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Understanding Number Names in Different Numbering Systems When you come across the numbers 236749 and 48670002, it’s interesting to see how they are represented in both the Indian and international numbering systems. 1. Number: 236749 Indian Numbering System: Two Lakh Thirty Six Thousand Seven Hundred Forty Nine International Numbering System: Two Hundred Thirty Six Thousand … Read more

Converting a mixed number into an improper fraction is a straightforward process, and once you understand the steps, you’ll find it easy to do! A mixed number consists of a whole number and a proper fraction. For example, in the mixed number 2 1/3, the whole number is 2, and the proper fraction is 1/3. … Read more

To find the coefficient of x in the division of the polynomial expression, we first need to clarify the operation. It appears that you are interested in dividing the polynomial expression 18×3 by the polynomial 12×2 + 3x + 6×2. 1. **Combine like terms** in the denominator: 12×2 and 6×2 combine to give 18×2. So … Read more

To calculate the percentage increase from 60 to 75, you can use the following formula: Percentage Increase = ((New Value – Old Value) / Old Value) × 100 In this case, the old value is 60 and the new value is 75. Plugging these numbers into the formula gives us: Percentage Increase = ((75 – … Read more

Let’s break down the scenario: a man who is 6 feet tall is walking away from a light located 15 feet high above the ground at a speed of 5 feet per second. To understand the relationship between the distance he walks and the light’s height, we can use some basic geometry and trigonometry. 1. … Read more

To calculate the future value of a deposit with simple interest, we can use the formula: Future Value (FV) = Principal Amount (P) + Interest (I) Where: Principal Amount (P): This is the initial amount of money deposited, which in this case is $10,000. Interest (I): This is calculated using the formula I = P … Read more

To verify that g(x) is the inverse of f(x), we need to check two key conditions. In general, if g is the inverse of f, then the following two equations must hold: f(g(x)) = x g(f(x)) = x Let’s calculate each of these: 1. Checking f(g(x)) First, we will substitute g(x) into f: f(g(x)) = … Read more

The function y = 2sin(x) is a transformation of the basic sine function, which has a known range. To understand the range of this function, let’s first recall a couple of key points about the sine function: The basic sine function, sin(x), has a range of [-1, 1]. This means that the function sin(x) will … Read more