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mathematics
college algebra graphs and models
College Algebra With Modeling And Visualization 6th Edition Gary Rockswold - Solutions
Suppose T varies directly with the 3/2 power of x. When x = 4, T = 20. Find when x = 16.
Solve the variation problem.Suppose y varies directly with the second power of x. When x = 3, y = 10.8. Find y when x = 1.5.
Solve the variation problem.Let y be inversely proportional to x. When x = 6. y = 5. Find y when .x = 15.
Solve the variation problem.Let z be inversely proportional to the third power of 1. When t = 5, z = 0.08. Find z when t = 2.
Assume that the constant of proportionality is positive.Let y be inversely proportional to x. If x doubles, what happens to y?
Assume that the constant of proportionality is positive.Let y vary inversely with the second power of x. If x doubles, what happens to y?
Assume that the constant of proportionality is positive.Suppose y varies directly with the third power of x. If x triples, what happens to y?
If a car is moving at 50 miles per hour on a level highway, then its braking distance depends on the road conditions. This distance in feet can be computed by D(x) = 250/30x where x is the coefficient of friction between the tires and the road and 0 < x ≤ 1. A smaller value of x indicates that
Discuss how to find the domain of a rational function symbolically and graphically.
Assume that the constant of proportionality is positive.Suppose y is directly proportional to the second power of x. If x is halved, what happens to y?
The data satisfy the equation y = kxn, where n is a positive integer. Determine k and n. X 2 ' 2 3 4.5 4 8 5 12.5
Describe the steps to graphically solve a polynomial inequality in the form p(x) > 0.
Describe the steps to inequality in the form f(x) > 0. symbolically solve a rational
Let f(x) be the formula for a rational function. (a) Explain how to find any vertical or horizontal asymptotes of the graph of f.(b) Discuss what a horizontal asymptote represents.
The volume V of a cylinder with a fixed height is directly proportional to the square of its radius r. If a cylinder with a radius of 10 inches has a volume of 200 cubic inches, what is the volume of a cylinder with the same height and a radius of 5 inches?
The brightness, or intensity, of starlight varies inversely with the square of its distance from Earth. The Hubble Telescope can see stars whose intensities are 1/50 that of the faintest star now seen by ground-based telescopes. Determine how much farther the Hubble Telescope can see into space
The data in the table satisfy the equation y = k/xn, where n is a positive integer. Determine k and n. X y 2 9 4 2.25 6 1 8 0.5625
The data in the table satisfy the equation y = k/xn, where n is a positive integer. Determine k and n. H y 2 1.5 3 1 4 0.75 5 0.6
The data satisfy the equation y = kxn, where n is a positive integer. Determine k and n. x 3 y 32.4 5 150 150 7 411.6 9 874.8
The weight y of a fiddler crab is directly proportional to the 1.25 power of the weight x of its claws. A crab with a body weight of 1.9 grams has claws weighing 1.1 grams. Estimate the weight of a fiddler crab with claws weighing 0.75 gram.
The weight of an object varies inversely with the second power of the distance from the center of Earth. The radius of Earth is approxi- mately 4000 miles. If a person weighs 160 pounds on Earth's surface, what would this individual weigh 8000 miles above the surface of Earth?
The electrical resistance R of a wire varies inversely with the square of its diameter d. If a 25-foot wire with a diameter of 2 millimeters has a resistance of 0.5 ohm, find the resistance of a wire having the same length and a diameter of 3 millimeters.
The frequency F of a vibrating string is directly proportional to the square root of the tension T on the string and inversely proportional to the length L of the string.Give two ways to double the frequency F.
The frequency F of a vibrating string is directly proportional to the square root of the tension T on the string and inversely proportional to the length L of the string.If both the tension and the length are doubled, what happens to F?
The strength of a rectangular wood beam varies directly with the square of the depth of its cross section. If a beam with a depth of 3.5 inches can support 1000 pounds, how much weight can the same type of beam hold if its depth is 12 inches?
Divide. Check your answer. x² + 3x² - 4x + 1 x + 2
Use the graph off to estimate the (a) Local extrema and (b) Absolute extrema. 3 -3 3
Use graphing to factor f(x). 9 - XLI + ₂x01 = (x)/
Divide the expression. 5x4 - 2x² + 6 x² + 2
Find any horizontal or vertical asymptotes. f(x) = 4x 2x6
Find all real solutions. Check your results. 8x 4x²1 3 3 + 2x + 12x - 1
Complete the following. (a) Graph y = f(x) in the standard viewing rectangle. (b) Approximate the coordinates of each turning point.(c) Estimate any local extrema. f(x) = = x² + x³ + ¾x² − 3x + 3 -
Complete the following. (a) Graph y = f(x) in the standard viewing rectangle. (b) Approximate the coordinates of each turning point.(c) Estimate any local extrema. f(x) = 0.025x¹-0.45x² - 5
Use the graph off to estimate the (a) Local extrema and (b) Absolute extrema. 2
Complete the following. (a) Graph y = f(x) in the standard viewing rectangle. (b) Approximate the coordinates of each turning point.(c) Estimate any local extrema. f(x)=x² - 4x - 3
Divide the expression. 3x - 7x3 + 6x - 16 3x - 7
Find all real solutions. Check your results. 2x - - 1 2 x+1 x 1 1
Divide the expression. 20x² + 6x³ - 2x² + 15x2 5x - |
Use the graph off to estimate the (a) Local extrema and (b) Absolute extrema. 732 3 X
Find any horizontal or vertical asymptotes. f(x) = x + 3 x-3
The graph of a polynomial f(x) with integer zeros is shown in the figure. Write its complete factored form. Note that the leading coefficient of f(x) is not ±1. -6 2 -y = f(x)
The graph of a polynomial f(x) with integer zeros is shown in the figure. Write its complete factored form. Note that the leading coefficient of f(x) is not ±1. 12 예 y = f(x) 3
Find all real solutions. Check your results. r - 1 3 +1 4
Use the graph off to estimate the (a) Local extrema and (b) Absolute extrema. 65 3 12 4 x
Find any horizontal or vertical asymptotes. f(x)=x-1 x+1
Complete the following. (a) Graph y = f(x) in the standard viewing rectangle. (b) Approximate the coordinates of each turning point.(c) Estimate any local extrema. f(x) = ÷r³ - 3x
Divide. Check your answer. 12x³ - 14x² + 7x -7 3x - 2
Find all real solutions. Check your results. 1 x-2 2 x-3 -1 xả - 5x + 6
The graph of a polynomial f(x) with integer zeros is shown in the figure. Write its complete factored form. Note that the leading coefficient of f(x) is not ±1. y = f(x) 23
Complete the following without a calculator. (a) Match the equation with its graph (a-f). (b) Identify the turning points. (c) Estimate the x-intercepts. (d) Estimate any local extrema. (e) Estimate any absolute extrema. f(x) = x³ + x² = x²³5x² -
Identify any horizontal or vertical asymptotes in the graph. State the domain of f. 564 X. 68 [ ï † ☞ ጘ
Divide. Check your answer. 6x³ + 5x²8x + 4 2x - 1
The graph of a polynomial f(x) with integer zeros is shown in the figure. Write its complete factored form. Note that the leading coefficient of f(x) is not ±1. 32 3 y = f(x) X
In the table, Y is a rational function. Give a possible equation for a horizontal asymptote. X 10 -20 -30 -40 -50 Y₁ 4.8922 4.9726 4.9878 4.9931 4.9956 -60 4.9969 -70 4.9978 X=-10
In the table, Y is a rational function. Give a possible equation for a horizontal asymptote. X 50 100 150 Y1 2.8654 2.9314 2.9539 200 2.9653 250 2.9722 300 2.9768 350 2.9801 X=50
Divide. Check your answer. ³+3x²-x-3 x +3
Use the graph off to estimate the (a) Local extrema and (b) Absolute extrema. 5 I X
Find all real solutions. Check your results. x-1 x + 1 x + 3 x-4
Use the graph off to estimate the (a) Local extrema and (b) Absolute extrema. 6 6 -12 6 12
Identify any horizontal or vertical asymptotes in the graph. State the domain of f. 34
Let g(x) be a quartic polynomial with zeros -2, -1, 1, and 2. If the graph of g passes through the point (0,8), write the complete factored form of g(x).
Find all real solutions. Check your results. 6 35 + 36 = 0
Divide. Check your answer. +1 x + 1
Complete the following without a calculator. (a) Match the equation with its graph (a-f). (b) Identify the turning points. (c) Estimate the x-intercepts. (d) Estimate any local extrema. (e) Estimate any absolute extrema. f(x) = 8x² - x²
Let an be the leading coefficient. (a) Find the complete factored form of a polynomial with real coefficients f(x) that satisfy the conditions. (b) Express f(x) in expanded form. Degree 4; a = 7; zeros 2i and 3i
Identify any horizontal or vertical asymptotes in the graph. State the domain of f. -3 3
Complete the following without a calculator. (a) Match the equation with its graph (a-f). (b) Identify the turning points. (c) Estimate the x-intercepts. (d) Estimate any local extrema. (e) Estimate any absolute extrema. f(x) = x² = 8x²
Use the graph off to estimate the (a) Local extrema and (b) Absolute extrema. ми
The graph of a polynomial f(x) with leading coefficient ±1 and integer zeros is shown in the figure. Write its complete factored form. 75 50
Use the graph off to estimate the (a) Local extrema (b) Absolute extrema. 2 77
Complete the following without a calculator. (a) Match the equation with its graph (a-f). (b) Identify the turning points. (c) Estimate the x-intercepts. (d) Estimate any local extrema. (e) Estimate any absolute extrema. x6 = ₂X{ + £* = (x)f
Let an be the leading coefficient. (a) Find the complete factored form of a polynomial with real coefficients f(x) that satisfy the conditions. (b) Express f(x) in expanded form. Degree 3; a = -2; an zeros 1 i and 3 -
Find all real solutions. Check your results. 35 4 X +15
Let an be the leading coefficient. (a) Find the complete factored form of a polynomial with real coefficients f(x) that satisfy the conditions. (b) Express f(x) in expanded form. Degree 3; an = elw zeros -3i and
Let f(x) be a cubic polynomial with zeros -1, 2, and 3. If the graph of f passes through the point (0, 3), write the complete factored form of f(x).
Divide. Check your answer. 4x³x²5x + 6 x-1
Complete the following without a calculator. (a) Match the equation with its graph (a-f). (b) Identify the turning points. (c) Estimate the x-intercepts. (d) Estimate any local extrema. (e) Estimate any absolute extrema. f(x) = 3x - x²³
Let an be the leading coefficient. (a) Find the complete factored form of a polynomial with real coefficients f(x) that satisfy the conditions. (b) Express f(x) in expanded form. Degree 4; an = zeros -i and 2i
Identify any horizontal or vertical asymptotes in the graph. State the domain of f. 3 2 -1 1
The graph of a polynomial f(x) with leading coefficient ±1 and integer zeros is shown in the figure. Write its complete factored form. 300 -300 y = f(x) 2 6
Complete the following without a calculator. (a) Match the equation with its graph (a-f). (b) Identify the turning points. (c) Estimate the x-intercepts. (d) Estimate any local extrema. (e) Estimate any absolute extrema. f(x) = 1-2x + x²
Divide. Check your answer. x³2x²-x+3 x + 1
Identify any horizontal or vertical asymptotes in the graph. State the domain of f. -12-8 48 12 X
Find all real solutions. Check your results. 1 r + B 1 x + 3 2 x + 5x +6
Use the graph off to estimate the (a) Local extrema and (b) Absolute extrema. 1000 500 8
The graph of a polynomial f(x) with leading coefficient ±1 and integer zeros is shown in the figure. Write its complete factored form. 20 -10 -20 y = f(x)
Use the graph off to estimate the (a) Local extrema (b) Absolute extrema. -2 32 3 ليا
Identify any horizontal or vertical asymptotes in the graph. State the domain of f. 8
Find all real solutions. Check your results. x³ - 4x x²+1 = 0
The graph of a polynomial f(x) with leading coefficient ±1 and integer zeros is shown in the figure. Write its complete factored form. -6 100 50
Use the graph off to estimate the (a) Local extrema and (b) Absolute extrema. -2-1 32 123 X
Identify any horizontal or vertical asymptotes in the graph. State the domain of f. -10-6 10 01 89
Divide. Check your answer. x4-3x³-x + 3 x-3
Let an be the leading coefficient. (a) Find the complete factored form of a polynomial with real coefficients f(x) that satisfy the conditions. (b) Express f(x) in expanded form. Degree 2; a = -5; zeros 1 + i and 1
Divide the first polynomial by the second. State the quotient and remainder. x4 1 + zx91 x +4
Find all real solutions. Check your results. 1 -2 x
Let an be the leading coefficient. (a) Find the complete factored form of a polynomial with real coefficients f(x) that satisfy the conditions. (b) Express f(x) in expanded form. Degree 4; an 10; zeros 1. -1, 3i, and -3i
Identify any horizontal or vertical asymptotes in the graph. State the domain of f. 10- 6 -10-6-2 off -10 4 6 8 10
Use the graph off to estimate the (a) Local extrema (b) Absolute extrema.
Use the graph to factor f(x). Assume that all zeros are integers. f(x) = x² = ³x²³ + ²x² + ³x = 6 DO y = f(x) 2
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