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SCALCET8 3.9.003. Each side of a square is increasing at a rate of 4 cm/s. At what rate is the area of the square increasing when the area of the square is 9 cm2

Sagot :

Answer: [tex]24\ cm^2/s[/tex]

Step-by-step explanation:

Given

Each side of square is increasing at a rate of 4 cm/s

Side of a square when area is [tex]9\ cm^2[/tex]

Suppose a is side of the square

[tex]\Rightarrow a=\sqrt{9}\\\Rightarrow a=3\ cm[/tex]

Area is given by

[tex]\Rightarrow A=a^2\\\text{Differentiate area w.r.t time}\\\\\Rightarrow \dfrac{dA}{dt}=2a\dfrac{da}{dt}\\\\\Rightarrow \dfrac{dA}{dt}=2\times 3\times 4\\\\\Rightarrow \dfrac{dA}{dt}=24\ cm^2/s[/tex]

Area is increasing at a rate of [tex]24\ cm^2/s[/tex]

ledgred07

Answer:

24cm^2/ s

Step-by-step explanation:

View image ledgred07
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