A box without a top is to be made from a rectangular piece of cardboard, with dimensions 12 in. by 16 in., by cutting out square corners with side length x and folding up the sides. A) Write an equation for the volume V of the box in terms of x.
B) Use technology to estimate the value of x, to the nearest tenth, that gives the greatest volume.
Please explain how you go your answer

Step-by-step explanation:

Length (a) = 12-2x

Width (b) = 16-2x

Height (h) = x

Volume = a*b*h = x(12-2x)(16-2x) = 192x-56x^2+4x^3

Use derivative to find max.

dV/dx = 192-112x+12x^2 = 0

x = 7.07, 2.26

You can use second  derivative or take two closest points and find gradient of them to find max x.

Max(x) = 2.26

choice b is correct

step-by-step explanation:

we have been given the following system of linear inequalities;

we are required to graphically determine the solution to these system of inequalities. using a graphing tool, the solution is as shown in the attachment below;

$450.00 for 6 weeks

or

$300

step-by-step explanation:

$200.00 for first week $50.00 x5 equals $250 plus $200 equals $450.00 for six weeks.

$200 for first week

$200 x 0.10 = $20

$20 x 5 = $100

$200 + $100 = $300