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Calculus Volume 3 | 1st Edition | ISBN: 9781938168079 | Authors: Openstax ISBN: 9781938168079 2033

Solution for problem 284 Chapter 6.6

Calculus Volume 3 | 1st Edition

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Calculus Volume 3 | 1st Edition | ISBN: 9781938168079 | Authors: Openstax

Calculus Volume 3 | 1st Edition

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Problem 284

For the following exercises, evaluate \(\iint_{S} \mathbf{F} \cdot \mathbf{N} d s\) for vector field F, where N is an outward normal vector to surface S.

F(x, y, z) = xi + 2yj = 3zk, and S is that part of plane 15x − 12y + 3z = 6 that lies above unit square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1.

Text Transcription:

\iint_{S} \mathbf{F} \cdot \mathbf{N} d s

Step-by-Step Solution:
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1.8. Visual System Fovea: ​center of the retina. Vision is clearest in the fovea and it has the highest concentration of rods and cones (photoreceptors). The r ​etina​is a heterogeneous structure where cells get larger and less dense with greater distance from the fovea (also why our periphery is not as good). Rods: ​respond to dim light. Good at differentiating in black and white. Not very receptive to color. More concentrated around the periphery. Cones:​ respond to color, and are concentrated in fovea. Color is not a fundamental property of things around us. It is a trick of the visual system that understands the absorption properties of the object. Light conditions can change the perception of color­­ cones with different opsins are sensitive to different wavelengths of color. Short (blue) Medium (green) Long (red) Primary Projection Pathways Optic Chiasm: ​ crossing of optic nerves in the brain. 90% of nerves originate in Lateral Geniculate Nucleus (LGN). ​ This is the primary relay center for visual information received by the retina. It is found in the thalamus so it makes sense why it would be a relay. Remaining 10% terminate in the thalamus & superior colliculus. Eye­­>Optic Nerve→ Optic Chiasm→ LGN­­­>(slingshots over to) V1. ** Coding in Ganglion & LGN Neurons Visual neurons have receptive fields too so the stimulus must be in a particular region of space. Ganglion & LGN cells have a center/surround organization that makes them very sensitive to contrast. Primary Visual Cortex (V1): ​ Info from LGN

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Chapter 6.6, Problem 284 is Solved
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Textbook: Calculus Volume 3
Edition: 1
Author: Openstax
ISBN: 9781938168079

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