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The area of a rectangular shape is the product of its dimensions.
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:
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