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Verify the following statements.a. 128 2 (mod 7) and 61 5

Discrete Mathematics with Applications | 4th Edition | ISBN: 9780495391326 | Authors: Susanna S. Epp ISBN: 9780495391326 48

Solution for problem 7E Chapter 8.4

Discrete Mathematics with Applications | 4th Edition

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Discrete Mathematics with Applications | 4th Edition | ISBN: 9780495391326 | Authors: Susanna S. Epp

Discrete Mathematics with Applications | 4th Edition

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Problem 7E

Verify the following statements.a. 128 ? 2 (mod 7) and 61 ? 5 (mod 7)________________b. (128 + 61) ? (2 + 5) (mod 7)________________c. (128 –61) ? (2 – 5) (mod 7)________________d. (128• 61) ? (2•5) (mod 7)________________e. 1282 ? 22 (mod 7)

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Life 103 Exam 3 Study Guide Light • Light and Plants -Light cues many key events in plant growth and development -Effects of light on plant morphology are called photomorphogenesis -Plants detect light direction, intensity, and wavelength -Action spectrum depicts relative response of a process to different wavelengths • Classes of Light Receptors -Blue-light photoreceptors ~Control hypocotyl elongation ~Control stomatal opening ~Control phototropism -Phytochromes ~Pigments that regulate many of a plant’s response to light throughout its life ~Seed germination ~Shade avoidance Animal Diversity and Evolution • Themes of Biology -Organization-structure and function, emergent properties, reductionism -Information-information is transferred between generations through genes (heredity) -Energy and Matter-all organisms require energy and matter, resources are often limited, look for trade-offs -Interactions-interactions are important at all levels of organization (cell to organisms to communities to the biosphere) -Evolution-nothing in biology makes sense except in the light of evolution • Themes in Animal Diversity -Trends in evolution -Tradeoffs and constraints -Different perspectives and ways of life • What is science -Asking testable questions, formulated as hypotheses -Using evidence to answer those questions -Employing parsimony-simple explanations are preferred -Biology is a science -Science is a way of approaching problems that is applicable to nearly every aspect of your life • Eukaryan Diversity -Protists -Plants -Fungi -Animals • What are animals -Metazoans -zoo or zoa=animals ~Ex.) Zoology • How well do we know animals -<1million named species -Estimates up to 7.8 million total -86% of species on land yet to be discovered -91% of marine species yet to be discovered -Even in very common places, there are still many more species to be discovered -Most species on this planet are animals -70% of animals are insects -Animals have been around for a long time, but relative to every other species, they’re relatively recent • Ediacaran Origin -Animals evolved, including extant taxa and extinct forms -Only a few animal phyla evolved • Cambrian Explosion -Oldest fossils of half of extant animal phyla -Most major animal body plans evolve -Almost every other animal phyla that didn’t evolve in Ediacaran evolved in Cambrian • What are animals =Metazoans -Multicellular -Ingestive heterotrophs ~Do not produce own food; take food into body and digest internally -Move under own volition at some point in life ~At some point they were motile -Lack cell walls, have structural proteins (extracellular matrix) -Unique, specialized cells: nerve and muscle (except sponges) ~Most animals have these cells, whereas they aren’t found in any other species -Sexual reproduction -2n (diploid) dominant -Flagellated sperm, non-motile egg -Most have larval stage -Cells are organized into tissues -Conserved genes control development (Hox genes) -Zygote undergoes cleavage, forms blastula, gastrulation • Eumetazoa=true tissues -Doesn’t include sponges because they don’t have true tissues -Metazoa includes sponges, but eumetazoa doesn’t • Themes in animal evolution (see textbook figure 32.11) -Origin of multicellularity -Origin of bilateral symmetry, cephalization, and the nervous system -Origin of embryonic tissue layers -Origin of a coelom -Origin of protostome and deuterostome development -Origin of segmentation • Origin of multicellularity -Choanoflagellates are the unicellular sister group to animals (see textbook figure 32.3) -Evolved at the origin of animals (Metazoa; includes sponges and all other animals) • Origin of bilateral symmetry, cephalization (formation of a head), and the nervous system -Types of symmetry ~Bilateral symmetry (Ex. Beetle) ~Radial symmetry (Ex. Coral polyp) ~No symmetry (Ex. Sponge) ~Pentaradial symmetry/pentamerism (echinoderms, except their larvae have bilateral symmetry) -Bilateral symmetry means you can have a head = cephalization ~Having a head gives the animal directionality (front and a back) ~Having a head gives the animal the ability to eat/be a predator -Concentrate sensory apparatus and nervous system at head -Evolved at the Bilateria origin (has bilateral symmetry if ancestor is Bilateria, Ctenophora and Cnidaria have radial symmetry, and sponges have no symmetry) -Genetic mechanisms responsible for bilateral symmetry and cephalization are shared (homologous) • Origin of embryonic tissue layers -Diploblastic=2 tissue layers (Endoderm and Ectoderm) -Triploblastic=3 tissue layers (Endoderm, Mesoderm, and Ectoderm) -Species with Bilateria ancestor are triploblastic, while Ctenophora and Cnidaria are diploblastic • Origin of a coelom -Animals are tubular-tubes within tubes -Coelom- a fluid-filled body cavity between the inner and outer tubes; disengages gut from outer layers, space for nutrients to move, forms basis of hydrostatic skeleton -3 body plans (see textbook figure 32.9) ~Acoelomate=no coelom ~Coelomate=has coelom ~Pseudocoelomate=false coelom (not a true coelom) -Pseudocoelomate has the space touching both the mesoderm and endoderm, while a true coelom only touches the mesoderm -Cannot say the coelomate evolved at a specific point of the tree because the body plans are randomly distributed ~Diploblastic and sponges don’t have coeloms ~Body plans scattered among Bilateria species • Origin of protostome and deuterostome development -“Stoma”=opening or mouth -Protostome-the mouth is formed before the anus ~”First mouth” -Deuterostome-the anus is formed before the mouth ~”Second mouth -The first opening in protostomes is the mouth, while the first opening in deuterostomes is the anus -Deuterostomes evolved at Deuterostomia -Protosomes, or “Spiralia,” evolved at Lophotrochozoa and Ecdysozoa • Origin of segmentation -Not all animal groups show segmentation -Common genes called Hox genes control segmentation -Suggesting flexible response through evolutionary history -Why segmentation ~Permits specialization-genetic duplication releases copies to be modified for new purposes-look for this theme in vertebrate evolution Animal Taxa: Invertebrates I (Diversity) • Invertebrate Diversity (see textbook figure 33.3) -Morphological and molecular data are combined to understand relationships among animal phyla -Molecular (DNA) data has revolutionized our understanding • “Big 9” animal phyla -Porifera -Cnidaria -Platyhelminthes -Mollusca -Annelida -Nematoda -Arthropoda -Echinodermata -Chordata • *Porifera (sponges) -5,000-10,000 species -Filter feeding -No symmetry -Sessile -Mostly marine • Ctenophora (comb jellies) -100-150 species -Predatory -Radially symmetrical -Motile (via cilia) -Entirely marine • *Cnidaria (jellyfish, corals, anemones) -Over 10,000 species -Predatory or filter feeding -Radially symmetrical -Both motile and sessile -Mostly marine • Placozoa (“flat animals”) -1 to a few species -Detritivore -Radially symmetrical -Motile (via flagella) -Entirely marine • Acoela (acoel flatworms) -Approximately 400 species -Predatory -Bilaterally symmetrical -Motile (via cilia) -Mostly marine • Rotifera (wheel animals) -Filter feeding -Bilaterally symmetrical -Motile -Mostly freshwater • Acanthocephala (spiny headed worms) -1150 species -Parasitic -Bilaterally symmetrical -Motile -Parasitic (freshwater) • Cycliophora -1-2 species -Discovered in 1995, found on the mouthparts of lobsters -Parasitic or commensal -Symmetry is not clear -Motile -Marine • Gastrotricha (hairybacks) -790 species -Detritivores -Motile -Marine and freshwater • Gnathostomulida (jaw worms) -100 species -Detritivore -Motile (via cilia) -Marine • *Platyhelminthes (flatworms) -25,000 species -Predators or parasites -Motile -Moist habitats • Entoprocta (“anus inside”) -150 species -Filter feeding -Sessile and colonial -Mostly marine • *Mollusca (mollusks) -85,000 species -More varied forms than any other phylum -Predatory, filter feeding, detritivores -Both motile and sessile -Marine, freshwater, terrestrial • Sipunculida (peanut worms) -320 species -Filter feeding -Motile -Marine • Brachiopoda (lamp shells) -330 species -Filter feeding -Sessile -Marine • Phoronida (horseshoe worms) -25 species -Filter feeding -Sessile -Marine • Ectoprocta/Bryzoa (moss animals “anus outside”) -4,000 species -Filter feeding -Sessile -Mostly marine • Nemertea (ribbon worms) -1,800 species -Predatory and parasitic -Motile -Mostly marine, some freshwater and terrestrial • *Annelida (segmented worms) -22,000 species -Predatory, filter feeding, detritivores, sanguivores -Both motile and sessile -Marine, freshwater, terrestrial • Priapulida (penis worm) -16 species -Detritivore -Motile -Marine • Kinorhyncha (mud dragons) -Detritivore/predatory -Motile -Marina • Loricifera -120 species -Discovered in 1983 in anoxic, deep sea brine -No mitochondria -Feeding style unknown -Sessile -Marine • Nematomorpha (horsehair worms) -2,000 species -Parasitic -Motile -Freshwater or moist habitats • *Nematoda (roundworms) -15,000 species or up to 1 million -Half parasitic, half free living -Motile -Nearly all habitats and all elevations • Chaetognatha (arrow worms) -120 species -Predatory -Motile -Marine planktonic • Tardigrada (water bears) -1,150 species -Predatory -Motile -Moist habitats, extreme environments • Onychophora (velvet worms) -180 species -Predatory -Motile -Terrestrial • *Arthropoda (arthropods) -Many millions -Every feeding style imaginable -Motile -Marine, freshwater, terrestrial • What are the patterns you observe in the diversity of animal phyla -Most phyla live in marine habitats, however, terrestrial phyla tend to have more overall diversity Animal Taxa: Invertebrates II (Lophotrochozoa) • Three major clades of Bilateria -Deuterostomia, Lophotrochozoa, Ecdysozoa • Lophotrochozoa -United by molecular characters -Named for two morphological characters that are not universal; in other words, not all members of Lophotrochozoa have the two characters for which they are named ~Lophophore-feeding morphology ~Trochophore larvae-larval morphology -Most diverse body plans -Largest number of phyla -Platyhelminthes-flatworms (25,000 species) ~Predators or parasites ~Motile ~Moist habitats, including terrestrial, freshwater, marine ~Acoelomate ~Flattened bodies increase surface area to volume ratio ~Gas exchange and diffusion of nitrogenous wastes across body surface ~Gastrovascular cavity (not a tube) -Have no anus ~More than half are parasitic, some with complex life cycles ~Complex life cycles -Schistosomiasis 2 nd only to malaria as far as devastating infectious diseases to humans go -Definitive host (a human; where the organism sexually reproduces) -Intermediate host(s) (often a snail; where the larvae produced in the definitive host develop/mature, after which they go back out to find the definitive host again) -Mollusca-molluscs (>85,000 species) ~More varied forms than any other phylum ~Predatory, filter-feeding, detritivores ~Motile and sessile ~Marine, freshwater, terrestrial ~Second only to arthropods in diversity ~Soft bodied with a hardened calcium carbonate shell (sometimes reduced) ~Shared body plan in spite of all looking very different (foot, visceral mass, mantle) (see textbook figure 33.15) ~Radula ~80% snails and slugs ~Cephalopods are most neurologically advanced invertebrates ~Some are quite toxic (blue-ringed octopus, cone snails) ~Most endangered group of animals (see textbook figure 33.21) ~Gastropods -Snails and slugs -Marine, terrestrial, freshwater -Foot is used for locomotion -Visceral mass is the gut -Mantle secretes the calcium carbonate shell ~Bivalves -Clams, mussels, oysters, etc. -Marine and freshwater -Bivalve=two shells (secreted by the mantle) -Foot holds them in one place -Visceral mass is the gut ~Cephalopods -Octopuses, squids, nautilus -Camouflage and chromatophores -Neurologically advance-eye, behavior, intelligence -Usually no calcium carbonate shell-sometimes internally (a greatly reduced mantle can be found near that) -Visceral mass is the gut -Foot is modified-tentacles and siphon -Annelida-segmented or ringed worms (22,000 species) ~Predatory, filter feeding, detritivores, sanguivores ~Motile and sessile ~Marine, freshwater, terrestrial ~Chaetae-bristles made of chitin ~Predators, grazers, filter-feeders, parasites ~Marine worms -Errantians (move around on their own) -Sedentarians (just sit in one place) ~Leeches -Secrete anesthetics and hirudin, which dissolves clots ~Earthworms -Circulate nutrients and aerate soil -Most common North American earthworms are not native and have transformed ecosystems Animal Taxa: Invertebrates III (Ecdysozoa) • Ecdysozoa -Defined by molecular evidence -Common morphological character that unites Ecdysozoa-ecdysis-external covering (cuticle or exoskeleton) is molted with growth -Most diverse animal group -Nematoda-roundworms (15,000 species or up to 1 million) ~15,000 recognized species, but estimated up to 1 million in actuality ~Half parasitic, half free-living ~Motile ~Nearly all habitats and elevations ~Important in decomposition and nutrient cycling ~Caenorhabditis elegans -1 mm long, simple organism -Important model organism in many research fields -959 total cells in adults-all mapped -Arthropoda-arthropods (many millions) ~Every feeding style imaginable ~Motile ~Marine, freshwater, terrestrial ~Most successful of all animal phyla-make up 2 out of every 3 species ~Characteristics of Arthropoda -“arthro”=joint -“pod”=foot -Segmented body -Paired limbs on segments -Hard exoskeleton (chitin) -Jointed appendages -Open circulatory system (hemolymph circulates through hemocoel) -Chelicerata-spiders, mites, scorpions, etc. ~Get their name because all of them have chelicerae (feeding appendages, often venomous) ~Cephalothorax ~Abdomen ~4 pairs of walking legs ~Pedipalps ~Behavior can be very complex -Crustacea-crabs, shrimp, amphipods, barnacles, etc. ~Many pairs of walking legs (great variation among species) ~Antennae ~Cephalon, thorax, abdomen ~Copepods may be the most numerous of animals on Earth ~Barnacles have to get creative: sessile and sexual hermaphroditism, sperm casting, very large intromittent organs -Insecta-insects (beetles, butterflies, ants, bees, cockroaches, flies, etc. ~Abdomen, thorax, head ~Antennae ~Wings (have true flight-can propel themselves through the air, not just gliding flight) ~Three pairs of walking legs ~Metamorphosis-a form of development (complete metamorphosis is when an organisms completely changes between larva and adult; incomplete metamorphosis is when there is no significant changes between larva and adult; see textbook figure 33.41) ~Why aren’t insects larger An evolutionary constraint -The oxygen content of the air has changed over time; oxygen concentrations used to be much higher than they are today, and, consequently, insects used to be much larger Animal Taxa: Vertebrates I (Chordate Evolution to Amniotes) (see textbook figure 34.2) • Deuterostomia -Defined by molecular evidence -Deuterostome development -Echinoderms-starfish, sea urchins, sea cucumbers (~7,000 species) ~Predators and filter-feeders ~Motile ~Marine -Chordata-chordates (~65,000 species) ~All feeding styles ~Motile and sessile ~Nearly all habitats and all elevations throughout the world ~4 things that bind all chordates together (see textbook figure 34.3) -Notochord, dorsal hollow nerve cord, pharyngeal slits, post anal tail ~Notochord-flexible rodin chordate embryos, becomes spine in vertebrates ~Pharyngeal slits-develop into gills and eventually elements of the head, jaw, and ears ~Cephalochordata (see textbook figure 34.4) ~Urochordata (see textbook figure 34.5) -Vertebrates ~Duplication of Hox genes, possibly useful in increasingly complex body plans ~Bony vertebrae (usually surrounding spinal cord) -Gnathostomes (“jawed mouth”) ~Jaws-arose from support structure for pharyngeal slits (see textbook figure 34.12) ~More gene duplication ~Enhanced smell and vision ~Lateral line system -Osteichthyes (majority of vertebrates)=”bony fish” ~Ossified endoskeleton ~Actinopterygii -Ray finned fishes; most diverse vertebrate group; over 30,000 species (see textbook figure 34.15, 34.16) -In all aquatic habitats -From 8 mm to 11 m in length -Any possible aquatic niche -Lobe fins (Sarcopterygii) (see textbook figure 34.17) ~Lobed fins with bony and muscular support -Tetrapods ~4 limbs with digits (see textbook figure 34.20) ~Adults lack gills ~Vertebrae in neck permit head movement ~Pelvic girdle fused to spine ~Amphibia -Frogs and toads-5,000 species ~One of the most diverse vertebrates globally ~Many habitats ~Often specialized for leaping ~Tadpoles=aquatic larvae -Salamanders and newts-700 species ~Northern hemisphere ~Temperate ~Predators ~Aquatic larvae -Caecilians-200 species ~Burrowing ~Soil dwelling ~Tropical ~Viviparous -Amniotes (see textbook figure 34.24) ~Amniotic egg-specialized extraembryonic membranes (+shell) (see textbook figure 34.25) ~Ventilate with rib cage ~Reptilia -20,500 species -Scales composed of keratin -Shelled eggs on land/ovoviviparity -Internal fertilization -Ectothermic + endothermic • Evolution of limbless forms -If a tetrapod lacks limbs, is it still a tetrapod ~Yes, because the term tetrapod just refers to ancestry Animal Taxa: Vertebrates II (Mammals and Metabolic Trade-offs) • Amniotes -Reptilia + Mammalia -Extra embryonic membranes protect embryo from desiccation ~Terrestrial habitats can be colonized • 3 Main Groups of Mammals (see textbook figure 34.40) -Monotremes (5 species) -Marsupials (324 species) -Eutherians (placental mammals; 5,010 species) • Mammalia -Hair -Young fed with milk produced by modified sweat glands (mammary glands) -Sound conducted through middle ear by 3 bones (malleus, incus, stapes) -Each side of lower jaw made up of a single bone, the dentary • Hair -No other animal group has it -Found on all mammals at some point in development -Keratin -Molt patterns -Complex anatomy ~Arrector muscles ~Sebaceous glands ~Color variation ~Vibrissae vs. underfur vs. fur • Young fed with milk produced by modified sweat glands (mammary glands) -Also not found in any other group (with the exception of pigeons and caecilians) -Intense parental investment in offspring -Obligates female parent to invest heavily (lactation is often more expensive than gestation) Animal Taxa: Vertebrates II (Mammals and Metabolic Trade-offs) ctn. • Mammalia -Sound conducted through middle ear by 3 bones (malleus, incus, stapes) -Each side of lower jaw made up of a single bone, the dentary -Remember, our perceptions about perception are influenced by our evolutionary history. Primates are very visual. Most use olfaction and hearing more. • Mammal evolution -Pelycosaurs-evolution of homoiothermy (or homeothermy) ~Homeothermy: stable internal body temperature in spite of external influence; can be regulated behaviorally or metabolically • Thermoregulation -Homeotherm: relatively constant temperature -Poikilotherm: variable temperature -Ectotherm: uses environmental heat -Endotherm: generates metabolic heat • Trends -Larger brains -Larger and more muscles -Upright limb posture -Nocturnal habits ~All of these trends are very metabolically expensive • Metabolic expense -How to address this problem ~Heterodonty (specialized teeth): efficiency in processing food; pre- process before it enters the stomach, most other animals don’t chew ~Secondary palate: can breathe while eating; uninterrupted oxygen supply ~Endothermy: blood vessels in fossilized bones; evidence of whiskers (maybe fur) Body Structure & Function • Form and Function -Animals must obtain nutrients and oxygen, excrete wastes, and move -Animals live in nearly every conceivable kind of environment (temperature, pressure, salinity, oxygen concentrations, light levels, selective pressures, etc.) -Natural selection acts on heritable variation to favor the most successful solutions to these challenges -So if a trait has an adaptive function (influences the successful survival and reproduction of individuals) then its form reflects its function ~Ex) Darwin’s finches -Natural selection acts on variation in bill shape and size in populations to favor particular bill morphologies well suited to particular foods -Bill shape (form) tells you what the diet is (function) -Exchange with the environment is ultimately at the cellular level- substances in solution travel across the plasma membrane of cells -How is this accomplished in complex multicellular organisms -Reflected at all scales ~Molecular-cellular-tissues-organs-organ systems-organism -Molecular-enzyme structure and substrate specificity; phospholipid characteristics -Cell structure- cell with extensive endoplasmic reticulum and Golgi apparatus is likely to have what function Protein synthesis ~Cell shapes -Neuron cells-function in communication -Epithelial cells-function in lining surfaces -Muscle cells-function in contraction ~Tissues- groups of cells that together serve a particular function -Embryonic tissue layers: endoderm, mesoderm ectoderm ~Give rise to 4 kinds of tissues 1. Connective-support, connect, or separate 2. Nervous-regulation, control, communication 3. Muscle-support, movement (contraction) 4. Epithelial-lining/covering -Tissues reflect function (see textbook figure 40.5) ~Example: Hydrodynamics is a physical constraint of the environment -Water is 1000x denser than air -Problem-how to travel quickly and efficiently through water -Solution-fusiforms (streamlined) body shape -Diverse organisms face similar challenges and arrive at similar solutions=convergent evolution ~Example: Increasing stride length to run fast ~Example: Evolution of flight in vertebrates -Similar physical constraints (generate lift) -Solutions reflect evolutionary constraint as well -Benefits of flight-powered flight has evolved four times (three times in vertebrates)-insects, pterosaurs, birds, bats -Problem-How to generate sufficient lift for sustained flight -Solution ~Flight membranes ~Generally small body size ~Lighten bony elements -Specific solutions vary ~Pterodactyl-elongate single digit ~Bird-fuse distal bony elements and feathers ~Bat-elongate four digits • Locomotion -Adaptations for different forms of locomotion are based on the same basic tetrapod body plan • Form and Function: two general principles that influence form and function in organ systems -Body size and surface area to volume relationships -Homeostasis and Regulation • Body size and surface are to volume relationships -Large ~Need more food ~Take longer to mature ~Lost heat slowly ~Lose water slowly ~Reproduce slowly -Small ~Need less food ~Shorter time to maturity ~Lose heat quickly ~Lose water quickly ~Reproduce quickly -There are many consequences of body size ~While the large aren’t very subject to the environment, they have much slower cycles ~While the small have fast cycles, they are very subject to environmental extremes -Example: body mass (size) and metabolic rate (see textbook figure 40.20) ~Metabolic rate-oxygen consumption per unit of time=a measure of metabolic activity ~Metabolic rates vary with activity, so basal metabolic rate is measured (at rest) ~What is the relationship between body mass and basal metabolic rate -Bigger animals eat less proportionally because they generally have a slower metabolism -Example: Relationship between body mass and lifespan ~What is the relationship between body mass and lifespan -Larger animals tend to live longer -As volume increases, surface area increases less -Surface area is critical for exchange -Example: salmon hatchlings ~Oxygen exchange across skin and gills ~At hatching, most oxygen exchange is across the skin ~As they grow, the gills take over -Every cell must exchange with its environment (see textbook figure 40.3) -Complex animals: vastly increased surface areas for exchange of nutrients, oxygen, and wastes (see textbook figure 40.4) -Adaptations to increase surface area ~Flattening ~Folding ~Branching Regulating Internal Environments: Homeostasis and Thermoregulation • Homeostasis and Regulation -Conformers vs. Regulators (see textbook figure 40.7) ~Conformers-conform to the environment; as the environmental temperature changes, so does the body temperature ~Regulators-don’t conform to the environment; as the environmental temperature changes, body temperature stays relatively the same -Homeostasis: maintaining internal chemical and physical environments within a tolerable range, independent of external environmental states -Why is homeostasis important ~Enzyme function is impacted by temperature, pH, other reactants, etc. ~Other chemical reactions in the body are sensitive to conditions ~Extremes also destroy proteins (high heat, pH) and cells (freezing, high heat) -Metabolic rate of a thermoconformer ~Do thermoconformers operate equally well at all temperatures -No, thermoconformers have an optimal range of metabolic activity that is influenced by environmental temperatures ~Acclimatization-organisms adjust to gradual environmental changes to maintain optimal (or near optimal) performance (see textbook figure 40.10) -Homeostasis: How is it maintained ~Set point-optimal temperature ~Stimulus-a variation from optimal temperature ~Sensor/control center-senses the stimulus and regulates response ~Response-brings temperature back to optimal ~Negative feedback-response is to minimize the effect- this is the feedback mechanism used to maintain homeostasis ~Positive feedback- response is to amplify the effect -Thermoregulation (thermoregulators): temperature maintained within a normal range ~Example: circadian rhythms-normal daily variation in body temperature (see textbook figure 40.9) • Energetic trade offs of ectothermy and endothermy -Able to maintain activity in different conditions ~Endotherms are able to do this much more efficiently than ectoderms -Require more or less energy ~Ectotherms require substantially less energy than endotherms • Mechanisms of Heat Exchange (see textbook figure 40.12) -Conduction: direct contact between solids -Convection: direct contact between solid and gas or liquid -Radiation: no direct contact -Evaporation: high heat of vaporization; a special property of water -In which direction does heat flow ~Heat always flows from areas of high heat to areas of low heat; from high to low; from hotter to colder temperatures • Generating and retaining heat -Insulation helps retain heat in mammals and birds -Behavioral heat absorption and regulation -Circulatory adaptations ~Vasodilation and vasoconstriction-delivering different amounts of heated blood to skin surface to heat or cool ~Countercurrent heat exchange (see textbook figure 40.13) -Evaporative heat loss -Metabolic heat production ~Shivering and non-shivering thermogenesis ~Some ectotherms use shivering thermogenesis to generate heat • Thermoregulation and energy conservation -Torpor: a state of decrease physiological activity ~Small endotherms (birds and mammals) that are active, with high metabolic rates ~Daily pattern -Hibernation: seasonal state of reduced physiological activity ~Mostly mammals ~Aestivation-“summer hibernation”- often facultative ~”Set point” is greatly reduced, sometimes to nearly 0 degrees Celsius ~Often accompanied by periodic arousals -Adaptive heterothermy ~The ability of an endothermic animal to allow its body temperature to fluctuate in response to some form of environmental stress, saving significant amount of energy and water ~Heterothermy: endothermic animals allow body temperature to fluctuate in response to an environmental stress (hibernation, aestivation, torpor, daily changes) Dietary Strategies and Digestion: Tongues, Teeth, and Venom • Dietary Strategies and Digestion -Remember that all animals are ingestive heterotrophs -Why eat ~Obtain chemical energy (sugars; respiration) ~Obtain organic molecules (building blocks for tissues) ~Obtain essential nutrients-cannot synthesize, must obtain from food -Essential amino acids-for protein synthesis -Essential fatty acids-for fatty acid synthesis -Vitamins-organic compounds with a variety of functions; “a substance that makes you ill if you don’t eat it” -Minerals-inorganic compounds, diverse functions, includes electrolytes -This is all done to support ~Survival ~Growth ~Reproduction -3 classes of molecules are sources of chemical energy, building blocks, and essential nutrients ~Carbohydrates-sugars and polymers of sugars, including glycogen and cellulose ~Proteins-polymers of amino acids ~Lipids-complex carbon molecules that are hydrophobic (fats-made up of fatty acids, phospholipids, steroids) Clicker Question • Nearly all animal phyla evolved in which era Cambrian • Do jellyfish have a coelom No • Where did protostome development evolve Lophotrochozoa and Ecdysozoa • Where did triploblastic tissue organization arise Deuterostomia, Lophotrochozoa, Ecdysozoa • Where did deuterostome development arise Deuterostomia • Although mollusks have the most varied body forms of any animal phylum, they all share a common body plan that includes a visceral mass, foot, and mantle • The phylum Arthropoda is made up of these living groups: Crustaceans (including insects), chelicerates, and myriapods • Insect size is most likely limited by the maximum distance that oxygen can efficiently diffuse into tissue • In chordates, some of the pharyngeal slits become the jaw/mouth in vertebrates • The hallmark characteristics of mammals are three inner ear bones, a single lower jaw bone, hair, and mammary glands • The most diverse animal phyla have colonized terrestrial habitats • Compared to their amphibian relatives, amniotes have reduced their reliance on water in their reproductive cycle • Lophotrochozoa, Ecdysozoa, and Deuterostomia are all made up of animal phyla that share molecular characteristics • All mammals are endothermic, most are homeothermic, some are heterothermic Homework Quiz 6 • All animals are multicellular, ingestive, heterotrophs with a diploid dominant life cycle • Lophotrochozoa, Ecdysozoa, and Deuterostomia are all made up of animal phyla that share molecular characteristics • Examples of lophotrochozoans are octopuses, slugs, leeches, flatworms • Compared to their amphibian relatives, amniotes have reduced their reliance on water in their reproductive cycle • Deuterostome development is characterized by spiral and determinate cleavage, blastopore forms the mouth Homework Quiz 7 • What is the importance of consuming an adequate amount of proteins in the diet Proteins serve a variety of functions, and the body does not store excess quantities of protein • Evolutionary adaptations that help diverse animals directly exchange matter between cells an the environment include an external respiratory surface, a small body size, and a two-cell-layered body • Penguins, seals, and tuna have body forms that permit rapid swimming, because the shape is a convergent evolutionary solution, which reduces drag while swimming • Hibernation and torpor are similar because they allow animals to escape seasonal climate changes and conserve metabolic energy • Ectothermic homeotherms are able to maintain a constant body temperature because they are found in environments with temperatures that don’t change

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Textbook: Discrete Mathematics with Applications
Edition: 4
Author: Susanna S. Epp
ISBN: 9780495391326

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Verify the following statements.a. 128 2 (mod 7) and 61 5