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A metal plate is situated in the xy-plane and occupies the

Calculus: Early Transcendentals | 8th Edition | ISBN: 9781285741550 | Authors: James Stewart ISBN: 9781285741550 124

Solution for problem 11 Chapter 14

Calculus: Early Transcendentals | 8th Edition

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Calculus: Early Transcendentals | 8th Edition | ISBN: 9781285741550 | Authors: James Stewart

Calculus: Early Transcendentals | 8th Edition

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Problem 11

A metal plate is situated in the xy-plane and occupies the rectangle 0 < x < 10, 0 < y < 8, where x and y are measured in meters. The temperature at the point sx, yd in the plate is Tsx, yd, where T is measured in degrees Celsius. Temperatures at equally spaced points were measured and recorded in the table. (a) Estimate the values of the partial derivatives Txs6, 4d and Tys6, 4d. What are the units? (b) Estimate the value of Du Ts6, 4d, where u si 1 jdys2 . Interpret your result. (c) Estimate the value of Txys6, 4d.

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Lecture Notes March 11 , 2016 Nondisjunction  Sometimes during meiosis the chromosomes don’t separate properly  Results in gametes lined up with too many/ too few chromosomes  Frequency of this increases in women in their late 30’s  Homologous chromosomes pairs in every cell are balanced against each other- when an individual has a double dose of some genes and a single dose of others shit happens o Down’s Syndrome- extra chromosome 21  47 total chromosomes in the zygote and in all other cells of the individual  Low level of intelligence, thickened eye lids, faulty speech o Turner’s Syndrome  Results when a person only has one X chromosome- 45 chromosomes in zygote  One of the gametes was missing a sex chromosome  Female, sterile, short, webbed neck, and have problems with math and special relationships o Klinefelter’s Syndrome  Extra sex chromosome- 2X 1Y- 47 chromosomes  Egg having 2X chromosomes  Tall, sterile, male, often with a lowered mental capacity Hormonal Control  Hormones- chemicals, usually proteins or steroids, produced by one part of the body (usually a gland) that alters the activity of another part of the body called the target organ  Important to the bodily functions of many animals- focus on male and female hormones o Males- during embryotic development of the male, the testes produce small amounts of the male sex hormone- testosterone  These small amounts result in the formation of male structures (differentiation) but no sperm is produced  At puberty- the hypothalamus (part of the brain) begins to secrete Gonadotrophic Releasing Hormone- GnRH  GnRH acts on the pituitary gland- which is a “master” gland near the brain- causes the pituitary gland to release a luteinizing hormone (LH) and follicle stimulating hormone (FSH)  LH- causes the interstitial cells in the testes to produce more testosterone  FSH- along with extra testosterone causes maturation of the seminiferous tubules and the production of sperm  Once the LH causes more testosterone to be produced it causes the maturation of the accessory reproductive structures- penis and testes- testosterone triggers secondary sexual characteristics- pubic hair, beard growth, deeper voice, larger and stronger muscles o Females- reproductive cycle Lecture Notes  As in the male- at puberty the hypothalamus releases GnRH which causes the pituitary gland to release LH and FSH  FSH and LH causes the ovaries to mature and begin secreting the two female sex hormones estrogen and progesterone  Estrogen- stimulates maturation of accessory reproductive structures- increases the size of the uterus and vagina- causes the development of secondary sexual characteristics- pubic hair, breasts, broadening of pelvis, redistribution of body fat, and some change in voice  As the hormone balance changes the menstrual cycle is initiated  Estrous Cycle- in most mammals the rhythmic changes in the female reproductive tract is called an EC- female receptive to the male only at certain times during EC- uterine lining build up is reabsorbed if fertilization does not occur  Humans and other higher primates differ from other mammals in that:  Female is somewhat receptive to the male at all times  If fertilization does not occur the thickened uterine lined is shed during a period of bleeding known as menstruation o Human menstrual cycle is about 28 days Lecture Notes March 11 , 2016 Nondisjunction  Sometimes during meiosis the chromosomes don’t separate properly  Results in gametes lined up with too many/ too few chromosomes  Frequency of this increases in women in their late 30’s  Homologous chromosomes pairs in every cell are balanced against each other- when an individual has a double dose of some genes and a single dose of others shit happens o Down’s Syndrome- extra chromosome 21  47 total chromosomes in the zygote and in all other cells of the individual  Low level of intelligence, thickened eye lids, faulty speech o Turner’s Syndrome  Results when a person only has one X chromosome- 45 chromosomes in zygote  One of the gametes was missing a sex chromosome  Female, sterile, short, webbed neck, and have problems with math and special relationships o Klinefelter’s Syndrome  Extra sex chromosome- 2X 1Y- 47 chromosomes  Egg having 2X chromosomes  Tall, sterile, male, often with a lowered mental capacity Hormonal Control  Hormones- chemicals, usually proteins or steroids, produced by one part of the body (usually a gland) that alters the activity of another part of the body called the target organ  Important to the bodily functions of many animals- focus on male and female hormones o Males- during embryotic development of the male, the testes produce small amounts of the male sex hormone- testosterone  These small amounts result in the formation of male structures (differentiation) but no sperm is produced  At puberty- the hypothalamus (part of the brain) begins to secrete Gonadotrophic Releasing Hormone- GnRH  GnRH acts on the pituitary gland- which is a “master” gland near the brain- causes the pituitary gland to release a luteinizing hormone (LH) and follicle stimulating hormone (FSH)  LH- causes the interstitial cells in the testes to produce more testosterone  FSH- along with extra testosterone causes maturation of the seminiferous tubules and the production of sperm  Once the LH causes more testosterone to be produced it causes the maturation of the accessory reproductive structures- penis and testes- testosterone triggers secondary sexual characteristics- pubic hair, beard growth, deeper voice, larger and stronger muscles o Females- reproductive cycle Lecture Notes  As in the male- at puberty the hypothalamus releases GnRH which causes the pituitary gland to release LH and FSH  FSH and LH causes the ovaries to mature and begin secreting the two female sex hormones estrogen and progesterone  Estrogen- stimulates maturation of accessory reproductive structures- increases the size of the uterus and vagina- causes the development of secondary sexual characteristics- pubic hair, breasts, broadening of pelvis, redistribution of body fat, and some change in voice  As the hormone balance changes the menstrual cycle is initiated  Estrous Cycle- in most mammals the rhythmic changes in the female reproductive tract is called an EC- female receptive to the male only at certain times during EC- uterine lining build up is reabsorbed if fertilization does not occur  Humans and other higher primates differ from other mammals in that:  Female is somewhat receptive to the male at all times  If fertilization does not occur the thickened uterine lined is shed during a period of bleeding known as menstruation o Human menstrual cycle is about 28 days

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Chapter 14, Problem 11 is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 8
Author: James Stewart
ISBN: 9781285741550

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