How to Find the Slope of a Curve at a Given Point
To find the slope of a curve at a specific point, you need to use calculus, specifically the concept of derivatives. The slope of a curve at a given point is defined as the derivative of the function at that point. Here are the steps to determine the slope: Identify the Function: First, you need […]
How to Find the Nth Term of an Arithmetic Sequence
To find the nth term of an arithmetic sequence, you can follow a straightforward formula. An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the ‘common difference’ and is usually denoted as ‘d’. The formula for the nth term (often represented as an) […]
How to Write 56 4 as a Fraction?
To convert the mixed number 56 4 into a fraction, start by recognizing what the mixed number represents. It consists of a whole number (56) and a fraction (4). 1. First, convert the whole number into a fraction by writing it as 56/1. 2. Now, to combine the whole number and the fractional part, we […]
What is 10 to the power of negative 7?
10 to the power of negative 7, written as 10-7, is equal to 0.0000001. This is derived from the rules of exponents in mathematics. When we have a negative exponent, it indicates the reciprocal of the base raised to the corresponding positive exponent. So, 10-7 can be rewritten as: 1 / 107 Calculating 107 gives […]
How to Find the Radius of a Sphere with the Volume
To find the radius of a sphere when you know its volume, you can use the formula for the volume of a sphere, which is: V = \( \frac{4}{3} \pi r^3 \) Where: V is the volume of the sphere. r is the radius of the sphere. \( \pi \) is a constant approximately equal […]
What is the simple interest of a loan for $1000 with 5 percent interest after 3 years?
To calculate the simple interest on a loan, you can use the formula: Simple Interest = Principal × Rate × Time Where: Principal is the initial amount of the loan. Rate is the interest rate (as a decimal). Time is the duration the money is borrowed for, in years. In this case: Principal = $1000 […]
What is 0015625 as a fraction?
The number 0015625 can be simplified to 0.0015625. To express this decimal as a fraction, we can follow these steps: Understanding the Position: The last digit (5) is in the millionth place, which means we can represent 0.0015625 as a fraction with a denominator of 1,000,000. Writing in Fraction Form: Thus, we write: 0.0015625 = […]
What is 90 of 20?
To find out what 90 of 20 means, we need to interpret it as calculating 90 percent of 20. To calculate this, we can use the formula: Percentage Value = (Percentage / 100) * Total In this case, the percentage is 90 and the total is 20. So we can set it up like this: […]
What is 7 to the power of 0?
7 to the power of 0 is equal to 1. This is a fundamental rule in mathematics that applies to all non-zero numbers, not just 7. The reason behind this is based on the properties of exponents. When you divide a number by itself, you get 1. For example, if we consider 7n (where n […]
What is 14 of 12?
To find out what ’14 of 12′ means, we interpret it as calculating 14 percent of the number 12. To do this, you can use the formula: Percentage = (Percent / 100) * Total In this case, you would substitute the values: Percentage = (14 / 100) * 12 Now, performing the calculation: Percentage = […]