Solve the inequality-3x - 2 6 7
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R.1
Real Numbers
R.2
Algebra Essentials
R.3
Geometry Essentials
R.4
Polynomials
R.5
Factoring Polynomials
R.6
Synthetic Division
R.7
Rational Expressions
R.8
nth Roots; Rational Exponents
1
Equations and Inequalities
1.1
Linear Functions
1.2
Quadratic Equations
1.3
Complex Numbers; Quadratic Equations in the Complex Number System
1.4
Radical Equations;Equations Quadratic in Form; Factorable Equations
1.5
Solving Inequalities
1.6
Equations and Inequalities Involving Absolute Value
1.7
Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
2
Graphs
2.1
The Distance and Midpoint Formulas
2.2
Graphs of Equations in Two Variables; Intercepts; Symmetry
2.3
Lines
2.4
Circles
2.5
Variation
3
Functions and Their Graphs
3.1
Functions
3.2
The Graph of a Function
3.3
Properties of Functions
3.4
Library of Functions; Piecewise-defined Functions
3.5
Graphing Techniques:Transformations
3.6
Mathematical Models: Building Functions
4
Linear and Quadratic Functions
4.1
Linear Functions and Their Properties
4.2
Linear Models: Building Linear Functions from Data
4.3
Quadratic Functions and Their Properties
4.4
Build Quadratic Models from Verbal Descriptions and from Data
4.5
Inequalities Involving Quadratic Functions
5
Polynomial and Rational Functions
5.1
Polynomial Functions and Models
5.2
Properties of Rational Functions
5.3
The Graph of a Rational Function
5.4
Polynomial and Rational Inequalities
5.5
The Real Zeros of a Polynomial Function
5.6
Complex Zeros; Fundamental Theorem of Algebra
6
Exponential and Logarithmic Functions
6.1
Composite Functions
6.2
One-to-One Functions; Inverse Functions
6.3
Exponential Functions
6.4
Logarithmic Functions
6.5
Properties of Logarithms
6.6
Logarithmic and Exponential Equations
6.7
Financial Models
6.8
Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
6.9
Building Exponential, Logarithmic, and Logistic Models from Data
7
Trigonometric Functions
7.1
Angles and Their Measure
7.2
Right Triangle Trigonometry
7.3
Computing the Values of Trigonometric Functions of Acute Angles
7.4
Trigonometric Functions of Any Angle
7.5
Unit Circle Approach; Properties of the Trigonometric Functions
7.6
Graphs of the Sine and Cosine Functions
7.7
Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
7.8
Phase Shift; Sinusoidal Curve Fitting
8
Analytic Trigonometry
8.1
The Inverse Sine, Cosine, and Tangent Functions
8.2
The Inverse Trigonometric Functions (Continued)
8.3
Trigonometric Equations
8.4
Trigonometric Identities
8.5
Sum and Difference Formulas
8.6
Double-angle and Half-angle Formulas
8.7
Product-to-Sum and Sum-to-Product Formulas
9
Applications of Trigonometric Functions
9.1
Applications Involving Right Triangles
9.2
The Law of Sines
9.3
The Law of Cosines
9.4
Area of a Triangle
9.5
Simple Harmonic Motion; Damped Motion; Combining Waves
10
Polar Coordinates;Vectors
10.1
Polar Coordinates
10.2
Polar Equations and Graphs
10.3
The Complex Plane; De Moivre’s Theorem
10.4
Vectors
10.5
The Dot Product
11
Analytic Geometry
11.2
The Parabola
11.3
The Ellipse
11.4
The Hyperbola
11.5
Rotation of Axes; General Form of a Conic
11.6
Polar Equations of Conics
11.7
Plane Curves and Parametric Equations
12
Systems of Equations and Inequalities
12.1
Systems of Linear Equations: Substitution and Elimination
12.2
Systems of Linear Equations: Matrices
12.3
Systems of Linear Equations: Determinants
12.4
Matrix Algebra
12.5
Partial Fraction Decomposition
12.6
Systems of Nonlinear Equations
12.7
Systems of Inequalities
12.8
Linear Programming
13
Sequences; Induction; the Binomial Theorem
13.1
Sequences
13.2
Arithmetic Sequences
13.3
Geometric Sequences; Geometric Series
13.4
Mathematical Induction
13.5
The Binomial Theorem
14
Counting and Probability
14.1
Counting
14.2
Permutations and Combinations
14.3
Probability
Textbook Solutions for Algebra and Trigonometry
Chapter 4.5 Problem 37
Question
Artillery A projectile fired from the point (0, 0) at an angle to the positive x-axis has a trajectory given by
\(y=c x-\left(1+c^{2}\right)\left(\frac{g}{2}\right)\left(\frac{x}{v}\right)^{2}\)
where
x = horizontal distance in meters
y = height in meters
v = initial muzzle velocity in meters per second (m/sec)
g = acceleration due to gravity = 9.81 meters per second squared (\(\mathrm{m} / \mathrm{sec}^{2}\))
\(c>0\) is a constant determined by the angle of elevation. A howitzer fires an artillery round with a muzzle velocity of 897 m/sec.
(a) If the round must clear a hill 200 meters high at a distance of 2000 meters in front of the howitzer, what c values are permitted in the trajectory equation?
(b) If the goal in part (a) is to hit a target on the ground 75 kilometers away, is it possible to do so? If so,for what values of c? If not, what is the maximum distance the round will travel?
Solution
Step 1 of 5
The trajectory equation is :
\(y=c x-\left(1+c^{2}\right)\left(\frac{g}{2}\right)\left(\frac{x}{v}\right) 2\)
(a)
Given data:
\(\begin{array}{l}v=897\mathrm{\ m}/\mathrm{s}\\ y=200\mathrm{\ m}\\ x=2000\mathrm{\ m}\\ g=9.8\mathrm{\ m}/\mathrm{s}^2\end{array}\)
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full solution
Title
Algebra and Trigonometry 9
Author
Michael Sullivan
ISBN
9780321716569
Artillery A projectile fired from the point (0, 0) at an
Chapter 4.5 textbook questions
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Chapter 4: Problem 3 Algebra and Trigonometry 9
In Problems 36, use the figure to solve each inequality.!4 !3 3 3 (!2, 0) (2, 0) y " f(x) (a) (b) f1x2 0 f1x2 7 0
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Chapter 4: Problem 4 Algebra and Trigonometry 9
In Problems 36, use the figure to solve each inequality.y !5 !4 !2 2 4 5 (!1, 0) (4, 0) (1.5, 5) y " g(x) (a) (b) g1x2 0 g1x2 6 0
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Chapter 4: Problem 5 Algebra and Trigonometry 9
In Problems 36, use the figure to solve each inequality.y !4 !4 4 8 (!2, 8) (1, 2) (2, 8) y " g(x) y " f(x) a) (b) f1x2 7 g1x2 g1x2 f1x2
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Chapter 4: Problem 6 Algebra and Trigonometry 9
In Problems 36, use the figure to solve each inequality.y !12 !3 3 6 (!3, !12) (3, !12) (1, !3) y " g(x) (a) (b) f1x2 g1x2 f1x2 6 g1x2
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Chapter 4: Problem 7 Algebra and Trigonometry 9
In Problems 722,solve each inequality.- 3x - 10 6 0
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Chapter 4: Problem 8 Algebra and Trigonometry 9
In Problems 722,solve each inequality.+ 3x - 10 7 0
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Chapter 4: Problem 9 Algebra and Trigonometry 9
In Problems 722,solve each inequality.x + 8x 7 0 2 x - 4x 7 0
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Chapter 4: Problem 10 Algebra and Trigonometry 9
In Problems 722,solve each inequality.x2 x + 8x 7 0
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Chapter 4: Problem 11 Algebra and Trigonometry 9
In Problems 722,solve each inequality.x - 1 6 0 2 - 9 6 0
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Chapter 4: Problem 12 Algebra and Trigonometry 9
In Problems 722,solve each inequality.x + x 7 12 2 x - 1 6 0
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Chapter 4: Problem 13 Algebra and Trigonometry 9
In Problems 722,solve each inequality.x + 7x 6 -12 2 x + x 7 12
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Chapter 4: Problem 14 Algebra and Trigonometry 9
In Problems 722,solve each inequality.x2 x + 7x 6 -12
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Chapter 4: Problem 15 Algebra and Trigonometry 9
In Problems 722,solve each inequality.2x 6 6 + 5x 2 6 5x + 3
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Chapter 4: Problem 16 Algebra and Trigonometry 9
In Problems 722,solve each inequality.6x - x + 1 0 2 2x 6 6 + 5x
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Chapter 4: Problem 17 Algebra and Trigonometry 9
In Problems 722,solve each inequality.x + 2x + 4 7 0 2 6x - x + 1 0
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Chapter 4: Problem 18 Algebra and Trigonometry 9
In Problems 722,solve each inequality.x2 x + 2x + 4 7 0
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Chapter 4: Problem 19 Algebra and Trigonometry 9
In Problems 722,solve each inequality.4x + 16 6 40x 2 + 9 6 6x
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Chapter 4: Problem 20 Algebra and Trigonometry 9
In Problems 722,solve each inequality.25x - 12 7 5x 2 4x + 16 6 40x
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Chapter 4: Problem 21 Algebra and Trigonometry 9
In Problems 722,solve each inequality.61x - 3x2 7 -9 2 25x - 12 7 5x
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Chapter 4: Problem 22 Algebra and Trigonometry 9
In Problems 722,solve each inequality.212x2 61x - 3x2 7 -9
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Chapter 4: Problem 23 Algebra and Trigonometry 9
What is the domain of the functionf1x2 = 2x ? 2 - 16?
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Chapter 4: Problem 24 Algebra and Trigonometry 9
What is the domain of the functionf1x2 = 2x - 3x2?
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Chapter 4: Problem 25 Algebra and Trigonometry 9
In Problems 2532, use the given functions f and g. (a) Solve f1x2 = 0. (b) Solve g1x2 = 0. (c) Solve f1x2 = g1x2. (d) Solve f1x2 7 0. (e) Solve g1x2 0. (f) Solve f1x2 7 g1x2. (g) Solve f1x2 1.f1x2 = x2 - 1 g1x2 = 3x + 3
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Chapter 4: Problem 26 Algebra and Trigonometry 9
In Problems 2532, use the given functions f and g. (a) Solve f1x2 = 0. (b) Solve g1x2 = 0. (c) Solve f1x2 = g1x2. (d) Solve f1x2 7 0. (e) Solve g1x2 0. (f) Solve f1x2 7 g1x2. (g) Solve f1x2 1.f1x2 = -x2 + 3 g1x2 = -3x + 3
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Chapter 4: Problem 27 Algebra and Trigonometry 9
In Problems 2532, use the given functions f and g. (a) Solve f1x2 = 0. (b) Solve g1x2 = 0. (c) Solve f1x2 = g1x2. (d) Solve f1x2 7 0. (e) Solve g1x2 0. (f) Solve f1x2 7 g1x2. (g) Solve f1x2 1.f1x2 = -x2 + 1 g1x2 = 4x + 1
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Chapter 4: Problem 28 Algebra and Trigonometry 9
In Problems 2532, use the given functions f and g. (a) Solve f1x2 = 0. (b) Solve g1x2 = 0. (c) Solve f1x2 = g1x2. (d) Solve f1x2 7 0. (e) Solve g1x2 0. (f) Solve f1x2 7 g1x2. (g) Solve f1x2 1.f1x2 = -x2 + 4 g1x2 = -x - 2
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Chapter 4: Problem 29 Algebra and Trigonometry 9
In Problems 2532, use the given functions f and g. (a) Solve f1x2 = 0. (b) Solve g1x2 = 0. (c) Solve f1x2 = g1x2. (d) Solve f1x2 7 0. (e) Solve g1x2 0. (f) Solve f1x2 7 g1x2. (g) Solve f1x2 1.f1x2 = x2 - 4 g1x2 = -x2 + 4
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Chapter 4: Problem 30 Algebra and Trigonometry 9
In Problems 2532, use the given functions f and g. (a) Solve f1x2 = 0. (b) Solve g1x2 = 0. (c) Solve f1x2 = g1x2. (d) Solve f1x2 7 0. (e) Solve g1x2 0. (f) Solve f1x2 7 g1x2. (g) Solve f1x2 1.f1x2 = x2 - 2x + 1 g1x2 = -x2 + 1
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Chapter 4: Problem 31 Algebra and Trigonometry 9
In Problems 2532, use the given functions f and g. (a) Solve f1x2 = 0. (b) Solve g1x2 = 0. (c) Solve f1x2 = g1x2. (d) Solve f1x2 7 0. (e) Solve g1x2 0. (f) Solve f1x2 7 g1x2. (g) Solve f1x2 1.f1x2 = x2 - x - 2 g1x2 = x2 + x - 2
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Chapter 4: Problem 32 Algebra and Trigonometry 9
In Problems 2532, use the given functions f and g. (a) Solve f1x2 = 0. (b) Solve g1x2 = 0. (c) Solve f1x2 = g1x2. (d) Solve f1x2 7 0. (e) Solve g1x2 0. (f) Solve f1x2 7 g1x2. (g) Solve f1x2 1.f1x2 = -x2 - x + 1 g1x2 = -x2 + x + 6
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Chapter 4: Problem 33 Algebra and Trigonometry 9
Physics A ball is thrown vertically upward with an initial velocity of 80 feet per second. The distance s (in feet) of the ball from the ground after t seconds is (a) At what time t will the ball strike the ground? (b) For what time t is the ball more than 96 feet above the ground?
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Chapter 4: Problem 34 Algebra and Trigonometry 9
Physics A ball is thrown vertically upward with an initial velocity of 96 feet per second.The distance s (in feet) of the ball from the ground after t seconds is (a) At what time t will the ball strike the ground? (b) For what time t is the ball more than 128 feet above the ground?
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Chapter 4: Problem 35 Algebra and Trigonometry 9
Revenue Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is R1p2 = -4p2 + 4000p(a) At what prices p is revenue zero? (b) For what range of prices will revenue exceed $800,000?
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Chapter 4: Problem 36 Algebra and Trigonometry 9
Revenue The John Deere company has found that the revenue from sales of heavy-duty tractors is a function of the unit price p, in dollars, that it charges. If the revenue R, in dollars, is (a) At what prices p is revenue zero? (b) For what range of prices will revenue exceed $1,200,000?R1p2 = - 1 2 p2 + 1900p
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Chapter 4: Problem 37 Algebra and Trigonometry 9
Artillery A projectile fired from the point (0, 0) at an angle to the positive x-axis has a trajectory given by y = cx - 11 + c22ag2b axv b2 where x " horizontal distance in meters y " height in meters " initial muzzle velocity in meters per second (m/sec) g"acceleration due to gravity = 9.81 meters per second squared (m/sec2 ) is a constant determined by the angle of elevation. A howitzer fires an artillery round with a muzzle velocity of 897 m/sec.(a) If the round must clear a hill 200 meters high at a distance of 2000 meters in front of the howitzer, what c values are permitted in the trajectory equation? (b) If the goal in part (a) is to hit a target on the ground 75 kilometers away, is it possible to do so? If so,for what values of c? If not, what is the maximum distance the round will travel?
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Chapter 4: Problem 38 Algebra and Trigonometry 9
Runaway Car Using Hookes Law, we can show that the work done in compressing a spring a distance of x feet from its at-rest position is , where k is a stiffness constant depending on the spring. It can also be shown that the work done by a body in motion before it comes to rest is given by , where w = weight of the object (lb), g = acceleration due to gravity (32.2 ft/sec2 ), and objects velocity (in ft/sec). A parking garage has a spring shock absorber at the end of a ramp to stop runaway cars. The spring has a stiffness constant k = 9450 lb/ft and must be able to stop a 4000-lb car traveling at 25 mph.What is the least compression required of the spring? Express your answer using feet to the nearest tenth. [Hint: Solve ]. Source: www.sciforums.com W 7 W ' , x 0
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Chapter 4: Problem 39 Algebra and Trigonometry 9
Show that the inequality 1x - 422 0 has exactly one solution.
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Chapter 4: Problem 40 Algebra and Trigonometry 9
Show that the inequality 1x - 222 7 0 has one real number that is not a solution.
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Chapter 4: Problem 41 Algebra and Trigonometry 9
Explain why the inequality x2 + x + 1 7 0 has all real numbers as the solution set.
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Chapter 4: Problem 42 Algebra and Trigonometry 9
Explain why the inequality x2 - x + 1 6 0 has the empty set as solution set.
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Chapter 4: Problem 43 Algebra and Trigonometry 9
Explain the circumstances under which the x-intercepts of the graph of a quadratic function are included in the solution set of a quadratic inequality.
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