The circumference of a circle is directly related to its radius through the formula: C = 2πr Here, C represents the circumference, r is the radius, and π (pi) is a constant approximately equal to 3.14159. To find the area of the circle, we can follow these steps: Find the Radius: Given that the circumference … Read more
Triangular numbers are a special sequence of numbers that can be represented in the shape of an equilateral triangle. They are formed by the arrangement of objects in a triangular pattern, where each subsequent row of objects has one more item than the previous row. To understand triangular numbers better, let’s look at how they … Read more
To find the value of x such that sin(x) = cos(19) within the interval 0 ≤ x ≤ 90, we can use the trigonometric identity that states: sin(x) = cos(90 – x) Given this identity, we can rewrite the equation: sin(x) = cos(19) => cos(90 – x) = cos(19) From the equation cos(A) = cos(B), … Read more
To determine a possible value of x such that the expression simplifies to 12, we first need to understand the expression itself. Let’s say we have an expression in the form of an equation, for example: ax + b = 12 Here, a and b represent constants. The goal is to isolate x. To do … Read more
The sum of the angle measures of any polygon can be found using the formula: Sum of interior angles = (n – 2) × 180° where n is the number of sides of the polygon. For an octagon, which has 8 sides, we can substitute 8 for n in the formula: Sum of interior angles … Read more
To find the value of x in the equation 42x – 12 = 0, follow these steps: Add 12 to both sides of the equation: This gives: 42x – 12 + 12 = 0 + 12 So the equation simplifies to: 42x = 12 Divide both sides by 42: This allows us to isolate x: … Read more
The derivative of the function sin(2x) can be found using the chain rule, which is a fundamental theorem in calculus used for differentiating composite functions. To find the derivative, we first recognize that sin(2x) is a composition of two functions: the sine function and the linear function 2x. 1. **Differentiate the outer function**: The derivative … Read more
To solve the equation 2/5 * x + 4 + 2x = 0 for x, let’s follow a systematic approach: Combine like terms: First, rewrite the equation clearly. You want to consolidate all terms involving x: (2/5)x + 2x + 4 = 0 Convert 2x to a fraction: To combine coefficients easily, convert 2x into … Read more
To determine if a triangle can be formed with sides measuring 14 cm, 8 cm, and 5 cm, we need to check the Triangle Inequality Theorem. This theorem states that for any three sides to form a triangle, the sum of the lengths of any two sides must be greater than the length of the … Read more
Converting a percentage into a fraction is a straightforward process. Here’s how to do it step by step: Understand the Definition: A percentage represents a part of a whole out of 100. For example, 25% means 25 out of 100. Write the Percentage as a Fraction: To convert the percentage to a fraction, you can … Read more