Please correct your statement of the problem. It must be in error.CricK0es said:Homework Statement
Sketch the surface of a paraboloid z=9-x2 -92 in 3-dimensional xyz-space
Homework Equations
I assume partial derivatives are involved in some manner
The Attempt at a Solution
I attempted to solve by making each variable equal to zero... That didn't work xD. I would appreciate some guidance on how to go about sketching these things in general, many thanks [/B]
Y-comp is missing, So it can't be 3d shape.CricK0es said:Homework Statement
Sketch the surface of a paraboloid z=9-x2 -92 in 3-dimensional xyz-space
Homework Equations
I assume partial derivatives are involved in some manner
The Attempt at a Solution
I attempted to solve by making each variable equal to zero... That didn't work xD. I would appreciate some guidance on how to go about sketching these things in general, many thanks [/B]
Do you mean ##z = 9 - x^2 - y^2##?CricK0es said:Homework Statement
Sketch the surface of a paraboloid z=9-x2 -92 in 3-dimensional xyz-space
Neither ordinary derivatives nor partial derivatives are required in this problem.CricK0es said:Homework Equations
I assume partial derivatives are involved in some manner
Setting one variable to zero gives you what's called a trace, the intersection of the surface in one of the coordinate planes. For example, assuming the surface is as I wrote it above, setting x = 0, gives you the trace in the y-z plane. Setting y = 0, gives you the trace in the x-z plane.CricK0es said:The Attempt at a Solution
[/B]
I attempted to solve by making each variable equal to zero... That didn't work xD. I would appreciate some guidance on how to go about sketching these things in general, many thanks
Look for cross sections in a number of planes that are parallel to the x-y plane.CricK0es said:Yeah there was a mistake on the question paper 92 goes to y2.
I'll attempt it again with your advice. Thank you
A paraboloid is a three-dimensional shape that resembles a bowl or a dish. It is formed by rotating a parabola around its axis.
To sketch the surface of a paraboloid, you can start by drawing a parabola on a piece of paper. Then, rotate the parabola around its axis to create a bowl-shaped figure. Make sure to draw the curves accurately and symmetrically to create a smooth surface.
A paraboloid has a single axis of symmetry, and its cross-sections are all parabolas. It also has a vertex, which is the point where the parabola intersects with the axis of symmetry.
Paraboloids have many practical uses in daily life. They are commonly found in satellite dishes, flashlights, and reflectors. They are also used in architecture, such as in the design of domes and archways.
Yes, there are different types of paraboloids, including elliptic paraboloids, hyperbolic paraboloids, and circular paraboloids. Each type has a different shape and properties, but they all share the common characteristic of being formed by rotating a parabola.