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3 years ago

4,669.3455 in word form

Mathematics

1 answer:

Vikentia [17]3 years ago

8 0

Answer:

Four thousand six hundred sixty nine and three thousand four hundred fifty five ten thousandths

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A page should have perimeter of 42 inches. The printing area within the page

Tamiku [17]

Overall dimensions of the page in order to maximize the printing area is page should be 11 inches wide and 10 inches long .

<u>Step-by-step explanation:</u>

We have , A page should have perimeter of 42 inches. The printing area within the page would be determined by top and bottom margins of 1 inch from each side, and the left and right margins of 1.5 inches from each side. let's assume width of the page be x inches and its length be y inches So,

Perimeter = 42 inches

⇒ $2(x+y) = 42\\x+y = 21\\y = 21-x$

width of printed area = x-3 & length of printed area = y-2:

area = $length(width)$

$area = (x-3)(y-2)\\area = (x-3)(21-x-2)\\area = (x-3)(19-x)\\area = -x^{2} + 22x -57$

Let's find $\frac{d(area)}{dx}$ :

$\frac{d(area)}{dx}$ = $\frac{d(-x^{2}+22x-57)}{dx} = -2x +22$ , for area to be maximum $\frac{d(area)}{dx}$ = 0

⇒ $-2x+22 = 0\\2x =22\\x=11 inches$

And ,

$y = 21-x\\y = 21-11\\y = 10 inches$

∴ Overall dimensions of the page in order to maximize the printing area is page should be 11 inches wide and 10 inches long .

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