Rationalize the Numerator and Simplify $\frac { 7 - \sqrt { 7 } } { 5 }$

question 175

Multiple Choice

Rationalize the numerator and simplify. Assume all variables represent positive real numbers.
- $\frac { 7 - \sqrt { 7 } } { 5 }$

• A) \(\frac { 0 } { 35 + 5 \sqrt { 7 } }\)
• B) \(\frac { 42 } { 35 - 5 \sqrt { 7 } }\)
• C) \(\frac { 7 } { 5 } - \frac { \sqrt { 7 } } { 5 }\)
• D) \(\frac { 42 } { 35 + 5 \sqrt { 7 } }\)

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Definitions:

Tip Link

A filamentous protein structure that connects the tip of one stereocilium to the side of an adjacent taller stereocilium in the hair cells of the inner ear, crucial for mechanotransduction.

Sound Waves

Sound waves that move through air or different substances and become audible when they make contact with an individual's or creature's ear.

Tectorial Membrane

A gel-like structure in the inner ear's cochlea, playing a key role in the mechanical process that converts sound waves into nerve impulses.

Cochlear Neurons

Specialized neurons that transmit auditory information from the cochlea to the brain.