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In Exercises 17 22, find the angle between v and w. Round

Precalculus | 4th Edition | ISBN: 9780321559845 | Authors: Robert F. Blitzer ISBN: 9780321559845 209

Solution for problem 20 Chapter 6.7

Precalculus | 4th Edition

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Precalculus | 4th Edition | ISBN: 9780321559845 | Authors: Robert F. Blitzer

Precalculus | 4th Edition

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Problem 20

In Exercises 17 22, find the angle between v and w. Round to the nearest tenth of a degree.

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Test Number 3 Lectures 22 & 23 Circulation & Gas Exchange Overview  Circulatory systems: facilitate exchange with the environment o Different systems have evolved o Humans have a close system: heart, vessels, and blood  Not “respiration” but gas exchange occurs across surfaces o Different systems, aquatic vs. terrestrial o Humans have lungs with high surface area  Hemoglobin (a respiratory pigment) increases the ability of blood to carry oxygen o There are other types of cells in blood as well All Cells Need to be Capable of Exchange with Their Environment  All reactions in cells depend on resources moving in, waste products moving out o All cells must have access to this exchange  Single cells & simple multi celled: all cells have contact with medium o Diffusion distances are short  Larger multi celled: some/ most cells isolated from external environment o Diffusion distances are too long o Circulatory systems connect those cells to the outside o Bring resources to the cell, carry waste away Circulatory Systems Vary in Complexity  Gastrovascular cavities: lack specialized circulatory systems o Have highly branched gut/ body cavity o High surface area: volume, short diffusion differences o E.g., cnidarians, flatworms  Specialized circulatory system: 3 basic components o Circulatory fluid: carries resources/ wastes o Interconnecting tubes: thru which fluid travels o Heart: muscular pump  Open circulatory systems: e.g., arthropods, most mollusks o Circulatory fluid (hemolymph) in direct contact with organs; same as interstitial fluid o Advantages: lower pressures, can use fluid as hydrostatic skeleton  Closed circulatory systems: e.g., annelids, vertebrates o Circulatory fluid (blood) in vessels, separate from interstitial fluid o Advantages: faster delivery of O2, easier to regulate Even Among Vertebrates, There is Variation in Circulatory Systems  Parts of the vertebrate circulatory system= cardiovascular system: o Pumping heart with 2+ chambers  Atrium: receives blood  Ventricle: pumps blood away o Arteries: carry blood away from heart; branch into arterioles o Branch further into capillaries: where exchange takes places; capillary bed: network of capillaries o Capillaries converge into venules; converge into veins: carry blood back to heart o Remember: arteries & veins distinguished by direction they carry blood o More energy organisms/ organ needs, the more complex circulation  Single circulation: in fishes with 2-chambered hearts o Blood passes thru 2 capillary beds during circuit o Runs at lower pressure, so lower velocity  Aided by swimming muscles  Double circulation: in tetrapods with 3- or 4- chambered hearts (4 in mammals) o Blood pumped thru two separate circuits  Right side pulmonary circuit: to lungs  Left side systematic circuit: to body o Maintains higher pressure/ velocity of blood  Variation across major groups: amphibians and (non-bird) reptiles have 3-chambered heart 11 Steps in the Flow of Blood Thru Both Circuits 1. Right ventricle pumps blood to lungs 2. Via the pulmonary arteries 3. Blood flows thru capillary beds of the left & right lungs (gas exchange, etc.) 4. Blood returns to left atrium via pulmonary veins 5. Left ventricle pumps blood out to body 6. Via the aorta, including coronary arteries to the heart 7. One branch leads to capillary beds in the head & arms 8. Another branch leads to capillary beds in the abdomen & legs (gas exchange, etc.) 9. Deoxygenated blood drains head & arms via superior vena cava 10. Deoxygenated blood drains the abdomen & legs via the inferior vena cava 11. Both empty to the right atrium The Cardiac Cycle Alternates Pumping and Filing  Cardiac cycle: complete sequence of pumping (systole) and filling (diastole) o Heart rate: 72 beats per minute (average resting) o Stroke volume: 70 mL per ventricle o Cardiac output: ca. 5 L/ minute (per ventricle)  Increases with activity  4 valves keep blood from flowing wrong direction o One way flaps, bigger than the opening they cover o Atrioventricular valve (AV): between chambers o Semilunar valves: between ventricles and arteries o Heart murmur: defective valve leads to back flow The Heart Provides its Own “Pacemaker”  Pacemaker: autorhythmic cells of heart; contraction based upon own electrical impulses o Begins at sinoatrial node: cause atria to contract o Relayed by atrioventricular node: after 0.1s delay, ventricles contract o Nervous system can speed up or slow down rate with activity level Both Velocity and Pressure Drops as Blood Moves Through Capillary Beds  Arteries branch, total cross-section area increases: velocity of blood decreases thru the capillaries o Slow velocity facilitates efficient diffusion o Speeds up again as capillaries coalesce into veins (x-section area decreases)  Pressure highest during ventricular systole o Stretches arteries; heart beats again before pressure completely dissipated o Vasoconstriction/ vasodilation can change pressure: during activity, stress, thermoregulation, etc. Capillaries are the Sites of Exchange Between Blood and Tissues  Only a small fraction of capillaries have blood flowing thru them at any time; diverted to where it is needed o Head, heart, kidneys usually running at capacity o Blood to skin used to control temperature o Blood to digestive tract with meal o Blood to muscles during exercise  Flow controlled two ways o Muscle constriction of ateriole o Precapillary sphincters: close off paths thru capillary beds  Controlled both by nervous system and hormones Exchange Occurs by Both Pressure and Diffusion  O2 and CO2 exchanged by diffusion  Water moves by pressure o Blood pressure forces water out at arterial end o Osmotic pressure draws water back at venous end  Ca. 85% of water recovered by capillaries: rest returned via lymphatic system o Network of small vessels that drains excess interstitial fluid: lymph o Eventually returned to circulatory system o Moves by smooth muscle contraction, aided by skeletal muscle; with series of valves Blood is Composed of Various Cells & Proteins in a Liquid Matrix  Open circulatory system: circulatory fluid (hemolymph) continuous with interstitial fluid o Same composition  Closed circulatory system (like mammals): circulatory flood (blood) more complex o Connective tissue: cells (& cell fragments, 45%) in a liquid matrix (plasma)  Plasma: 90% water with dissolved salts, proteins (e.g., antibodies, lipid escorts, clotting factors) + gases, wastes, hormones, etc. o More protein than interstitial fluid  Cellular components: o Erythrocytes (red blood cells): 5 trillion per 1 L blood  Main function O2 transport  Lack nuclei, mitochondria, full of hemoglobin = oxygen transport protein o Leukocytes (white blood cells): up to 10 billion per 1 L blood  Perform various immune function: o Platelets: cell fragments involved in blood clotting  Clotting: damage plugged by platelets and reinforced by fibrin protein  Multipotent stem cells located in bone marrow: produce new blood cells o Negative feedback based on O2 Gas Exchange Occurs Across Respiratory Surfaces  Gas have pressures rather than concentrations o Partial pressure of O2 (Po2) is the fraction of the total pressure exerted by air  O2 21& by volume x 760 mmHg = 160 mmHg (sea level)  Pco2 = 0.29 mmHg o Partial pressure of dissolved gas equals partial pressure in air, but concentration depends on temperature, salinity, etc. o Gases always diffuse from higher pressure to lower pressure  O2 more available in air than in water o 21% of air, easier to move around o 40x less O2 in same volume water: warmer, saltier holds less  All oxygen must be exchanged thru water: cell membranes need moist surfaces o Entirely by diffusion; rate proportional to surface area, inversely proportional to distance o Respiratory surfaces are large and thin Aquatic Organisms Have More Efficient Gas Exchange Surfaces  Less O2 available, so less can be wasted  Various respiratory surfaces among invertebrates: high vascularized or connected to body cavity  Fish have gills: delicate out-foldings of body surface o Surface area much grater than that of body o Countercurrent exchange of respiratory medium maintained by ventilation  Move surface thru medium  Capillaries flow in the opposite direction: Po2 in blood always less than in medium  Very efficient: removes 80% of dissolved O2  Won’t work on land: dry out There are Two Common Terrestrial Adaptations for Breathing Air  Most common: tracheal system; insects o Series of air tubes that branches throughout body o Gas exchange does not involve circulatory system  Most familiar: lungs; vertebrates o Large in-foldings of the body surface, subdivided to increase surface area o Air in thru nostrils: filtered, warmed, moistened o To larynx via pharynx: held open by cartilage; opens to trachea o Trachea branches into two bronchi, which continue to branch into bronchioles  Surface covered by cilia and mucus to remove waste o Tiniest bronchioles end in alveoli: terminal sacs where gas exchange happens  Total area about 50x skin Ventilation of Exchange Surfaces is Achieved by Breathing  Amphibians: positive pressure breathing o Push air in by shrinking oral cavity  Mammals: negative pressure breathing o Pull air in by expanding thoracic cavity with muscles and diaphragm (skeletal muscle) o Controlled by breathing control centers in brain by negative feedback (CO2 determined by pH)  Coordinated with circulatory system o Birds are more efficient (and complex)  Use posterior & anterior air sacs to regulate one way flow of air  No mixing of old air with new Hemoglobin is Necessary Because O2 Has Low Solubility in Water  During exercise, you need 2 L O2 per minute o Under normal conditions, 1 L water has 0.045 L O2  Instead O2 transported attached to respiratory pigment: hemoglobin; reduces necessary cardiac output to 12.5 L per minute o In erythrocytes o Four protein subunits, each with Fe atom: reversibly binds O2 o Subunits cooperative: affinity varies as Po2 varies  One binds O2, the others increase affinity for O2  One releases O2, the others lower their affinity for O2 o Presence of CO2 causes O2 unloading

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Chapter 6.7, Problem 20 is Solved
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Textbook: Precalculus
Edition: 4
Author: Robert F. Blitzer
ISBN: 9780321559845

This textbook survival guide was created for the textbook: Precalculus, edition: 4. Precalculus was written by and is associated to the ISBN: 9780321559845. Since the solution to 20 from 6.7 chapter was answered, more than 251 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 20 from chapter: 6.7 was answered by , our top Calculus solution expert on 01/04/18, 08:34PM. The answer to “In Exercises 17 22, find the angle between v and w. Round to the nearest tenth of a degree.” is broken down into a number of easy to follow steps, and 19 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 92 chapters, and 9372 solutions.

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In Exercises 17 22, find the angle between v and w. Round