Provide an Appropriate Answer $x ^ { 2 } + y ^ { 2 } = r ^ { 2 }$

question 305

Multiple Choice

Provide an appropriate answer.
-Suppose that $x ^ { 2 } + y ^ { 2 } = r ^ { 2 }$ and $x = r \cos \theta$ , as in polar coordinates. Find $\left( \frac { \partial y } { \partial \theta } \right) _ { r }$ .

• A) \(\left( \frac { \partial y } { \partial \theta } \right) _ { r } = - r \sin \theta\)
• B) \(\left( \frac { \partial y } { \partial \theta } \right) _ { r } = r \cos \theta\)
• C) \(\left( \frac { \partial y } { \partial \theta } \right) _ { r } = r ( \cos \theta - \sin \theta )\)
• D) \(\left( \frac { \partial y } { \partial \theta } \right) _ { \mathrm { r } } = 0\)

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Definitions:

Acetylcholine

A neurotransmitter involved in many functions including muscle movement and memory.

Catecholamines

Organic compounds, including epinephrine (adrenaline), norepinephrine, and dopamine, that function as neurotransmitters and hormones in the body.

Myelin Sheath

The fatty covering around nerve fibers that increases the speed and efficiency of electrical signal transmission in the nervous system.

Neuron

A specialized cell transmitting nerve impulses; a nerve cell, consisting of a cell body, dendrites, and an axon.