Mathematics: 10 1/2 x 1/3 help me pls

10 1/2 x 1/3 help me pls - id1012138962630, kivking12

Ответ:

jahnoibenjamin

08.12.2022

Mathematics

Length = 20 ft

Height = 10 ft

Step-by-step explanation:

Let 'X' be the total width of the billboard and 'Y' the total height of the billboard. The total area and printed area (excluding margins) are, respectively:

$200 = x*y\\A_p = (x-4)*(y-2)$

Replacing the total area equation into the printed area equation, gives as an expression for the printed area as a function of 'X':

$y=\frac{200}{x} \\A_p = (x-4)*(\frac{200}{x} -2)\\A_p=208 -2x -\frac{800}{x}$

Finding the point at which the derivate for this expression is zero gives us the value of 'x' that maximizes the printed area:

$\frac{dA_p(x)}{dx} =\frac{d(208 -2x -\frac{800}{x})}{dx}=0\\0=-2 +\frac{800}{x^2} \\x=\sqrt{400}\\x=20\ ft$

If x = 20 ft, then y=200/20. Y= 10 ft.

The dimensions that maximize the printed area are:

Length = 20 ft

Height = 10 ft

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10 1/2 x 1/3 help me pls

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