1 Introduction To Common Fractions And Mixed Numbers 2 Addition Of Common Fractions And Mixed Numbers 3 Subtraction Of Common Fractions And Mixed Numbers 4 Multiplication Of Common Fractions And Mixed Numbers 5 Division Of Common Fractions And Mixed Numbers 6 Combined Operations Of Common Fractions And Mixed Numbers 7 Computing With A Calculator 8 Computing With A Spreadsheet 9 Introduction To Decimal Fractions 10 Rounding Decimal Fractions And Equivalent Decimal And Common Fractions 11 Addition And Subtraction Of Decimal Fractions 12 Multiplication Of Decimal Fractions 13 Division Of Decimal Fractions 14 Powers 15 Roots 16 Table Of Decimal Equivalents And Combined Operations Of Decimal Fractions 17 Computing With A Calculator 18 Computing With A Spreadsheet 19 Achievement Review—section One 20 Ratio And Propor Tion 21 Direct And Inverse Proportions 22 Introduction To Percents 23 Basic Calculations Of Percentages, Percents, And Rates 24 Percent Practical Applications 25 Achievement Review—section Two 26 Customary (english) Units Of Measure 27 Metric Units Of Linear Measure 28 Degree Of Precision, Greatest Possible Error, Absolute Error, And Relative Error 29 Tolerance, Clearance, And Interference 30 Customary And Metric Steel Rules 31 Customary Vernier Calipers And Height Gages 32 Metric Vernier Calipers And Height Gages 33 Digital Calipers And Height Gages 34 Customary Micrometers 35 Metric Vernier Micrometers 36 Digital Micrometers 37 Customary And Metric Gage Blocks 38 Achievement Review—section Three 39 Symbolism And Algebraic Expressions 40 Signed Numbers 41 Algebraic Operations Of Addition, Subtraction, And Multiplication 42 Algebraic Operations Of Division, Powers, And Roots 43 Introduction To Equations 44 Solution Of Equations By The Subtraction, Addition, And Division Principles Of Equality 45 Solution Of Equations By The Multiplication, Root, And Power Principles Of Equality 46 Solution Of Equations Consisting Of Combined Operations And Rearrangement Of Formulas 47 Applications Of Formulas To Cutting Speed, Revolutions Per Minute, And Cutting Time 48 Applications Of Formulas To Spur Gears 49 Achievement Review—section Four 50 Lines And Angular Measure 51 Protractors—simple Semicircular And Vernier 52 Types Of Angles And Angular Geometric Principles 53 Introduction To Triangles 54 Geometric Principles For Triangles And Other Common Polygons 55 Introduction To Circles 56 Arcs And Angles Of Circles, Tangent Circles 57 Fundamental Geometric Constructions 58 Achievement Review—section Five 59 Areas Of Rectangles, Parallelograms, And Trapezoids 60 Areas Of Triangles 61 Areas Of Circles, Sectors, And Segments 62 Volumes Of Prisms And Cylinders 63 Volumes Of Pyramids And Cones 64 Volumes Of Spheres And Composite Solid Figures 65 Achievement Review—section Six 66 Introduction To Trigonometric Functions 67 Analysis Of Trigonometric Functions 68 Basic Calculations Of Angles And Sides Of Right Triangles 69 Simple Practical Machine Applications 70 Complex Practical Machine Applications 71 The Cartesian Coordinate System 72 Oblique Triangles 73 Achievement Review—section Seven 74 Introduction To Compound Angles 75 Drilling And Boring Compound-angular Holes 76 Drilling And Boring Compound-angular Holes 77 Machining Compound-angular Surfaces 78 Computing Angles Made By The Intersection Of Two Angular Surfaces 79 Computing Compound Angles On Cutting And Forming Tools 80 Achievement Review—section Eight 81 Introduction To Computer Numerical Control (cnc) 82 Control Systems, Absolute Positioning, Incremental Positioning 83 Location Of Points 84 Binary Numeration System 85 Hexadecimal Numeration System 86 Bcd (binary Coded Decimal) Numeration Systems 87 An Introduction To G- And M-codes For Cnc Programming 88 Achievement Review—section Nine Chapter44: Solution Of Equations By The Subtraction, Addition, And Division Principles Of Equality
Chapter Questions Section: Chapter Questions
Problem 1A: Write the expression "A number divided by 7 plus twice the number equals 75" as an equation with the... Problem 2A: Use scientific notation to solve (6.325 108)(9.4 109)5105 . Leave the answer in scientific notation... Problem 3A Problem 4A: If a=7.5 and b=9.45 , what is the value of a+4bb2a ? If necessary, round the answer to 2 decimal... Problem 5A Problem 6A Problem 7A Problem 8A Problem 9A Problem 10A: Solve each of the following equations using the subtraction principle of equality. Check each... Problem 11A Problem 12A: Solve each of the following equations using the subtraction principle of equality. Check each... Problem 13A Problem 14A Problem 15A Problem 16A Problem 17A Problem 18A Problem 19A Problem 20A Problem 21A Problem 22A Problem 23A: Solve each of the following equations using the subtraction principle of equality. Check each... Problem 24A: Solve each of the following equations using the subtraction principle of equality. Check each... Problem 25A: Solve each of the following equations using the subtraction principle of equality. Check each... Problem 26A Problem 27A Problem 28A: Solve each of the following equations using the subtraction principle of equality. Check each... Problem 29A: Solve each of the following equations using the subtraction principle of equality. Check each... Problem 30A: Solve each of the following equations using the subtraction principle of equality. Check each... Problem 31A: Write an equation for each of the following problems, solve for the unknown, and check. All... Problem 32A: Write an equation for each of the following problems, solve for the unknown, and check. All... Problem 33A Problem 34A: Write an equation for each of the following problems, solve for the unknown, and check. All... Problem 35A: Write an equation for each of the following problems, solve for the unknown, and check. All... Problem 36A: Write an equation for each of the following problems, solve for the unknown, and check. All... Problem 37A Problem 38A Problem 39A Problem 40A: A Shaft rotates in a bearing that is 0.3968 inch in diameter. The total between the shaft and... Problem 41A: For each of the following problems, substitute the given values in the formula and solve for the... Problem 42A: For each of the following problems, substitute the given values in the formula and solve for the... Problem 43A Problem 44A: For each of the following problems, substitute the given values in the formula and solve for the... Problem 45A Problem 46A Problem 47A Problem 48A Problem 49A Problem 50A Problem 51A Problem 52A: Solve each of the following equations using the addition principle of equality. Check each answer.... Problem 53A Problem 54A Problem 55A Problem 56A Problem 57A Problem 58A: Solve each of the following equations using the addition principle of equality. Check each answer.... Problem 59A: Solve each of the following equations using the addition principle of equality. Check each answer.... Problem 60A Problem 61A Problem 62A: Solve each of the following equations using the addition principle of equality. Check each answer.... Problem 63A Problem 64A: Solve each of the following equations using the addition principle of equality. Check each answer.... Problem 65A: Solve each of the following equations using the addition principle of equality. Check each answer.... Problem 66A Problem 67A: Solve each of the following equations using the addition principle of equality. Check each answer.... Problem 68A Problem 69A Problem 70A Problem 71A Problem 72A Problem 73A Problem 74A Problem 75A Problem 76A: For each of the following problems, substitute the given values in the formula and solve for the... Problem 77A Problem 78A Problem 79A Problem 80A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 81A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 82A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 83A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 84A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 85A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 86A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 87A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 88A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 89A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 90A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 91A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 92A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 93A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 94A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 95A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 96A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 97A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 98A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 99A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 100A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 101A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 102A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 103A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 104A: Solve each of the following equations using the division principle of equality. Check each answer.... Problem 105A: Write an equation for each of the following problems, and solve for the unknown. The depth, D, of an... Problem 106A: Write an equation for each of the following problems, and solve for the unknown. All dimensions are... Problem 107A: Write an equation for each of the following problems, and solve for the unknown. Find x. Problem 108A: The feed of a drill is the depth of material that the drill penetrates in one revolution. The total... Problem 109A Problem 110A: For each of the following problems, substitute the given values in the formula and solve for the... Problem 111A: For each of the following problems, substitute the given values in the formula and solve for the... Problem 112A: For each of the following problems, substitute the given values in the formula and solve for the... Problem 113A: Solve each of the following equations using either the addition, subtraction, or division principle... Problem 114A: Solve each of the following equations using either the addition, subtraction, or division principle... Problem 115A: Solve each of the following equations using either the addition, subtraction, or division principle... Problem 116A: Solve each of the following equations using either the addition, subtraction, or division principle... Problem 117A: Solve each of the following equations using either the addition, subtraction, or division principle... Problem 118A Problem 119A Problem 120A Problem 121A Problem 122A Problem 123A Problem 124A Problem 125A: Solve each of the following equations using either the addition, subtraction, or division principle... Problem 126A Problem 127A: Solve each of the following equations using either the addition, subtraction, or division principle... Problem 128A Problem 129A Problem 130A Problem 38A
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Concept explainers
In the circle below, segment AB is a diameter. If the length of arc is 6 , what is the length of the radius of the circle?
Transcribed Image Text: **Problem**
In the circle below, segment \( AB \) is a diameter. If the length of arc \( ACB \) is \( 6\pi \), what is the length of the radius of the circle?
**Diagram Explanation**
- A circle is shown with a diameter labeled \( AB \).
- Three points are marked on the circumference: \( A \), \( B \), and \( C \).
- The diameter \( AB \) connects two points on the circle, passing through the center.
- An arc is indicated by \( \overset{\frown}{ACB} \), covering part of the circle's circumference from point \( A \) to point \( B \) through point \( C \).
**Calculation & Conclusion**
To solve for the radius, we use the relationship between the arc length and the circumference of the circle. The given arc length \( \overset{\frown}{ACB} = 6\pi \), which is the length of a semicircle (half of the circle’s circumference).
Thus, the entire circumference of the circle would be:
\[ 2 \times 6\pi = 12\pi \]
The circumference \( C \) of a circle is also given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius. Setting the two expressions for the circumference equal gives:
\[ 2\pi r = 12\pi \]
Solving for \( r \):
\[ r = \frac{12\pi}{2\pi} = 6 \]
So, the radius of the circle is \( \boxed{6} \).
Two-dimensional figure measured in terms of radius. It is formed by a set of points that are at a constant or fixed distance from a fixed point in the center of the plane. The parts of the circle are circumference, radius, diameter, chord, tangent, secant, arc of a circle, and segment in a circle.
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![**Problem**
In the circle below, segment \( AB \) is a diameter. If the length of arc \( ACB \) is \( 6\pi \), what is the length of the radius of the circle?
**Diagram Explanation**
- A circle is shown with a diameter labeled \( AB \).
- Three points are marked on the circumference: \( A \), \( B \), and \( C \).
- The diameter \( AB \) connects two points on the circle, passing through the center.
- An arc is indicated by \( \overset{\frown}{ACB} \), covering part of the circle's circumference from point \( A \) to point \( B \) through point \( C \).
**Calculation & Conclusion**
To solve for the radius, we use the relationship between the arc length and the circumference of the circle. The given arc length \( \overset{\frown}{ACB} = 6\pi \), which is the length of a semicircle (half of the circle’s circumference).
Thus, the entire circumference of the circle would be:
\[ 2 \times 6\pi = 12\pi \]
The circumference \( C \) of a circle is also given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius. Setting the two expressions for the circumference equal gives:
\[ 2\pi r = 12\pi \]
Solving for \( r \):
\[ r = \frac{12\pi}{2\pi} = 6 \]
So, the radius of the circle is \( \boxed{6} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5cae965-fbbf-45bc-b876-726779e5ae34%2F27aef100-eee8-46ad-899a-c2c7be7238d2%2F51phndb_processed.jpeg&w=3840&q=75)
