The Surface of a Mountain Is Modeled by the Equation $h ( x , y ) = 4000 - 0.005 x ^ { 2 } - 0.007 y ^ { 2 }$

question 121

Multiple Choice

The surface of a mountain is modeled by the equation $h ( x , y ) = 4000 - 0.005 x ^ { 2 } - 0.007 y ^ { 2 }$ . A mountain climber is at the point $( 400,600,4390 )$ . In what direction should the climber move in order to ascend at the greatest rate? Round all numerical values in your answer to one decimal place.

• A) \(13.2 \hat { \mathbf { i } } - 8.4 \hat { \mathbf { j } }\)
• B) \(- 6.4 \hat { \mathbf { i } } - 13.2 \hat { \mathbf { j } }\)
• C) \(- 4.0 \hat { \mathbf { i } } - 8.4 \hat { \mathbf { j } }\)
• D) \(10.8 \hat { \mathbf { i } } + 4.0 \hat { \mathbf { j } }\)
• E) \(- 5.6 \hat { \mathbf { i } } + 10.8 \hat { \mathbf { j } }\)

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Definitions:

Cognitive Limits

The boundaries or constraints on a person's mental abilities, such as memory capacity, attention span, and the ability to process information.

Serial Processing

The act of processing information in a sequential manner, one operation at a time.

Parallel Processing

The ability of the brain to simultaneously process incoming stimuli of differing quality, a fundamental method of information processing in the human mind.

Overextension

A language development error in which a child applies a word too broadly, beyond its appropriate context.