Final answer:
To find dy/dt, use the relationship dx/dt = 3dy/dt and substitute the given value dx/dt = 1. This gives dy/dt = 1/3, so the value of dy/dt at the instant when x = 4 and y = 3 is 1/3.
Step-by-step explanation:
The student is dealing with a derivative problem in calculus, specifically related to rates of change. Given that dz/dt is constant and equal to 1, and that dx/dt is 3 times dy/dt, we need to solve for dy/dt. Using the information that x = 4 and y = 3 at a particular instant:
From dx/dt = 3dy/dt, we can isolate dy/dt:
dy/dt = (dx/dt) / 3.
Substituting the given rate of change for x:
dy/dt = 1 / 3.
If dx/dt is 1, then:
dy/dt = 1 / 3.
Therefore, the value of dy/dt when x = 4 and y = 3 is 1/3.