devyy To find the radius of a sphere using its circumference, you can apply a simple mathematical formula. The circumference (C) of a sphere is related to its radius (r) through the formula: C = 2πr Where: C is the circumference of the sphere. r is the radius of the sphere. π (Pi) is approximately 3.14159. … Read more
A polyhedron with twelve flat faces is known as a dodecahedron. The term ‘dodecahedron’ is derived from the Greek words ‘dodeka’, meaning twelve, and ‘hedron’, which refers to faces or surfaces. This geometric shape is part of the family of Platonic solids, which are convex polyhedra with identical faces of regular polygons. In the case … Read more
The probability of rolling a sum of 6 with two dice can be calculated by determining the total possible outcomes and the favorable outcomes that result in that sum. When rolling two dice, each die has 6 faces, leading to a total of 36 possible outcomes (6 faces on die one multiplied by 6 faces … Read more
To find the surface area of a square pyramid, you can use a straightforward formula that combines both the area of the base and the area of the triangular faces. The formula for the surface area (SA) of a square pyramid is: SA = b² + 2 * (b * l / 2) where: b … Read more
When delving into the world of mathematics, it’s essential to understand the fundamental differences between an equation and an expression. Here’s a comprehensive breakdown: What is an Expression? An expression is a mathematical phrase that combines numbers, variables, and operators (such as +, −, ×, ÷) but does not contain an equality sign. Expressions can … Read more
To factor the polynomial expression 3x² + 5x + 1, we need to find two numbers that multiply to the product of the coefficient of x² (which is 3) and the constant term (which is 1), so 3 * 1 = 3. Additionally, we need these two numbers to add up to the coefficient of … Read more
The expression x2y2 can be simplified using the properties of exponents. Here are the steps to correctly simplify this expression: Identify the coefficients: In the expression, there are no additional coefficients in front of x and y, implying both are equal to 1 by default. Apply the exponent rule: According to the exponent rule, when … Read more
Solving the Equation x² – 20x + 100 = 36 To solve the equation x² – 20x + 100 = 36, we first need to rearrange it in the standard quadratic form. 1. **Rearranging the equation:** We subtract 36 from both sides, giving us: x² – 20x + 100 – 36 = 0. This simplifies … Read more
To expand the expression x(y + 3), you can use the distributive property, which states that a(b + c) = ab + ac. Essentially, you need to multiply each term inside the parentheses by the term outside the parentheses. Starting with the expression: x(y + 3) We can apply the distributive property: Multiply x by … Read more
To determine the next number in the series 5000, 1000, 200, 40, we need to identify the pattern that governs the progression of these numbers. If we observe closely, we can see that each number is being divided by a certain factor to yield the next number: 5000 divided by 5 equals 1000 1000 divided … Read more