Focus on Engineering It's Time for the School of Engineering $y=e^{-x}$

question 54

Multiple Choice

Focus on Engineering It's time for the School of Engineering class picture and you are the photographer! You stand at the origin with your camera and your classmates are strung out along the curve $y=e^{-x}$ from (0, 1) to $\left(3, e^{-3}\right)$ . What is the formula for the average value of the distance from you to your classmates at points (x, y) on the curve?

• A) \(\frac{1}{3} \int_{0}^{3} \sqrt{x^{2}+e^{-2 x}} d x\)
• B) \(\int_{0}^{3} \sqrt{x^{2}+e^{-x}} d x\)
• C) \(\frac{1}{3} \int_{0}^{3}\left(x+e^{-x}\right) d x\)
• D) \(\int_{0}^{3} \sqrt{x^{2}-e^{-2 x}} d x\)

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Definitions:

Shoplifting

The act of stealing merchandise from a retail establishment without paying for it.

Opportunist Robber

A criminal who takes advantage of a situation to commit theft, often acting on impulse when a vulnerable target presents itself.

Deep Commitment

A profound dedication or strong emotional bond to a cause, activity, or another person.

Shoplifts

The act of stealing goods from a store, violating legal or ethical standards.