A Hydraulic Cylinder on an Industrial Machine Pushes a Steel $( 0 \leq x \leq 4 )$

question 23

Multiple Choice

A hydraulic cylinder on an industrial machine pushes a steel block a distance of x feet $( 0 \leq x \leq 4 )$ , where the variable force required is $F ( x ) = 3000 x e ^ { - x }$ pounds. Find the work done in pushing the block the full 4 feet through the machine. Round your answer to three decimal places.

• A) \(2725.265 \mathrm { ft } . \mathrm { lbs }\)
• B) \(2890.106 \mathrm { ft } . \mathrm { lbs }\)
• C) \(1655.749 \mathrm { ft } . \mathrm { lbs }\)
• D) \(2839.235 \mathrm { ft } . \mathrm { lbs }\)
• E) \(3219.788 \mathrm { ft }\).lbs

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Definitions:

Production Quality

The standard of the final output or product, measured in terms of its craftsmanship, durability, and attention to detail.

White Space

The unmarked or empty areas in a design or layout, which can help to create a clean appearance and improve readability.

Haptics

Refers to the use of touch in communication or interaction with technology, providing feedback through vibrations or movements.

Poor Design Decisions

Choices made during the design process that negatively affect the usability, functionality, or aesthetic appeal of a product or service.