What is the domain of

Mathematics

1 answer:

ddd [48]3 years ago

4 0

All real numbers is the correct answer

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A billboard designer has decided that a sign should have 4-ft margins at the top and bottom and 1-ft margins on the left and rig

givi [52]

An equation is formed of two equal expressions. The value of x that maximizes the area of the printed region of the billboard is 9.655 ft.

<h3>What is an equation?</h3>

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given x is the left-right width of the billboard and y is the height of the billboard. Therefore,

The total area of the billboard, A= x·y

The total printed area of the billboard, $A_p=(x-2)(y-8)$

Given in problem that the area of the billboard is 3600 ft².

x·y = 3600

y = (3600)/x

Substituting the value of y in the equation of the total printed area of the billboard,

$A_p = (x-2)(\dfrac{3600}{x}-8)\\\\A_p = 3600 -8x -\dfrac{7200}{x} + 16\\\\A_p =3616-8x - \dfrac{7200}{x}$

Now, the value of x is needed to be minimum, therefore, differentiating the given function,

$\dfrac{d}{dx}A_p =\dfrac{d}{dx}3616-8x - \dfrac{7200}{x}\\\\\dfrac{d}{dx}A_p =-8 - \dfrac{7200}{x^2}$

Equate the differentiated function with 0,

$0=-8x - \dfrac{7200}{x^2}\\\\8x = - \dfrac{7200}{x^2}\\\\x^3 = 900\\\\x = 9.655 ft.$

Hence, the value of x that maximizes the area of the printed region of the billboard is 9.655 ft.

Learn more about Equation:

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4 0

1 year ago

Use a property of equality to solve this equation:<br><br> 4.5x = 18<br><br> x =

liberstina [14]

Answer:

Step-by-step explanation:

x= 18÷4.5=4

hope it helps

4 0

2 years ago

Read 2 more answers

Factor completely 64x2 − 49. (1 point)

Roman55 [17]

Answer:

(8x-7)(8x+7)

Step-by-step explanation:

This is a difference of squares polynomial of the form $a^2-b^2=(a+b)(a-b)$ . Since 64 and 9 are both perfect squares then take the square root of each so a=8 and b=7.