Final answer:
To find dt / dz, use the chain rule to differentiate z with respect to t. Substitute given values for dx/dt and dy/dt and simplify the equation.
Step-by-step explanation:
To find dt / dz, we need to find the derivative of t with respect to z. Given that z^2 = x^2 + y^2, we can rewrite the equation as z = sqrt(x^2 + y^2).
Now, we can differentiate both sides of the equation with respect to t. Since x and y are functions of t, we use the chain rule to differentiate z with respect to t.
dz/dt = dz/dx * dx/dt + dz/dy * dy/dt
Since dx/dt and dy/dt are given, we can substitute them into the equation and simplify to find dz/dt.