Question

Given the parametric equations x=eᵗ, y=te−t, these equations describe the motion of a point in the:

a) Cartesian plane.
b) Polar coordinate system.
c) Parametric curve in 3D space.
d) Complex plane.

Answer 1

The given parametric equations x=eᵗ, y=te−t describe the motion of a point in the Cartesian plane.

Step-by-step explanation:

The given parametric equations x=eᵗ, y=te−t describe the motion of a point in the Cartesian plane (option a).

In the Cartesian coordinate system, the x-axis represents the horizontal direction and the y-axis represents the vertical direction. The equations x=eᵗ and y=te−t provide the coordinates for the point as the parameter t changes.

For example, when t=0, the point is located at the origin (0,0) and as t increases, the point moves along a specific path in the Cartesian plane.