(1 point) An open box will be made by cutting a square from each corner of a 10 ft by 16 ft piece of cardboard and then folding up the sides. What size square should be cut from each corner in order to produce a box of maximum volume

2 feet

Step-by-step explanation:

We are given that

Length of piece,l=10ft

Width of piece,b=16ft

Let x be the side of square

Length of box=10-2x

Width of  box=16-2x

Height of box=x

Volume of box=lbh

Differentiate w.r.t x

Because when substitute the value x=20/3

Then, the width of box is negative which is not possible.

Substitute x=2

Hence, the volume is maximum at x=2

Side of square=2 feet

Hence, square of side 2 feet should be cut from each corner in order to produce a box of maximum volume.

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

definition: a circle is the  set of all points in a plane that are equidistant  from a given  point  called the center of the circle. we use the symbol ⊙ to represent a circle. the a line segment from the center of the circle to  any point  on the circle is a radius of the circle.

step-by-step explanation:

i googled it and this is what i got i don't know how it is. sorry.