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study help
mathematics
precalculus
Precalculus 9th edition Michael Sullivan - Solutions
Write each expression in the standard form a + bi.i14
Write each expression in the standard form a + bi.i23
Write each expression in the standard form a + bi. (1 – i)? 2
Write each expression in the standard form a + bi. (1 + i)?
Write each expression in the standard form a + bi. V3 1 2
Write each expression in the standard form a + bi. 1 V3 \2 2 2 +
When dividing a polynomial by x - c do you prefer to use long division or synthetic division? Does the value of c make a difference to you in choosing? Give reasons.
Write each expression in the standard form a + bi. 2 + 3i 1 - i
Write each expression in the standard form a + bi. 6 - i 1 + i
Write each expression in the standard form a + bi. 2 - i -2i
Write each expression in the standard form a + bi. 2 + i i
Write each expression in the standard form a + bi. 13 5 – 12i
Write each expression in the standard form a + bi. 10 3 – 4i
Write each expression in the standard form a + bi.(-3 + i)(3 + i)
Write each expression in the standard form a + bi.(-6 + i)(-6 - i)
Write each expression in the standard form a + bi.(5 + 3i)(2 - i)
Write each expression in the standard form a + bi.(3 - 4i)(2 + i)
Write each expression in the standard form a + bi.3i(-3 + 4i)
Write each expression in the standard form a + bi.2i(2 - 3i)
Write each expression in the standard form a + bi.-4(2 + 8i)
Write each expression in the standard form a + bi.3(2 - 6i)
Write each expression in the standard form a + bi.(-8 + 4i) - (2 - 2i)
Write each expression in the standard form a + bi.(2 - 5i) - (8 + 6i)
Write each expression in the standard form a + bi.(3 - 4i) - (-3 - 4i)
Write each expression in the standard form a + bi.(-3 + 2i) - (4 - 4i)
Write each expression in the standard form a + bi.(4 + 5i) + (-8 + 2i)
Write each expression in the standard form a + bi.(2 - 3i) + (6 + 8i)
Create a problem different from any found in the text that requires a combination to solve. Give it to a friend to solve and critique.
Create a problem different from any found in the text that requires a permutation to solve. Give it to a friend to solve and critique.
Investigate the notion of counting as it relates to infinite sets. Write an essay on your findings.
Make up a problem different from any found in the text that requires the addition principle of counting to solve. Give it to a friend to solve and critique.
Make up two infinite geometric series, one that has a sum and one that does not. Give them to a friend and ask for the sum of each series.
Write a paragraph that explains why the numbers found in Problem 97 are called triangular. Data from Problem 97A triangular number is a term of the sequence u1 = 1, un +1 = un + (n + 1). Write down the first seven triangular numbers.
Investigate various applications that lead to a Fibonacci sequence, such as art, architecture, or financial markets. Write an essay on these applications.
Make up an arithmetic sequence. Give it to a friend and ask for its twentieth term.
How would you explain the Principle of Mathematical Induction to a friend?
Describe four ways of solving a system of three linear equations containing three variables. Which method do you prefer? Why?
Make up a system of three linear equations containing three variables that has: (a) No solution (b) Exactly one solution (c) Infinitely many solutions. Give the three systems to a friend to solve and critique.
Create a situation different from any found in the text that can be represented by a matrix.
When solving a system of linear equations using matrices, do you prefer to place the augmented matrix in row echelon form or in reduced row echelon form? Give reasons for your choice.
Do you prefer the method of substitution or the method of elimination for solving a system of two linear equations containing two variables? Give reasons.
Make up a system of three linear equations containing three variables that has: (a) No solution (b) Exactly one solution (c) Infinitely many solutions Give the three systems to a friend to solve and critique.
Explain in your own words what a linear programming problem is and how it can be solved.
The eccentricity e of an ellipse is defined as the number c/a where a is the distance of a vertex from the center and c is the distance of a focus from the center. Because a > c, it follows that e < 1. Write a brief paragraph about the general shape of each of the following ellipses. Be
Formulate a strategy for discussing and graphing an equation of the form Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
Look up the curves called hypocycloid and epicycloid. Write a report on what you find. Be sure to draw comparisons with the cycloid.
In Problem 62, we graphed the hypocycloid. Now graph the rectangular equations of the hypocycloid. Did you obtain a complete graph? If not, experiment until you do. Data From Problem 62.The hypocycloid is a curve defined by the parametric equations x(t) = cos3t, y(t) = sin3 t, 0 ≤ t ≤
How does your strategy change if the equation is of the following form?Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
Formulate a strategy for discussing and graphing an equation of the formAx2 + Bxy + Cy2 + Dx + Ey + F = 0
Explain the difference between an algebraic vector and a position vector.
Explain in your own words what a vector is. Give an example of a vector.
Write a brief paragraph comparing the algebra of complex numbers and the algebra of vectors.
Open the Vectors applet. Suppose v = 2i + 3j and w = 4i - 3j.
Open the Vectors applet. Draw the directed line segment from P1= (1,2) to P2= (5,4). Then draw the position vector v = P1P2(vector)
Explain why the vertical-line test used to identify functions in rectangular coordinates does not work for equations expressed in polar coordinates.
Write down two different tests for symmetry with respect to the polar axis. Find examples in which one test works and the other fails. Which test do you prefer to use? Justify your answer.
Is the street system in your town based on a rectangular coordinate system, a polar coordinate system, or some other system? Explain.
Explain how you proceed to convert from rectangular coordinates to polar coordinates.
1. Go to http://www.mindomo.com and register. Learn how to use Mindomo. Agreat video on using Mindomo can be found at http://www.screencast.com/users/Rose_Jenkins/folders/Default/media/edd9bd1b-62a7-45b3-9dd2-fa467d2e8eb3.2. Use an Internet search engine to research Mind Mapping. Write a few
Create an application different from any found in the text that requires a dot product.
Explain how you would measure the height of a TV tower that is on the roof of a tall building.
Explain how you would measure the width of the Grand Canyon from a point on its ridge.
What do you do first if you are asked to solve a triangle and are given two sides and the angle opposite one of them?
What do you do first if you are asked to solve a triangle and are given one side and two angles?
How would you explain to a friend what simple harmonic motion is? How would you explain damped motion?
Make up three problems involving oblique triangles. One should result in one triangle, the second in two triangles, and the third in no triangle.
Write down your strategy for solving an oblique triangle.
Make up an applied problem that requires using the Law of Cosines.
What do you do first if you are asked to solve a triangle and are given three sides?
The sound from a tuning fork is collected over time. Determine the amplitude, frequency, and period of the graph.A model of the form y = A cos[B(x - C)] is fitted to the data. (Activity 23, Real-World Math with the CBL System.)
What do you do first if you are asked to solve a triangle and are given two sides and the included angle?
Pendulum motion is analyzed to estimate simple harmonic motion. A plot is generated with the position of the pendulum over time.The graph is used to find a sinusoidal curve of the form y = A cos[B(x - C)] + D. Determine the amplitude, period, and frequency. (Activity 16, Real-World Math with the
State the area of an SAS triangle in words.
What do you do first if you are asked to find the area of a triangle and are given three sides?
What do you do first if you are asked to find the area of a triangle and are given two sides and the included angle?
Explain in your own words how you would use your calculator to solve the equation cos x = -0.6, 0 ≤ x < 2π. How would you modify your approach to solve the equation cot x = 5,0 < x < 2π?
Go to the library and research Chebyshëv polynomials. Write a report on your findings.
Make up an identity that is not a Fundamental Identity.
Why do you think it is usually preferable to start with the side containing the more complicated expression when establishing an identity?
Write a few paragraphs outlining your strategy for establishing identities.
Consult three books on calculus and write down the definition in each of y = sec-1 x and y = csc-1 x. Compare these with the definitions given in this book.
Explain in your own words how you would use your calculator to find the value of cot-1 10.
Explain how to find the value of sin 390° and cos (-45°) using the unit circle.
Explain how to find the value of cos( -45°) using even-odd properties.
How would you explain the meaning of the sine function to a fellow student who has just completed college algebra?
Explain how to find the value of sin 390° using periodic properties.
Write a brief paragraph that explains how to quickly compute the trigonometric functions of 0°, 90°, 180°, and 270°.
Describe your understanding of the meaning of a periodic function.
Write a brief paragraph that explains how to quickly compute the trigonometric functions of 30°, 45°, and 60°.
Write down five properties of the tangent function. Explain the meaning of each.
Investigate the way that speed bicycles work. In particular, explain the differences and similarities between 5-speed and 9-speed derailleurs. Be sure to include a discussion of linear speed and angular speed.
Discuss why ships and airplanes use nautical miles to measure distance. Explain the difference between a nautical mile and a statute mile.
Do you prefer to measure angles using degrees or radians? Provide justification and a rationale for your choice.
On the screen you will see a slider. Move the point along the slider to see the role v plays in the graph of f(x) = sin(ωx). Pay particular attention to the key points matched by color on each graph. For convenience the graph of g(x) = sin x is shown as a dashed, gray curve.
On the screen you will see a slider. Move the point along the slider to see the role a plays in the graph of f(x) = a sin x.
On the screen you will see the graph of the unit circle with a point C labeled. Use your mouse and move point C around the unit circle in the counterclockwise direction.What do you notice? In particular, what is the relation between the angle and the x-coordinate of point C?
On the screen you will see the graph of the unit circle with a point C labeled. Use your mouse and move point C around the unit circle in the counterclockwise direction.What do you notice? In particular, what is the relation between the angle and the y- coordinate of point C?
Find an application in your major field that leads to a sinusoidal graph. Write a paper about your findings.
Explain how the amplitude and period of a sinusoidal graph are used to establish the scale on each coordinate axis.
Explain the term period as it relates to the graph of a sinusoidal function.
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