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mariasoledad1
17.12.2020 •
Engineering
An engineer must design a rectangular box that has a volume of 9 m3 and that has a bottom whose length is twice its width. What are the dimensions of the box so that the total surface area (of all six sides) of the box is minimized
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Ответ:
Explanation:
Given
Represent the height as h, the length as l and the width as w.
From the question:
Volume of a box is calculated as:
This gives:
Substitute 9 for V
Make h the subject:
The surface area is calculated as:
Recall that:![l = 2w](/tpl/images/0996/3011/6b30b.png)
Recall that:![h = \frac{9}{2w^2}](/tpl/images/0996/3011/7a30d.png)
So:
To minimize the surface area, we have to differentiate with respect to w
Set A' to 0
Add
to both sides
Multiply both sides by![w^2](/tpl/images/0996/3011/4bc84.png)
Make
the subject
Solve for w
Recall that :
and ![l = 2w](/tpl/images/0996/3011/6b30b.png)
Hence, the dimension that minimizes the surface area is:
Ответ:
Step-by-step explanation:
If x is the number of hours, then:
48 = 10x + 7
41 = 10x
x = 4.1