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Solved: In 5–8, rewrite the given scalar equation as a

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

Solution for problem 6E Chapter 9.4

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 6E

Problem 6E

In Problems 5–8, rewrite the given scalar equation as a first-order system in normal form. Express the system in the matrix form x’ = Ax + f.

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BIOL 120 Principles of Biology (Dr. Partain) Week 3 Notes (2/19­2/26) GENETICS Heirarchy of Genetic Information  Traits: o an inherited characteristic controlled by genes found on DNA  Chromosomes: o structural unit containing part or all of an organisms genome consisting of DNA and its associated proteins o Pairs:  in sexually reproducing organisms, one of the pair in inherited from dad, one from mom  These are called homologous pairs o Karyotype:  A pictorial arrangement of a full set of an organism’s chromosomes  In humans, there are 22 pairs of autosomes and 1 pair of sex chromosomes o Chromatids:  One of the two identical strands of chromatin or half of a replicated chromosome  Genes: o A segment of a chromosome that carries specific information about a trait o Contains info about anything your body needs o Sometimes, genes carry mutations that cause disease or changes in traits o They are instructions carried by DNA  These instructions are for building all of the proteins that the cells require  Genome: o The entire suite of genes present in an organism o Each cell in your body has a complete set of instructions about how to make your cells, their components, and their component’s components  This set of instructions is called your genome  Your body has about 100,000,000,000,000 cells  Francis Watson & James Crick described DNA’s structure in 1953, won Nobel Prize in 1962 o Description was built largely on work of Rosalin Franklin, who took x­ray diffraction images of DNA DNA & It’s Structure  Deoxyribonucleic Acid  The information molecule stored in the nucleus of eukaryotic cells and in the cytoplasm of prokaryotic cells  Composed of nucleotides  Nucleotides have 3 parts: o a phosphate o a sugar (deoxyribose for DNA nucleotides) o one of 4 bases:  Adenine (A)  Guanine (G)  Thymine (T)  Cytosine (C)  Complementary Bases: o There is a specific pattern of the bases that connect the two strands o Called complementary base pairs, like the steps of a spiral staircase  A always bonds across from T  C always bonds across from G  Because of this, if only one strand of DNA is known, the other can be easily deciphered  Ex: one side  ATCGGCA  Other side  TAGCCGT  Sugar­Phosphate Backbone: o Connected end to end to form a structure that is like the hand rail of the spiral staircase o Like you backbone, the sugar­phosphate backbone supports and gives shape to the DNA molecule Chromosome A long, single molecule of DNA and associated proteins Housed in nucleus Can carry hundreds of genes along its length Each cell has a complete set of chromosomes o All genes are present DNA:  molecule of heredity that stores info required for making all of the proteins required in a cell o Manages information o stores information o duplicates information when needed o transfers and decodes information when needed RNA:  information carrying molecule composed of nucleotides PROTEIN SYNTHESIS  2­Step Process o 1. Transcription  DNA­polymer of nucleotides (two complementary strands)  copying of DNA gene into RNA o 2. Translation  RNA­polymer of nucleotides (single strand)  Decoding the copied RNA sequences and producing the protein for which it codes  RNA is translated into a protein (polymer of amino acids), enzyme is made o Example:  DNA one side TAGCAG  DNA other side ATCGTC  RNA Translation AUCGUC (RNA does not have T, it has U) MEITOSIS  Happens in Somatic Cells  (body cells) o Mitosis (happens everywhere but sex cells)  For growth and repair  Makes identical copies  Happens in Germ Cells  (sex cells) o Meiosis  To make gametes (eggs/sperm)  Makes unique cells  ½ chromosomes #  one of each type of chromosome OVERVIEW OF CELL DIVISION  Interphase  Mitosos  Cytokinesis CELL CYCLE  Interphase: o longest phase of cell o Protein synthesis o Suicide o DNA is copied (replication)  Chromosomes are uncondensed (when they can be used) (unduplicated)  Mitosis: o Chromosomes are condensed (X shape) (duplicated) (duplicated splits) o DNA is split equally into two halves of the chromosome o Moving to opposite sides of the cell  Cytokinesis: o Parent cell is divided in half into two daughter cells PROTEIN SNYTHESIS VS. DNA REPLICATION  SIMILARITES: A. DNA unzips and unwinds B. Free nucleotides are matched C. Takes place during Interphase  DIFFERENCES: A. Protein Synthesis starts in the nucleus, continues in Ribsomones a. DNA Replication all takes place in the nucleus B. Protein Synth. is a 2­step process a. DNA rep. is not VARIATIONS  Brain and nerve cells form in the embryo and then never divide  Many leaf cells: divide as young leaves, stop dividing and simple increased in size by growing  Bone marrow cells: divide rapidly; forming as many as 20,000 new cells per minute CANCER  Is a two part failure in the cell cycle o When the cell is unable to repair DNA, stop growth, or commit suicide  Benign tumor­ not mutated, just a mass of cells, not aggressive o Formed if cell division is over stimulated  Malignant tumor­ mutation occurred o Formed if cell cannot correct mutation, supposed to kill the cell  Problem with tumor suppressor gene  mutated cell will keep going, invading surrounding tissue  become malignant, cancerous tumor SUMMARY of CANCEROUS CELLS  Uncontrolled cell division  Suppressor genes are unable to turn off growth, repair DNA, or cause cell suicide  Metastasis causes cells to migrate  They are immortal Detecting Cancer  Risk factors: chemical, sun exposure, nutrition & health, age  Genetic testing: looking for mutations  Detecting chemicals in the blood: certain cancer cells secrete proteins that are detectable in the blood  Biopsy: take a portion of tumor and examine the cells Treating Cancer  Chemotherapy: highly toxic chemicals that will kill cells  Cancer cells become resistance at 1 cell per million. Average tumor contains 1 billion cells, so ~1,000 are resistant  Radiation Therapy: high energy radiation pointed at tumor cells will destroy DNA, therefore destroying the cell What do we need to Pass along our heritage  Something to pass along: info about the organism  A mode of passing it along  A way of determining its value to the organism What are we passing along DNA… has all the instructions for making a new organism What is the Mode  Sexual Reproduction: o Two unique individuals contrinbuting half of their own DNA toward the production of a new individual o New individual has its own unique set of DNA  Asexual Reproduction: o A single individual gives rise to identical offspring o No new combos of DNA are produced except through random mutation  Asexual Reproduction: o Passing along an exact copy of instructions to an individual o ADVANTAGES:  Guarantees passing along genes to one’s offspring  No care for young required  All individuals can reproduce  Easier to carry out/more efficient  Happens at a faster rate  more offspring can be made o DISADVANTAGES:  No genetic diversity produced  Large accumulation of mutations  Possible increased susceptibility to diseases or environmental change  Sexual Reproduction: o Combines info from 2 individuals to produce a new, unique individual o ADVANTAGES:  Huge amount of genetic diversity  Fewer amounts of mutations  Fights disease o DISADVANTAGES:  Social behavior increases risk of spreading disease  Physically demanding/time consuming: growing and raising offspring  Requires time at the cellular level  Time & energy devoted to finding the “right” mate  Only some can reproduce How Many Chromosomes are In Our Gametes  Germ Cells (gametes): egg and sperm: in humans 23 chromosomes, one form each of the pairs  Somatic cells: every other cell in the body: in humans 23 pairs or 46  How Are Gametes Made o Diploid “stem” cells undergo Meiosis and become haploid cells o Diploid: having a full set of chromosomes, one from each parent. IN humans that means 23 pairs of chromosomes for a total of 46. o Haploid: having half the # of chromosomes, one form pair, for a total of 23 (in eggs and sperm)  8 million gamete possibilities per individual  With sexual reproduction:  8 million (male) x 8 million (female) = 64 trillion possible differing offspring  *not including mutations Meiosis  process by which chromosomes number is reduced in half to produce the gametes  diploid cells are put through a process  Chromosomes match up as a homologous pair, one from mom and one from dad  They trade genes  Two sets pulled to opp ends of the cell  that turns them into haploid cells  these cells then become sperm or egg Diversity Arises From  Sexual Reproduction & Random Fertilization o Alleles from 2 parents  Genetic Recombination: o Independent Assortment  Homologous pairs (one from mom & one from dad) are situated at the metaphase state. The homolog’s orientation is as random as the flip of a coin o Crossing Over:  Gene for gene exchange of genetic info between members of a homologous pair of chromosomes occurs during meiosis I, it is believed to occur several times on each homologous pair o Diploid cells have 23 pairs Sex Determination in Humans  Formation of Twins o Identical:  One sperm has fertilized one egg, it splits, and the genetics are identical o Fraternal:  Two eggs, fertilized by different sperm Modern Genetics  Gregor Mendel: o Father of genetics o Published his work on peas in 1865  Mendel’s ideas… o Law of Segregation (from meiosis):  Each organism has 2 hereditary unites for each trait and during gamete formation  These units segregate from each other and pass on to different gametes. Each gamete receives only one copy (allele) o Law of Independent Assortment (from meiosis I):  In the formation of gametes, the distribution of hereditary unites for one trait is independent of the distribution of hereditary units for the other unit  Different traits are inherited independently of each other Mendelian Inheritance Terms  Genotype: genetic composition of an individual  Phenotype: physical traits  Allele: alternate versions of the same gene o The effect of and individual’s genotype on her phenotype depends on the nature of the alleles she carries  Dominant: when one allele completely covers up the other allele for a gene  Recessive: when one allele is completely covered up by the other allele in a gene  Homozygous: genotype where the alleles are the same  Heterozygous: genotype where the alleles are different o Heterozygous genotype carries the gene but does not have it themselves. Ex: BALDNESS, GENOTYPE Bb= not bald, but carries gene Punnett Square P p P Homozygous Heterozygous Dominant p Pp pp HeterozygouHRecessive

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Chapter 9.4, Problem 6E is Solved
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Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. The full step-by-step solution to problem: 6E from chapter: 9.4 was answered by , our top Calculus solution expert on 07/11/17, 04:37AM. This full solution covers the following key subjects: system, form, normal, given, Matrix. This expansive textbook survival guide covers 67 chapters, and 2118 solutions. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. Since the solution to 6E from 9.4 chapter was answered, more than 286 students have viewed the full step-by-step answer. The answer to “In 5–8, rewrite the given scalar equation as a first-order system in normal form. Express the system in the matrix form x’ = Ax + f.” is broken down into a number of easy to follow steps, and 26 words.

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Solved: In 5–8, rewrite the given scalar equation as a