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Solved: In 11–16, find a general solution of the system

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider ISBN: 9780321747730 43

Solution for problem 14E Chapter 9.5

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Fundamentals of Differential Equations | 8th Edition

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Problem 14E

In 11–16, find a general solution of the system x’(t) = Ax(t) for the given matrix A .

Step-by-Step Solution:
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Tuesday, March 22, 2016 Nervous System II Lecture 16 - Na+ and K+ Voltage Gated Channels • K+ (passively flows into the cell) - Resting state - closed by activation gate - Active state - open - The voltage across the membrane determines whether the channels will be open or closed. • Channels open at +30 mV. • Repolarization causes the gates to close. - second gate that opens during the action potential • Na+ (passively flows out of the cell) - Resting state - closed by activation gate • Repolarization (> -55 mV) closes the activation gate and opens the inactivation gate. - Activated state - open The activation gate is opened at -55 mV. • - Inactivated state - closed by inactivation gate • The inactivation gate closes at +30 mV. - first gate to open during the action potential - The Action Potential: Trigger Zone • A large concentration of voltage-gated Na+ channels is in the axon hillock. • A local potential arrives (> -55 mV), causing activation gates of Na+ channels to open. - Positive feedback loop: more Na+ activation gates open, resulting in a massive depolarization (potential reaches +30 mV). 1 Tuesday, March 22, 2016 • At +30 mV: inactivation gate of Na+ channel closes and K+ channel is open - Na+ channels return to resting state (> -55 mV), causing activation gates to close. K+ channels also close (slowly). • Hyperpolarization occurs because K+ channels are slow to close. - Both channels return to resting state. - The Na+/K+ pump brings Na+ and K+ ions back to their original side of the membrane. - Refractory Periods • Absolute refractory period - the neuron cannot fire another action potential during this time - occurs while Na+ and/or K+ channels are activated • Relative refractory period - it is difficult to generate an action potential during this time 2 Tuesday, March 22, 2016 Lecture 17 The Integumentary System - Organs • skin - cutaneous membrane (epidermis and dermis) - epidermis (epithelial tissue) is the outer layer and dermis (connective tissue) is the inner layer • hair • nails • exocrine glands (contain ducts) - sweat glands - sebacious glands (oils) • sensory receptors and arrector pili (muscles surrounding hair) - Integument Structure • Cutaneous membrane (skin) - Epidermis (outer layer; epithelial tissue) • not vascularized • keratinized stratified squamous - Dermis (inner layer; connective tissue - loose and dense irregular) • vascularized (supplies nutrients to epidermis) - Hypodermis (loose connective and adipose tissues) • Hair - loose connective tissue derived from dermal cells Sebacious glands - exocrine glands (oil) • • Arrector pili muscles - surround hair • Sensory receptors - Your skin is the closest point of contact to the outside world. 1 Tuesday, March 22, 2016 • Sweat glands (exocrine) - Integument Functions • protection (mechanical trauma, pathogens, outside environment) • sensation (sensory receptors) • thermoregulation (sweat glands and vasomotion) - vasomotion - the ability to open and close arteries vasoconstriction (pulls arteries away from the surface of the skin; conserves • heat) and vasodilation (widens arteries, bringing them closer to the surface of the skin; makes heat release easier) • excretion (lactic acid and urea) • vitamin D synthesis (cholesterol precursors are exposed to UV radiation) - cholecalciferol —> liver —> kidneys —> calitriol (vitamin D) 2 Thursday, March 24, 2016 Lecture 17 con’t The Integumentary System - Thermal Regulation Feedback Loop • Stimulus: body temperature increases • Receptors: thermoreceptors (nerves) in skin - Afferent signals are sent from receptors to control center. • Control center: hypothalamus of brain - Efferent signals are sent from control center to effectors. • Effectors: dermal blood vessels and sweat glands • Outcome: return to normal body temperature (homeostasis) - The Epidermis • Cells - 95% keratinocytes (able to produce keratin) • contain desmosomes (link cells together, provide strength) - 5% dendritic cells (immune cells), merkel cells (involved in sense), melanocytes (dark pigment) • Dendritic (langerhans) cells - found mostly in stratum spinosum - phagocytes • Merkel cells - found in stratum basale - sensory cells associated with neurons - detect light touch and texture • Melanocytes - found in stratum basale 1 Thursday, March 24, 2016 - produce melanin pigment • Layers - Squamous cells are not born with a squamous shape, they flatten as they are pushed to the surface (of the skin). - Stratum basale (closest to the bottom) • single layer of mitotically active stem cells - Stratum spinosum • some cells are still mitotically active • keratin production begins - Stratum granulosum (everything above here is cut off from the blood supply (dead)) • some cells produce an oily substance - cuts the above layers off from the blood supply - Stratum lucidum (ONLY FOUND IN THICK SKIN; provides an additional layer) • dead keratinocytes - Stratum corneum (much thicker in thick skin) • This is found at the top (surface of the skin). • dead keratinocytes • The most superficial layers lose desmosomes and slough off. - The Dermis • Papillary Layer - loose connective tissue - Dermal papillae extend up into epidermis (increase surface area) • contain capillary networks (provide nutrients to epidermis) - tactile (Meisner) corpuscles - sense deep touch • Reticular Layer - dense irregule connective tissue 2 Thursday, March 24, 2016 - gives skin its strength (collagen) and elasticity (elastic fibers) - hydration (due to proteoglycans) - contains blood vessels, sweat glands, sebaceous glands, and lamented (Pacinian) corpuscle - Skin Patterns • Fingerprints - prominent dermal papillae arranged into dermal ridges by thick collage fibers - enhance gripping ability - sweat glands along ridges leave fingerprints • Flexure lines - reticular layer bound tightly to deeper tissues - prominent around joints and palms • Tension lines - formed by gaps between collagen bundles in reticular layers that indent epidermis - Skin Pigments • Melanin - orange-red to black pigment - protects DNA from UV radiation • Melanin in keratinocytes accumulates above the nucleus, shielding the DNA from UV radiation. - dipeptide (two amino acids) • specific amino acid: tyrosine - produced by melanocytes (in the stratum basale) • Melanin is synthesized in melanosomes. Tyrosinase catalyzes peptide bond formation between 2 tyrosine molecules. • Melanin is released (exocytosis) and taken up by keratinocytes (endocytosis). • Carotene - yellow-orange pigment - vitamin A precursor - unsaturated lipids 3 Thursday, March 24, 2016 - obtained from diet (egg yolk, carrots), stored in adipose tissue • Hemoglobin - red pigment - binds oxygen in erythrocytes (transport) - protein with quaternary structure - protein synthesis in erythrocytes - Accessory Structures Hair • - derived from skin epithelium - protective and sensory functions • eyebrows stop sweat (containing pathogens) from getting into eyes • hair protects DNA from UV light • nose hair traps pathogens • 3 Types of Hair - Lanugo - thin, non-pigmented hair on fetus - Terminal hair - scalp and around eyes - Vellus hair - body hair • Nails - derived from skin epithelium - protective and gripping functions • Glands - derived from skin epithelium - various functions - What does pigmentation variation tell us (My research answers) • Freckles and moles - increased melanin in concentrated areas • Albinism - absence of melanin 4 Thursday, March 24, 2016 • healthy tans - there are no healthy tans because tan = exposure to UV radiation • Red lips - lips contain fewer melanocytes, so you can see your blood vessels • Erythema - superficial reddening of skin as a result of injury or irritation (more blood in that area due to vasodilation) • Pallor - pale color of skin caused by illness, shock, stress, etc. (caused by reduced amount of hemoglobin) • Why were Gregorie Rasputin’s cheeks so red - cyanide poisoning disrupts an electron carrier in mitochondria, causing erythrocytes to hold on to oxygen through venous circulation • Cyanosis - bluish discoloration of skin due to poor circulation/inadequate oxygen in blood 5

Step 2 of 3

Chapter 9.5, Problem 14E is Solved
Step 3 of 3

Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

This full solution covers the following key subjects: Find, general, given, Matrix, solution. This expansive textbook survival guide covers 67 chapters, and 2118 solutions. The answer to “In 11–16, find a general solution of the system x’(t) = Ax(t) for the given matrix A .” is broken down into a number of easy to follow steps, and 18 words. Since the solution to 14E from 9.5 chapter was answered, more than 277 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. The full step-by-step solution to problem: 14E from chapter: 9.5 was answered by , our top Calculus solution expert on 07/11/17, 04:37AM. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730.

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Solved: In 11–16, find a general solution of the system