Noelle and karina both leave the Internet cafe at the same time, but in opposite directions. If karina travels 9 mph faster than
1 answer:
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Answer:
x = 0.53 cm
Maximum volume = 1.75 cm³
Step-by-step explanation:
Refer to the attached diagram:
The volume of the box is given by
Let x denote the length of the sides of the square as shown in the diagram.
The width of the shaded region is given by
The length of the shaded region is given by
So, the volume of the box becomes,
In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.
We are left with a quadratic equation.
We may solve the quadratic equation using quadratic formula.
The quadratic formula is given by
Where
Volume of the box at x= 1.59:
Volume of the box at x= 0.53:
The volume of the box is maximized when x = 0.53 cm
Therefore,
x = 0.53 cm
Maximum volume = 1.75 cm³
