≡It was noted that four-legged chairs usually present imbalance
It was noted that four-legged chairs usually present imbalance, while three-legged ones do not. Mathematics explains this fact, but it is difficult to understand. To understand why, look at a farm gate. It has a diagonal board, forming two triangles. In this way, it is more resistant to deformation and the maintenance of its balance is guaranteed. Likewise, the three legs of a chair form a triangle, making it more robust and stable.
Pi Approximation
Pi Approximation Day, also known as Pi Approximation Day or Approximate Pi Day, is celebrated on July 22 . This date is a reference to the approximate value of Pi (π), which is often rounded to 3.14. Pi is a mathematical constant that represents the relationship between the circumference of a circle and its diameter. The value of Pi is an infinite, non-repeating sequence of decimal digits, and its approximation to 3.14 is often used in calculations and mathematical problems. Pi Approximation Day is an opportunity to celebrate the importance of this mathematical constant and its application in various areas of science and engineering.
Discover some interesting facts about Math
International Mathematics Day is celebrated on March 14
International Mathematics Day is celebrated on March 14 , known as Pi Day due to the numerical representation of the date (3/14), which corresponds to the first digits of the number pi. As of 2020, by decision of UNESCO, the day began to be officially recognized to celebrate the importance of mathematics around the world. Each year has a specific theme, and celebrations include a variety of educational events and activities to promote interest and understanding of mathematics.
celebrate in March 14
Addition
Addition. Properties
30 + 11 = 50 (read: The sum of thirty-nine and eleven is equal to 50.)
39 and 11 are the installments and 50 is the sum.
Addition properties:
- Commutative: a + b = b + a
Changing the order of the installments the sum does not change.
39 + 11 = 11 + 39 = 50
- Associative: (a + b) + c (b + c)
The sum does not change when associating the installments differently.
(39 + 11) + 28 = 39 + (11 + 28) = 78
- Existence of neutral elements : a + 0 = 0 + a = a
o (zero) is the neutral element of addition.
To make an estimate for a sum, we usually round numbers to the nearest tens or hundreds.
39 + 11 + 28 = 78 (Exact value)
40 + 10 + 30 = 80 (Estimate)
Subtraction
Subtraction. Properties
39 - 28 = 11 (It reads: The difference between thirty-nine and twenty-eight is equal to eleven.)
39 (Additive), 28(Subtractive) and 11(Difference)
Note: To check whether the subtraction is carried out correctly, the fundamental property of subtraction can be applied:
The sum of the subtractive and the difference is equal to the additive.
To make an estimate of a difference, we normally round the numbers to the nearest tens or hundreds.
903 + 288 = 615 (Exact value)
900 - 300 = 600 (Estimate)
Quadratic equations and their solutions
A quadratic equation (or second-degree equation) is a polynomial equation in which the highest exponent of the variable is 2.
General form:
It is written as:
\( ax^2 + bx + c = 0 \)
Where:
a, b, c → are constant numbers (with \( a \neq 0 \)).
x → is the unknown variable.
How to find the solutions?
First, we calculate the discriminant (Δ):
\( \Delta = b^2 - 4ac \)
It determines how many solutions the equation has.
Types of solutions:
1. Two real and different roots:
When: \( \Delta > 0 \)
✔️ The equation has two distinct real solutions.
✔️ The x values are different.
2. Two equal real roots:
When: \( \Delta = 0 \)
✔️ The equation has one repeated solution.
✔️ Both roots are equal.
3. No real roots:
When: \( \Delta < 0 \)
❌ There are no real solutions.
✔️ The solutions are complex numbers.
Simple summary:
Second-degree equation: \( ax^2 + bx + c = 0 \).
Discriminant: \( \Delta = b^2 - 4ac \).
Types of solutions:
\( \Delta > 0 \) → 2 different roots.
\( \Delta = 0 \) → 1 double root.
\( \Delta < 0 \) → no real roots.
First-degree equation and how to solve it.
A first-degree equation is a polynomial equation in which the highest exponent of the variable is 1.
General form:
It is written as:
\( ax + b = 0 \)
Where:
a and b → are known numbers (constants).
x → is the unknown variable.
What is the solution?
The solution is the value of x that makes the equation true.
How to solve (step by step):
1️⃣ Isolate the term with x:
Put the term with x alone on one side.
Move the other terms to the other side.
2️⃣ Simplify the equation:
Perform operations on both sides.
Add or subtract values.
3️⃣ Isolate the variable:
Divide both sides by the coefficient of x.
Leave x alone.
4️⃣ Find the solution:
The value obtained for x is the solution of the equation.
It makes the equality true.
Example of General Form:
Equation: \( ax + b = 0 \)
Goal: find x.
Simple summary:
First-degree equation: \( ax + b = 0 \)
Steps:
isolate x.
simplify.
divide.
solve.
Special case:
Usually there is one unique solution.
If any value of x works, it is an identity.
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