To determine the measure of angle 7 when it is known to be twice the measure of angle 2, we need to set up a simple equation based on the relationship given. Let’s denote the measure of angle 2 as x. According to the problem, angle 7 is twice the measure of angle 2, which … Read more
Circular permutations are a fascinating concept in combinatorics, particularly when arranging items in a circular formation. Unlike linear permutations, where the arrangement is sensitive to the order, circular permutations treat arrangements that can be rotated as identical. To calculate the circular permutation of 5 items taken all at once, we can follow a simple formula: … Read more
To solve the equation log₂(x) + 6 = 256 – 4, we will first simplify the right side: 256 – 4 = 252. Now our equation looks like this: log₂(x) + 6 = 252. Next, we can isolate log₂(x) by subtracting 6 from both sides: log₂(x) = 252 – 6 log₂(x) = 246 To eliminate … Read more
To prove that the number \(3 + \sqrt{5}\) is irrational, we can start by examining the definition of rational and irrational numbers. A rational number is any number that can be expressed as the fraction \(\frac{a}{b}\) where \(a\) and \(b\) are integers and \(b \neq 0\). An irrational number, on the other hand, cannot be … Read more
To find the point on the parabola y² = 2x that is closest to the point (1, 4), we can use the method of minimizing the distance between a point on the parabola and the given point. First, we express the distance D between a point (x, y) on the parabola and the point (1, … Read more
To find the value of 12 divided by 23, we perform a simple division operation. This can be expressed as: 12 ÷ 23 When you carry out this division, you get: 12 ÷ 23 ≈ 0.5217391304347826 So, to simplify, we can say: The answer is approximately 0.52 when rounded to two decimal places. In simple … Read more
To find the value of x rounded to the nearest tenth, you’ll need to follow these steps: Identify the Value: First, determine the value of x that you need to round. For instance, let’s say x = 5.67. Locate the Tenths and Hundredths Place: In the number 5.67, the tenths place is the first digit … Read more
To find the zeroes of the function f(x) = x² – 2, we need to determine the values of x that make the function equal to zero. This means we are looking for x such that: f(x) = 0 Substituting into the equation, we get: x² – 2 = 0 Now, we can solve for … Read more
To solve the logarithmic equation log(x) log(x) = 5 log(6x) 12, let’s rewrite and analyze the equation step by step. Let’s begin by understanding the components: log(x) indicates the logarithm of x, typically in base 10, unless otherwise specified. log(6x) can be expanded using the logarithm properties: log(6x) = log(6) + log(x). We have the … Read more
To find the domain of the expression cdx, where cx = 5x^2 and dx = x^3, we first need to analyze the individual components of both cx and dx. 1. **Definition of the Components**: For cx = 5x^2: The expression is defined for all real numbers, since polynomial functions such as this do not have … Read more