## System of NonLinear Equations problems

## System of NonLinear Equations problem example

Find Real and Imaginary solutions, whichever exist, to the Systems of NonLinear Equations:

**a)**

**b)**

Solution to these **Systems of NonLinear Equations** practice problems is provided in the video below!

## HARD System of NonLinear Equations example question

Determine Real and Imaginary solutions, whichever exist, to the given System of NonLinear Equations:

Solution to this **Hard System of NonLinear Equations** practice problem is provided in the video below!

## VERY HARD System of NonLinear Equations example

Solve the System of NonLinear Equations provided below:

Solution to this **Very Hard System of NonLinear Equations** practice problem is provided in the video below!

## HARDEST System of NonLinear Equations example problem

Find the solutions to the System of NonLinear Equations provided below:

Solution to this **Most Difficult System of NonLinear Equations** practice problem is provided in the video below!

## NonLinear System of Equations Word Problem

A rectangle of perimeter 100 meters is to be constructed to have area 100 square meters. What dimensions are required?

Solution to this **NonLinear System of Equations** word practice problem is provided in the video below!

## Partial Fraction Decomposition problems

## Linear Factors Partial Fraction Decomposition problem example

Find the Partial Fraction Decomposition for the following Fraction:

Solution to this **Linear Factors Partial Fraction Decomposition** practice problem is provided in the video below!

## Linear Factors Partial Fraction Decomposition ALTERNATE Method example question

Alternate method takes into account the *x*-values in the equation that one can test to find the constants immediately instead of comparing coefficients.

Find the Partial Fraction Decomposition for the same example as above by using the Alternate Method:

Solution to this **Alternate Method Linear Factors Partial Fraction Decomposition** practice problem is provided in the video below!

## QUADRATIC Factors Partial Fraction Decomposition example

Find the Partial Fraction Decomposition for the Fraction provided below:

Solution to this **Quadratic Factors Partial Fraction Decomposition** practice problem is provided in the video below!

## HARD QUADRATIC Factors Partial Fraction Decomposition example problem

Determine the Partial Fraction Decomposition for the Fraction provided below:

Solution to this **Difficult Quadratic Factors Partial Fraction Decomposition** practice problem is provided in the video below!

## Multiple Integral problems (complete Playlist)

The following playlist shows a variety of **Calculus** examples and practice problems dealing with **Double Integration**, **Changing Order of Integration**, **Triple Integration**, **Cylindrical Coordinates**, **Spherical Coordinates**, and more!

## Trigonometric Form of Complex Numbers problems

## Complex Number Trigonometric Form Representation problem example

Express the following Complex Numbers in Trigonometric Form:

-12

-8*i *

2 – 2*i *

Solution to this **Complex Number Trigonometric Form Representation** practice problem is provided in the video below!

## Trigonometric Complex Number Product Quotient Power Rectangular Standard Form Representation example question

Find the resulting Complex Number in standard (rectangular) form for the following:

Solution to this **Trigonometric Complex Number Product Quotient Power Rectangular Standard Form Representation **practice problem is provided in the video below!

## Square Roots of a Complex Number example

Find the two Square Roots of

Solution to this **Square Roots of a Complex Number** practice problem is provided in the video below!

## Complex Number Rectangular POLAR Form Conversion example problem

Express the following POLAR Complex Number in Trigonometric and Rectangular Form:

Express the following Rectangular Complex Number in Trigonometric Form and POLAR Form:

5*i*

Solution to this **Complex Number Polar Rectangular Form Conversion** practice problem is provided in the video below!

## Complex Number POLAR Product Quotient Power example question

Find the resulting Complex Number in POLAR form for the following:

a)

b)

Find the resulting Complex Number in POLAR and RECTANGULAR (standard) form:

Solution to this **Complex Number Polar Product Quotient Power** practice problem is provided in the video below!

## POLAR Complex Number Nth Root Theorem example

Find the Four 4th (Fourth) Roots of

Solution to this **Polar Complex Number Nth Root Theorem** practice problem is provided in the video below!

## Vector word problems

## Horizontal and Vertical Components of a Force Vector problem example

A force of 46.3 pounds is applied at an angle of 34.8º to the horizontal. Resolve the force into horizontal and vertical components.

Solution to this **Horizontal Vertical Components of a Force Vector word** practice problem is provided in the video below!

## HARD Parallel Perpendicular Weight Vector Components to Surface word problem

A weight of 75 pounds is resting on a surface inclined at an angle of 25º to the ground. Find the components of the weight parallel and perpendicular to the surface.

Solution to this **Parallel Perpendicular Weight Vector Components word** practice problem is provided in the video below!

## VERY HARD Resultant Force Vector example question

Find the resultant of two forces, one with magnitude 155 pounds and direction *N*50º*W*, and a second with magnitude 305 pounds and direction *S*55º*W*.

Solution to this **Resultant Force Vector word** practice problem is provided in the video below!

## Plane Wind vector example problem

An airplane has an airspeed of 430 miles per hour at a bearing of *E*45º*S* (45 degrees South of East). The wind velocity is 35 miles per hour in the direction of *N*30º*E* (30 degrees East of North). Find the ground speed and true course of the plane using vectors.

Solution to this **Plane Wind vector word** practice problem is provided in the video below!

## Law of Cosines problems

## Law of Cosines word problem example

Two sides of a parallelogram are 9 and 15 units in length. The length of the shorter diagonal of the parallelogram is 14 units. Find the length of the long diagonal.

Solution to this **Law of Cosines word** practice problem is provided in the video below!

## HARD Law of Cosines word problem

A new car leaves an auto transport trailer for a test drive in the flat surface desert in the direction N47ºW at constant speed of 65 miles per hour. The trailer proceeds at constant rate of 50 miles per hour due East. If the car has enough fuel for exactly 3 hours of riding at constant speed, what is the maximum distance in the same direction that the car can cover in order to safely return to the trailer?

Solution to this **Law of Cosines word** practice problem is provided in the video below!

## Law of Sines problems

## Law of Sines word problem example

A radio antenna is attached to the top of the building. From a point 12.5 meters from the base of the building, on level ground, the angle of elevation of the bottom of the antenna is 47.2 degrees and the angle of elevation of the top is 51.8 degrees. Find the height of the antenna.

Solution to this **Law of Sines word** practice problem is provided in the video below!

## Law of Sines Triangle Area PROOF problem

Show that for any triangle the area is one-half the product of any two sides and sine of the angle formed between these sides. That is,

Solution to this **Law of Sines Triangle Area PROOF** practice problem is provided in the video below!

## Inverse Trigonometric Functions problems

## Hard Inverse Trigonometric Expression Value example question

Evaluate the following Trigonometric Expression:

Solution to this **Inverse Trigonometric Expression Value** practice problem is provided in the video below!

## Rectangle Word Problem with ArcTangent example

A rectangle is 173 meters long and 106 meters high. Find the angle between diagonal and the longer side.

Solution to this **Inverse Trigonometric Function word** practice problem is provided in the video below!

## Trigonometric Equations with Angle Sum, Difference, Multiple, Half-Angle Formulas problems

## Trigonometric Equation Double-Angle and Product-To-Sum example

Solve the following Trigonometric Equations using Double-Angle and Product-To-Sum formulas:

sin2** θ** – sin

**= 0**

*θ*cos** x** + cos3

**= cos2**

*x*

*x*

Solution to this **Trigonometric Equation Double-Angle Product-To-Sum** practice problem is provided in the video below!

## Trigonometric Angle Sum, Difference, Multiple, Half-Angle Formulas problems

## Trigonometric Angle Sum and Difference example question

Find the value of the following Trigonometric Expressions using Angle Sum or Difference formulas:

cos(105º)

Solution to this **Trigonometric Angle Sum Difference** practice problem is provided in the video below!

## Trigonometric Equations problems

## Solution to Trigonometric Equation example question

Solve the following Trigonometric Equations:

tan(3*t*) = 1

2cos^{2}*u* = cos*u*

ln(sin*x*) = 0

Solution to this **Trigonometric Equations** practice problem is provided in the video below!

## Conversion of Radians, Degrees, Minutes, and Seconds problems

## Radian Degree Minute Second Transformation example question

a) Convert the following angle measure given in Radians into Degrees, Minutes and Seconds:

**5 Radians**

b) Convert the following angle measure in Degrees, Minute and Seconds into Radians:

**424 ^{o}34‘ 24”**

Solution to this **Angle Measure Radian Degree Minutes Seconds Conversion** practice problem is provided in the video below!

## Graphing Trigonometric Functions problems

## Amplitude Period Phase Shift of Trigonometric Functions example

Find the Amplitude, Period, Phase Shift, and Vertical Shift for each of the following Trigonometric Functions:

Solution to this **Trigonometric Function Graph** practice problem is provided in the video below!

## All Key Features of Trigonometric Functions example problem

For each of the following Trigonometric Functions, find the Amplitude, Period, Frequency, Midline Equation, Phase Shift, Vertical Shift, Horizontal Stretch or Shrink, Vertical Stretch or Shrink, Domain, and Range.

Solution to this **Trigonometric Function Graph** practice problem is provided in the video below!

## GRAPH of Trigonometric Functions example question

Draw a Graph of the following Trigonometric Functions:

Solution to this **Graph of Trigonometric Function** practice problem is provided in the video below!

## Basic Trigonometric Angles and Values problems

## Find ANY Known Trigonometric Value by Hand example question

How do you find the values like or or ?

There is a way to use the Unit Circle information and fill out your own Table of Values fast!

All you need is to start with sine function values in the interval [0, ]

Watch the video below with a detailed tutorial and start being a **pro** at this!

Solution to this **Basic Trigonometric Function Values** practice problem is provided in the video below!

## Linear Functions problems

## Linear Function Word Problem example question

It is common that a piece of equipment has a residual value after it has been depreciated over its entire lifetime.

(a) Find the rule for * V*(

**), the value of a piece of equipment, assuming that the value at time**

*t**= 0 is*

**t**

**V****and that the value after 20 years is**

_{o}*.*

**R**(b) Use the rule to find the value after 12 years of a piece of equipment originally valued at $7500, assuming that it has a residual value after 20 years of $500.

Solution to this **Linear Function** practice problem is provided in the video below!

## Transformation and Graphs of Functions problems

## Transformation and Graphs of Functions SKETCHING example question

(a) Describe how the graph of * x* =

**(**

*f**) relates to the graph of*

**y***=*

**y****(**

*f***)**

*x*(b) Sketch the Graphs of and

Solution to this **Transformation and Graph of a Function** practice problem is provided in the video below!

## Reference Angles problems

## Finding Trigonometric Values Using Reference Angles example question

Find the value of the following Trigonometric Expressions using appropriate Reference Angles:

a) sin(120º)

b)

c) tan(-45º)

d)

e) sec(240º)

f)

Solution to this **Reference Angle** practice problem is provided in the video below!

## Trigonometric Functions problems

## Find All Six Trigonometric Functions using Rectangular Coordinates or given Angle example question

a) If ** t** is a point on the unit circle with coordinates , find the six Trigonometric Functions of

*t*b) Find the six Trigonometric Functions of

Solution to this **Trigonometric Function** practice problem is provided in the video below!

## World’s HARDEST Easy Geometry problems

## World’s HARDEST Easy Geometry problem example question

The following triangle, , shows angle measures in the base angles ** A **and

**, as well as line segments , and . Find the measure of angle**

*C**AED*, that is, .

**Note:** Do not use Trigonometry or Calculus to solve this problem

Solution to this **World’s Hardest Easy Geometry** practice problem is provided in the video below!

## Algebraic and Graph Symmetry Test problems

## Algebraic Symmetry Test example problem

Determine if any of the following Equations and their respective Graphs have ** x-axis** symmetry,

**symmetry, or**

*y*-axis**origin**symmetry.

a.

b.

Solution to these **Algebra Symmetry Tests** practice problems is provided in the video below!

## Symmetry Test GRAPHING example question

Determine if any of the following Equations and their respective Graphs have ** x-axis** symmetry,

**symmetry, or**

*y*-axis**origin**symmetry, and then graph each Equation.

a.

b.

Solution to these **Graphical Symmetry Tests** practice problems is provided in the video below!

## Rational and Radical Expressions problems

## HARD Rational Expression example question

Reduce and Simplify the following Rational Expressions to lowest terms:

a.

b.

c.

d.

Solution to these **Rational Expression** practice problems is provided in the video below!

## HARD Radical Expression example problem

Reduce and Simplify the following Radical Expressions to lowest terms:

a.

b.

c.

d.

Solution to these **Radical Expression** practice problems is provided in the video below!

## Finding Inverse Functions using Algebra & Graphing Techniques problems

## Inverse Function Algebra example problem

Determine the Inverse function of the Square Root function provided below:

Solution to this **Inverse Function** practice problem is provided in the video below!

## HARD Inverse Function Algebra Graphing example question

Determine Inverse functions of the following functions:

Solution to this **Inverse Function** practice problem is provided in the video below!

## Recent Comments