To express a complex number in trigonometric form, we typically use the format: z = r (cos θ + i sin θ) where: r is the modulus (magnitude) of the complex number θ is the argument (angle) of the complex number Let’s break down the steps to express the complex number 3 + 3i in … Read more
To solve the equation x4 + 6×2 + 5 = 0 using u-substitution, we first make a substitution that simplifies the equation. Let u = x2. Then, we can express x4 as u2, leading to the transformation of the equation: u2 + 6u + 5 = 0 This quadratic equation can now be solved using … Read more
Arranging a set of rational numbers from least to greatest involves a few straightforward steps. Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. Here’s how you can effectively sort them: Understanding Rational Numbers: Ensure you know what rational numbers are. Examples … Read more
To find three irrational numbers between √2 and √3, we first need to establish the approximate values of these square roots. The value of √2 is approximately 1.414 and √3 is approximately 1.732. Knowing this, we can look for numbers that fall between these two square roots. 1. **Number 1:** One straightforward example is the … Read more
Understanding Odd Functions An odd function is defined mathematically by the property that for all x in the function’s domain, the following condition holds: f(-x) = -f(x) This means that if you take the input of a function, switch its sign (i.e., replace x with -x), the output should also switch sign. Examples of Odd … Read more
To convert the linear equation y = 2x + 32 into the standard form of a quadratic equation, we need to first understand what the standard form of a quadratic equation looks like. The standard form of a quadratic equation is generally expressed as: Ax2 + Bx + C = 0 However, the equation provided … Read more
To find the value of x for the bigger polygon using the sides of two similar polygons, we need to understand the property that corresponding sides of similar polygons are proportional. Let’s denote the side lengths of the bigger polygon as follows: Side A: 3 Side B: 8 Side C: 16 And for the smaller … Read more
The product of a number and its reciprocal is always one. To understand why, let’s break it down a bit. A reciprocal of a number is simply what you get when you divide 1 by that number. For instance, if you take the number 5, its reciprocal would be 1/5. When you multiply these two … Read more
The equation given is m² – 9 = 0, which is a quadratic equation. To find the solutions, we can start by rearranging the equation. First, we can add 9 to both sides of the equation: m² = 9 Next, to solve for m, we can take the square root of both sides: m = … Read more
To find the vector function that represents the curve of intersection between the cylinder x2 + y2 = 4 and the surface z = xy, we first need to express the points on the cylinder in a suitable parametric form. The equation of the cylinder describes a circle of radius 2 in the xy-plane. We … Read more