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The circumference of a circle is the distance around it, and it’s calculated using the formula: C = 2πr In this formula: C represents the circumference of the circle. π (pi) is a mathematical constant approximately equal to 3.14159, but it is often expressed simply as π in equations. r represents the radius of the … Read more

To find the exact value of tan 15 degrees, we can utilize the half angle formula for tangent. The formula states: tan(θ/2) = sqrt((1-cos θ)/(1+cos θ)) In our case, we can consider 15 degrees as half of 30 degrees; therefore, we set θ = 30 degrees. First, we need the cosine of 30 degrees, which … Read more

The binary number 10010 can be simplified by converting it to its decimal equivalent. To do this, we will assign powers of 2 to each digit, starting from the rightmost digit, which represents 20. Here’s a breakdown of the conversion: The rightmost digit (0) is 20 = 0 The next digit to the left (1) … Read more

To find the equation of the line that passes through the two given points, (0, 1) and (2, 3), we can follow these steps: Step 1: Determine the Slope The slope (m) of a line that passes through two points, (x1, y1) and (x2, y2), can be calculated using the formula: m = (y2 – … Read more

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