in the case of the cone any number satisfy the inequality, but what if i want the external points of the coneMath_QED said:Take a simple test point and see if its coordinates satisfy the inequalities.
That's not true about the cone. For example, the point (1, 1, 2) is outside the cone.DottZakapa said:in the case of the cone any number satisfy the inequality, but what if i want the external points of the cone
A 3d quadratic surface is a three-dimensional shape that can be represented by a quadratic equation, where the highest power of the variables is two. It is a type of geometric surface that can be described as a curved or rounded shape.
The domain of a 3d quadratic surface refers to the set of all possible input values that can be plugged into the equation to produce a valid output. To find the domain, you can analyze the equation and determine any restrictions on the variables, such as square roots or fractions. These restrictions will give you the range of values that are allowed in the domain.
Yes, a 3d quadratic surface can have an infinite domain. This can occur when there are no restrictions on the variables in the equation, or when the equation contains variables with an infinite range, such as x or y. In these cases, the surface will extend infinitely in all directions.
To graph a 3d quadratic surface, you can use a three-dimensional coordinate system and plot points that satisfy the equation. You can also use software or online tools to create a 3d graph of the surface. It is important to remember that a 3d quadratic surface is not a flat shape, so it may be difficult to visualize on a two-dimensional surface.
3d quadratic surfaces have many real-world applications in fields such as engineering, physics, and computer graphics. They can be used to model the shape of objects, such as buildings or bridges, and to analyze their structural stability. In physics, 3d quadratic surfaces are used to represent the path of projectiles or the shape of gravitational fields. In computer graphics, they are used to create realistic 3d models of objects and environments.