Respuesta :
Answer:
Minimum value: 6 inches,
Maximum value: 8 inches.
Step-by-step explanation:
To find the minimum length of s, we need to use the minimum volume of the shipping box in the equation, so:
s_minimum = ^3√(2*108) = ^3√216 = 6 inches
The maximum value of the volume will give us the maximum value of the length:
s_maximum = ^3√(2*256) = ^3√512 = 8 inches
So the minimum value of the length is 6 inches and the maximum value is 8 inches.
The required minimum value of the length is 6 inches and the maximum value is 8 inches.
Given that,
The length of one side, s, of a shipping box is [tex]s(x) = \sqrt[3]{2x}[/tex],
Where x is the volume of the box in cubic inches.
A manufacturer needs the volume of the box to be between 108 inches and 256 inches
We have to determine,
The minimum and maximum possible lengths of s.
According to the question,
To obtain the minimum length of s, using the minimum volume of the shipping box in the equation.
[tex]s(x) = \sqrt[3]{2x} \\\\[/tex]
Where, x = 108
Substitute the value of x in the given equation,
Then,
[tex]s(x) = \sqrt[3]{2x} \\\\\ s(108) = \sqrt[3]{(2).(108)} \\\\s(108) = \sqrt[3]{216} \\\\s(108) = 6 \ inches[/tex]
And, Where x = 256
Substitute x = 256 in the given equation,
[tex]s(x) = \sqrt[3]{2x} \\\\\ s(256) = \sqrt[3]{(2).(256)} \\\\s(256) = \sqrt[3]{512} \\\\s(256) = 8 \ inches[/tex]
Hence, The required minimum value of the length is 6 inches and the maximum value is 8 inches.
To know more about Minima and Maxima click the kink given below.
https://brainly.com/question/14553532
