This works out beautifully. You COULD use long division here, but since your numerator is a quadratic, your first instinct should be to try and factor it. If you factor it, it works out to be (x - 3)(x + 2). Now it just so happens that when you do that, the (x - 3) in the numerator will cancel with the (x - 3) in the denominator leaving you with one sad and lonely (x + 2) as your answer.

3 0

3 years ago

A rectangular poster is to contain 882 square inches of print. The margins at the top and bottom of the poster are to be 2 inche

Zinaida [17]

Answer:

L = 23 in

h = 46 in

Step-by-step explanation:

Let call " x " and " y " dimensions of the print area of the poster then:

882 = x*y and y = 882/x

We also know that dimensions of the poster is:

L = x + 2 in and h = y + 4 in

Therefore area of the poster is:

A(p) = ( x + 2 ) * ( y + 4 ) And area as function of x is:

A(x) = ( x + 2 ) * ( 882/x + 4 )

A(x) = 882 + 4*x + 1764 /x + 8

Taking derivatives on both sides of the equation we have:

A´(x) = 4 - 1764/x²

A´(x) = 0 ⇒ 4 - 1764/x² = 0 ⇒ 4*x² - 1764 = 0

x² = 1764 / 4

x² = 441

x = 21 in and y = 882/x y = 42

The second derivative A´´(x) is > 0 ( the second term changes its sign to +) there is a minimum for the function at the point x = 21

As x and y are dimensions of the printing area of the poster, dimensions of the poster are

L = x + 2 = 21 + 2 = 23 in and

h = y + 4 = 42 + 4 = 46 in

4 0

4 years ago