Final answer:
When x = x(t) and y = y(t) are functions of t, you can plot them on a graph, solve for their derivatives, differentiate them with respect to t, and evaluate them at specific values of t.
Step-by-step explanation:
If x = x(t) and y = y(t) are both functions of t, you can plot the functions on a graph by assigning values to t and finding the corresponding values of x and y. For example, if x = 2t and y = 3t^2, you can choose different values for t, calculate x and y, and plot the points on a graph.
To solve for the derivatives of x and y, you can use the rules of differentiation. For example, if x = 2t, the derivative of x with respect to t is dx/dt = 2. Similarly, if y = 3t^2, the derivative of y with respect to t is dy/dt = 6t.
To evaluate the functions at specific values, simply substitute the desired value of t into the equations and calculate the corresponding values of x and y. For example, if x = 2t and y = 3t^2, substituting t = 5 would give x = 2(5) = 10 and y = 3(5^2) = 75.