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Why the water is blue?

Have you ever asked yourself a question – why the water is blue? Obviously,we mean something large like sea or the ocean. If you take a glass of water, the liquid seems transparent and colorless, yet vast amounts of water possess certain colors. Let’s try to understand why it happens.

The color of the ocean is defined by the mechanism of absorption and dissipation of light by water molecules. Geoscientist Vasily V. Shuleikin described this complicated mechanism only in 1923. It turned out that water molecules move oscillatory, thus, they absorb waves of different length. Red wavelengths are predominantly absorbed, blue are less. Water molecules scatter blue wavelengths by absorbing the light waves and reemit those waves in different directions into the air, while red wavelengths are “swallowed” by the ocean. This makes ocean seem blue, and this is exactly why underwater photos are so full of blueness. (more…)

Assignment help on Master’s and Ph.D. level

We continue to study and analyze effiсiency and reliability of our helping service. It turns out that we increasingly often help students, teachers, researchers in carrying out their research papers and assignments.

You probably know that assignments leveled as Masters and Ph.D. are very complicated, and that’s so to a great extent because they are usually highly specialized. It is very important that among our staff there are specialists who can help to carry out such kind of tasks. Normally, we are asked by our customers to fulfill certain part of the paper – to describe a mathematical model or to write a program performing the calculations, to build a probabilistic or statistical model of the process under investigation. (more…)

How to calculate 4X4 determinant? Do math with our expert

We’re continuing to prepare math tutorials. Hopefully, it will be helpful for you and you won’t be in need asking our experts something like “Do my math homework for me, please! I’m stuck..” This is the second part of our tutorial explaining how to calculate determinants. We’re asked to calculate the determinant of the following 4×4 matrix:

$A=\begin{pmatrix}-1 & {1} & 4 & 2 \\2 & -1 & 2 & 5 \\1 &2 & 3& 4\\3& 4& -1 & 2\end{pmatrix}$

Recall that only square matrices have a determinant, for non-square ones it’s not defined. Matrix $A$ is a square 4×4 matrix so it has determinant. Here we have no zero entries, so, actually, it doesn’t matter what row or column to pick to perform so called Laplace expansion. Let it be the first column. It means that we set $j=1$ in general formula for calculating determinants which works for determinants of any size (more…)

Website that does your homework wherever you are

Surfing the Internet to find a website that does homework for you? Great news, you’re at the right place!

We do our best to help you doing your assignments as good as possible. We’re fully aware that homework quality is very important and delicate matter and that’s why we’re aiming at constant improvement of our homework making service. We understand that when our clients are in need of help it’s our duty to minimize risks and provide excellent results within your deadlines. We have analyzed our work and got unbelievable results. It appeared that we have already helped a great number of people from 120 countries. (more…)

Gaussian elimination method – case of inconsistent system

We’re continuing to consider Gaussian elimination method. Earlier we’ve prepared several tutorials covering theoretical background and examples including application of matrix representation. Yet, all those examples suggested systems of linear equations which have a solution. That’s not always so, though. In your homework or linear algebra assignment you can face different situations. In fact, there are three possibilities: system of linear equations can have either unique solution, or infinitely many solutions, or no solution at all. We’ll discuss the last case in this section.

Let’s solve the following system of linear algebraic equations:

$\left\{ \begin{aligned}2x_1-x_2+3x_3=4\\-3x_1+2x_2+x_3=5\\-4x_1+2x_2-6x_3=1 \end{aligned}\right.$ (more…)

Basic Properties of Parabolas

In this section we’re going to discuss the most important properties of parabola, also we’ll show how to find its vertex, roots and intercepts. This information is needed to sketch the graph and also allows to analyze the behavior of given parabola. We’ve already shown how to sketch graphs of quadratic function, and now we’re going through most essential details. Let’s start with considering the equation of parabola. (more…)

How to graph parabolas

What is a parabola? How to sketch its graph? These are the questions for this section. Sketching parabolas is commonly asked in algebra homework tasks, so some tips will be helpful. We’ll discuss the basic concepts and show you on simple examples how to deal with parabolas.

Let’s get started. In simple words, parabola is a U-shaped curve with some specific properties. However, note that not any U-shaped curve can be called parabola. It’s a common fact that math likes to describe everything by formulas. No surprises here, we also can write a formula for parabola. Basically, any parabola is described by some quadratic equation. (more…)