Question

Two varibble quartities A and B are found to be relited by the equation given below What is the nte of change dA/de at the moment when A=2 and oB/dt =1 ? A 3 +B 3 =133 d1/ dA = when A=2 and dB/di=1

Answer 1

The rate of change dA/dB is found by differentiating the given equation A^3 + B^3 = 133 with respect to time, solving for dA/dt, and then dividing by dB/dt. Without additional information about the relationship between A and B, a numerical value for dA/dB when A=2 and dB/dt=1 cannot be determined.

Step-by-step explanation:

We are given that A and B are related by the equation A^3 + B^3 =133. To find dA/dB, we would differentiate both sides of the equation with respect to t, then isolate dA/dt and divide by dB/dt to get dA/dB. Using the Chain Rule, we get 3A^2dA/dt + 3B^2dB/dt = 0. Then, we can solve for dA/dt when A=2, and dB/dt=1 which gives us dA/dt = -B^2. By substitution, the final answer is the negative square of B when A=2. Without a given function to relate A and B directly or an initial condition for B, we cannot numerically solve for B, and thus we cannot give a numerical value for the rate of change dA/dB at the moment when A=2.