Answered

Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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
Submit Answer
MY NOTES
8. [-/1 Points)
DETAILS
X
►
X

Sagot :

MrRoyal

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

View image MrRoyal
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.