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Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728

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Chapter
Section
BuyFindarrow_forward

Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter 8.CR, Problem 23CR
Textbook Problem
1 views

For Problems 17 24 , find the length of the major axis and the length of the minor axis of each ellipse.

9 x 2 + 72 x + 4 y 2 8 y + 112 = 0

To determine

To find:

The length of the major axis and the length of the minor axis of the given ellipse

Explanation of Solution

Given:

The given equation of the ellipse is,

9x2+72x+4y28y+112=0

Approach:

The standard equation of ellipse whose center is not at origin is,

A(xh)2+B(yk)2=C

Here, A,BandC are nonzero real numbers and center is at (h,k).

The formula to calculate the distance of a line segment with the given endpoints is,

d=(x2x1)2+(y2y1)2

Here, d is the length of the line segment.

Calculation:

Consider the given equation of ellipse.

9x2+72x+4y28y+112=0

Express the above equation in the standard form by completing the square.

9x2+72x+4y28y+112=09(x2+8x)+4(y22y)=1129(x2+8x+42)+4(y22y+12)=112+9(42)+4(12)9(x+4)2+4(y1)2=36(1)

Compare the equation (1) with the standard equation A(xh)2+B(yk)2=C. The value of h is 4 and k is 1.

Thus, the center of the ellipse is (h,k)=(4,1).

To find the horizontal endpoints, substitute 1 for y in equation (1).

9(x+4)2+4(11)2=369(x+4)2=36(x+4)2=4x=4±2

Solve for the two values of x.

x=4+2=2

And,

x=42=6

Thus, the end points are (2,1) and (6,1).

To find the vertical endpoints, substitute 4 for x in equation (1)

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Chapter 8 Solutions

Intermediate Algebra
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Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - For Problems 130, graph each parabola. Objective 1...Ch. 8.1 - Write a few paragraphs that summarize the ideas we...Ch. 8.1 - How would you convince someone that y=(x+3)2 is...Ch. 8.1 - How does the graph of y=x2 compare to the graph of...Ch. 8.1 - How does the graph of y=4x2 compare to the graph...Ch. 8.1 - Use a graphing calculator to check your graphs for...Ch. 8.1 - a. Graph y=x2, y=2x2, y=3x2, and y=4x2 on the same...Ch. 8.1 - a. Graph y=x2, y=(x2)2, y=(x3)2, and y=(x5)2 on...Ch. 8.1 - a. Graph y=x2, y=(x2)2+3, y=(x+4)22, and y=(x6)24...Ch. 8.1 - a Graph y=x212x+41 and y=x2+12x+41 on the same set...Ch. 8.2 - For Problems 110, answer true or false. Equations...Ch. 8.2 - For Problems 110, answer true or false. A circle...Ch. 8.2 - For Problems 110, answer true or false. A line...Ch. 8.2 - For Problems 110, answer true or false. The circle...Ch. 8.2 - For Problems 110, answer true or false. The circle...Ch. 8.2 - For Problems 110, answer true or false. The circle...Ch. 8.2 - For Problems 110, answer true or false. The graph...Ch. 8.2 - For Problems 110, answer true or false. The only x...Ch. 8.2 - For Problems 110, answer true or false. The origin...Ch. 8.2 - For Problems 110, answer true or false. The vertex...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 122, graph each parabola. Objective 1...Ch. 8.2 - For Problems 2334, find the centre and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 2334, find the centre and the length...Ch. 8.2 - For Problems 2334, find the center and the length...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 3544, graph each circle. Objective 3...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - For Problems 4554, write the equation of each...Ch. 8.2 - Find the equation of the circle that passes...Ch. 8.2 - Find the equation of the circle that passes...Ch. 8.2 - Find the equation of the circle that passes...Ch. 8.2 - Find the equation of the circle that passes...Ch. 8.2 - What is the graph of x2+y2=4? Explain your answer.Ch. 8.2 - On which axis does the centre of the circle...Ch. 8.2 - Give a step-by-step description of how you would...Ch. 8.2 - Further Investigations The points (x,y) and (y,x)...Ch. 8.2 - Use a graphing calculator to check your graphs for...Ch. 8.2 - Use a graphing calculator to graph the circles in...Ch. 8.3 - For Problems 110, answer true or false. The length...Ch. 8.3 - For Problems 110, answer true or false. The major...Ch. 8.3 - For Problems 110, answer true or false. The axes...Ch. 8.3 - For Problems 110, answer true or false. The...Ch. 8.3 - For Problems 110, answer true or false. The x and...Ch. 8.3 - For Problems 110, answer true or false. The...Ch. 8.3 - For Problems 110, answer true or false. The...Ch. 8.3 - For Problems 110, answer true or false. The...Ch. 8.3 - For Problems 110, answer true or false. The center...Ch. 8.3 - For Problems 110, answer true or false. The center...Ch. 8.3 - For Problems 124, graph each ellipse. 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The graph...Ch. 8.4 - For Problems 110, answer true or false. Each...Ch. 8.4 - For Problems 110, answer true or false. To find...Ch. 8.4 - For Problem 110, answer true or false. The...Ch. 8.4 - For Problems 110, answer true or false. The...Ch. 8.4 - For Problem 110, answer true or false. The...Ch. 8.4 - For Problems 110, answer true or false. The center...Ch. 8.4 - For Problems 110, answer true or false. The...Ch. 8.4 - For Problem 110, answer true or false. The center...Ch. 8.4 - For Problems 16, find the intercepts and the...Ch. 8.4 - For Problems 16, find the intercepts and the...Ch. 8.4 - For Problems 16, find the intercepts and the...Ch. 8.4 - For Problems 16, find the intercepts and the...Ch. 8.4 - For Problems 16, find the intercepts and the...Ch. 8.4 - For Problems 16, find the intercepts and the...Ch. 8.4 - For Problems 718, graph each hyperbola. Objective...Ch. 8.4 - For Problems 718, graph each hyperbola. Objective...Ch. 8.4 - For Problems 718, graph each hyperbola. Objective...Ch. 8.4 - For Problems 718, graph each hyperbola. Objective...Ch. 8.4 - For Problems 718, graph each hyperbola. Objective...Ch. 8.4 - For Problems 718, graph each hyperbola. Objective...Ch. 8.4 - For Problems 718, graph each hyperbola. Objective...Ch. 8.4 - For Problems 718, graph each hyperbola. Objective...Ch. 8.4 - For Problems 718, graph each hyperbola. Objective...Ch. 8.4 - For Problems 718, graph each hyperbola. Objective...Ch. 8.4 - For Problems 718, graph each hyperbola. Objective...Ch. 8.4 - For Problem 718, graph each hyperbola. Objective 1...Ch. 8.4 - For Problems 922, find the equation for the...Ch. 8.4 - For Problems 1922, find the equation for the...Ch. 8.4 - For Problems 1922, find the equation for the...Ch. 8.4 - For Problems 1922, find the equation for the...Ch. 8.4 - For Problems 2332, graph each hyperbola.Objective...Ch. 8.4 - For Problem 2332, graph each hyperbola. Objective...Ch. 8.4 - For Problem 2332, graph each hyperbola. Objective...Ch. 8.4 - For Problem 2332, graph each hyperbola. Objective...Ch. 8.4 - For Problem 2332, graph each hyperbola. Objective...Ch. 8.4 - For Problem 2332, graph each hyperbola. Objective...Ch. 8.4 - For Problem 2332, graph each hyperbola. Objective...Ch. 8.4 - For Problem 2332, graph each hyperbola. Objective...Ch. 8.4 - For Problem 2332, graph each hyperbola. Objective...Ch. 8.4 - For Problem 2332, graph each hyperbola. Objective...Ch. 8.4 - The graph of equations of the form xy=k, where k...Ch. 8.4 - What is the graph of xy=0? Defend your answer.Ch. 8.4 - We have graphed various equations of the form...Ch. 8.4 - Explain the concept of an asymptote.Ch. 8.4 - Explain how asymptotes can be used to help graph...Ch. 8.4 - Are the graphs of x2y2=0 and y2x2=0 identical? Are...Ch. 8.4 - Graphing Calculator Activities To graph the...Ch. 8.4 - Graphing Calculator Activities For each of the...Ch. 8.S - Graph y=(x1)23.Ch. 8.S - Graph y=x26x11.Ch. 8.S - Write the equation of a circle that has its center...Ch. 8.S - Graph x24x+y2+6y+4=0.Ch. 8.S - Graph x2+25y2=25.Ch. 8.S - Graph 9x218x+y22y26=0.Ch. 8.S - Graph x24y2=4.Ch. 8.S - Graph 9x2+36x4y240y100=0.Ch. 8.CR - For Problems 18, find the vertex of each parabola....Ch. 8.CR - For Problems 18, find the vertex of each parabola....Ch. 8.CR - For Problems 18, find the vertex of each parabola....Ch. 8.CR - For Problems 18, find the vertex of each parabola....Ch. 8.CR - For Problems 18, find the vertex of each parabola....Ch. 8.CR - For Problems 18, find the vertex of each parabola....Ch. 8.CR - For Problems 18, find the vertex of each parabola....Ch. 8.CR - For Problems 18, find the vertex of each parabola....Ch. 8.CR - For Problems 912, write the equation of the circle...Ch. 8.CR - For Problems 912, write the equation of the circle...Ch. 8.CR - For Problems 912, write the equation of the circle...Ch. 8.CR - For Problems 912, write the equation of the circle...Ch. 8.CR - For Problems 1316, find the center and the length...Ch. 8.CR - For Problems 1316, find the center and the length...Ch. 8.CR - For Problems 1316, find the center and the length...Ch. 8.CR - For Problems 1316, find the center and the length...Ch. 8.CR - For Problems 1724, find the length of the major...Ch. 8.CR - For Problems 1724, find the length of the major...Ch. 8.CR - For Problems 1724, find the length of the major...Ch. 8.CR - For Problems 1724, find the length of the major...Ch. 8.CR - For Problems 1724, find the length of the major...Ch. 8.CR - For Problems 1724, find the length of the major...Ch. 8.CR - For Problems 1724, find the length of the major...Ch. 8.CR - For Problems 1724, find the length of the major...Ch. 8.CR - For Problems 2530, find the equations of the...Ch. 8.CR - For Problems 2530, find the equations of the...Ch. 8.CR - For Problems 2530, find the equations of the...Ch. 8.CR - For Problems 2530, find the equations of the...Ch. 8.CR - For Problems 2530, find the equations of the...Ch. 8.CR - For Problems 2530, find the equations of the...Ch. 8.CR - For Problems 3150, graph each equation. 9x2+y2=81Ch. 8.CR - For Problems 3150, graph each equation. 9x2y2=81Ch. 8.CR - For Problems 3150, graph each equation. y=2x2+3Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation. y=2x24x3Ch. 8.CR - For Problems 3150, graph each equation. x2y2=9Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation. x2+y22y8=0Ch. 8.CR - For Problems 3150, graph each equation. y=(x+1)2+5Ch. 8.CR - For Problems 3150, graph each equation. y=12(x3)24Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation. x2+4y2=4Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CR - For Problems 3150, graph each equation....Ch. 8.CT - For Problems 14, find the vertex of each parabola....Ch. 8.CT - For Problems 14, find the vertex of each parabola....Ch. 8.CT - For Problems 14, find the vertex of each parabola....Ch. 8.CT - For Problems 14, find the vertex of each parabola....Ch. 8.CT - For Problems 57, write the equation of the circle...Ch. 8.CT - For Problems 57, write the equation of the circle...Ch. 8.CT - For Problems 57, write the equation of the circle...Ch. 8.CT - Find the length of minor axis of the ellipse...Ch. 8.CT - Find the length of major axis of the ellipse...Ch. 8.CT - Find the length of minor axis of the ellipse...Ch. 8.CT - For Problems 1517, find the equation of the...Ch. 8.CT - For Problems 1517, find the equation of the...Ch. 8.CT - For Problems 1517, find the equation of the...Ch. 8.CT - For Problems 1825, graph each equation. x24y2=16Ch. 8.CT - For Problem 1825 graph each equation. y=x2+4xCh. 8.CT - For Problems 1825, graph each equation....Ch. 8.CT - For Problems 1825 graph each equation. 2x2+3y2=12Ch. 8.CT - For Problem 1825 graph each equation. y=2x2+12x+22Ch. 8.CT - For Problems 1825, graph each equation. 9x2y2=9Ch. 8.CT - For Problems 1825, graph each equation....Ch. 8.CT - For Problems 1825, graph each equation....Ch. 8.CM - For Problems 14, evaluate each algebraic...Ch. 8.CM - For Problems 14, evaluate each algebraic...Ch. 8.CM - For Problems 14, evaluate each algebraic...Ch. 8.CM - For Problems 14, evaluate each algebraic...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 516, perform the indicated operations...Ch. 8.CM - For Problems 1724, evaluate each of the numerical...Ch. 8.CM - For Problems 1724, evaluate each of the numerical...Ch. 8.CM - For Problems 1724, evaluate each of the numerical...Ch. 8.CM - For Problems 1724, evaluate each of the numerical...Ch. 8.CM - For Problems 1724, evaluate each of the numerical...Ch. 8.CM - For Problems 1724, evaluate each of the numerical...Ch. 8.CM - For Problems 1724, evaluate each of the numerical...Ch. 8.CM - For Problems 1724, evaluate each of the numerical...Ch. 8.CM - For Problems 2530, factor each of the algebraic...Ch. 8.CM - For Problems 2530, factor each of the algebraic...Ch. 8.CM - For Problems 2530, factor each of the algebraic...Ch. 8.CM - For Problems 2530, factor each of the algebraic...Ch. 8.CM - For Problems 2530, factor each of the algebraic...Ch. 8.CM - For Problems 2530, factor each of the algebraic...Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve of the equations....Ch. 8.CM - For Problems 3154, solve of the equations....Ch. 8.CM - For Problems 3154, solve of the equations....Ch. 8.CM - For Problems 3154, solve of the equations....Ch. 8.CM - For Problems 31-54, solve each of the equations....Ch. 8.CM - For Problems 31-54, solve each of the equations....Ch. 8.CM - For Problems 31-54, solve each of the equations....Ch. 8.CM - For Problems 3154, solve of the equations....Ch. 8.CM - For Problems 3154, solve of the equations....Ch. 8.CM - For Problems 3154, solve of the equations....Ch. 8.CM - For Problems 3154, solve of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 3154, solve each of the equations....Ch. 8.CM - For Problems 5564, solve inequality and express...Ch. 8.CM - For Problems 5564, solve inequality and express...Ch. 8.CM - For Problems 5564, solve inequality and express...Ch. 8.CM - For Problem 5564, solve inequality and express the...Ch. 8.CM - For Problems 5564, solve inequality and express...Ch. 8.CM - For Problems 5564, solve inequality and express...Ch. 8.CM - For Problems 5564, solve inequality and express...Ch. 8.CM - For Problem 5564, solve inequality and express the...Ch. 8.CM - For problem 55-64, solve each inequality and...Ch. 8.CM - For problem 55-64, solve each inequality and...Ch. 8.CM - For Problems 65-70, graph the following equations....Ch. 8.CM - For Problems 65-70, graph the following equations....Ch. 8.CM - For Problems 65-70, graph the following equations....Ch. 8.CM - For Problems 65-70, graph the following equations....Ch. 8.CM - For Problems 65-70, graph the following equations....Ch. 8.CM - For Problems 65-70, graph the following equations....Ch. 8.CM - For Problems 71 and 72, find the distance between...Ch. 8.CM - For Problems 71 and 72, find the distance between...Ch. 8.CM - For Problems 73-76, write the equation of a line...Ch. 8.CM - For Problems 73-76, write the equation of a line...Ch. 8.CM - For Problems 73-76, write the equation of a line...Ch. 8.CM - For Problem 73-76, write the equation of a line...Ch. 8.CM - Find the center and the length of a radius of the...Ch. 8.CM - Find the coordinates of the vertex of the...Ch. 8.CM - Find the equations of the asymptotes for the...Ch. 8.CM - Graph the ellipse 25x2+4y2=100Ch. 8.CM - Graph the hyperbola 9x24y2=36Ch. 8.CM - Graph the parabola y=2(x1)2+4Ch. 8.CM - For Problems 83-88, solve each problem by setting...Ch. 8.CM - For Problems 83-88, solve each problem by setting...Ch. 8.CM - For Problems 83-88, solve each problem by setting...Ch. 8.CM - For Problems 83-88, solve each problem by setting...Ch. 8.CM - For Problems 83-88, solve each problem by setting...Ch. 8.CM - For Problems 83-88, solve each problem by setting...

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