3x3 − 2x2 + 6)
In Problems 11 – 54, simplify each expression. Assume that all variables are positive when they appear. 2 ( 5 29 )²
In Problems 33–44, find the one-sided limit. lim (2x³ + 5x) x-1-
In Problems 23–42, graph each function. Use the graph to investigate the indicated limit. lim f(x), f(x) = { x² 2x if x ≥ 0 if x < 0
In Problems 11–48, write each expression in the standard form a + bi.i23
In Problems 33–40, write each interval as an inequality involving x, and illustrate each inequality using the real number line.(−3, −2)
In Problems 27 – 36, factor the perfect squares.16x2 + 8x + 1
In Problems 29 – 48, add, subtract, or multiply, as indicated. Express your answer as a single polynomial in standard form.(x2 − 3x + 1) + 2(3x2 + x − 4)
In Problems 79–86, solve each system of equations using any method you wish. 2x+3y-z = -2 7= 4x + 3z = 6 бу - 27 = 2
In Problems 79–86, solve each system of equations using any method you wish. x-2y + 4z = 2 -3x+5y-2z = 17 4x-3y =-22
Solve for x and y in terms of a ≠ 0 and b ≠ 0: + ४/० b² || y - ²/² = b + a a² + b² a²b² a+b ab
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.Writein rectangular form x + yi and in exponential form reiθ. |√6( cos 57 5T 12 S7)/²* 12 + i sin
Iffind a and b so that A2 + A = 0. A = a b b a
Refer to Problem 68. Show that the complex nth roots of a nonzero complex number w are equally spaced on the circle.Data from problem 68Use the result of Problem 67 to draw the conclusion that each complex nth root lies on a circle with center at the origin. What is the radius of this circle?Data
A Broadway theater has 500 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $150, main seats for $135, and balcony seats for $110. If all the seats are sold, the gross revenue to the theater is $64,250. If all the main and balcony seats are sold, but only half 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.Find the average rate of change of f (x) = cos−1x from x = −1/2 to x = 1/2.
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 an equation of the hyperbola with vertices (4, 1) and (4, 9) and foci (4, 0) and (4, 10).
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 area of the triangle with vertices at ( 0, 5) , (3, 9) , and ( 12, 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.What is the amount that results if $2700 is invested at 3.6% compounded monthly for 3 years?
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 average rate of change of f (x) = sin−1x from x = −1 to x = 1.
Suppose you are the manager of a sheet metal shop. A customer asks you to manufacture 10,000 boxes, each box being open on top. The boxes are required to have a square base and a 9-cubic-foot capacity. You construct the boxes by cutting out a square from each corner of a square piece of sheet metal
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 for f (x) = −1/x2. Express the answer as a single fraction.
Problems 103–112. 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: 7x2 = 8 − 6x
Problems 104 – 113. 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 a polynomial with minimum degree and leading coefficient 1 that has zeros x = 3 (multiplicity
Problems 103–112. 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 with slope −2/5 that contains the point (10, −7).
Problems 104 – 113. 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 = −2i − j and w = 2i + j, find the dot product v · w and the angle between v and w .
Problems 103–112. 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 cotθ= 24/7 and cosθ < 0, find the exact value of each of the remaining trigonometric
Problems 103–112. 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 straight trail with uniform inclination leads from a hotel, elevation 5300 feet, to a lake in the

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