Mathematics plays a crucial role in various aspects of daily life, from simple calculations to complex problem-solving. Here are some common mathematical formulas and their daily applications:

**Area of a Rectangle (A = l * w):****Application:**Calculating the area of a room or a piece of land.

**Volume of a Cylinder (V = π * r^2 * h):****Application:**Determining the amount of liquid a cylindrical container can hold, like a water tank or a soda can.

**Simple Interest (I = P * R * T / 100):****Application:**Calculating interest on loans, savings, or investments.

**Pythagorean Theorem (a^2 + b^2 = c^2):****Application:**Measuring distances, such as when constructing buildings or determining the length of a ladder needed to reach a certain height.

**Quadratic Formula (x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}***x*=2*a*−*b*±*b*2−4*a**c*):**Application:**Solving quadratic equations, which can arise in various real-world problems.

**Percentage Change (\frac{New – Old}{Old} \times 100%***Ol**d**N**e**w*−*Ol**d*×100):**Application:**Calculating changes in prices, discounts, or increases/decreases in values.

**Gross Domestic Product (GDP) Calculation:****Application:**Assessing the economic health of a country.

**Probability (P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}Total number of outcomesNumber of favorable outcomes):****Application:**Predicting the likelihood of events, such as weather forecasts or game outcomes.

**Compound Interest (A = P (1 + \frac{r}{n})^{nt}(1+***n**r*)*n**t*):**Application:**Computing interest on savings or investments that compound over time.

**Speed, Distance, Time Relationship (Speed = \frac{\text{Distance}}{\text{Time}}TimeDistance):****Application:**Planning travel time or calculating the speed of a moving object.

**Binomial Distribution Probability (P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}***P*(*X*=*k*)=(*k**n*)*p**k*(1−*p*)*n*−*k*):**Application:**Used in statistics to model the number of successes in a fixed number of independent trials.

**Linear Regression Equation (y = mx + b):****Application:**Predicting trends and relationships between variables, commonly used in data analysis.

**Newton’s Law of Universal Gravitation (F = \frac{G \cdot m_1 \cdot m_2}{r^2}***r*2*G*⋅*m*1⋅*m*2):**Application:**Calculating gravitational forces between objects, crucial in physics and astronomy.

**Euler’s Formula (e^{ix} = \cos(x) + i \sin(x)***e**i**x*=cos(*x*)+*i*sin(*x*)):**Application:**Used in complex number analysis, signal processing, and electrical engineering.

These are just a few examples, and mathematics is deeply woven into everyday life in various fields, including finance, engineering, science, and technology. Understanding and applying mathematical concepts can enhance problem-solving skills and contribute to informed decision-making.

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