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Angular size A boat sails directly toward a 150-meter

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

Solution for problem 35 Chapter 3.10

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 35

Angular size A boat sails directly toward a 150-meter skyscraper that stands on the edge of a harbor. The angular size u of the building is the angle formed by lines from the top and bottom of the building to the observer (see figure). a. What is the rate of change of the angular size du>dx when the boat is x = 500 m from the building? b. Graph du>dx as a function of x and determine the point at which the angular size changes most rapidly. 150 m x

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REPRODUCTION IN PLANTS Leaves stems roots – means of reprod asexually  A sexual reproduction (stems) o Rhizomes – horizontal underground stem  Irises and grass are examples --- many not all grass o Tubers – enlarged storage stems  Ex) potato  Sprouts buds that become new plants o Bulbs – shortened underground stems  Have very fleshy leaves attached  Ex) tulips, lilies, daffodils, and onions o Stolons – horizontal above ground stem  Strawberries are an example  ALSO called runners  Flower is organ of reproduction o Two outer whorls are for protection and luring organism to the flower for fertilization o Two inside are the sexual organs o Innermost whorl  Carper or Pistil (female)  Consist of a sticky pad called the stigma which is where pollen will attach … pollen is the male gamete  Style – tube that takes pollen into the last part of the carpel which is the ovary(w/female gametes)  Male gamete is the STAMEN  Consists of anther and the filament  Anther is where the pollen is produced  Filament holds anther in place  Flower does no need to have both male and female gametes  When it has both many times it is not self-fertilizing – like animals  Needs to cross fertilize o Petals are the next whorl  Lure birds bees etc to the flower  Function is to lure organism to the plant for cross fertilization o OUTER MOST WHORL  Sepals – protects the flower when it was a bud  In fruit the seeds  Gametogenesis  Formation and Maturation both controlled by anterior pituitary hormones o FSH (follicle stimulating)-female o LH (Lutenizing H)-female o Interstitial cell hormone –male  In the male o Spermatogenesis – formation o Spermiogenesis – maturation o Both take place in seminiferous tubules of the testes  IN the female o Oogenesis – formation and maturation occur at the same time  Oacyte forms and matures egg all in one step  Difference is timing BIG ISSUE o Male – gametogenesis not until puberty …  Nothing happens until puberty  Process will continue throughout sexual life once puberty happens  NO SET END  There may be decrease but no end o Female  Begins when FETUS – in uterus … not born yet  By the time she is born the process stops … not completed  Starts again at puberty  Not continuing  Starts and stops monthly  ENDS @ menopause MALE  He can make batches of sperm throughout his life  Spermatogonia in testes o Stem cells  Make more by mitosis  Stem cells make more stem cells  MAJOR DIFFERENCE o Diploid o At some point in life it decides not to make any more stem cells but decides to become a sperm o Primary spermatocyte commits to become sperm  Cannot go back  Uses meiosis o Primary spermatocyte = 2n/4n = chrm# / DNA  LOOK AT SLIDE 26 o One primary spermatocyte form four spermatids then becomes four sperm (haploid)  Does not look like sperm… it is round  Spermiogenesis does not divide  Head of sperm is basically a nucleus (LOOK @ 27)  Acrosome is sack filled with enzymes that break barrier of egg o Derived from golgi  Upper end of tail has mitochondria  Tail is flagellum  NEED TO KNOW o Head is nucleus with acrosome o Neck is upper part  Flexible region to connect tail to head  Needs to be flexible or else tail snaps o Tail then upper tail has mitochondria  Sperm does not leave on its own OOGENESIS (female)  Begins before puberty  Starts before born with oogonium (diploid) o Make more through mitosis  When ovaries reach certain number of these stem cells all of them stop dividing by mitosis and commit to meiosis @ the same time o CANNOT MAKE ANYMORE ONCE ALL ENTER MEIOSIS o She’ll have all the eggs shell ever have  The committed cell is primary ooacyte  She gets larger through own synthesis or from external needs o Gets what she needs to get started o Yolk is nutritive needed to develop o Ovaries don’t make yolk because we have placenta  When primary ooacyte in womb she is in prophase one  Still in prophase I after birth o Ooacyte arrested at this stage  No oogonium in ovaries – ONLY OOACYTE IN PRO 1  In puberty ooacyte completes meiosis I o At the end first polar body and secondary oacyte are made o Has exocentic nucleus o Both are 1n/2n st Meiosis 1 sep homologs o 1 polar body removes set of homologs because we need 1n/1n o Secondary oacyte undergoes meiosis 2  Not completed until sperm enters  Metaphase II aresst happens until sperm  When sperm enters meiosis II is completed o Second polar body result of meiosis 2  releases set of chromatids o If no sperm the egg is shed during mensis  DIFFERENCE IN MALE AND FEMALE o HE STREAMLINES SHE ENLARGES Ovarion menstrual cycle  2 cycles that occur at the same time but at diff places o Ovarion takes place in ovary  Takes primary follicle to maturation  Leads to the release of a fertilizable secondary oacyte o Mentstrual cyce occurs in uterus  Starts with shedding of the endometrium from the previous month  Whole does not shed but most of it does  Starts building a new one  If no pregnancy then starts shedding again  Get rids of old enodmitrium then gets new endo thingy o Both controlled by hormones o Lsh controls first half and LH is second halfe o Hormones produced during ovarion cycle o FSH reactiveates immature follicles  FSH  causes proliferation of follicle cells  Makes more cells with mitosis  FSH Also responsible for causing follicle cells to produce and secrete the female hormone estrogen  FSH completes meiosis one and begins meiosis 2  ALL TAKES PLACE IN FIRST 14 DAAYS  Only ONE of reactivated follicles will complete meiosis 1 and go to meiosis 2  Rest die and become scar tissue  Corpora Albicantia  Dead follicles – scar tissue  Why reactivated o One will not produce enough estrogen  When enough estrogen is there all but one o LH  responsible for ovulation  Release of secondary ooacyte and surrounding follicle cells  Heals ruptured follicle and forms CORPUS LUTEUM  Causes CL to produce and secrete progesterone  LH Maintains the corpus luteum (keeps it alive) o In ovarion cycle when progesterone beomces o MENTSTRUAL CYCLE  Estrogen renew endo to certain height  Prog complete endo to maximum height  No Pregnancy o CL dies becase  Pregnancy Plant Nutrients  Of 13 minerals  12found in soil o Broken down into macronutrients and micronutrients  Macronutrients used in large quantities  Micro used in small  Macro broken into primary and secondy  Primary are nitrogen, p and k  Secondary are ca, mg, and s  Soil o Has 3 components :  Mineral (inorganic matter)  Organic matter  Pore spaces o Inorganic material o Organic matter – decaying or dead  Humus made up of decaying or dead org matter  Roots – organs of procurement o The organ that allows minerals into the plant o Can also act as storage  Carrot example that stores its food o Act as procurement of water and minerals o And anchors o Types of roots:  Fibrous root system – aerial roots  Many small branching roots  No one main root  Taproot system  ONE large root  Adventitious roots (not talking about today) o Structure  Epidermis  Has root hairs o Extension of cell out into soil o Function to increase surface area  Cortex  Endodermis –(inner most layer) is the limiting factor for what goes into plant o If it cannot pass through the cell membrane it cannot go in o Casparian strip on top side and bottom  Prevents or allows material to get into steel where transporting tissue is  Kinda like a barrier  It has to go through the cell membrane and no where else  Xylem –big cell  Transports water and minerals  Only in one direction – UP  Phloem – smaller cell  For organic material – food it makes  Transports in all directions  Xylem and phloem in the steel  Absorption of nutrients o Ions available to plants for absorption are in the solution in the soil water o The absorption of minerals by roots is essentially independent of rates of water absorption. o Factors for rate of mineral movement into root:  Concentration inside and outside  Can it passively flow through membranes or ion channels  If it cant get through are there carrier moelcules to get them there  2 routes water and minerals can take o Symplast  Where mineral crosses the root hair and moves from cell to cell through the cortex .  Uses plasma dismoda to move  Moves through plant cells  When gets to endodermis it can pass through because it already pass through the membrane of the root hair o Apoplast  Enters from soil into space between cell walls and cell membrane and continues to move through the spaces until it gets to the endodermis where it is forced to go through because of the casparian strip. .  NITROGEN DOES NOT COME FROM WEATHERED ROCK  Nitrogen comes from nitro-fixing bacteria through nitrogen fixation o Example of bacteria is rhizobium o Process is symbiotic  Plant cannot get nitrogen from soil bc no nzymes to do it o The bacteria breaks it down and makes it a usable form for the plants o Example  Legumes and rhizobium have the symbiotic relationship  Utilize enzyme nitrogenase  Bacteria enters root through root hairs and goes into the cortex where it begins to divide o Bacteria needs plant in order to multiply o As it divides it forms a nodule which continues to grow but also as growing its fixing nitrogen in soil to a usable form.  There are mechanisms/ signals where the legume can lure the rhizobium  Bacterium also has signals to enter root hairs and begin process of division.  NUTRITION.DIGESTION IN ANIMAL  Autotrophs o Get nutrients from inorganic material  Used by plant to produce organic food o Most are photosynthetic and are plants o Nutrients are from soil, withered rock  Heterotrophs o Have to eat organic material made by other organisms o Food either made by autotrophs or eating other heterotrophs a  Digestion – break down material o THreee classifications  Carnivores mainly meat  Herbivores mainly plants  Omnivores both o Based on the category the org is in you will see anatomical and physiological mods to deal with that type of food  Carnivores have sharp teeth because they have to be able to tear meat  Herbivores have flat teeth because they have to grind cellulose  Omni have both flat and sharp o In carnivores the jaw can usually open up larger than their own size o Modifications in the tract  Herbis have three to four compartments in their stomach that have different  Types of Digestion (heterotrops) o Intracellular – withing the cella  Most primitive type o Extracellular – digestion outside of the cell  In the envioment  In some kind of digestive cavity – advanced o Protista only have intracellular digestion o Porifera  Sponges – least complex of multicell organism (KNOW THE DIAGRAM FOR THE TEST)  Intracellular digestion o Choanocyte- cells involved in digestion o Amoebocytes – Assosciated with choan  Endocytotes food from choanocytes  Called amoeba because mobile  ADVANCED EXTRACELLULAR DIGESTION o Advantage of digestive cavity allows one to take in larger food o CNIDARIANS – know both diagrams  Hydra – have extracellular and intracellular digestion  Aquatic  Gastrovascular cavity o Extends throughout body  Body only two layers thick o Epidermis o Gastroderms – lining cavity  Surrounding the mouth are tentacles o Helps lure prey toward moth  Tentacless have cnidocytes o Cnidocyte cell have a nematocyst  Nema has a coiled thread as a part of its structure  Outside of cell has a trigger  When trigger touched thread comes out and captures or wraps prey  All cells of cavity are digestive cell  Gastrodermal cells digest by releasing digestive enzymes into the cavity  Digestion completed intracellularly o SKIP PLANARIA o NEMATODA  DIGESTION IS COUPLED WITH ABSORPTION  One way flow  Vertebrate Digestion o Fish o Amphi VERTIBRATE DIGESTION PART ii SMALL INTESTINES • Components- duodenum, jejunum and ileum • Functions: • completes digestion and most of absorption occurs here THREE PRETIN SPLITTING ENZYMES RELEASED FROM PANCREAS:  TRYPSINOGEN  Procarboxypeptidase  Chymotripsinogen  All three in inactive from when released by pancreatic cells into the duodenum  Not active until in duodenum  In duodenum there are membrane bound enzymes called enterokinase or enteropeptidase o Enterkinase activates trypsinogen to active from trypsin o Trypsin activates the other two zimogens o  IN DUODENUM o Chyme(acidic) needs to be neutralized by sodium bicarbonate salts that come from the pancreas  Makes it a little bit alkaline o What causes the release of the pancreatic enzymes  When chyme enters small intestine parasympathetic nerves turn on and sends:  The two hormones released by the krypts of liber (all released from pancreas)  Secretin – causes pancreas to release sodium bicarb salts o Salts neutralize acid chyme  CKP (cholecystokinin pancreozymin) – causes pancreas to release digestive enzymes all of them  Liver – produces bile  Gall Bladder – stores and concentrates bile (removes some of the water) o Release of Bile is caused by CKP  CKP travels to liver/gall bladder to release  Bile contains billy ruben – that is a waste product o Needs to be excreted o If not you get a jontus condition o Can cause brain damage o Physiological damadge due to immature liver at birth  Billy is being stored in tissues COLON  Functions: o Absorbs necessary water (for hydration) o Forms the feces  Components: o cecum , ascending, transverse and descending colon, sigmoid colon and rectum

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Chapter 3.10, Problem 35 is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 2
Author: William L. Briggs
ISBN: 9780321947345

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Angular size A boat sails directly toward a 150-meter