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UPPER AND LOWER BOUNDS
a book has a front and a back and 400 pages. the front and back cover are each 0.9 mm thick, measured to 1 decimal place. each page is 0.13 min thick, measured to two decimal places. calculate the minimum thickness of the book. some working must be shown

Answer :

opudodennis

Answer:

51.7mm

Step-by-step explanation:

#Find the minimum bound of the back/front thickness:

-Given that it's rounded to one decimal point, the margin or error will be:

[tex]ME=\frac{1}{2}\times0.1\\\\=0.05[/tex]

We subtract this ME from the front thickness to get the minimum thickness:

[tex]M_t=0.9-0.05\\\\=0.85\ mm[/tex]

#Find the minimum bound of the pages:

-Given that it's rounded to one decimal point, the margin or error will be:

[tex]ME=\frac{1}{2}\times0.01\\\\=0.005[/tex]

We subtract this ME from the page thickness to get the minimum thickness:

[tex]M_p=0.13-0.005\\\\=0.125\ mm[/tex]

The minimum book thickness is thus calculated as:

[tex]M_[bt}=2\times M_t+400\times M_p\\\\=0.85\times 2+400\times 0.125\\\\=51.7\ mm[/tex]

Hence, the minimum thickness of the book is 51.7 mm

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