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To find the value of f(12) for the function f(x) = log₅(x + 1), we will substitute 12 into the function. First, we will calculate x + 1 when x = 12: 12 + 1 = 13 Next, we need to find f(12) = log₅(13). This means we need the base 5 logarithm of 13. … Read more

To find the equation of the line of intersection of two planes, we start with their equations: Plane q: x + y + 2z = 1 Plane r: x + y + z = 1 1. **Identifying the System of Equations**: We have the following system: x + y + 2z = 1 (1) x … Read more

The conversion between inches and centimeters can sometimes be confusing, but it’s a simple process once you know the ratio! There are 2.54 centimeters in one inch. Therefore, to convert centimeters into inches, you can use the following formula: Inches = Centimeters / 2.54 So, if you have a measurement in centimeters and you want … Read more

To solve for the measure of angle A (ma), we first need to understand that vertical angles are equal. This means that if angle A is represented as ma and angle B as mb, then: ma = mb According to the problem, we have: ma = 5x – 80 and since angles A and B … Read more

Rolling a six-sided die is a common probability problem. To understand the probability of rolling a number less than 5, we first need to define the possible outcomes when the die is rolled. A standard six-sided die has the numbers 1, 2, 3, 4, 5, and 6 on its faces. Therefore, the possible outcomes are: … Read more

The domain of a function refers to the set of all possible input values (or ‘x’ values) that can be used in the function. In the context of the function you’ve provided, which has a specified range of {25, 64}, we need to deduce what values of ‘x’ correspond to these outputs. Assuming the function … Read more

To simplify the expression tan(x) sec(x), it’s important to recall the definitions of these two trigonometric functions. The tangent and secant functions can be expressed in terms of sine and cosine: tan(x) = sin(x) / cos(x) sec(x) = 1 / cos(x) Using these definitions, we can rewrite the expression: tan(x) sec(x) = (sin(x) / cos(x)) … Read more

To determine how much money is due to the vendor for the milk supplied to the hotel each day, we need to first calculate the total amount of milk supplied in both the morning and the evening. The vendor delivers: 32 liters of milk in the morning 68 liters of milk in the evening Now, … Read more

The sequence defined by the formula an = 2n + 4 generates terms based on the natural numbers where n starts from 1. To find the first four terms, we replace n with 1, 2, 3, and 4: For n = 1: a1 = 2(1) + 4 = 2 + 4 = 6 For n … Read more

To find the relative and absolute extrema of the function f(x) = x³ – 6x² + 9x + 2, we will follow a systematic approach involving first and second derivatives. Step 1: Find the first derivative The first step is to find the first derivative of the function, which will help us to determine the … Read more