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If Psa, a2 d is any point on the parabola y x 2 , except

Calculus | 8th Edition | ISBN: 9781285740621 | Authors: James Stewart ISBN: 9781285740621 127

Solution for problem 11 Chapter 4

Calculus | 8th Edition

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Calculus | 8th Edition | ISBN: 9781285740621 | Authors: James Stewart

Calculus | 8th Edition

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Problem 11

If Psa, a2 d is any point on the parabola y x 2 , except for the origin, let Q be the point where the normal line at P intersects the parabola again (see the figure). (a) Show that the y-coordinate of Q is smallest when a 1ys2 . (b) Show that the line segment PQ has the shortest possible length when a 1ys2 .

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Study Guide 4 mechanisms for controlling enzyme activity:  Feedback inhibition  Degredation  Protein protein interactions  Covalent modifications 2 major levels if regulation in the cell:  Post translational regulation: one controls the activity of preexisting enzymes  One controls the amount of an enzyme Classes of protein domains  Zinc fingers- protein structure that binds a zinc ion  Leucine zipper – functions to hold 2 recognition helices in the corset orientation Effectors affect transcription indirectly by binding to specific DNA binding proteins. Activator proteins help RNA polymerase recognize promoters. It may cause a change in DNA structure and may interact directly with RNA polymerase. Repression typically affects anabolic enzymes. Induction typically affects catabolic enzymes. Most signal transduction systems are 2 component regulatory systems. 2 component regulatory systems are made of 2 different proteins: sensor kinase (in cytoplasmic membrane) and response regulator (in cytoplasm). Modified 2 component systems used in chemotaxis to: 1) sense temporal changes in attractants or repellents 2) regulate flagellar rotation. Quorum Sensing -bacteria know when other bacteria are around and how many there are -might start certain activity until there is a support group -secrete a chemical that acts as marco polo -communication mechanism -ex: virulence factors  E. Coli & Staphylococcus aureus autoinducer: molecule generate by the cell & secreted by the cell Caulobacter divides asymmetrically into swarmer cells (dispersal role) and stalked cells (reproductive role). -controlled by 3 major regulatory proteins  external stimuli & internal factors play a role in affecting life cycle Steps in viral replication: - attachment penetration of viral nucleic acids (injects DNA or RNA)  synthesis of viral nucleic acids & proteins  assembly & packaging of new viruses ( brings proteins & DNA together)  cell lysis or buds & releases of new viruses Example of a retrovirus is herpes or chicken pox (once you have had it once, the trace of it will always be there). All viruses have a specific host but have the capability to infect another host. Viruses: short genomic sequences that contain enough info to take over the cells causing it to replicate, divide, & express viral proteins -range from 0.02 to 0.3 um. Virus particle (virion) : extracellular form of a virus that contains nucleic acid genome surrounded by a protein coat & other layers of material Nitrogen fixation is a process of reducing N to2NH . 3 -in its original form, 2 is inorganic & in order for plants to be able to use it they must convert it to the organic form -if it isn’t converted, it will cause damage -only certain prokaryotes can fix nitrogen, those that cant don’t need it or don’t use it Response to signal: sensory proteins in cytoplasmic membrane sense attractants & repellents; methyl accepting chemotaxis proteins Controlling flagellar rotation: controlled by CheY protein -CheY results in counterclockwise rotations & runs -CheY-P results in clockwise rotation & tumbling Adaptation: feedback loop allows the system to reset itself to continue to sense the presence of a signal Riboswitches: RNA domains in an mRNA molecule that can bind small molecules to control translation of mRNA -located at the 5 prime end of mRNA from folding of RNA into a 3D structure -found in some bacteria, fungi, & plants The attachment of a virus to its host cell results in changes to both virus & cell surface that facilitate penetration. Process of replication of a retrovirus -Entrance into the cell removal of virion envelope at the membrane reverse transcription of 1 of the 2 RNA genomes  integration of retroviral DNA into host genome  transcription of retroviral DNA  assembly & packaging of genomic RNA  budding of enveloped virions; release from cell

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Chapter 4, Problem 11 is Solved
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Textbook: Calculus
Edition: 8
Author: James Stewart
ISBN: 9781285740621

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If Psa, a2 d is any point on the parabola y x 2 , except