To convert the improper fraction 11/2 into a mixed number, we start by dividing the numerator by the denominator. When we divide 11 by 2, we find: 11 ÷ 2 = 5 with a remainder of 1. So, 5 is the whole number part of our mixed number. Next, we take the remainder, which is … Read more
To find the value of 2 raised to the power of 8, we calculate: 21 = 2 22 = 2 × 2 = 4 23 = 2 × 2 × 2 = 8 24 = 2 × 2 × 2 × 2 = 16 25 = 2 × 2 × 2 × 2 × 2 … Read more
To find the x-intercepts of a quadratic function, you first need to understand that the x-intercepts are the points where the graph of the function crosses the x-axis. This occurs when the value of the function equals zero. For a quadratic function, which typically has the form: f(x) = ax2 + bx + c you … Read more
Calculating the Surface Area of a Right Triangular Prism A right triangular prism is a three-dimensional shape with two triangular bases and three rectangular faces connecting the corresponding sides of the triangles. To find the surface area of a right triangular prism, you can follow the steps below: Formula for Surface Area The surface area … Read more
To understand what fraction of a day is represented by 12 hours, we first need to recognize that a full day is typically considered to be 24 hours long. To find the fraction, we can set up a simple division: Fraction of the day = (Number of hours we are considering) / (Total hours in … Read more
To convert the improper fraction 11/3 into a mixed number, we follow a few simple steps. 1. **Divide** the numerator (11) by the denominator (3). In this case, 11 ÷ 3 = 3 with a remainder of 2. 2. **Write the whole number part**: The quotient from the division (3) becomes the whole number part … Read more
16 raised to the power of 2, often written as 16², is a mathematical expression that indicates multiplying 16 by itself. To calculate this, you simply perform the multiplication: 16 × 16 = 256 Therefore, 16² = 256. This means that if you have a square with each side measuring 16 units, the area of … Read more
The lowest common denominator (LCD) is the smallest number that can serve as a common multiple of the denominators of two or more fractions. In the case of the numbers 8 and 9, we are looking for the least common multiple (LCM), which will also act as the LCD when dealing with fractions. To find … Read more
To find the magnitude of a vector with three components (often denoted as v = (x, y, z)), you can use the formula derived from the Pythagorean theorem extended into three dimensions. The formula is as follows: Magnitude of the vector (|v|) = √(x² + y² + z²) Here’s a step-by-step approach on how to … Read more
Calculating 2 to the 5th power, written as 25, means multiplying the number 2 by itself a total of five times. In simpler terms, it is represented mathematically as: 25 = 2 × 2 × 2 × 2 × 2 Now, let’s break it down: First, we start with the first two: 2 × 2 … Read more