Elena is making an open-top box by cutting squares out of the corners of a piece of paper that is 11 inches wide and 17 inches long, and then folding up the sides. If the side lengths of her square cutouts are ???? inches, then the volume of the box is given by ????(????)=????(11−2????)(17−2????).
rectangle with dotted squares drawn at corners
Elena graphs the volume of the box along with the function ????(????)=140.
graph of v of x = x times parenthesis 11 - 2 x times parenthesis 17 minus 2x. x intercepts at 0, 5 point 5, and 8 point 5. horizontal line b of x = 140 graphed.
4a) What is a reasonable domain for ????(????)?

V(x) = (17 - 2x)(11 - 2x)x

Step-by-step explanation:

We are told that She is making an open top box. This means the box will have only 5 faces.

Now, she cuts squares out of the paper that measures 11 inches wide and 17 inches long.

Now, if the square side is x, it means the width of the box will be x. Since there are 2 upright faces that serve as width.

Thus, measurement of width from the 11 inches paper = (11 - 2x)

Now, similarly, there will be 2 upright sides that will serve as length. Thus, length from the 17 inches side is;

(17 - 2x)

Now,recall that a side of the square is x.

Thus, the depth is x.

Now, volume of a box is given by;

V = length x width x depth

Thus, in this case;

V(x) = (17 - 2x)(11 - 2x)x

V(x) = (17 - 2x)(11 - 2x)x

Step-by-step explanation:

We are told that She is making an open top box. This means the box will have only 5 faces.

Now, she cuts squares out of the paper that measures 11 inches wide and 17 inches long.

Now, if the square side is x, it means the width of the box will be x. Since there are 2 upright faces that serve as width.

Thus, measurement of width from the 11 inches paper = (11 - 2x)

Now, similarly, there will be 2 upright sides that will serve as length. Thus, length from the 17 inches side is;

(17 - 2x)

Now,recall that a side of the square is x.

Thus, the depth is x.

Now, volume of a box is given by;

V = length x width x depth

Thus, in this case;

V(x) = (17 - 2x)(11 - 2x)x

Step-by-step explanation:

Refer the attached picture for complete question

a) V(x)=x(11-2x)(17-2x)

B(x)=140

Side and volume cannot be negative

So, x> 0

11-2x>0   and 17-2x>0

and

Domain for V(x) :

b)For finding the greatest Volume

x=7.155 , 2.177

Consider the graph

So, Volume at 7.155 is negative

Thus x≈2 gives the greatest volume

c)

Consider the graph .

It is increasing from and

So, Graph increasing interval is [-1,2] ∪[7,∞)

d)

At the point of intersection, both graph has the same value .

The answer is in the image 

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

The total nom of  code that can be used is equal to 5+3 = 8

The answer is in the image