What are the formulae of 1 + cos(2x) and 2(1 + cos(2x))?
The formula for 1 + cos(2x) can be derived from the trigonometric identity for cosine. The expression simplifies using the double angle formula of cosine, which states: cos(2x) = 2cos²(x) – 1 Using this identity, we rewrite: 1 + cos(2x) = 1 + (2cos²(x) – 1) = 2cos²(x) So, 1 + cos(2x) = 2cos²(x). Next, […]
What is 9 to the power of 5?
9 to the power of 5, denoted as 95, is calculated by multiplying 9 by itself a total of five times. This can be expressed as: 9 × 9 × 9 × 9 × 9 To do the math step-by-step: First, calculate 9 × 9 = 81. Next, take that result and multiply it by […]
What is the missing number: 73, 17, 46?
To identify the missing number in the sequence of 73, 17, and 46, we first need to analyze the pattern that links these numbers. One way to examine these numbers is by looking at the differences between them: The difference between 73 and 46 is 27 (73 – 46 = 27). The difference between 46 […]
What is 4 to the power of 2?
4 to the power of 2, often written as 42, means that you multiply 4 by itself. So, it’s calculated as: 4 x 4 = 16 Therefore, 42 equals 16. This exponentiation demonstrates how many times a number is used as a factor, and in this case, it’s used twice. It’s a fundamental concept in […]
What is the value of x in the equation 2x + 3 = 9 – 3x + 1?
To find the value of x in the equation 2x + 3 = 9 – 3x + 1, we first need to simplify the equation. Step 1: Combine like terms on the right side of the equation: 9 – 3x + 1 = 10 – 3x So, the equation becomes: 2x + 3 = 10 […]
What is the area of a rectangle that is 8 inches wide and 12 inches long?
The area of a rectangle can be calculated using the formula: Area = Width × Length In this case, the width of the rectangle is 8 inches and the length is 12 inches. Plugging these values into the formula gives: Area = 8 inches × 12 inches Calculating this results in: Area = 96 square […]
A quadratic equation has exactly one real number solution. What is the value of its discriminant?
A quadratic equation can be expressed in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. The solutions to this equation can be determined using the quadratic formula: x = (-b ± √(b² – 4ac)) / (2a) The term under the square root, b² […]
What is the equation of the x-axis?
The equation of the x-axis is y = 0. This means that for any point on the x-axis, the value of y is always zero, regardless of the value of x. The x-axis is a horizontal line that runs through the origin (0,0) and extends infinitely to the left and right. Thus, every point on […]
What is 1 2 to the power of 5?
To solve the expression 1 2 to the power of 5, we first need to clarify what ‘1 2’ means. Assuming it refers to the number 12, we rewrite the expression as 125. Next, we calculate 12 raised to the power of 5: 121 = 12 122 = 144 123 = 1,728 124 = 20,736 […]
What are the first 10 prime numbers?
The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. A prime number is defined as a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In simple terms, a prime number has exactly two distinct positive divisors: 1 and itself. For […]