Answer:
-4 28/81 cm/min ≈ -4.346 cm/min
Step-by-step explanation:
Differentiating the formula for the area of a triangle gives the relationship between the various rates of change.
A = 1/2bh
A' = 1/2(b'h +bh') . . . . . relation of rates of change
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triangle dimensions
When the area is 83 cm², and the height is 9 cm, the base length is ...
83 cm² = 1/2b(9 cm)
b = 166/9 cm
rate of change
Filling in the given values and rates of change, we have ...
3.5 cm²/min = 1/2(b'·(9 cm) +(166/9 cm)(2.5 cm/min))
7 cm²/min -46 1/9 cm²/min = (b')(9 cm)
b' = (-39 1/9 cm²/min)/(9 cm) = -4 28/81 cm/min
The base of the triangle is changing at the rate of -4 28/81 cm/min, about -4.346 cm/min.
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