If a rectangle has a base of 2cm, and length of 3cm, and its base increases by 1cm/s and its length increases by 2cm/s, at what rate is the area increasing when the area is 28cm^2?
Is the answer to this 15cm^2/s?
If a rectangle has a base of 2cm, and length of 3cm, and its base increases by 1cm/s and its length increases by 2cm/s, at what rate is the area increasing when the area is 28cm^2?
Is the answer to this 15cm^2/s?
Ok
Think of the graph of time on x axis and length on y axis plot the lines of length and base:
(y=mx+c where c is value when t=0 and m is the rate of change of length)
Length y = 2+x
Base y= 3+2x
So
Area = (2+x)(3+2x)
solve 28=(2+x)(3+2x) to give 2 values for time when area=28.
One of these values are negative, and this clearly is invalid as you can't have negative time.
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Now the area at any point in time is (2+x)(3+2x) as shown above.
Put this equal to y and find "dy by dx"
Put your realistic value for time in here to get the rate of change of area at this point
It comes out at 15cm^2/s
EDIT:Aha i didn't read your post properly - you just wanted confirmation - well yea its 15 - sorry