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Julie S.

Syracuse University

Biography

Hi! My name is Julie and I have been a high school math teacher for 11 years. I have taught almost every math class offered at the high school level, for example Algebra 1, Geometry, Algebra 2, Trigonometry, PreCalculus, and AP Calculus. I enjoy helping students learn new mathematical concepts, so feel free to reach out if you have any questions.

Education

BA Mathematics and Mathematics Education
Syracuse University

Topics Covered

Functions
Functions
Rational Functions
Exponents and Polynomials
Polynomials
Graphs and Statistics
Equations and Inequalities
Linear Functions
Systems of Equations and Inequalities
Algebra Topics That are Reviewed at the Start of the Semester
Quadratic Functions
The Integers
An Introduction to Geometry
Introduction to Algebra
Introduction to Conic Sections
Introduction to Conic Section
Series
Introduction to Sequences and Series
The Language of Algebra
Introduction to Sequences and Series
Whole which of Numbers
Trigonometry
Introduction to Trigonometry
Exponential and Logarithmic Functions
Fractions and Mixed Numbers
Ratio, Proportion, and Measurement
Graph Linear Functions
Write Linear Equations
Linear Equations and Functions
Matrices and Determinants
Linear Equations and Inequalities
Complex Numbers
Right Triangles
Circles
Decimals
Introduction to Matrices
Introduction to Combinatorics and Probability
Sequences
Factoring Polynomials
Radicals and Rational Exponents
Quadratic Equations
Congruent Triangles
Solve Linear Inequalities
Introduction to Combinatorics and Probability
Introduction to Vectors
Area and Perimeter
Relationships Within Triangles
Logic
Parametric Equations
Polar Coordinates
Geometric Proof
Angles
Parallel and Perpendicular lines
Geometry Basics
Properties of Quadrilaterals
Limits
Derivatives
Differentiation
Integrals
Integration
Integration Techniques
Applications of Integration
Partial Derivatives
Functions of Several Variables

Julie's Textbook Answer Videos

02:42
Precalculus with Limits

In Exercises 35-38, find values for $b$ such that the triangle has (a) one solution, (b) two solutions, and (c) no solution.

$A\ =\ 36^{\circ}$,

$a\ =\ 5$

Chapter 6: Additional Topics in Trigonometry
Section 1: Law of Sines
Julie S.
04:07
Precalculus with Limits

HEIGHT A flagpole at a right angle to the horizontal is located on a slope that makes an angle of $12^{\circ}$ with the horizontal. The flagpole's shadow is 16 meters long and points directly up the slope. The angle of elevation from the tip of the shadow to the sun is $20^{\circ}$.

(a) Draw a triangle to represent the situation. Show the known quantities on the triangle and use a variable to indicate the height of the flagpole.

(b) Write an equation that can be used to find the height of the flagpole.

(c) Find the height of the flagpole.

Chapter 6: Additional Topics in Trigonometry
Section 1: Law of Sines
Julie S.
03:48
Precalculus with Limits

FLIGHT PATH A plane flies 500 kilometers with a bearing of $316^{\circ}$ from Naples to Elgin (see figure). The plane then flies 720 kilometers from Elgin to Canton(Canton is due west of Naples). Find the bearing of the flight from Elgin to Canton.

Chapter 6: Additional Topics in Trigonometry
Section 1: Law of Sines
Julie S.
03:43
Precalculus with Limits

BRIDGE DESIGN A bridge is to be built across a small lake from a gazebo to a dock (see figure). The bearing from the gazebo to the dock is S $41^{\circ}$W. From a tree 100 meters from the gazebo, the bearings to the gazebo and the dock are S $74^{\circ}$E and S $28^{\circ}$E, respectively. Find the distance from the gazebo to the dock.

Chapter 6: Additional Topics in Trigonometry
Section 1: Law of Sines
Julie S.
03:36
Precalculus with Limits

RAILROAD TRACK DESIGN The circular arc of a railroad curve has a chord of length 3000 feet corresponding to a central angle of $40^{\circ}$.

(a) Draw a diagram that visually represents the situation.Show the known quantities on the diagram and use the variables $r$ and $s$ to represent the radius of the arc and the length of the arc, respectively.

(b) Find the radius $r$ of the circular arc.

(c) Find the length $s$ of the circular arc.

Chapter 6: Additional Topics in Trigonometry
Section 1: Law of Sines
Julie S.
07:28
Precalculus with Limits

GLIDE PATH A pilot has just started on the glide path for landing at an airport with a runway of length 9000 feet. The angles of depression from the plane to the ends of the runway are $17.5^{\circ}$ and $18.8^{\circ}$.

(a) Draw a diagram that visually represents the situation.

(b) Find the air distance the plane must travel until touching down on the near end of the runway.

(c) Find the ground distance the plane must travel until touching down.

(d) Find the altitude of the plane when the pilot begins the descent.

Chapter 6: Additional Topics in Trigonometry
Section 1: Law of Sines
Julie S.
1 2 3 4 5 ... 1897

Julie's Conceptual Videos

01:32
Introduction to Algebra

Absolute Value - Example 1

In mathematics, the absolute value or modulus |x| of a real number x is its numerical value without regard to its sign. The absolute value of a number may be thought of as its distance from zero along a number line; this interpretation is analogous to the distance function assigned to a real number in the real number system. For example, the absolute value of ?4 is 4, and the absolute value of 4 is 4, both without regard to sign.
Julie Silva
01:11
Introduction to Algebra

Absolute Value - Example 2

In mathematics, the absolute value or modulus |x| of a real number x is its numerical value without regard to its sign. The absolute value of a number may be thought of as its distance from zero along a number line; this interpretation is analogous to the distance function assigned to a real number in the real number system. For example, the absolute value of ?4 is 4, and the absolute value of 4 is 4, both without regard to sign.
Julie Silva
00:59
Introduction to Algebra

Absolute Value - Example 3

In mathematics, the absolute value or modulus |x| of a real number x is its numerical value without regard to its sign. The absolute value of a number may be thought of as its distance from zero along a number line; this interpretation is analogous to the distance function assigned to a real number in the real number system. For example, the absolute value of ?4 is 4, and the absolute value of 4 is 4, both without regard to sign.
Julie Silva
01:43
Introduction to Algebra

Absolute Value - Example 4

In mathematics, the absolute value or modulus |x| of a real number x is its numerical value without regard to its sign. The absolute value of a number may be thought of as its distance from zero along a number line; this interpretation is analogous to the distance function assigned to a real number in the real number system. For example, the absolute value of ?4 is 4, and the absolute value of 4 is 4, both without regard to sign.
Julie Silva
04:56
Introduction to Algebra

Absolute Value - Overview

In mathematics, the absolute value or modulus |x| of a real number x is its numerical value without regard to its sign. The absolute value of a number may be thought of as its distance from zero along a number line; this interpretation is analogous to the distance function assigned to a real number in the real number system. For example, the absolute value of ?4 is 4, and the absolute value of 4 is 4, both without regard to sign.
Julie Silva
02:34
Introduction to Algebra

Adding and Subtracting Rational Numbers - Example 1

In mathematics, the term rational number refers to any number that can be expressed as the quotient or fraction of two integers, a numerator divided by a denominator. The set of all rational numbers is usually denoted by a boldface Q, and is thus the set of all fractions. Rational numbers include all integers, most fractions, and all other numbers that can be written as a/b, where a and b are integers and b is not zero. The numbers are formed by a sequence of numerals, where the denominator is either a single digit, or two or more digits.
Julie Silva
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