devyy The set of all numbers, often referred to as the set of real numbers, includes both rational and irrational numbers. To understand this better, let’s delve into each category. Rational Numbers Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. This means … Read more
To solve for c in the expression c = 5cos(35°) + 5sin(35°), we start by isolating c in the given equation. Reorganizing, we have: c = 5cos(35°) + 5sin(35°) Next, we can factor out the constant 5: c = 5(cos(35°) + sin(35°)) Now, we need to calculate cos(35°) and sin(35°). Using a calculator: cos(35°) ≈ … Read more
To determine how many thousands there are in 10 crores, we first need to understand the relationship between these two units of measurement. 1 crore is equivalent to 10 million, or 10,000,000. Thus, 10 crores can be calculated as follows: 10 crores = 10 x 1 crore = 10 x 10,000,000 = 100,000,000 (or 100 … Read more
Proving the Equation: sin(a + b) = sin(a)cos(b) + cos(a)sin(b) To prove the identity sin(a + b) = sin(a)cos(b) + cos(a)sin(b), we will use the unit circle and properties of sine and cosine functions. 1. Understanding the Unit Circle The unit circle is a circle with a radius of 1, centered at the origin (0,0) … Read more
A regular polygon is a polygon with all sides and all angles equal. In the case of a regular polygon with 22 sides, also known as a 22-gon, we can determine the number of lines of symmetry by understanding a few basic properties of regular polygons. Each regular polygon has as many lines of symmetry … Read more
To find a quadratic equation equivalent to the expression x² + 5x + 6, we can utilize factorization. A quadratic equation is typically in the form of ax² + bx + c = 0, and in this case, we have: a = 1, b = 5, c = 6 We begin by looking for two … Read more
When we say that the limit as x approaches infinity is 8, we are indicating a particular behavior of a function as the input (x) grows very large, without bound. This concept is a fundamental part of calculus, specifically in understanding limits. To break this down further, let’s explore what it means: Limit: In mathematics, … Read more
To find the value of cos(15°), we can utilize the cosine subtraction identity, which is given by: cos(a – b) = cos(a)cos(b) + sin(a)sin(b) In this case, we can express 15° as the difference of two angles: 45° and 30°. So, we set: a = 45° b = 30° Now substituting into the cosine subtraction … Read more
To find the quotient of the expression 6×4 ÷ 15×3 ÷ 2×2 ÷ 10x ÷ 4 ÷ 3×2 ÷ 2, we need to follow a systematic approach. First, let’s simplify each term in the numerator and the denominator: Numerator: The numerator is simply 6×4. Denominator: The terms we have in the denominator are: 15×3, 2×2, … Read more
To factor the expression x3 + 7×2 + 5x + 35 using the grouping method, we can follow these steps: First, we should group the terms in pairs: (x3 + 7×2) + (5x + 35) Next, we factor out the greatest common factor (GCF) from each group: From the first group (x3 + 7×2), the … Read more