In the metric system, the unit used to measure mass is the kilogram (kg). The kilogram is currently defined based on the International System of Units (SI) and has become a fundamental part of scientific and everyday measurements around the world. The kilogram is a base unit, and it is the only SI base unit … Read more
The mathematical expression i to the power of 4, which is written as i4, is equal to 1. To understand why, we first need to recall what i represents. In mathematics, i is the imaginary unit, defined by the equation i = √-1. The powers of i follow a specific cycle: i1 = i i2 … Read more
To convert the improper fraction 6/5 into a mixed number, you need to follow these simple steps: Identify the Whole Number: Divide the numerator (6) by the denominator (5). The whole number part of the mixed number is the quotient. In this case, 6 ÷ 5 = 1. This means our mixed number will have … Read more
To find out what percentage 8 is of 20, we can use a simple formula. Percentages are calculated using the following equation: Percentage = (Part / Whole) × 100 In this case, the ‘part’ is 8 and the ‘whole’ is 20. So we substitute these values into the formula: Percentage = (8 / 20) × … Read more
To determine the slope of a line that is perpendicular to another line, we need to understand a fundamental concept from geometry regarding slopes. The key principle is that the slopes of two perpendicular lines are negative reciprocals of each other. In mathematical terms, if you have a line with a slope m, the slope … Read more
To express the number 8 million in scientific notation, we first start by writing it in standard numerical form, which is 8,000,000. Scientific notation allows us to write large numbers in a more compact form, making it easier to read and work with, especially in scientific and mathematical contexts. The general format for scientific notation … Read more
To simplify the expression 1/tan(x), we can start by recalling the definition of the tangent function in terms of sine and cosine. The tangent of an angle x is defined as: tan(x) = sin(x) / cos(x) So, if we want to simplify 1/tan(x), we can substitute this definition into our expression: 1/tan(x) = 1/(sin(x)/cos(x)) Next, … Read more
The polynomial expression x² can be factored as follows: x² represents x multiplied by itself, so the factorization is: x² = x * x In terms of understanding this factorization, it’s important to recognize that when a variable is squared, it means it’s being used as a factor twice. Therefore, x² can be expressed as: … Read more
To write the equation of a sphere in standard form, you first need to understand what the equation entails. The standard form of the equation of a sphere is given by: (x – h)² + (y – k)² + (z – l)² = r² Here, (h, k, l) represents the coordinates of the center of … Read more
The expression “23 of 24” can be interpreted in a couple of ways depending on the context. Generally, it refers to a proportion or a fraction, specifically, it means 23 out of 24 parts or elements of a whole. In numerical terms, you can represent this as a fraction: 23/24. This means that if you … Read more