To find the inverse of the function f(x) = 4×3 + 5, we’ll follow a few steps: Rewrite the function: Set y equal to f(x): y = 4×3 + 5 Swap x and y: This step is essential for finding the inverse. Now we rewrite the equation as: x = 4y3 + 5 Solve for … Read more
Determining if a number is divisible by 4 is quite simple and can be done by following a specific rule. This rule states that a number is divisible by 4 if the number formed by its last two digits is divisible by 4. Here’s how you can apply this rule: Look at the Number: Take … Read more
Understanding the Derivative of sin(1/x) The function in question is sin(1/x). To find its derivative, we will use the chain rule of differentiation, which is a fundamental technique in calculus. Step-by-Step Derivation The chain rule states that if you have a composite function f(g(x)), the derivative is given by: f'(g(x)) * g'(x) In this case, … Read more
To eliminate the parameter in the equation x sin(1/2) + y cos(1/2) = p, we first need to understand the components involved: Identifying Parameters: Here, x, y, and p are the variables, while the equation includes trigonometric functions of a constant (1/2). Rearranging the Equation: We can rearrange the equation to isolate p: p = … Read more
The set of all possible outcomes of an experiment is known as the sample space. In the realm of probability and statistics, understanding the sample space is fundamental as it encompasses every possible result that could occur following a certain action or procedure. For instance, if you were to flip a coin, the sample space … Read more
To find the velocity of an object, you can use the formula for velocity: Velocity (v) = Distance (d) / Time (t) In this case: Distance (d): 100 meters Time (t): 10 seconds Now, we can plug in the values into the formula: Velocity (v) = 100 m / 10 s Calculating that gives: Velocity … Read more
To find the angle between two vectors, you can use the dot product formula. The dot product of two vectors u and v can be calculated as: u ⋅ v = |u| |v| cos(θ) Where: u ⋅ v is the dot product of the vectors. |u| and |v| are the magnitudes (lengths) of the vectors. … Read more
To find the value of ‘a’ such that the line x = a bisects the area under the curve y = 1/x² for the interval [1, 4], we need to follow a series of steps: Step 1: Calculate the total area under the curve. The area under the curve from x = 1 to x … Read more
To express the equation 64×6 + 27 as a sum of cubes, we first recognize that this can be rewritten in the form of a3 + b3, where: a corresponds to (4×2) since (4×2)3 = 64×6, and b corresponds to 3 since 33 = 27. Now we rewrite the expression: 64×6 + 27 = (4×2)3 … Read more
To find the next number in the series 16, 11, 13, 8, 10, 5, 7, let’s first analyze the pattern through the series. The series is formed through a combination of subtracting and then adding numbers alternately: From 16 to 11: subtract 5 From 11 to 13: add 2 From 13 to 8: subtract 5 … Read more