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College Algebra 11th Edition Michael Sullivan, Michael Sullivan III - Solutions
In Problems 17–26, analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it. 9 + = 1 25
In Problems 17–26, analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it. x2 + 16 = 1
In Problems 21–38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation. Focus at (0, -1); directrix the line y = 1
In Problems 21–38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation. Directrix the line y || 1 ; vertex at (0, 0) 2'
In Problems 21–38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation. Directrix the line x 1 2² vertex at (0, 0)
In Problems 27–38, find an equation for each ellipse. Graph the equation. Foci at (0, 2); length of the major axis is 8
In Problems 27–38, find an equation for each ellipse. Graph the equation. Focus at (-4, 0); vertices at (±5, 0)
In Problems 27–38, find an equation for each ellipse. Graph the equation. Foci at (±2,0); length of the major axis is 6
In Problems 17–26, analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it.x2 + 9y2 = 18
In Problems 17–26, analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it.4y2 + x2 = 8
In Problems 27–38, find an equation for each ellipse. Graph the equation. Focus at (0, -4); vertices at (0, ±8)
In Problems 17–26, analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it.4y2 + 9x2 = 36
In Problems 27–38, find an equation for each ellipse. Graph the equation. Foci at (0, 3); x-intercepts are ±2
In Problems 17–26, analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it.x2 + y2 = 16
In Problems 17–26, analyze each equation. That is, find the center, vertices, and foci of each ellipse and graph it.x2 + y2 = 4
In Problems 27–38, find an equation for each ellipse. Graph the equation. Center at (0, 0); vertex at (0, 4); b = 1
In Problems 39–42, find an equation for each ellipse. (-1, 1) -3 3 -3 3 x
In Problems 39–42, find an equation for each ellipse. -3 (-1,-1)" y 3 3 x
In Problems 39–42, find an equation for each ellipse. -3 УА 3 -3 (1, 0) 3 х
In Problems 21–38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation.Vertex at (3, 0); focus at (3, -2)
In Problems 21–38, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation.Focus at (2, 4); directrix the line x -4
In Problems 39–42, find an equation for each ellipse. -3 У 3 (0, 1) -3 3 x
In Problems 73–88, use the given function f.f(x) = ln(x - 3) (a) Find the domain of f (d) Find f¹, the inverse of f (b) Graph f (c) From the graph, determine the range and any asymptotes of f (e) Find the domain and the range of f-¹. (f) Graph f-¹.
In Problems 65–84, solve each equation. 4x² = 2
You have just contracted to buy a house and will seek financing in the amount of $100,000. You go to several banks. Bank 1 will lend you $100,000 at the rate of 4.125% amortized over 30 years with a loan origination fee of 0.45%. Bank 2 will lend you $100,000 at the rate of 3.375% amortized over 15
In Problems 55–72, the function f is one-to-one. (a) Find its inverse function f-1 and check your answer. (b) Find the domain and the range of f and f-1. f(x) = 2√x + 3-5
In Problems 71–78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. log√27
In Problems 71–78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. log1/2 15
In Problems 71–78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. log1/3 71
In Problems 65–84, solve each equation. 5x+3 1 5
In Problems 55–72, the function f is one-to-one. (a) Find its inverse function f-1 and check your answer. (b) Find the domain and the range of f and f-1. f(x)=√x²³ +13
In Problems 55–72, the function f is one-to-one. (a) Find its inverse function f-1 and check your answer. (b) Find the domain and the range of f and f-1 . f(x) = (x - 1)² + 2, x ≥ 1
In Problems 73–86, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.ex = -x
In Problems 55–72, the function f is one-to-one. (a) Find its inverse function f-1 and check your answer. (b) Find the domain and the range of f and f-1. f(x) = √√x5-2
In Problems 65–84, solve each equation.8-x+11 = 162x
In Problems 65–84, solve each equation. 4 X 1 64
In Problems 55–72, the function f is one-to-one. (a) Find its inverse function f-1 and check your answer. (b) Find the domain and the range of f and f-1 . f(x) = x² + 5
In Problems 45–72, solve each exponential equation. Express irrational solutions in exact form. 2.49 +11.7% + 5 = 0
In Problems 57–70, write each expression as a single logarithm. 2 log₂ (x + 1) = log₂ (x + 3) = log₂ (x - 1) - -
In Problems 57–70, write each expression as a single logarithm. 3 logs (3x + 1) - 2 logs (2x - 1) - logs x
In Problems 65–84, solve each equation.3x3 = 9x
In Problems 65–84, solve each equation. 1 25
In Problems 65–84, solve each equation. 3* = 81
In Problems 45–72, solve each exponential equation. Express irrational solutions in exact form. 3.4 +4.2 + 8 = 0
In Problems 57–70, write each expression as a single logarithm. 1 log(x³ + 1) + -log(x² + 1)
In Problems 55–72, the function f is one-to-one. (a) Find its inverse function f-1 and check your answer. (b) Find the domain and the range of f and f-1 . f(x) = x³ - 4₁ x ≥ 0 4,
Traders often buy foreign currency in the hope of making money when the currency’s value changes. For example, on April 10, 2018, one U.S. dollar could purchase 0.8101 euro, and one euro could purchase 132.317 yen. Let f(x) represent the number of euros you can buy with x dollars, and let g(x)
In Problems 71–78, use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places.log5 18
In Problems 65–84, solve each equation.32x-5 = 9
In Problems 45–72, solve each exponential equation. Express irrational solutions in exact form. 25 8.5 = -16 -
In Problems 57–70, write each expression as a single logarithm. 2 loga (5x³) 2 loga (2x + 3)
In Problems 65–84, solve each equation. 5 = 56
The following data represent the average in-state tuition and fees (in 2017 dollars) at public four-year colleges and universities in the United States from the academic year 1990–91 to the academic year 2017–18. (a) Using a graphing utility, draw a scatter plot with academic year as the
In Problems 57–70, write each expression as a single logarithm. 8 log2 √3x - 2 - log2 + log₂ 4
In Problems 57–70, write each expression as a single logarithm. 21 log3 √x + log3 (9x²) - log3 9
In Problems 65–84, solve each equation.2-x = 16
In Problems 57–64, begin with the graph of y = ex (Figure 27) and use transformations to graph each function. Determine the domain, range, horizontal asymptote, and y-intercept of each function.f(x) = 7 - 3e2x (-1,-¹) y = 0 (-2,-2) Figure 27 y = ex YA 6 3 (2, e²) (1, e) (0, 1) 3 X
In Problems 55–72, the function f is one-to-one. (a) Find its inverse function f-1 and check your answer. (b) Find the domain and the range of f and f-1. f(x) 3x + 4 2x - 3
In Problems 61–64, graph each function and its inverse on the same set of axes. f(x) = (-/-)²; ƒ^¹ (x) 51/2 X
In Problems 57–70, write each expression as a single logarithm. 7x log (x² + 2x - 3) - log(+²+7+2+6) x² - 4 x
In Problems 57–70, write each expression as a single logarithm. in (₁ x ₁ ) + ²m ( x + ¹) = ¹ ( x + ¹) - In (x² - 1) In In - X
In Problems 57–64, begin with the graph of y = ex (Figure 27) and use transformations to graph each function. Determine the domain, range, horizontal asymptote, and y-intercept of each function.f(x) = 2 - e-x/2 (-1,-¹) y = 0 (-2,-2) Figure 27 y = ex YA 6 3 (2, e²) (1, e) (0, 1) 3 X
In Problems 57–70, write each expression as a single logarithm. log(x² + 3x + 2) - 2 log(x + 1)
Problems 63–66 involve zero-coupon bonds. A zero-coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it matures; no interest payments are made.If Pat pays $15,334.65 for a $25,000 face-value, zero-coupon bond that matures in 8 years, what is his
In Problems 55–72, the function f is one-to-one. (a) Find its inverse function f-1 and check your answer. (b) Find the domain and the range of f and f-1. f(x) = 3x + 1 X
In Problems 55–72, the function f is one-to-one. (a) Find its inverse function f-1 and check your answer. (b) Find the domain and the range of f and f-1 . f(x) = 2x 3x - 1
In Problems 65–84, solve each equation.6x = 65
Problems 57–62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3%, then $1000 worth of purchasing power now will have only $970 worth of purchasing power in 1 year because 3% of the
In Problems 45–72, solve each exponential equation. Express irrational solutions in exact form.16x + 4x+1 - 3 = 0
In Problems 45–72, solve each exponential equation. Express irrational solutions in exact form. ex+3 x
Problems 63–66 involve zero-coupon bonds. A zero-coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it matures; no interest payments are made.How much should a $10,000 face-value, zero-coupon bond, maturing in 10 years, be sold for now if its rate of
In Problems 57–70, write each expression as a single logarithm. loga + log2| X 1 2 +
Problems 57–62 require the following discussion. Inflation is a term used to describe the erosion of the purchasing power of money. For example, if the annual inflation rate is 3%, then $1000 worth of purchasing power now will have only $970 worth of purchasing power in 1 year because 3% of the
In Problems 57–70, write each expression as a single logarithm. log4 (x² - 1) - 5 log4(x + 1)
In Problems 45–72, solve each exponential equation. Express irrational solutions in exact form.22x + 2x+2 - 12 = 0
Problems 63–66 involve zero-coupon bonds. A zero-coupon bond is a bond that is sold now at a discount and will pay its face value at the time when it matures; no interest payments are made.A child’s grandparents are considering buying an $80,000 face-value, zero-coupon bond at her birth so that
In Problems 57–70, write each expression as a single logarithm. log3 √x - log3 x³
In Problems 45–72, solve each exponential equation. Express irrational solutions in exact form. 1-x = et
In Problems 55–72, the function f is one-to-one. (a) Find its inverse function f-1 and check your answer. (b) Find the domain and the range of f and f-1. f(x) 2x x 1
In Problems 55–72, the function f is one-to-one. (a) Find its inverse function f-1 and check your answer. (b) Find the domain and the range of f and f-1. f(x) 3x x + 2
In Problems 45–72, solve each exponential equation. Express irrational solutions in exact form.32x + 3x+1 - 4 = 0
In Problems 57–70, write each expression as a single logarithm. 2 log3 u log3 V
In Problems 51–58, use a calculator to evaluate each expression. Round your answer to three decimal places. log 15 + log 20 In 15 + In 20
In Problems 55–72, the function f is one-to-one. (a) Find its inverse function f-1 and check your answer. (b) Find the domain and the range of f and f-1. f(x) 4 2-x
In Problems 57–70, write each expression as a single logarithm. 3 log5 u + 4 log5 v
In Problems 55–72, the function f is one-to-one. (a) Find its inverse function f-1 and check your answer. (b) Find the domain and the range of f and f-1. f(x) = 2 3 + x
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. In [5x² V/1-x X 4(x + 1)² 0
In Problems 45–72, solve each exponential equation. Express irrational solutions in exact form. 413 1-x = 5x =
In Problems 45–72, solve each exponential equation. Express irrational solutions in exact form.0.31+x = 1.72x-1
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. In 5x V1 + 3x (x-4)³ x > 4
In Problems 45–72, solve each exponential equation. Express irrational solutions in exact form. 5 X = 71-x
In Problems 45–56, use transformations to graph each function. Determine the domain, range, horizontal asymptote, and y-intercept of each function.f(x) = 1 - 2-x/3
In 2018, the federal debt was about $21 trillion. In 2018, the U.S. population was about 327 million. Assuming that the federal debt is increasing about 5.5% per year and the U.S. population is increasing about 0.7% per year, determine the per capita debt (total debt divided by population) in 2030.
Colleen and Bill have just purchased a house for $650,000, with the seller holding a second mortgage of $100,000. They promise to pay the seller $100,000 plus all accrued interest 5 years from now. The seller offers them three interest options on the second mortgage: (a) Simple interest at 6%
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. In (x-4) ²72/3 I - zx 1 x > 4
In Problems 37–56, write each expression as a sum and/or difference of logarithms. Express powers as factors. In x²-x-2 (x + 4)² 11/3 x > 2
In Problems 51–58, use a calculator to evaluate each expression. Round your answer to three decimal places. In 5 3
The annual growth rate of the world’s population in 2018 was k = 1.1% = 0.011. The population of the world in 2018 was 7,632,819,325. Letting t = 0 represent 2018, use the uninhibited growth model to predict the world’s population in the year 2024.
In Problems 45–56, use transformations to graph each function. Determine the domain, range, horizontal asymptote, and y-intercept of each function.f(x) = 2 + 3x/2
Two bank accounts are opened at the same time. The first has a principal of $1000 in an account earning 5% compounded monthly. The second has a principal of $2000 in an account earning 4% interest compounded annually. Determine the number of years, to the nearest tenth, at which the account
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