Answer:
8.5 square mm per minute
Step-by-step explanation:
A = 1/2bh
A' = (1/2)(b'h +bh') . . . . differentiating with respect to time
A' = (1/2)((-13)(1) +(5)(6)) = (1/2)(17) = 8.5 . . . . mm²/min
The area is increasing at the rate of 8.5 mm²/min.
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<em>Numerical solution</em>
Consider the triangle dimensions .01 minutes before and after the time of interest.
before: base = 5 + 0.13 = 5.13 mm; height = 1 - 0.06 = 0.94 mm. area = 2.4111 mm²
after: base = 5 -0.13 = 4.87 mm; height = 1 +.06 = 1.06 mm. area = 2.5811 mm²
Average rate of change in that period is
(2.5811 -2.4111)/0.02 = .17/.02 = 8.5 . . . . mm²/min
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<em>Comment on the numbers</em>
Note that we have assumed the base is decreasing at 13 mm/min. Quite often, division bars get lost on Brainly, so we're not sure this isn't 1/3 mm/min. At the assumed rate, the triangle will disappear in 5/13 minutes, about 23.08 seconds, when the base becomes zero. Of course, it only came into existence 1/6 minute (10 seconds) ago, when the height became non-zero.
