A baker is folding up open-topped boxes to package up her baked goods. She has flat, rectangular pieces of cardboard that are 10 inches by 6 inches. She wants to

maximize the volume of the box. What size squares should she cut from the corners

of the cardboard?

She should cut 1.21 inches (or a square of area 1.46 inch²) from 4 corners to get the maximum volume

Step-by-step explanation:

Length = L = 10 inches

Width = W = 6 inches

Suppose x is cut from the 4 corners to make a box.

Dimensions of the Box:

L= 10 - 2x

W = 6 - 2x

H = x

Volume of the Box:

V = (L)(W)(H)

V = (10-2x)(6-2x)(x)

V = 4x³ -  32x² + 60x

For Maximum value:

The values of x found are:

x= 4.12 , x = 1.21

If we put x= 4.12 in W= 6-2x , the value of width becomes negative, so that is not possible.

We discard 4.12. Now x=1.21

So,

If 1.21 inches are cut from 4 corners, or a square of 1.21*1.21 = 1.46 inch² is cut from 4 corners, we get the maximum value of V

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.