A Closed Box Is to Be Constructed from a Rectangular

question 28

Multiple Choice

A closed box is to be constructed from a rectangular sheet of cardboard that measures 21 inches by 10 inches. The box is made by cutting rectangles that measure x inches by 2 x inches from two of the corners and by cutting two squares that measure x inches by x inches from the top and from the bottom of the rectangle, as shown in the following figure. Use a graphing calculator to determine what value of x (to the nearest thousandth of an inch) will produce a box with maximum volume?

• A)1.918
• B)7.709
• C)1.352
• D)1.513
• E)6.082

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Definitions:

Transmission ECU

An electronic control unit responsible for managing the operation of a vehicle's transmission, ensuring optimal performance and fuel efficiency.

Hall-effect Sensors

Sensors that detect the presence of a magnetic field and convert it into an electrical signal.

Variable Capacitance Sensors

Sensors that detect changes in capacitance, which can be used to measure various parameters, such as pressure, position, or acceleration.

Potentiometers

Potentiometers are variable resistors used to measure the electrical potential (voltage), often found in devices for adjusting volume or tuning.