A regular pentagon is a polygon with five equal sides and five equal angles. To find the measure of each interior angle, we can use the formula for calculating the interior angles of any polygon: Interior Angle = (n – 2) × 180° / n In this formula, n represents the number of sides in … Read more
The term mantissa refers to the significant digits of a number in scientific notation. In a scientific notation format, a number is expressed as the product of a number (the mantissa) and a power of ten. For example, in the number 6.02 x 10^23, the mantissa is 6.02, while 10^23 is the exponential part that … Read more
To simplify the expression 1 + tan²(x), you can use a fundamental identity from trigonometry known as the Pythagorean identity. According to this identity: 1 + tan²(x) = sec²(x) Here’s a breakdown of the steps involved in this simplification: Recall the definition of tan(x): tan(x) is defined as the ratio of the opposite side to … Read more
To find the solution to the equation 21x + 3 = 14, we start by isolating the variable x. Here are the steps: Subtract 3 from both sides: This gives us: 21x + 3 – 3 = 14 – 3 which simplifies to: 21x = 11 Divide both sides by 21: Now, we can isolate … Read more
To solve the equation 2x + 5x + 3x = 4, we first need to combine like terms on the left side of the equation. 1. Combine the coefficients of x: 2x + 5x + 3x = (2 + 5 + 3)x = 10x This simplifies our equation to: 10x = 4 2. Next, we … Read more
To solve the equation 5x + 8 = 3x + 10, follow these steps: Start with the original equation: 5x + 8 = 3x + 10 Isolate the variable (x) on one side: First, subtract 3x from both sides to move all terms containing x to one side of the equation: 5x – 3x + … Read more
To find the area of a circle when you have its circumference, you can follow these steps: Understand the relationship between circumference and radius: The formula for the circumference (C) of a circle is given by: C = 2 × π × r where r is the radius of the circle. Rearrange the formula to … Read more
The expression you provided seems to involve multiple variables and perhaps a multiplication notation. It’s important to clarify some details about the properties of multiplication that might be illustrated through these variables. Let’s break down the properties of multiplication that are relevant when dealing with variables: Commutative Property: This property states that changing the order … Read more
To determine the values of r for which the function y = erx satisfies the differential equation 2yy’ = y, we first need to differentiate the function with respect to x. The function y = erx is an exponential function, where e is the base of the natural logarithm. The derivative of y with respect … Read more
To determine how many notepads can fit in a box that is 2 feet wide, we first need to convert the width of the box from feet to inches, since the width of the notepad is given in inches. Since there are 12 inches in a foot, we can calculate the width of the box … Read more