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822. Identifying surfaces Consider the surfaces defined by | Ch 12 - 13 |

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

Solution for problem 13 Chapter 12

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 13

822. Identifying surfaces Consider the surfaces defined by the following equations. a. Identify and briefly describe the surface. b. Find the xy@, xz@, and yz@traces, when they exist. c. Find the intercepts with the three coordinate axes, when they exist. d. Make a sketch of the surface. 4z = x2 4 + y2 9

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1 Reproductive Systems Male vs Female  Primary reproductive structure in males are the testicles. o Occurs in pairs.  Internally divided into sections. (if dissected, would look internally same as an orange)  Each section (lobe) has a seminiferous tubules.  Each tubule is roughly 3 feet long.  Seminiferous Tubules are where sperm production occurs. Epididymis o Extension of the tubules on the outside of the testicle.  This is where sperm is stored for brief periods of time  Vas deferens  Connects to the epididymis moves sperm from the testicle to the urethra. o (Urethra) This is the only structure shared by the reproductive and urinary system in males. o No structures are shared between the female reproductive and urinary systems.  Production of Semen  Seminal vesicle­Near the prostate gland toward the end of the Vas Deferens.  Prostate gland: production of semen. o Surrounds the urethra, located at the base of the bladder o The prostate continues to grow throughout life.  Has a very fibrous outer covering which restricts oenlargement o As it grows, it may restrict flow within the urethra making it difficult to completely empty the bladder. o Prostate is prone to develop cancer, easily treatable if caught early.  Cowper’s gland 2 o Located at the base of the prostate o Connects to the urethra Urethra:  Drains the bladder and facilitates the introduction of sperm into the female reproductive tract. Penile Shaft  Made up of 2 types of tissue (Corpus Cavernosum and Corpus Spongiosum)  Collectively known as erectile tissue o When stimulated, these tissue fill with blood causing an erection  Interstitial Cells  Found in the testicles  Major function: production of testosterone  Sperm:  main regions o Tail: used for swimming o Midpiece: has numerous mitochondria  Mitochondria provide ATP needed by tail o Head region:  Nucleus (needed for fertilization)  Acrosome: package of digestive enzymes  Enzymes are used to degrade the outer portion of an ova (egg)  Seminal Fluid (Semen)  structures that produce semen o Testicles: contribute sperm to the semen o Seminal vesicle & Prostate & Cowper’s Gland: Produce the rest of the semen  Contained in it: Sperm, Alkali Solution (Used to neutralize the pH of the female reproductive system.  Sperm are most active in a neutral environment (pH around 7)  Female reproductive tract tends to be acidic o Fructose: produced by one of the 3 glands. o Broken down by the sperm in order to produce ATP 3 o Prostoglandins:  Hormones that cause uterine contractions  Force sperm higher into the female reproductive tract  External Genitals Testicles: o Surrounded by scrotal sac  Scrotal sac expands and contracts under the influence of temperature  Suspended outside of the body (usually mammals)  Sperm production is greatly influenced by temperature  98.6 is too hot for functional sperm  93 is optimal temperature  Female reproductive system ovary: Primary reproductive structure oProduces Ova oSolid Structure oProduces some hormones (estrogen) o The ovaries take turns during each uterine cycle Oviduct:is a tube that is loosely attached to the ovary o Captures an ova when released conducts it towards the uterus is where fertilization occurs Fallopian tubes; uterine tubes o At the tip of the oviduct where it loosely attaches to the ovary is fingerlike growths called fimbriae o Are in constant motion and create a “water” current which forces any released ova into the oviduct  Uterus oPear shaped organ, mostly smooth muscle, sits on top of the urinary bladder, where development will take place if fertilization occurs Vagina (Vaginal Canal) oFacilitates intercourse oreceives male penis oserves as the birth canal olined with erectile tissue Cervix oJunction between the vagina and the uterus 4 External Genitals: oClitoris  Female organ of arousal; made up of erectile tissue, almost identical in structure to the male penis. oLabia Majoria and Minora:  Folds of skin that cover the vaginal opening  produce lubricants during intercourse  Menstrual Cycle (Uterine Cycle) Average length 28 days (can run anywhere from 18­40 days) oDays 1­5:  Menstruation, inner lining of uterus is discharged o Days 6­13  Proliferation stage (build up) o Day 14  Ovulation (ova released from ovaries) o Days 15­28  Secretory phase, uterus prepares for implantation o Birth Control: o Abstinence 100% o Vasectomy almost 100% o Tubal ligation (uterine tubes clipped) almost 100% o Oral contraception (pill) almost 100%  When tracked, it’s actually closer to 85% because the pill needs to be taken approx same time every day o Contraceptive implants 95% o Contraceptive injections 99% o Intruterine Device (IUD) 90%  Device inserted into the cervix; usually made of copper or some kind of metal.  does not prevent fertilization, just implantation o Diaphragm 90%  A device that covers the cervix; prevents sperm from reaching the ova o Cervical Cap 85%  Plugs the cervix; prevents sperm from reaching the ova o Male Condom 85%  sleeve that fits the penis and traps sperm; the most effective method at preventing STD’s o Female Condom 85% 5  sleeve that fits into the vagina and traps sperm very good at preventing STD’s o Coitus interruptus 75%  removal of penis before ejaculation; couples that are attempting to get pregnant have only a roughly 25%  success rate and 25% failure rate o Jellies, creams and foams 75%  chemicals that have spermicidal effects (kills sperm)  are intended to be used with other forms of birth control o Natural family planning 70%  plan days of ovulation, avoid sex several days around that time o Douche 70%  Contains spermicidal chemicals; while flushing some sperm out and some higher o Sexually Transmitted Diseases  AIDS caused by a virus; treatable but at present not curable  acquired from an exchange of body fluids the immune system degenerates (targets helper t­cells)  victims tend to die from rare type of diseases  Genital Herpes  Caused by a virus; treatable but not curable  open sores on the genitals  tend to be self­healing  tend to reoccur  closely related to the virus that causes cold sores  active outbreaks (individuals) tend to be caused by stress  Genital Warts  Caused by a virus, warts develop on the genitals  treatable but not curable;  they tend to reoccur  in females, there appears to be a link between genital warts and certain types of uterine/ovarian cancer Gonorrhea  Caused by bacteria  easily curable with antibiotics 6  one of the more common types of STD’s  Symptoms: o white discharge from the penis/vagina o painful urination o in men: scar tissue can develop in the urethra may lead to a complete blockage medical intervention is required o in females: symptoms seem to go unnoticed  scar tissue develops in the uterine tubes  leading to sterility o at one point, was the most common cause of sterility medical intervention is required Chlamydia  Probably the most common type of STD but least reported  most people are a­symptomatic  some people develop flu like symptoms but recover quickly  some develop painful urination but recover quickly  Easily treated with antibiotics  Has a very weak immune response  Predisposes a person to contracting other STD’s o Most people diagnosed with an STD, have chlamydia (85%)  Syphilis  caused by bacteria  easily treated in the early stages (antibiotics)  impossible to treat in later stages  Stage 1: an (painless) ulcer develops on the genitals  usually heal within a couple of weeks and may leave a scar  Stage 2: a rash develops on the palms of the hand/soles of the feet  usually occompanied by flu like symptoms; may occur several months after the ulcer heals; rash clears in a couple of weeks  Stage 3: development of gumas (large weeping ulcers that develop throughout the body)  The worst ones are the ones that develop on the internal organs (lead to death)  untreatable 7  Parasitic infection  Initial symptoms can last up to 9 months  Secondary can last up to 30­40 years  o Fertilization: union of a sperm and an ova which forms a Zygote.  Only 1 sperm penetrates the egg and the nucleus of the sperm and ova combine o Takes place in the Oviduct (fallopian tubes)  Requires hundreds of sperm/but only one penetrates the ova  Sperm: o Head: acrosome, nucelus o Middle piece: mitochondria for power o Tail: swimming  Ova: o Corona radiata: thick outer layer  Consists of cells from the ovary o Zona pellucida: thickened middle layer o Plasma membrane  Is not degraded during a fertilization event o The events of fertilization: o 1: thousands of sperm reach the ova and release the contents of their acrosome o 2: enzymes from the acrosome begin to degrade the corona radiata and zona pellucida o 3: eventually, one sperm comes in contact with the plasma membrane the remaining events take place within microseconds.  a: plasma membrane separates from the zone pellucida this creates a gap making it difficult for additional sperm to enter  b. a gap created fills with fluid  c. the interior of the ova begins to spin o Sperm and ova are unique because they each have a haploid nucleus so that when they combine they maintain the original chromosome count  Haploid means half. o Development after Fertilization: o Cleavage: the zygote begins to divide without increasing in size, the cells numbers double after each division 8 (the cell size decreases by half during each division) o Morula: solid ball of cells produced by cleavage events (mulberry) o Blastula: cells from the center of the morula migrate to the outside leaving a hollow ball  some cells remain in the cavity o Gastrula: cells invade the space between the endoderm and the ectoderm (forming endoderm and ectoderm)  Cells reinvade the hollow space left by the blastula.  This forms 2 layers of cells  Inner layer: endoderm o will eventually produce most of the internal organs  Outer layer: ectoderm o will eventually form the skin and nervous system  Toward the end of gastrulation, the cells invade the space between the endoderm and ectoderm (these cells form mesoderm)  Mesoderm will eventually produce skeletal and muscle tissue o Neurula: notochord develops which will eventually be replaced by the spinal cord o Germ Layers:  Ectoderm: skin, brain and neurons, linings of the nose mouth and anus  Mesoderm: muscles, connective tissue, reproductive organs  Endoderm: digestive tract, glands, bladder (other internal organs) o Implantation  Zygote embeds into the uterine lining oPlacenta:  A huge capillary bed (exchanges w/tissues)  Forms from fetal cells/blood vessels from the fetus intertwine with mothers blood vessels (forming a huge capillary bed) to provide nutrients and remove waste from developing embryo.  Is only present during pregnancy  Delivered after the baby (afterbirth)  The placenta can develop anywhere within the uterus.  Umbilical cord attaches from the fetus to the placenta o Embryonic Development o 1st Stages: First and second months of pregnancy 9 o Week 1: pre­embryonic development implantation has not occurred, cleavage events occurring, nutrients are supplied by yolk, and blastula formation occur  Cell mass may split to form identical twins  Week 2: Cell mass arrives at the uterus  implantation occurs  placenta begins to form  Tissues are being produced  Week 3: Nervous system begins to develop (first system) o Circulatory system begins to develop  Week 4: the appearance of a tail is present on embryo o Head is much larger than rest of embryo o Limb buds are present o Eyes, ears, and nose all begin to appear o Heart beats o Liver produces blood cells oSecond Month: oArms and legs become more developed oStart getting fingers and toes  By end of second month all major organ systems have developed o Fetal Development o Third and Fourth month:  Head growth slows (does not stop)  Eye­lashes and eye­brows, hair on head, fingernails and nipples begin to appear  Bone begins to replace cartilage  Heartbeat may be heard  Approximately 6 in/6oz  Amniotic Sac: filled with fluid, prevents drastic temp change, protects against mechanical damage. o Fifth through Seventh month:  Movement may be felt  Lanugo covers the baby (fine downy hair covering the entire body)  Eyelids open 12 in/3 pounds  Also covered with Vernix Casiosis (waxy substance looks like cheese) 10  Prevents the fetus from becoming water­logged o Eighth and Ninth Month  Head begins to point down towards the cervix  Growth of Fetus  21 inches/7.5 pounds o Birth o Stage 1: Mucus plug, which has been at the cervix, is expelled  Amniotic sac breaks (water breaking)  Cervix dilates to 4 inches o Stage 2: Contractions every 1­2 minutes  The uterus began contracting somewhere in the second/third month  (called braxton hicks contractions)  Crowning: Baby’s head appears in birth canal  Baby is expelled head first  Umbilical cord is cut after baby begins to breath normally o Stage 3:  Delivery of the placenta

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Chapter 12, Problem 13 is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 2
Author: William L. Briggs
ISBN: 9780321947345

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822. Identifying surfaces Consider the surfaces defined by | Ch 12 - 13 |