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To calculate the number of minutes that have elapsed between 1:30 PM and 4:45 PM, we can break the problem down into smaller parts. First, let’s find the total hours and minutes: The start time is 1:30 PM. The end time is 4:45 PM. Now, let’s break it down: The time from 1:30 PM to … Read more

In a right triangle, we can use trigonometric functions to find the lengths of sides based on angles. Here, we have a right triangle ABC where angle B measures 60 degrees, and side BC is 18. To find the length of AC, we can use the sine function. The sine of an angle in a … Read more

To use substitution for writing an equivalent quadratic equation based on the equation 3x² + 7x + 8 = 0, we can follow a structured approach. First, let’s rewrite the equation in standard form: 3x² + 7x + 8 = 0 Next, we can choose a substitution variable to simplify the equation. A common method … Read more

A corollary is a statement that follows readily from a previously proven statement, often a theorem. In simpler terms, once a theorem is established, some conclusions can be drawn from it without requiring extensive additional proof. Corollaries serve as a way to extend the implications of a theorem, making it easier to understand and apply … Read more

To write the equation of a line in slope-intercept form, which is y = mx + b, we need to find the slope (m) and the y-intercept (b) of the line passing through the given points (3, 1) and (2, 5). Step 1: Calculate the slope (m). The formula for the slope (m) between two … Read more

To find cot x from the equation sin x × cot x × csc x = √2, we can start by breaking down the trigonometric functions involved. The cotangent function can be defined in terms of sine and cosine: cot x = cos x / sin x The cosecant function is the reciprocal of sine: … Read more

The function f(x) = |x – 2| is an absolute value function, which means it takes any input value (x), calculates the expression inside the absolute value bars, and returns the non-negative value of that expression. In this case, we can break down the function: The expression inside the absolute value is (x – 2). … Read more

The sequence of numbers you’ve provided is 1, 1, 2, 3, 4, 5, 8, 13, 21. At first glance, it may not be immediately clear that these numbers have a particular pattern. However, this sequence resembles the famous Fibonacci sequence, where each number is the sum of the two preceding ones. In the Fibonacci series, … Read more

Calculating the Volume of a Cylinder To find the volume of a cylinder, we need to use a specific formula. The volume (V) of a cylinder can be calculated using the following equation: V = πr2h where: V is the volume of the cylinder r is the radius of the base of the cylinder h … Read more