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Linear Equations...?Linear **Equations**: Linear **equation**, an important concept in algebra was invented by Rane Descartes. Descartes was born in 1596 in France. He studied mathematics from the book of Culvius. Linear algebra was followed by the development of determinants in 1693 and Cramer presented his theory to solve systems of linear **equations** in 1750. Dependent and Independent Variables analysis started developing thereafter. Linear models formation was naturally a next step further for the solution of several real life issues. (A Brief History) Linear **equation** concept gave birth to the dependent and independent variables. Linear **equation** shows a relationship between two...

3 Pages(750 words)Research Paper

Equations of Motion... and the particle, and w represents the angular velocity of the rolling object. Mechanical energy of a rolling object can be defined as kinetic energy plus potential energy in the system of an object. For mechanical energy to be conserved, the sum of kinetic and potential energies within the system should always remain constant especially when the object is only affected (Adams. 2008) by conservative forces. For uniform acceleration to occur, the **equations** that would describe the object’s **motion** include: V= u +at ............................................................................................................................(2) S= ?(u+ v) t... ...

7 Pages(1750 words)Essay

Solving Equations...In this project, Bluman (2004, p. 331) challenged students to examine an **equation**, x2 – x + 41, which purportedly yields prime numbers. Students choose numbers to substitute to x in the formula and observe if prime numbers occur. An added challenge was to venture into finding a number, which when substituted in the given **equation**, will result in a composite number.
It is presupposed that a prime number is one whose factors are itself and 1, is common knowledge. On the other hand, a composite number may not be that much of a common knowledge. A definition is thus, provided: a composite number is “any whole number greater than one that is not a prime number … [it] always has at least one divisor other...

4 Pages(1000 words)Assignment

Application of the equations of motion...Applications of Newton’s Laws of **Motion** – Measurement of the acceleration due to gravity g using gym weights Introduction and Principle Newton’s **equations** of **motion** form the basis of all engineering and constitute the quantitative framework of Newton’s laws of **motion**. If a body with initial velocity u undergoes uniform acceleration a and covers a distance s in the time t,
Where v is the final velocity.
When applied to rotating bodies, these **equations** undergo a change of terms. The terms corresponding to distance, velocity, acceleration and force, change respectively to angle, angular velocity, angular acceleration and torque. Mass is similarly replaced...

5 Pages(1250 words)Book Report/Review

Application of the equations of motion...Applications of Laws of **Motion** – Projectile **Motion** Introduction The aim of this project is to design an experiment that will test and vali the concepts of Newton’s **equation** of **motion**, conservation of energy and rotational **motion**. These principles form the basics of all of physics and applied engineering. In this experiment, all the three concepts are applied in deriving the final position of a steel ball ejected as a projectile through an inclined tube; leading to not only greater understanding of the concepts but also a more holistic approach to engineering as none of these concepts occur in isolation in real life.
Principles Involved
Newton’s Laws of...

5 Pages(1250 words)Book Report/Review

Quadratic Equations...Quadratic **Equations** Introduction Raising a pet is not as easy as it looks. To keep a pet one must possess patience and a passion forthe pet that one is raising. Space is vital for the provision of an enabling environment for the rearing of pet. Different pets need different amounts of space for the provision of enough areas for their survival. My pet is a cat, which naturally spends a better part of its day in the house.
This does not make it “a potato couch” and; thus, the need to fence my backyard arises. The backyard is of a rectangular shape with its length, L = 2W- 2 and a width W=13-L. All these measurements are in meters. This area encompasses the whole of my backyard, and it is large enough to provide an ample...

1 Pages(250 words)Assignment

Equations.... Explain why your example does not model a function.
A function is not modelled in this example because of the repeating value of ‘x’ in ordered pairs (8, -7) and (8, -1) which fail to show the correspondence that must be one-to-one for the relation to be considered a function.
Part 2
f. Select any two integers between -12 and +12 which will become solutions to a system of two **equations**.
The two integers are: 3 and 8
g. Write two **equations** that have your two integers as solutions. Show how you built the **equations** using your integers. Your solution and **equations** should not be the same as those of other students or the textbook. There are...

1 Pages(250 words)Assignment

Equations of motion...Introduction In this experiment the moment of inertia of a solid disk was determined by studying and analyzing the dynamics of a rotating disk when a constant torque was applied to it. From it, it should be evident that the value of moment of inertia calculated experimentally is equal
to the theoretical value within experimental error. Furthermore, the conservation of
Mechanical energy in rotational **motion** was studied and also the effect of any non-conservative
Forces on the **motion** were investigated, reduced and compensated.
The **equations** of **motion** are used to describe the movement in a straight line that is in uniform acceleration. There are three...

10 Pages(2500 words)Assignment

Quadratic equations...Can you think of examples of processes that could be modeled with quadratic **equations**? In the real world, ‘Quadratic **Equations**’ can prove useful in a number of ways as –
(1) Modeling costs for a general store –
In C(x) = -0.03x2 + 57x + 310, for instance, the independent variable ‘x’ may refer to the number of materials bought which a store needs in order to produce sellable items. These materials are worth the variable cost C(x) with fixed cost of $310. Since the parabolic curve opens downward, as characterized by the negative leading coefficient, one manages to determine that a maximum cost is reached when x = -57/[ 2(-0.03) ]. The cost may be predicted to decline once the store decides to...

1 Pages(250 words)Assignment

Molecular and ionic equations...s Post-Laboratory Assignment Molecular and ionic **equations** Step1 Molecular **equation** Cu(s)+4NHO3 (aq) Cu(NO3)2 (aq)+2NO2 (g)+2H2O (g)
Ironic **equation**
Cu(s)+4H+(aq)+4NO3-(aq) Cu2+(aq)+2NO3-(aq)+ 2N3+(aq)+4O2-(aq)+ 2H2O (g)
Step 2
Molecular **equation**
Cu(NO3)2 (aq)+2NaOH(aq) Cu(OH)2 (s)+2NaNO3 (aq)
Ionic **equation**
Cu2+(aq)+ 2NO3-(aq)+2Na+(aq)+2OH-(aq) Cu2+(aq)+ 2OH-(aq)+2 Na+(aq)+ 2NO3-(aq)
Step 3
Molecular **equation**
Cu(OH)2 (s) CuO(s) +H2O(g)
Ionic **equation**
Cu2+(aq)+ 2OH-(aq) Cu2+(aq)+O2-+ H2O(g)
Step...

1 Pages(250 words)Assignment