A rectangular page is to contain 24 square inches of printed material. The margins at the top and at the bottom are each 1.5 inches. The margins at the left and at the right are each 1 inch. What dimensions should the page have so that the least amount of material is used?

Height: 9 in

Length: 6 in

Width: 4 in

Step-by-step explanation:

Given that A rectangular page is to contain 24 square inches

We know that:

The area of the the rectangle: A = length* width =24

<=> x*y = 24

<=> y = 24/x

As given in the question:

<=> The area = h*l

= (y  + 3  ) (x + 2 )

=  (24/x+3) (x+2)

= 30  +  48 /x  +  3x

Taking derivatives on both sides of the equation

A´(x)  =  -48/x²  + 3

Let A´(x) = 0, we have:

-48/x²  + 3  = 0

<=> x = 4 in

When x=4 in we have y = 24/4 = 6  and h = 6+3 = 9

=> A (min) = 6*9 = 54

So the dimensions are:

Height: 9 in

Length: 6 in

Width: 4 in

15

step-by-step explanation:

we are given the following expression and we are to solve it and find the product:

-13 × (-5)

solving the given expression in the standard order of solving a mathematical expression, beginning with the opening of brackets and then multiplying the terms and changing their signs.

-3 × -5 = 15 (answer is positive because when negative is multiplied with negative, it gives a positive answer)