The values for the trigonometric functions at 60 degrees are: cosec 60°: The cosecant function is the reciprocal of the sine function. Therefore, cosec 60° = 1/sin(60°) = 1/(√3/2) = 2/√3 or √3/3 simplifying gives us approximately 1.1547. sec 60°: Similar to cosecant, the secant function is the reciprocal of the cosine function. So, sec … Read more
Understanding the Probability of Rolling a Sum of 9 or Higher When rolling two fair six-sided dice, we want to find the probability that the sum of the numbers on the top faces of the dice is 9 or greater. Let’s break this down step by step. Step 1: Total Possible Outcomes Each die has … Read more
The prime numbers are those natural numbers greater than 1 that can only be divided by 1 and themselves without leaving a remainder. To find the set of prime numbers that are less than 15, we can list the natural numbers starting from 2 and check each number for primality: 2 (Prime) 3 (Prime) 4 … Read more
To solve the problem, we first need to find the difference between 14 and 5. This can be calculated as follows: Difference = 14 – 5 = 9 Now we have the difference, which is 9. Next, we check the conditions given in the question: If the difference is less than 6, we add 2. … Read more
The end behavior of the logarithmic function f(x) = log3(x2) can be analyzed by considering its limits as x approaches both positive and negative infinity. First, as x approaches infinity (x → ∞), we observe that: As x becomes larger, x2 also becomes larger. Therefore, the logarithm of x2 will also increase. This means that … Read more
To analyze the sequence of numbers: 2, 1, 9, 4, 2, 18, 5, 3, 18, 6, 3, 27, we should look for patterns or relationships among them. Each number can represent different elements depending on the context, but let’s explore them individually and in pairs to uncover any significance. First, we can check if there … Read more
The equation xy = 6 can be rewritten in slope-intercept form (y = mx + b) or by obtaining y’s value in terms of x. To do this, we can rearrange the equation as follows: 1. Start with the equation: xy = 6. 2. To isolate y, divide both sides by x (assuming that x … Read more
To solve the equation 2x – 20 = 3(2x), we will follow these steps: Distribute: Begin by distributing the 3 on the right side of the equation. This gives us: 2x – 20 = 6x Rearrange the equation: To isolate the variable terms on one side, we need to subtract 2x from both sides. This … Read more
To convert radians to degrees, we use the conversion factor that 180 degrees is equal to π radians. This means that 1 radian can be expressed as: 1 radian = (180/π) degrees Calculating this gives: 1 radian ≈ 57.2958 degrees This means that if you’re working with a circle or any kind of angular measurement, … Read more