Project #4767 - Algebra assessment task

Hi

I had personal issues so couldn't complete this assessment myself, I need this quite urgently.

See questions below

 

Task 1: The ratio problem

A line of Army men starts marching along the road. The length of the line is X metre

and is moving at a constant speed. A Sergeant, doing inspections, begins at the rear of

the line, marches forward toward the front of the line. When he reaches the front of

the line, he promptly turns around, and marches back to the rear of the line. While the

sergeant was performing his inspection, the line moved X metre. Assuming that all

people travel at constant speeds, what was the ratio between the speed of the sergeant

and the speed of the Army line?

 

 

Task 2: The Poles Problem

The sports arena has two poles for flags out front. One is for the national flag (this

pole is 7.2m tall), while the other is for a flag of the school mascot (this pole is 3.6m

tall). The poles are 9m apart. To stabilize the poles, there are two wires attached to a

stake somewhere between the poles. Where should the stake be placed to use the least

amount of wire?

 

Here are some questions you need to consider:

 

·         Must the sides be integers?

·         Must the triangles created be right triangles?

·         How can we find the length of the wire for each triangle?

·         What is a reasonable domain for the base of a triangle created by a pole and

·         its “base” on the ground with the guy wire?

·         What is the minimum length? Is this the absolute minimum?

·         All necessary working must be shown including diagrams, graphs or computer

·         application outputs.

 

 

Task 3: Exploring Polynomial Functions

Polynomial functions play a fundamental role in mathematics. In an important sense,

they are the ‘building blocks’ for all the functions. Discovering the amazing variety of

patterns and symmetries in polynomials kept mathematicians busy for several centuries.

 

For this task you become a mathematical explorer and discover some of the patterns

and symmetries of polynomials for yourself!

 

Your first step should be to read from page 222 in your textbook to get a clear

understanding of what a polynomial is. You need to understand the definitions of the

following terms: leading coefficient, constant term, degree of a polynomial, roots or 18/03/13 6

zeros of a polynomial, turning point (or stationary point), and point of inflection.

 

Your response to this task should include definitions of these terms.

 

Next, using Graphmatica, or similar software, plot some polynomials and take note of

any interesting patterns or symmetries that you observe. Work systematically. Begin

with the simplest polynomials and gradually work towards more complex ones. There

are many aspects you might consider.

 

Here are some questions you should consider:

 

·         What patterns arise for polynomials of the form y = axn

·         (called mononomials)?

·         What happens when the leading coefficient of a polynomial is changed?

·         What happens when the constant term is changed?

·         Is there are connection between the number of roots and the order of the

·         polynomial?

·         In there a connection between the number of turning points and the order of the

·         polynomial?

·         What if the polynomial equations are written in factorised form? What

·         information do the factors give?

 

Finally, you should write a report of your observations, making sure to attach printed

copies of your graphs as supporting evidence.* As a rough guide, you should aim to

make around 10 observations. The more general and insightful your observations the

better! Also, try to suggest why you think a certain pattern is happening.

 

* Remember, with Graphmatica you can plot any number of graphs on a single set of

axes. Also, be sure to label your graphs by clicking on ANNOTATIONS in the

EDIT menu.

 

 

Thanks

Subject Mathematics
Due By (Pacific Time) 04/25/2013 12:00 am
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