The area of the square increasing at 30 [tex]\frac{cm^{2} }{sec}[/tex]
The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another
Let the side of a square be x.
So,
Area of square = [tex]x^{2}[/tex]
A =[tex]x^{2}[/tex]
Differentiating with respect to time we get,
dA/dt = 2x dx/dt
When area = 9 [tex]cm^{2}[/tex] the side becomes 3 cm
At x = 3cm and dx/dt = 5 cm/s (Given)
dA/dt = 2.3.5 = 30 [tex]\frac{cm^{2} }{sec}[/tex]
Thus the area of the square increasing at 30 [tex]\frac{cm^{2} }{sec}[/tex]
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