devyy The equation of a parabola in the form y² = 4px describes a parabola that opens to the right. Here, p represents the distance from the vertex to the focus of the parabola, which is a crucial parameter in defining its shape and position. In the specific case of the equation y² = 4x, we … Read more
Finding Solutions Using the Zero Product Property To solve the equation x² – 30x + 12 = 0 using the zero product property, we first need to break it down into a suitable format. The zero product property states that if the product of two factors equals zero, then at least one of those factors … Read more
To find the point-slope form of a line that is perpendicular to another line, we first need to determine the slope of the given line. The equation given is y = 3x. This is in the slope-intercept form (y = mx + b), where m represents the slope. From this equation, we can see that … Read more
The given vector equation can be expressed in the parametric form as: x = s y = sin(4t) z = s^2 w = cos(4t) To identify the surface defined by this vector equation, we can analyze the relationship between the variables x, y, z, and w. Firstly, observe that: From the first equation x = … Read more
To find the equation for the directrix of a parabola with a vertex at the origin and a focus at (0, 20), we first need to understand the basic properties of a parabola. A parabola is defined as the set of all points that are equidistant from a fixed point, called the focus, and a … Read more
In geometry, triangles are classified based on their sides and angles. When we consider a triangle where all three sides are equal in length, such as the scenario given with each side measuring 80 units, we can effectively conclude the following: Types of Triangles: 1. Equilateral Triangle: An equilateral triangle is defined as a triangle … Read more
The equation given is in the form of a circle’s equation in standard form, which is typically expressed as: x² + y² = r² In this case, we can see that the equation is: x² + y² = 42 To find the center of the circle, we recall that the standard form of a circle … Read more
The letter in the word ‘happy’ that displays order 2 rotational symmetry is the letter ‘h’. To understand this better, let’s break down the concept of order 2 rotational symmetry. A shape has order 2 rotational symmetry if it looks the same after being rotated 180 degrees around a central point. In the case of … Read more
Finding the Equation of a Hyperbola To find the equation of a hyperbola that models the path of a satellite, we first need to understand the parameters given. In this case, we have: a = 55000 km (the distance from the center to the vertex along the transverse axis) c = 81000 km (the distance … Read more
Finding the Range of the Function y = 2x + 3 To determine the range of the function y = 2x + 3 given the domain {0, 2, 6}, we will evaluate the function at each value of x in the specified domain. Step 1: Evaluate y at x = 0 When x = 0: … Read more