NEWrelated_rates

# NEWrelated_rates - PROBLEM1 /sec andthepropor= ?

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A screen saver displays the outline of a 3 cm by 2 cm rectangle and then expands the rectangle in such a way that the 2 cm side is expanding at the rate of 4 cm/sec and the propor=ons of the rectangle never change. How fast is the area of the rectangle increasing when its dimensions are 12 cm by 8 cm? PROBLEM 1

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A screen saver displays the outline of a 3 cm by 2 cm rectangle and then expands the rectangle in such a way that the 2 cm side is expanding at the rate of 4 cm/sec and the propor=ons of the rectangle never change. How fast is the area of the rectangle increasing when its dimensions are 12 cm by 8 cm? Rela%ons among variables: A=xy x=(3/2)y Variables: =me independent: t dependent: x, y and A dimensions area x y A Diagram: Known: dy/dt = 4 cm/sec Unknown: dA/dt when x=12 and y=8 MATHEMATICAL MODEL OF THE PROBLEM
Rela%ons among variables: A=xy x=(3/2)y Variables: =me independent: t dependent: x, y and A dimensions area x y A Diagram: Known: dy/dt = 4 cm/sec Unknown: dA/dt when x=12 and y=8 Rela=on among variables Rela=on among rates Step 1 : List the rates Rates: dx/dt dy/dt dA/dt Step 2 : List the rela=ons among the rates Chain rule

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• Fall '10
• AlessandraPANTANO

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