The smallest whole number is 0. Whole numbers are defined as the set of non-negative integers that include zero and all positive integers. Therefore, the set of whole numbers can be represented as follows: 0 1 2 3 4 5 This sequence continues indefinitely, meaning that whole numbers extend infinitely towards positive values. It’s important … Read more
To integrate the function int cos(2x) dx using the method of integration by parts, we start by recalling the integration by parts formula: ∫u dv = uv – ∫v du Here, we will need to choose parts of the integral. Let’s set: u = cos(2x) –> this implies du = -2sin(2x)dx dv = dx –> … Read more
To solve the equation 6y + 2y + 1 – 3y + 2 = 6, we will first combine like terms and simplify the equation step by step. Step 1: Combine Like Terms In the given equation, we can first combine the coefficients of y: 6y + 2y – 3y = (6 + 2 – … Read more
In the equation of a line expressed as y = mx + b, the letter b represents the y-intercept of the line. This is the point where the line crosses the y-axis on a graph. To provide further clarity, let’s break down the components of this equation: y: This is the dependent variable, which represents … Read more
To factor the quadratic expression 3x² + 8x + 5, we seek two binomials that multiply to give the original expression. The general form of factoring a quadratic equation is: ax² + bx + c = (px + q)(rx + s) In this case, a = 3, b = 8, and c = 5. Next, … Read more
To simplify the function sectan(1x), it’s essential to first understand the terms involved: secant: In trigonometric functions, the secant function is defined as sec(x) = 1/cos(x). tangent: Similarly, the tangent function is defined as tan(x) = sin(x)/cos(x). Therefore, sectan(1x) can be expressed as: sectan(1x) = sec(1x) * tan(1x) Substituting the definitions of secant and tangent … Read more
The sequence you’ve presented is 2, 4, 8, 16, 32. To find the general term of this sequence, we first need to identify the pattern between the numbers. Each term in the sequence is obtained by multiplying the previous term by 2: 2 × 2 = 4 4 × 2 = 8 8 × 2 … Read more
The Formula for sin(3x) The formula for sinus of a triple angle, specifically sin(3x), can be derived using the angle addition formulas and identities from trigonometry. The formula is given by: sin(3x) = 3sin(x) – 4sin3(x) This means that the sine of three times an angle x can be expressed in terms of the sine … Read more
To factor the polynomial f(x) = x³ + 2x² + 5x – 6, we will follow a systematic approach involving a combination of factoring techniques. Step 1: Identify potential rational roots We can use the Rational Root Theorem to identify possible rational roots of the polynomial. The potential rational roots are the factors of the … Read more
In India, the monetary system uses different units to make large sums of money easier to understand. One of these units is the crore. To clarify, 1 crore is equal to 10 million (10,000,000). Now, when it comes to larger amounts, such as a trillion, the calculation becomes quite straightforward: 1 trillion = 1,000,000,000,000 (1 … Read more