A 2 column table with 5 rows. The first column, x, has the entries, negative 4, negative 3, negative 2, negative 1. The second c
olumn, y, has the entries 11.5, 17.25, 23, 28.75. A 2 column table with 5 rows. The first column, x, has the entries, negative 4, negative 3, negative 2, negative 1. The second column, y, has the entries, negative 5, negative 7.5, negative 10, negative 12.5. The tables represent two linear functions. The equation represented by the first table is given below. y = 5.75x + 34.5 What linear equation is represented by the second table? What is the solution to the system of equations?
3 answers:
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Answer:
The variable x lies within the interval of all positive real numbers less than 5 cm.
Detailed solution:
Problem statement:
Determine the volume of the open-topped box as a function of the side length x (in centimeters) of the square cutouts.
Refer to the provided diagram for clarity.
Define:
x → length in centimeters of each square cutout side
The volume of the box with open top can be written as:
Given this, we have:
By substitution:
Determine the domain of x:
Because:
Therefore:
Domain is the interval (0,5)
That means all real numbers strictly greater than zero and less than 5 cm are valid for x.
Hence, the volume V as a function of x is:
