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Calculating the Volume of a Cylinder To find the volume of a cylinder, you can use the formula: Volume = π * r² * h Where: π (Pi) is approximately 3.14159, r is the radius of the cylinder, and h is the height of the cylinder. In your case, the diameter of the cylinder is … Read more

To simplify the sum of the expression 2x + 3 + 10 + x + 2 + 9, we start by combining like terms. First, let’s group the terms: Coefficients of x: 2x and x (which is equivalent to 1x) Constant terms: 3, 10, 2, and 9 Now, combine the coefficients of x: 2x + … Read more

To calculate the volume of a ball (or sphere), you can use the formula: Volume = (4/3) × π × r³ Where: Volume is the volume of the sphere. π (pi) is approximately 3.14159. r is the radius of the sphere. In this case, we need to find the radius first. The radius (r) is … Read more

To find a vector of a specific magnitude that points in the same direction as a given vector, we can follow these steps: Identify the original vector: The vector given is v = 10i + 24k. Calculate the magnitude of the original vector: The magnitude (length) of a vector v = ai + bj + … Read more

To calculate the distance between two points M(6, 16) and Z(1, 14) in a two-dimensional space, we can use the distance formula: Distance Formula: d = √((x₂ – x₁)² + (y₂ – y₁)²) Where: (x₁, y₁) and (x₂, y₂) are the coordinates of points M and Z, respectively. d is the distance between the two … Read more

To calculate the probability of being dealt a 5-card hand that consists solely of hearts from a standard deck of 52 cards, we need to consider a few key elements. A standard deck of 52 cards contains 4 suits: hearts, diamonds, clubs, and spades, with each suit containing 13 cards. Therefore, when we are dealing … Read more

To calculate the measure of angle A in a triangle, you can use various methods depending on the information you have about the triangle. Here are some ways to determine angle A: Using the Sum of Angles in a Triangle: The sum of the interior angles of any triangle is always 180 degrees. If you … Read more

To determine when the function g(x) = 6x² + 23x + 4 equals zero, we need to find the roots of the equation. This means solving the equation: 6x² + 23x + 4 = 0 We can apply the quadratic formula, which is given by: x = (-b ± √(b² – 4ac)) / 2a In … Read more

Finding g(f(x)) and f(g(x)) To solve the problem, we need to find two compositions of functions: g(f(x)) f(g(x)) Step 1: Finding g(f(x)) Given: f(x) = sin(x) g(x) = cos(x) To find g(f(x)), we substitute f(x) into g(x): g(f(x)) = g(sin(x)) = cos(sin(x)) Final Result for g(f(x)) Thus, g(f(x)) = cos(sin(x)). Step 2: Finding f(g(x)) Next, … Read more

To divide the expressions 3×3, 2×2, 61x, and 20 by 5x, we will work through each term step by step. 1. Dividing 3×3 by 5x: To divide these two, we can apply the rules of division for algebraic expressions. We separate the coefficients and the variable. So: Coefficients: 3 / 5 gives us 3/5 Variables: … Read more