Question

The sides of the rectangle increase in such a way that dz/dt = 1 and dx/dt = 3dy/dt. At the instant when x = 4 and y = 3, what is the value of dy/dt?

Answer 1

When x = 4 and y = 3, the value of dy/dt is 1/3.

Step-by-step explanation:

Given that dz/dt = 1 and dx/dt = 3dy/dt, we can find the value of dy/dt when x = 4 and y = 3.

Substituting the values into the given equations, we have 1 = 3(dy/dt). Rearranging the equation, we get dy/dt = 1/3.

Therefore, at the instant when x = 4 and y = 3, the value of dy/dt is 1/3.

Answer 2

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.