Mathematics, 31.03.2020 03:01 belferfex
A rectangle has area 64 cm^2. A straight line is to be drawn from one corner of the rectangle to the midpoint of one of the two more distant sides. What is the minimum possible length of such a line
Answers: 3
![dL/db=\frac{d}{db} [(\frac{1024}{b^2}+b^2)^{\frac{1}{2}} ]\\\\dL/db=\frac{1}{2} (\frac{1024}{b^2}+b^2)^{(-\frac{1}{2})}\cdot \frac{d}{db} [\frac{1024}{b^2}+b^2]\\\\ dL/db=\frac{2b+1024\cdot(-2)\cdot b^{-3}}{2\sqrt{(\frac{1024}{b^2}+b^2)}} \\\\\\ dL/db=\frac{2b-2048\cdot b^{-3}}{2\sqrt{(\frac{1024}{b^2}+b^2)}}](/tpl/images/0572/6050/8e978.png)
![dL/db=\frac{2b-2048\cdot b^{-3}}{2\sqrt{(\frac{1024}{b^2}+b^2)}}=0\\\\\\2b-2048b^{-3}=0\\\\2b=\frac{2048}{b^3}\\\\b^4=\frac{2048}{2} =1024\\\\b=\sqrt[5]{1024}\approx5.66](/tpl/images/0572/6050/57b15.png)
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A rectangle has area 64 cm^2. A straight line is to be drawn from one corner of the rectangle to the...
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