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Joseph-Louis Lagrange

Born January 25, 1736, Turin, Sardinia-Piedmont [Italy]

Died April 10, 1813, Paris, France

Mathematician who made great contributions to number theory and to analytic and celestial mechanics. His most important book, Mécanique analytique (1788; “Analytic Mechanics”), was the basis for all later work in this field.

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Proof

The following is what seems to be a mathematical proof that two equals one.

What's wrong with it?

a = b
aa = ab
aa - bb = ab - bb

(a + b)(a - b) = b(a - b)
a + b = b

a + a = a

2a = a

2 = 1

Dots

Nine dots are arranged in a three by three square. Connect each of the nine dots using only four straight lines and without lifting your pen from the paper.

domain and range

Identify the domain and range of the graph

Long-Distance Phone Calls

A long-distance telephone company charges a monthly fee of $2.95 and a per minute charge of $0.04.The monthly cost for long distance is given by C=2´95+0'04x where x is the number of minutes used.
(a) Solve the equation for x.
(b) How many full minutes can Debbie use in one month on this plan if she does not want to spend more than $20 in long distance in one month?

Uniform Motion

Roger and Bill decide to have a 10-mile race. Roger can run at an average speed of 12 miles per hour while Bill can run at an average speed of 10 miles per hour.To “even things up,” Roger agrees to give Bill a head start of 0.15 hour.When will Roger catch up to Bill?

Numbers

Can you place the numbers 1,2,3,4,5,6,7 and 8 in the squares below so that no two consecutive numbers are next to each other, either vertically, horizontally or diagonally?

Interesting digit patterns

You may have seen this:

1/81 = 0.012345679012345679...

But you may not have seen this:

1/243 = 0.004115226337448559...

What is special about the number 243? How does the pattern continue?

Mathematicals operations

Choose complete mathematical operations for example : 2-5=-3 (maybe you need install java from http://www.java.com/en/download/windows_ie.jsp

Problems

1.Going into the final exam, which counts as two grades,Kendra has test scores of 84, 78, 64, and 88.What score does Kendra need on the final exam in order to have an average of 80?

2.Maria has just been offered two sales jobs.The first job offer is a base monthly salary of 2500 euros plus a commission of 3% of total sales.The second job offer is a base monthly salary of 1500 euros plus a commission of 3.5% of total sales. For what level of monthly sales is the salary of the two jobs equivalent?

3.Pedro wants to invest his 25,000 euros bonus check. His investment advisor has recommended that he put some of the money in a bond fund that yields 5% per annum and the rest in a stock fund that yields 9% per annum. If Pedro wants to earn 1875 euros each year from his investments, how much should he place in each investment?

Projectile Motion

The graph below shows the height, in feet, of a ball thrown straight up with an initial speed of 80 feet per second from an initial height of 96 feet after t seconds.

a) What is the height of the object after 1.5 seconds?
b) At what time is the height a maximum? What is the maximum height?
c) Identify and interpret the intercepts.

d) Do you konw the equation of the projectile?

Measuring Temperature

The relationship between Celsius (°C) and Fahrenheit (°F) degrees for measuring temperature is linear. Find an equation relating °C and °F if 0°C corresponds to 32°F and 100°C corresponds to 212°F. Use the equation to find the Celsius measure of 60°F.

Formula

Solve the formula for the indicated variable:
y=mx+n for m
S-rS=a-ar⁵ for S
C=(5/9)·(F-32) for F
A=(1/2)·h·(B+b) for b
E=(Z·s)/n^1/2 for n
Z= (x-u)/s for x

Georg Cantor

Born March 3, 1845, St. Petersburg, Russia
Died Jan. 6, 1918, Halle, Ger.
German mathematician who founded set theory and introduced the mathematically meaningful concept of transfinite numbers, indefinitely large but distinct from one another.

Area

An artist wants to place a piece of round stained glass into a square that is made of copper wire. See the figure. If the perimeter of the square is 4 metres, what is the area of the largest circular piece of stained glass that can fit into the copper square?

Equations

Which of the following equations might have the graph shown? (More than one answer is possible)

a) y = 2x - 5
b) y =-x + 2
c) y = (-2/3)x – 3
d) 4x + 3y = -5
e) -2x + y = -4

Numbers

1. Real numbers that can be represented with a terminating decimal are called _____ numbers.
2. Real numbers that cannot be represented as a ratio of integers are called _____numbers.
3. The distance from zero to a point on the number line is called the _____ _____ of the number.

Mathematicians

Look for five famous mathematicians (maybe you need install java from http://www.java.com/en/download/windows_ie.jsp

Welcome

Hello everybody and welcome to the project :"365 days with mathematics"
I am Nacho , the maths teacher from Spain and I would like to write the first question of the year :
What does the word ''mathematics'' mean ?

Help: The word "mathematics" come from the Greek mathēmatiká

If you can write the answer in the comments , remember that your names are:
poland group 1 : a365dayswithmaths@hotmail.com
poland group 2 : b365dayswithmaths@hotmail.com
poland group 3 : c365dayswithmaths@hotmail.com
poland group 4 : d365dayswithmaths@hotmail.com
poland group 5 : e365dayswithmaths@hotmail.com
spain group 1 : f365dayswithmaths@hotmail.com
spain group 2 : g365dayswithmaths@hotmail.com
spain group 3 : h365dayswithmaths@hotmail.com
spain group 4 : i365dayswithmaths@hotmail.com
spain group 5 : j365dayswithmaths@hotmail.com

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