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satela [25.4K]
3 years ago
13

A square with side x is changing with time where x(t)=3t+1. What is rate of change of the area of the square when t=2 seconds.

Mathematics
1 answer:
GuDViN [60]3 years ago
7 0

Answer:

Rate of change of the area of the square is 42 units at t = 2.

Step-by-step explanation:

We note that the area of the square is given by: A(x) = x^2 but we aim to find \frac{dA}{dt}. But we can use the chain rule to pull out that dA/dt. Doing so gives us:

\frac{dA}{dt} = \frac{dA}{dx} \times \frac{dx}{dt}.

Now, \frac{dA}{dx} = 2x (by the power rule and \frac{dx}{dt} = 3.

But since we have "x" and not "t", we want to find what x is when t = 2. Substituting t = 2 gives us x(2) = 3(2) + 1 = 7.

So, finally, we see that:

\frac{dA}{dt} = 2(7) \times 3 = 14 \times 3 = 42.

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