Suppose you wish to test if a number cube (die) is loaded or not. if the die is not loaded, the theoretical probabilities for ea
1 answer:
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Answer: look at the picture
Step-by-step explanation:
Answer:
<em>x</em> = 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 = <em>x</em>
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 - 2<em>x</em>
width = 2 - 2<em>x</em>
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Volume,
To find the maximum, we differentiate <em>V</em> with respect to <em>x</em> and equate the derivative to 0.
Simplify by dividing by 4.
Using the quadratic formula,
<em>x</em> = 0.423 m or <em>x</em> = 1.577 m
To determine which values gives maximum, we differentiate the first derivative which gives
The maximum value occurs when is negative.
At <em>x</em> = 1.577,
This is positive, so it is minimum.
At <em>x</em> = 0.423,
This gives a negative value. Therefore, it is a maximum.
Hence, the maximum volume is obtained when <em>x</em> = 0.423 m.