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:
Answer:
To summarize the answer:
Step-by-step explanation:
Given:
Here is the graph associated with this question:
The second function, denoted as 
, does not qualify as a function.
Keep in mind that the g(x) function is the inversion of the f(x) function. Recognizing this pattern indicates a reflection on the Y-axis.
Reflection on the axes:
In the x-axis:
Enhance the function by -1 to illustrate an exponential curve around the x-axis.
In the y-axis:
Decrease the input of the function by -1 to depict the exponential function around the y-axis.
Answer:
Step-by-step breakdown:
The necessary formula for this problem is
which resolves to
leading to
36 + 6x = 40 + 5x, and consequently
x = 4
Thus, DG equals 5 + 4 + 3, resulting in 12
Answer:
D
Step-by-step explanation:
it represents entire F as shown in the diagram
The maximum number of plates Lenin can create is 4, with each plate containing 3 pieces of chicken and 4 rolls. Step-by-step explanation: Lenin is preparing dinner plates with 12 pieces of chicken and 16 rolls. To ensure all plates are identical without any leftover food, the greatest number of plates he can prepare is represented by the G.C.D.(12,16) = 4. Each plate will therefore include 3 pieces of chicken and 4 rolls.
