Final answer:
To eliminate the parameter t in the given pair of parametric equations x=4t² and y=8t³, we can express t in terms of x and substitute it into the equation for y. Simplifying further, we obtain the rectangular-coordinate equation y = sqrt(x)³.
Step-by-step explanation:
To eliminate the parameter t, we can express t in terms of x and substitute it into the equation for y. From the equation x = 4t², we can solve for t:
t = sqrt(x/4)
Substituting this value of t into the equation for y = 8t³, we get:
y = 8(sqrt(x/4))³
Simplifying further, we have:
y = 8(sqrt(x/4))³
y = 8(sqrt(x)/2)³
y = 8(sqrt(x)³/8)
y = sqrt(x)³
Therefore, the rectangular-coordinate equation for the curve is y = sqrt(x)³.