2 years ago

Pls help thanks.....

Mathematics

1 answer:

ivolga24 [154]2 years ago

8 0

Answer: 60

Step-by-step explanation:

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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.

GuDViN [60]

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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.

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