javascript
DownloadCopy code
function greetFromLocation(location) {
    console.log(`Hello from ${location}`);
}

// Example usage:
greetFromLocation("New York");
greetFromLocation("Tokyo");
greetFromLocation("Paris");

• The greetFromLocation function takes one parameter, location.
• It uses template literals (the backticks ``) to create a string that includes the location.
• The console.log function is used to print the message to the console.

1. Area of a Triangle:
   • Using base and height: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$
   • Using Heron's formula (when you know all three sides $a$, $b$, and $c$): $$s = \frac{a + b + c}{2} \quad \text{(semi-perimeter)}$$ $$\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$$
2. Perimeter of a Triangle:
   • If you know the lengths of all three sides $a$, $b$, and $c$: $$\text{Perimeter} = a + b + c$$
3. Pythagorean Theorem (for right triangles):
   • If $c$ is the length of the hypotenuse and $a$ and $b$ are the lengths of the other two sides: $$c^2 = a^2 + b^2$$
4. Angles:
   • To find angles using the sides (Law of Cosines): $$c^2 = a^2 + b^2 - 2ab \cdot \cos(C)$$
   • Rearranging gives: $$\cos(C) = \frac{a^2 + b^2 - c^2}{2ab}$$

javascript
DownloadCopy code
function calculateTriangleArea(base, height) {
    if (base <= 0 || height <= 0) {
        throw new Error("Base and height must be positive numbers.");
    }
    return 0.5 * base * height;
}

// Example usage:
const base = 5; // Example base length
const height = 10; // Example height length

try {
    const area = calculateTriangleArea(base, height);
    console.log(`The area of the triangle is: ${area}`);
} catch (error) {
    console.error(error.message);
}

Explanation:

1. Function Definition: The function calculateTriangleArea takes two parameters: base and height.
2. Input Validation: It checks if the base and height are positive numbers. If not, it throws an error.
3. Area Calculation: It calculates the area using the formula and returns the result.
4. Example Usage: The example shows how to call the function and log the result to the console.

Algebra

1. Quadratic Formula:
   $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
   (Used to find the roots of a quadratic equation $ax^2 + bx + c = 0$)
2. Difference of Squares:
   $$a^2 - b^2 = (a - b)(a + b)$$
3. Factoring a Perfect Square:
   $$a^2 + 2ab + b^2 = (a + b)^2$$ $$a^2 - 2ab + b^2 = (a - b)^2$$

Geometry

1. Area of a Circle:
   $$A = \pi r^2$$
2. Circumference of a Circle:
   $$C = 2\pi r$$
3. Pythagorean Theorem:
   $$a^2 + b^2 = c^2$$
   (In a right triangle, where $c$ is the hypotenuse)
4. Area of a Triangle:
   $$A = \frac{1}{2} \times \text{base} \times \text{height}$$

Trigonometry

1. Sine, Cosine, and Tangent:
   $$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}, \quad \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}, \quad \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$
2. Pythagorean Identity:
   $$\sin^2(\theta) + \cos^2(\theta) = 1$$

Calculus

1. Derivative of a Function:
   $$\frac{d}{dx}(x^n) = nx^{n-1}$$
2. Integral of a Function:
   $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C \quad (n \neq -1)$$
3. Fundamental Theorem of Calculus:
   $$\int_a^b f(x) \, dx = F(b) - F(a)$$
   (Where $F$ is an antiderivative of $f$)

Statistics

1. Mean:
   $$\text{Mean} = \frac{\sum_{i=1}^{n} x_i}{n}$$
2. Variance:
   $$\sigma^2 = \frac{\sum_{i=1}^{n} (x_i - \mu)^2}{n}$$
   (Where $\mu$ is the mean)
3. Standard Deviation:
   $$\sigma = \sqrt{\sigma^2}$$

Probability

1. Probability of an Event:
   $$P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$
2. Bayes' Theorem:
   $$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$$