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Answer:
The width of billboard is "[x]" and the height of billboard is "[y"]. If total area of billboard is [tex]9000 ft^2[/tex] then [tex]9000=xy[/tex]
Step-by-step explanation:
• The total width of billboard is [x]. Therefore the width of printed area will be (x-10) by excluding margin of left and right side.
• The total height of billboard is [y]. Therefore the height of printed area will be [(y-6)] by excluding the margin of top and bottom from the total height.
• To find the printed area of billboard calculations are given below:
[tex]& 9000=xy[/tex]
[tex]& y=\frac{9000}{x} \\ & A=(x-10)(y-6) \\ & A=xy-6x-10y+60 \\ & A=x\left( \frac{9000}{x} \right)-6x-10\left( \frac{9000}{x} \right)+60 \\ & A=9060-6x-\frac{9000}{x} \\[/tex]
On taking the first order derivative of A
[tex]\[A'=-6+\left( \frac{90000}{{{x}^{2}}} \right)\][/tex]
[tex]& \left( \frac{90000}{{{x}^{2}}} \right)-6=0 \\ & 6{{x}^{2}}=90000 \\ & x=\sqrt{15000} \\ & y=\frac{9000}{x}=\frac{90000}{\sqrt{15000}}=10\sqrt{150} \\[/tex]
• Hence [tex]\[x=10\sqrt{150}\][/tex] and [tex]\[y=\frac{900}{\sqrt{150}}\][/tex]
Learn More about Differentiation Here:
https://brainly.com/question/13012860
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