Final answer:
The rate at which the side lengths of the ice cube are decreasing when the volume is 5mm³ is -1/10 mm/min.
Step-by-step explanation:
To find the rate at which the side lengths of the ice cube are decreasing when the volume is 5mm³, we need to use the relationship between the volume and the side length of a cube. The volume of a cube is given by V = s³, where s is the side length. We are given that the volume is decreasing at a rate of -9mm³/min. Taking the derivative of the volume formula with respect to time, we get dV/dt = 3s²(ds/dt), where ds/dt is the rate at which the side length is changing. Plugging in the values, we have -9 = 3(5)²(ds/dt). Solving for ds/dt, we get ds/dt = -9 / (3(5)²) = -1/10 mm/min.