Annaleya Hamilton
1
PreCalculus: Unit 7: Lesson 3: Apply
November 16, 2016
Write a short paragraph explaining why parametric equations are useful.
Parametric equations allow you to graph the complete position of an object over time. For
example, parametri
Annaleya Hamilton
PreCalculus: Unit 7: Lesson 2: Apply
November 16, 2016
Explain how the equation of a hyperbola and an ellipse are related. Point out any
similarities and differences between the two. Graph the equations of a hyperbola
and ellipse with th
576 Chapter 7 Linear Systems and Matrices
7 Chapter TCSt See www.0alcChat.c0m for worked-out solutions to odd-numbered exercises.
Take this test as you would take a test in class. After you are nished, check your
work against the answers given in the ba
Annaleya Hamilton
1
PreCalculus: Unit 7: Lesson 4: Apply
November 16, 2016
Write a short paragraph explaining the differences between the rectangular
coordinate system and the polar coordinate system.
The polar coordinate system and the rectangular coordi
Annaleya Hamilton
Unit 5: Lesson 5: Apply
November 11, 2016
The famous formula shown below is called Eulers formula, after the Swiss
mathematician Leonhard Euler (1707-1783).
ea + bi = ea(cos b + i sin b)
This formula gives rise to the equation ei + 1 = 0
Annaleya Hamilton
PreCalculus: Unit 6: Lesson 3: Apply
November 15, 2016
In your own words, describe the difference between a matrix in row-echelon form
and a matrix in reduced row-echelon form.
Row echelon form: Have to have a zero below the leading ones
Annaleya Hamilton
1
Precalculus: Unit 6: Lesson 1: Apply
November 15, 2016
Write a short paragraph comparing the three methods of solving systems
of equations. Describe the advantages and disadvantages of each method.
Graphing is the easiest method to sol
Annaleya Hamilton
Precalculus: Unit 6: Lesson 2: Apply
November 15, 2016
When using Gaussian elimination to solve a system of linear equations, explain
how you can recognize that the system has no solution. Give an example that
illustrates your answer.
Wh
Annaleya Hamilton
Precalculus: Unit 7: Lesson 1: Apply
November 16, 2016
Explain what each of the following represents, and how equations (a) and (b) are
equivalent.
(a) y = a(x - h)2 + k, a 0
Quadratic: Standard (Vertex) Form
(b) (x - h)2 = 4p(y - k), p
Annaleya Hamilton
Unit 5: Lesson 1: Apply
November 7, 2016
Can the Law of Sines be used to solve a right triangle? Write a short paragraph
explaining why it can or cannot be used. If it can be used, explain how to use it.
Is there an easier way to solve t
Annaleya Hamilton
Pre-Calculus: Unit 5: Lesson 2: Apply
November 7, 2016
Describe how the Law of Cosines can be used to solve the ambiguous case of
the oblique triangle ABC, where a = 12 feet, b = 30 feet, and A = 20. Is the result
the same as when the La
Annaleya Hamilton
1
Pre-Calculus: Unit 5: Lesson 3: Apply
November 8, 2016
In your own words, state the difference between a scalar and a vector.
Give examples of each.
Vectors have magnitude and direction (Ex: Displacement), scalars only have
magnitude a
Annaleya Hamilton
Pre-Calculus: Unit 5: Lesson 4: Apply
November 8, 2016
What is known about , the angle between two nonzero vectors u and v, if each
of the following is true? Explain your answers.
1 u v = 0 -> = +/- pi/2: u and v are orthogonal: u _|_ v
Annaleya Hamilton
Pre-Calculus: Unit 2: Lesson 2: Apply
September 23, 2016
Complete and submit the assignment below, then you can proceed onto the next
lesson.
1 Let y = f(x) be a cubic polynomial with leading coefficient a = 2 and f(-2) =
f(1) = f(2) = 0
Annaleya Hamilton
Pre-Calculus: Unit 4: Lesson 2: Apply
October 26, 2016
For both problems:
A
B
1.
Verify the identity.
Determine if the identity is true for the given value of x. Explain.
Annaleya Hamilton
2.
Pre-Calculus: Unit 4: Lesson 2: Apply
October
Annaleya Hamilton
Pre-Calculus: Unit 2: Lesson 3: Apply
September 23, 2016
Determine whether the statement is true or false. Justify your reasoning.
1 There is no complex number that is equal to its conjugate.
False. Real numbers are a subset of complex n
Annaleya Hamilton
Pre-Calculus: Unit 3: Lesson 2: Apply
October 4, 2016
Determine whether the statement is True or False. Justify your answer.
1
sin a = sin(a - 6)
True.
sin(a - 6pi)
(using the following identity: sin (s - t) = - cos(s)sin(t) + cos(t)sin(
Annaleya Hamilton
Pre-Calculus: Unit 3: Lesson 3: Apply
October 4, 2016
You are given the value of tan . is it possible to find the value of sec without
finding the measure of ? Explain.
It is not possible to find the value of sec without finding the meas
Annaleya Hamilton
Pre-Calculus: Unit 2: Lesson 5: Apply
September 26, 2016
Determine whether the statement is true or false. Justify your answer.
1. A rational function must have at least one vertical asymptote.
False. Not every rational function must hav
Annaleya Hamilton
Pre-Calculus: Unit 2: Lesson 4: Apply
September 26, 2016
Compile a list of all the various techniques for factoring a polynomial that have
been covered so far in the course. Give an example illustrating each technique,
and write a paragr
Annaleya Hamilton
Pre-Calculus: Unit 3: Lesson 4: Apply
September 5, 2016
Consider an angle in standard position with r = 12 centimeters, as shown in the
figure. Write a short paragraph describing the changes in the magnitudes of x, y,
sin , cos , and tan
Annaleya Hamilton
Pre-Calculus: Unit 2: Lesson 6: Apply
September 26, 2016
Explain why the parabola shown in the figure below is not a good fit for the data.
The parabola shown is not a good fit because it is far away from all the data
points. It looks li
Annaleya Hamilton
Pre-Calculus: Unit 3: Lesson 5: Apply
October 5, 2016
Use a graphing utility to graph the function y = d + a sin (bx - c) for different
values of a, b, c, and d. Write a paragraph describing the changes in the graph
corresponding to chan
Annaleya Hamilton
Pre-Calculus: Unit 4: Lesson 1: Apply
October 11, 2016
Use the Pythagorean identity sin2 + cos2 = 1 to derive the other
Pythagorean identities, 1 + tan2 = sec2 and 1 + cot2 = csc2 . Discuss
how to remember these identities and other fund
Annaleya Hamilton
Unit 2: Lesson 1: Apply
September 13, 2016
The parabola in the figure below has an equation of the form y = ax2 + bx - 4.
Find the equation of the parabola using two different methods, by hand and with
technology (graphing utility or com
Annaleya Hamilton
Pre-Calculus: Unit 3: Lesson 6: Apply
October 6, 2016
Define the inverse secant function by restricting the domain of the secant
function to the intervals:
and sketch the inverse
functions graph.
The blue function is y = sec(x) = 1/cos(x
Pre-Calculus: Unit 3:
Unit Project
Annaleya Hamilton
October 13, 2016
1a)
Graphs for #5)
in standard position
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