You are constructing a cardboard box with the dimensions 2 m by 4 m. You then cut equal-size squares ( x by x squares) from each corner so that you may fold the edges to get a box. How long should x be to get a box with the maximum volume?Round your answer to three decimal places

x = 0.423 m

Step-by-step explanation:

Volume of the box = length × width × height

The height is given by the length of a side of the square.

height = x

The width and height are gotten by subtracting twice the side of the square form each dimension of the cardboard (since two squares are cut along each dimension).

length = 4 - 2x

width = 2 - 2x

Volume,

To find the maximum, we differentiate V with respect to x and equate the derivative to 0.

Simplify by dividing by 4.

Using the quadratic formula,

x = 0.423 m or x = 1.577 m

To determine which values gives maximum, we differentiate the first derivative which gives

The maximum value occurs when is negative.

At x = 1.577,

This is positive, so it is minimum.

At x = 0.423,

This gives a negative value. Therefore, it is a maximum.

Hence, the maximum volume is obtained when x = 0.423 m.

36 girls

step-by-step explanation:

the 48 boys is 4 parts of the ratio

divide 48 by 4 to obtain one part of the ratio

= 12 ← 1 part of the ratio

3 parts = 3 × 12 = 36 ← number of girls

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.