Math Homework Help

Yesterday I couldn’t write. Today I hoped to write about basic geometric concepts. But today also I am very busy and I haven’t enough time to write a long topic.

So we can have a small puzzle today. This is an ancient problem dating back to about 310 A.D.
Demochares had one-fourth of his life as a boy, one-fifth as a youth , one-third as a man, and has spent 13 years in his dotage. How old was Demochares?

Another problem of this kind:
A stone weights one Kilogram and half of its weight. What is the actual weight of the stone?

Solutions:
First Question
Let x be Demochares’s age.
Then, x/4+x/5+x/3+13=x
ie 47x/ 60+13=60
==>47x/60=47
==>x=60
So, Demochares was 60 years.

Second Question
2 kilogram

It is very important for a math student to learn the basic concepts in mathematics. It is a common fact that most children find math is very hard and in particular Geometry. The main reason behind this is that they don’t have the basics in maths.
and in Geometry the concepts are more abstract. If the students get some good basic help in math, I am sure most of them do better in maths. So let us learn some basics of Geometry today.
There are three basic concepts of geometry. These are “point“, “line” and “plane“. I am not attempting to define them as it is not possible to define them precisely. We can however, have a good idea of these three by considering examples. A fine dot made by a sharp pencil on a sheet of paper, resembles a geometrical point very closely. The sharper the pencil, the closer is the dot to the concept of a point.

The surface of a sheet of paper or the surface of a smooth table are examples of plane. But these surfaces limited in extent. The geometrical plane extends endlessly in all directions.
A straight line, drawn on a sheet of paper with a sharp pencil, is a close example of a geometrical straight line. A geometrical line is a set of points and extends endlessly in both the directions. To emphasize this we use two arrowheads.
It is impossible to find exact example for point,line and plane in nature. The geometrical point, line and plane are ideal concepts. but for practical purpose it is enough to deal with close examples.
So, a plane is a set of points, line is a subset of plane. Moreover all the other figures in geometry are sets of points. But they are not just set of points. They are special set of points possessing some properties.

Notation
We use capital letters such as A, B, C, P, Q, R, X, Y, Z etc. to denote points.
We use small letters (lower case) such as l,m,n,p,q,r etc. to denote lines.

What is the peculiarity of 1729?

This number is known in the name of the famous mathematician Ramanujan.

Answer

This is the one and only one number which can be written as the sum of the cubes of two numbers in two different ways.

10^3 + 9^3 =1729
12^3 + 1^3 = 1729

I can help you in the following topics of Mathematics
You can send in me your math problems at getmath@gmail.com

All math solutions will be clearly demonstrated.

Algebra

Middle school and high school algebra
Functions
Linear Equations, Inequalities.
Quadratic Equations
Simultaneous System of Equations
Arithmetic and Geometric Progressions.
Sequences and Series
Binomial Theorem
Probability, Permutations, Combinations.
Logarithms
Matrices and Determinants

Trigonometry

Trigonometric Identities.
Trigonometric Functions
Solutions of Triangles
Heights and Distance Problems

Geometry

Middle school and High school Geometry
Prisms
Similar triangles,
Congruent Triangles

Analytic Geometry

The Straight Line.
The Circle.
Conic Sections (Parabola,Ellipse,Hyperbola)

Statistics

Probability
Mean Deviation
Standard Deviation

Calculus

Functions, Limits and Continuity.
Differentiation
Integration
Definite Integral
Definite Integral Applications (Areas and Volumes)

Today again I have a puzzle. This one is not a typical math puzzle. You should use your common sense to answer this simple puzzle. Here we go……

Two identical trains, at the equator start travelling round the world in opposite directions. They start together, run at the same speed and are on different tracks.
Which train will wear out its wheel treads first?

You can post your answers in the comments section.

Update
The train travelling against the spin of the earth will wear its wheel more quickly, as the centrifugal force is less in this train.

I offer math tutoring via email.This is a great option for students looking for an online tutor, or students who don’t necessarily need to sit down with a tutor for a long time. This can also be a good option for homeschooling students and those working in independent study situations.

For a long session, I will likely ask you to email me a sample or two of the types of questions you have, so that I can be sure that it looks like something I can help you with effectively and I can calculate my fee.Once you agreed to puchase my service,you can pay me through my Paypal account getmath@gmail.com. You do not need a Paypal account in order to use PayPal, as long as you have a credit card. (If you are under 13 years, you can ask your parents to open an account.)

IMPORTANT NOTE
It is highly recommended that, when you e-mail your questions to me, you include the area of study , the topic of study and your grade level.
Please feel free to describe all the difficulties you’ve been having and what you hope to achieve with tutoring.

Fifty minutes ago if it was four times as many minutes past 3 O’ clock, how many minutes is it to 6 O’ clock?

Got the answer?
Please feel free to put it in the comments section.

Wait for the correct answer till tomorrow.

Update
The answer was posted in the comments section.

We know Geometry is one of the most ancient branches of mathematics. The big step forward in geometry after the Greeks, was the development of a new method called Co-ordinate geometry or Analytical geometry. Modern analytical geometry is also called “Cartesian” after the name of Rene Decartes (1596-1665). But the fundamental principles and methods were already discovered by Pierre de Fermat(1601-1665). Unfortunately, Fermats treatise on the subject entitled “Ad locus planos et so lidos Isagoge“(Introduction to plane and solid loci) was published only published posthumously in 1679. So Decartes came to be regarded as the unique inventor of the analytical geometry.
In co-ordinate geometry, we enlist the services of Algebra in aid of Geometry.

There is a number which is very peculiar. This number is three times the sum of its digits. Can you find the number?
Answer
It is 27
2+7=9
3.9=27

We know the formula for finding the area of a triangle is 1/2 bh, where b is the base and h is the height of the altitude from the opposite vertex to the base.

Another important formula is given below. We can use this formula when two sides and the included angle are given. We can derive Hero’s formula from this.

The area of triangle is given by

Similarly other results can also prove.