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PSYCHO15rus [73]
2 years ago
12

Each side of a square is increasing at a rate of 6 cm/s. At what rate (in cm2/s) is the area of the square increasing when the a

rea of the square is 9 cm2
Mathematics
1 answer:
My name is Ann [436]2 years ago
6 0

36 cm²s⁻¹ is the rate at which the area of the square is increasing.

Given each side of the square is increasing at a rate of 6cm/s

Area, A = s², s is the side length

=> \frac{dA}{dt} =\frac{dA}{ds}* \frac{ds}{dt} =2s*(\frac{ds}{dt} ) {chain rule of differentiation}

\frac{ds}{dt} = 6 cm/s

When A = 9 cm² => 9 = s²

=> s = √(9) => s = 3 cm

Hence, \frac{dA}{dt} = 2 × 3 × 6 = 36 cm²s⁻¹

Hence, 36 cm²s⁻¹ is the rate at which the area of the square increases

Learn more about differentiation here brainly.com/question/3083587

#SPJ4

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