A rectangle initially has dimensions 3 cm by 6 cm. All sides begin increasing in length at a rate of 3 cm divided by s 3 cm/s. A
t what rate is the area of the rectangle increasing after 21 s?
1 answer:
Answer:
405 cm²/s
Step-by-step explanation:
The dimensions are increasing at the rate of 3 cm/s, so the dimensions in cm can be described as a function of time by ...
3 + 3t
and
6 + 3t
Then the area is the product of these, or ...
A = (3 +3t)(6 +3t)
A = 9t² +27t +18
and the rate of change of area is given by its derivative with respect to t:
A' = 18t +27
When t=21, the value of this is ...
A'(21) = 18·21 +27 = 405 . . . . cm²/s
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Step-by-step explanation:
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