A Particle Moves Along the Circle $x ^ { 2 } + y ^ { 2 } = 25$

question 238

Multiple Choice

A particle moves along the circle $x ^ { 2 } + y ^ { 2 } = 25$ . If x increases at a rate 2 units per minute, at what rate is y changing when $x = 3$ ?

• A) \(2 \text { unit } / \min\)
• B) \(\frac { 3 } { 2 } \text { unit } / \mathrm { min }\)
• C) \(3 \text { unit } / \mathrm { min }\)
• D) \(\frac { 1 } { 4 } \text { unit } / \mathrm { min }\)
• E) \(- 2 \text { unit } / \min\)
• F) \(- \frac { 3 } { 2 } \text { unit } / \mathrm { min }\)
• G) \(- 3 \text { unit } / \min\)
• H) \(- \frac { 1 } { 4 } \text { unit } / \mathrm { min }\)

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Definitions:

Adolescence

A developmental transition between childhood and adulthood involving significant physical, emotional, and psychological changes.

Young Adulthood

The stage of life following adolescence, roughly between the ages of 20 and 40, characterized by the pursuit of independence, relationships, and career development.

Revolving Door

A term often used to describe a situation where people or positions are frequently replaced or changed.

Emerging Adult

A phase of development spanning from late teens through twenties, characterized by exploration, instability, and self-focus in the transition to adulthood.