Question

Let be the surface in ℝ³ defined by the equation x² ⋅ y⁷ − 5z = 8. Find a real‑valued function (x,y) of two variables such that is the graph of .

Answer 1

To find the real-valued function (x, y) that represents the given surface equation, solve the equation for z.

Step-by-step explanation:

To find a real-valued function (x, y) such that the surface in ℝ³ defined by the equation x² ⋅ y⁷ − 5z = 8 is the graph of the function, we need to solve the given equation for z.

Starting with the original equation, x² ⋅ y⁷ − 5z = 8:

1. Add 5z to both sides: x² ⋅ y⁷ = 5z + 8
2. Divide both sides by 5: z = (x² ⋅ y⁷ + 8) / 5

So, the real-valued function (x, y) that represents the surface is z = (x² ⋅ y⁷ + 8) / 5.