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Solved: 1114. Working with parametric equations Consider

Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs ISBN: 9780321947345 167

Solution for problem 11 Chapter 10.1

Calculus: Early Transcendentals | 2nd Edition

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Calculus: Early Transcendentals | 2nd Edition | ISBN: 9780321947345 | Authors: William L. Briggs

Calculus: Early Transcendentals | 2nd Edition

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Problem 11

1114. Working with parametric equations Consider the following parametric equations. a. Make a brief table of values of t, x, and y. b. Plot the 1x, y2 pairs in the table and the complete parametric curve, indicating the positive orientation (the direction of increasing t). c. Eliminate the parameter to obtain an equation in x and y. d. Describe the curve. x = 2t, y = 3t - 4; -10 t 10 1

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Biology Exam 2 study guide Natural selection -Darwinism and its ideas Darwin made 2 major points: 1. Descent with modification a. All organisms are related through descent from an ancestor that lived in the remote past b. Implies that the relationships among organisms can be represented by a branching “tree” 2. Unity and diversity of life a. Unity come from a common ancestor - Small changes in organisms create new features and new species Ex. Whales have bones like humans -Natural Variation *Natural variation is created by both mutation and natural selection which creates variance *You have to have mutation for variance -Adaptations Adaptation by natural selection is based on: 1. Five observations a. Populations have the capacity to grow in size b. Populations tend to be stable in size i. Idea of the Logistic Curve explains the survival of the fittest c. Resources are limited d. Individuals in a population vary extensively in their traits e. Relatives resemble each other i. ***same variation are inherited from the parents to the offspring ii. Evolution cannot favor a gene if its not genetic/ passed down from generation to generation 2. Three logical inferences a. More individuals are produced than the environment can support -Mechanism -Definition of fitness A species that is more fit is adapted into its niche and its better off than other creates trying to go into the same niche -Morphological convergence 1. Morphological convergence happens if body parts with similar form or function evolve independently a. this is a result when different lineages are subjected to similar environments, and so therefore national selection favors similar modifications -Definition of diversifying (disruptive) selection Disruptive selection- select for extreme values (bell curve split in the middle favoring the 2 extremes) a. Describes changes in a population genetics in which extreme values for a trait are favored over intermediate values i. Example: the immune system ii. Examples: butterflies have different colors on their wings for a mating display (extreme differences) Stabilizing selection: (bell curve stabilized in the middle) a. a type of natural selection in which genetic diversity decreases and the population mean stabilizes on a particular trait value Directional selection: (bell curve leaning to one side of the extremes) a. in which an extreme phenotype is favored over other phenotypes, causing the allele frequency to shift in the direction of the phenotype -Speciation Speciation is a key problem that bridges micro and macro evolution a. Macro-evolution: - Refers to the evolutionary patterns seen at scales above the species level -Prezygotic barriers: (before the fertilized egg) a. Hinders the fertilization of the ova if members of different species attempt to mate b. impede mating between species Example: birds dance to attract a mate *if they do not come together to mate they cannot reproduce Example: seasonal habits might be different SeasonalCertain types of skunks only mate in the winter -Postzygotic barriers: (after the fertilized egg) a. prevent the hybrid zygote from developing b. prevent the hybrid adult from reproducing c. weakens the hybrid individual Example: horse + donkey = mule (cannot produce offspring) -Allopatric: a. Separated geographically - Geography makes new species Example: continental drift -Sympatric: Morphological divergent (separated by life history) -Character displacement (see textbook) Can be between species Example: the Galapagos birds have different beaks because they compete and different beak sizes evolve -Biological speciation concept Biological species concept is a difficult to apply to: a. Asexual organisms b. Fossils c. Organisms where distant hybridization can be successful d. Organisms about which little is known regarding their reproduction e. Populations that are widely separated f. “Ring” species -Population genetics (emphasize) Microevolution is change in the genetic composition of a population from one generation to the next  To understand evolution, you need to understand the dynamics of ‘genes’ in populations -Hardy-Weinberg model & assumptions Hardy Weinberg describes a population that is NOT evolving  It is at genetic equilibrium o A population at equilibrium, frequencies and alleles and genotypes in a populations gene pool remain constant from generation to generation  5 conditions for non- evolving populations are ‘rarely’ met in nature o Extremely large population size o No gene flow o No mutations o Random mating o No natural selection *if the conditions are met, we can predict the frequencies of genotypes in the population -know the definition of p, q, & 2pq Consider a gene with only two alleles in a population, A and B - Let P and Q represent the frequencies of the two possible alleles in a population - 2pq represents genotype -calculate allele & genotype frequencies P + Q = 1 P^2^ + 2pq + Q^2^ = 1 F(AA) = P ^2^ homozygous dominant F(Aa) = 2PQ heterozygote (represents genotype) F(aa) = Q^2^ homozygous recessive -calculate a percent frequency from a proportion -Understand dominant & recessive alleles (see textbook p. 116) Dominant: when both alleles are present, the dominant allele masks or hides the recessive Example: AA, Aa Recessive alleles: the weaker allele out the two alleles that hides in the background unless there are two recessive alleles which will conclude in a recessive gene Example: aa -Basic probability theory as applicable to alleles and genotypes frequencies * If we know genotype frequencies, we can always calculate allele frequencies * If we know allele frequencies, we can predict genotype frequencies- if we assume Hardy- Weinberg conditions hold -types of natural selection (important to know) Disruptive selection- select for extreme values (bell curve split in the middle favoring the 2 extremes) b. Describes changes in a population genetics in which extreme values for a trait are favored over intermediate values i. Example: the immune system ii. Examples: butterflies have different colors on their wings for a mating display (extreme differences) Stabilizing selection: (bell curve stabilized in the middle) b. a type of natural selection in which genetic diversity decreases and the population mean stabilizes on a particular trait value Directional selection: (bell curve leaning to one side of the extremes) b. in which an extreme phenotype is favored over other phenotypes, causing the allele frequency to shift in the direction of the phenotype -genetic drift (such as bottleneck or founder effect) Bottleneck: is a sudden drastic reduction in the size of a population The new population will have less genetic diversity than the original Founder effect: is the loss of genetic variation that occurs when a new population is established by a very small number of individuals from a larger population -Mutation *a population needs mutation for evolution - Mutation is the only source of new alleles, and is ultimately the source of all variation Mutations can NOT: a. generate new variation b. change allele frequencies c. change genotype frequencies -Gene Flow *Consists of genetic additions or subtractions from a population, resulting from movement of fertile individuals or gametes *Causes a population to gain or lose alleles *it tends to reduce differences between populations over time Example: adaptive divergence -Causes of genetic diversity Mutation causes genetic diversity -Definition of panmictic (it means random mating in a population) -Phylogenetics -Interpret phylogeny -Novel traits: *Are characteristics in an organism that have been created or introduced through a specific genetic change Novel traits for whales: a. body elongated and streamlined b. tall modified into fluke c. limbs reduced in size d. pelvis reduced in size and internalize into body -Hypothesize origin of novel trait -modern taxonomic relationship between birds and dinosaurs -Cetacean evolution Prior to Eocene epoch- all mammals were on land BUT Whales are mammals as well and they have placentas *Modern cetaceans - include whales, porpoises, and dolphins - order of placental mammals -Aquatic adaptations a. body elongated and streamlined b. tall modified into fluke c. limbs reduced in size d. pelvis reduced in size and internalize into body -"Missing link" fossils between ancient artiodactyls and cetaceans Pakicetids are the missing link between ancient artiodactyls and cetaceans - adapted to land - transitional fossil leading to whales - know the adaptation for underwater hearing

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Textbook: Calculus: Early Transcendentals
Edition: 2
Author: William L. Briggs
ISBN: 9780321947345

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Solved: 1114. Working with parametric equations Consider