Question

Rewrite the parametric equations in Cartesian form: x(t) = et, y(t) = –e3t.

Answer 1

To rewrite the parametric equations x(t) = et and y(t) = -e3t in Cartesian form, we can eliminate the parameter t. The Cartesian form equations are x = et and y = -yx^3.

Step-by-step explanation:

To rewrite the parametric equations x(t) = et and y(t) = -e3t in Cartesian form, we can eliminate the parameter t. Since x(t) = et, we can solve for t in terms of x by taking the natural logarithm of both sides: t = ln(x). Similarly, we can solve for t in terms of y by dividing both sides of y(t) = -e3t by -e3: t = ln(-y/(-e3)) = 3ln(-y/e). Therefore, the Cartesian form of the parametric equations is x = e^(ln(x)) = x and y = -e^(3ln(-y/e)) = -yx^3.