Two Insects Are Crawling Along Different Lines in Three-Space $( x , y , z )$

question 12

Multiple Choice

Two insects are crawling along different lines in three-space. At time t (in minutes) , the first insect is at the point $( x , y , z )$ where $x = 7 + t , y = 3 - t , z = 1 + t$ . Also, at time $t$ , the second insect is at the point $( x , y , z )$ where $x = 4 + t , y = 6 + t , z = t$ . Assume distances are given in inches. Find the distance between the two insects at time $t = 0$ . Round your answer to two decimal places.

• A) \(6.00\) inches
• B) \(7.81\) inches
• C) \(9.27\) inches
• D) \(4.36\) inches
• E) \(18.00\) inches

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Definitions:

Derived Demand

Derived demand occurs for a factor of production when the demand for another good or service drives it, such as the demand for raw materials increasing due to higher demand for the final product.

Factor of Production

An economic resource used in the production of goods and services, including labor, capital, land, and entrepreneurship.

Market

A group of buyers and sellers of a particular good or service.

Diminishing

A principle often referring to diminishing returns, where additional inputs result in progressively smaller increases in output.