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A billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 700ft2
(including the margins).
A. O
Printed Region
If x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard,
Area, as a function of x
X
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Question:

Reading Lis
7. (0.5/1 Points)
DETAILS
REVIOUS ANSWERS
MY NOTES
PRACTICE ANOTHER
A billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 700ft2
(including the margins).
A. O
Printed Region
If x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard,
Area, as a function of x
X
Sou
Determine the domain of the function for area. Enter your answer using interval notation
Domain of the function for area
X
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MY NOTES
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The area of a rectangular shape is the product of its dimensions. The area as a function of x is: [tex]A(x) = \frac{4(x - 10)(175-x)}x[/tex].The domain of x in interval notation is [tex][10, \infty)[/tex]Given that:[tex]x \to length[/tex][tex]y \to width[/tex]So, the area is:[tex]Area = Length \times Width[/tex][tex]A = x \times y[/tex][tex]x \times y =700[/tex]Make y the subject:[tex]y = \frac{700}x[/tex]When the margins are removed, the dimension of the billboard is:[tex]Length = x - 2\times 5[/tex][tex]Length = x - 10[/tex][tex]Width = y - 2 \times 2[/tex][tex]Width = y - 4[/tex]The print area is calculated as:[tex]A_p = (x - 10) \times (y -4)[/tex]So, we have:[tex]A_p = (x - 10) \times (\frac{700}x -4)[/tex]Take LCM[tex]A_p = (x - 10) \times (\frac{700-4x}x)[/tex][tex]A_p = \frac{(x - 10)(700-4x)}x[/tex]So, as a function of x;The print area is:[tex]A(x) = \frac{(x - 10)(700-4x)}x[/tex][tex]A(x) = \frac{4(x - 10)(175-x)}x[/tex]So, the area as a function of x is: [tex]A(x) = \frac{4(x - 10)(175-x)}x[/tex]To determine the domain of x, I will plot the graph of A(x) (See attachment).From the attached graph, we can see that the values of x starts from 10.Hence, the domain of x in interval notation is [tex](10, \infty)[/tex]Read more about areas at:https://brainly.com/question/16418397

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