Final answer:
The value of b in the equation r(t) = (t⁶/6, b, 80) can be any real number.
Step-by-step explanation:
To find the value of b in the equation r(t) = (t⁶/6, b, 80), we need to determine the expression for the y-component of the curve. From the given equation r(t) = (t⁶/6, b, 80), we can see that the y-component is always b and does not depend on t. Therefore, the value of b can be any real number.