$\text { Find the arc length of the graph of the function } y = \frac { 2 } { 3 } x ^ { \frac { 3 } { 2 } } + 2 \text { over the interval [14, }$

question 76

Multiple Choice

$\text { Find the arc length of the graph of the function } y = \frac { 2 } { 3 } x ^ { \frac { 3 } { 2 } } + 2 \text { over the interval [14, }$ $16$ ].

• A) \(17 \sqrt { 17 } - 15 \sqrt { 15 }\)
• B) \(\frac { 2 } { 3 } ( 17 \sqrt { 17 } - 15 \sqrt { 15 } )\)
• C) \(\frac { 3 } { 2 } ( 17 \sqrt { 17 } + 15 \sqrt { 15 } )\)
• D) \(\frac { 3 } { 2 } ( 17 \sqrt { 17 } - 15 \sqrt { 15 } )\)
• E) \(\frac { 2 } { 3 } ( 17 \sqrt { 17 } + 15 \sqrt { 15 } )\)

---

Definitions:

Biological Clock

An internal mechanism that regulates bodily rhythms and cycles, such as sleep and wakefulness, on a roughly 24-hour cycle.

Pineal Gland

A small endocrine gland in the brain that produces the hormone melatonin, which regulates sleep and wakefulness.

Melatonin

A hormone produced by the pineal gland that regulates sleep-wake cycles and is influenced by the presence of light.

Biological Clock

An internal mechanism in organisms that controls the cycle of biological processes and behaviors in a roughly 24-hour cycle.