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The side length of a square is increasing at a rate of 15 millimeters per second. At a certain instant, the side length is 22 millimeters.
What is the rate of change of the area of the square at that instant (in square millimeters per second)?

Respuesta :

okpalawalter8

Answer:

[tex]\frac{dA}{dt}=660 millimetre/sec[/tex]

Step-by-step explanation:

From the question we are told that

Increase rate  [tex]\triangle L=15 millimetre\ per\ second[/tex]

Length L=millimetre

Generally the area of  the square is given by [tex]A=L^2[/tex]

Therefore

[tex]\frac{dA}{dt}=\alpha S*\frac{dS}{dt}[/tex]

[tex]\frac{dA}{dt}=2*22*(15)[/tex]

Generally rate of change of area is given as

[tex]\frac{dA}{dt}=660 millimetre/sec[/tex]