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The solid formed when the region bounded by y = 2, y = 2x

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

Solution for problem 60 Chapter 6.4

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 60

The solid formed when the region bounded by y = 2, y = 2x + 2, and x = 6 is revolved about the y-axis

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Chapter 5: The Integumentary System Announcements:  Overall Exam 1 grades good o Grades will not be posted on BB o Will return scantrons  Wednesday labs canceled o All other labs will continue as normal Refer to Figure 5.1 Skin Structures (page 151)  Skin= Cutaneous membrane o Dry membrane o Not a simple organ  An organ system  Contains several organs o Blood vessels o Nerve fibers (4 type of tissue) rd o Muscles (3 type of tissue)  2 types of tissue: o Epithelial: stratified squamous (epidermis) o Connective: dermis  Dermis: made up of connective tissue o Papillary layer o Reticular layer  Integument- ‘covering’  Hypodermis: NOT considered part of the skin o Links skin to underlying muscles o Made up of adipose tissue o Superficial fascia: other name for hypodermis  Epidermis: outer most layer of skin o Stratified squamous epithelial tissue o Characteristics: keep in mind the characteristics of epithelial Refer to figure 5.2 Epidermal cells and layers of the epidermis (page 152)  Layers of epidermis dependent on the type discussed thin or thick  4 cells of epidermis: o Keratinocytes: most abundant and important epithelial cell in epidermis  Linked together by lateral contacts- desmosomes  Responsible for the fibrous protein: keratin  Arise from deepest layer of epidermis: Stratum Basale  Germ layer o Stratum Basale= Stratum Germinativum  Made up of stem cells o Stimulated by chemical: epidermal growth factor  Causes continuous mitotic division  All keratinocytes arise from this layer o Melanocyte: 2  Function: responsible for the production of skin pigment: melanin  Melanin surrounded by sac-like membrane (granule): melanosomes o Completed in melanocytes o Transferred to the keratinocytes  Modified epithelium cell  Has cytoplasmic extensions between keratinocytes FIGURE AL-DAWHI DRAWS  Moves melanosomes along acting filaments, motor protein helps lead melanosomes move to through the end of the process to the sunny side of keratinocyte o Protects keratinocytes from UV radiation SIDE NOTE: EXAM 2 may move from March 1 to March 3 rd o Epidermal dendritic cell: Langerhans cell  Associated with immune system  NOT an epithelial cell  Originates in red bone marrow and migrates to epidermis  Has cytoplasmic extensions  Help perform cell function  Enable cell to capture foreign pathogens (antigens: anything foreign to body) o Once stuck to the extension it is engulfed and broken-down into peptide fragments o Fragments presented to the T lymphocytes 3 o ANTIGEN PRESENTING CELLS  Located in epidermis: 1 line of dense o Tactile cell: Merkel cell  Usually located at junction of dermis and epidermis  Associated with nervous system  Sensory nerve ending (yellow colored fiber in figure)  Disk-like ending of sensory nerve: tactile or Merkel disk o Touch  Layers of the epidermis o # of layers dependent of type of skin o Thick skin located: palms of hands and soles of feet  Deepest: stratum basale  Stratum spinosum  Stratum granulosum  Stratum lucidum  Superficial layer: stratum corneum o Thin skin: ALL other areas  Deepest: Stratum Basale  Stratum Spinosum  Stratum granulosum  Superficial layer: stratum corneum  REPEATED: Keratinocytes most abundant cell & arise from stratum basale 4  Stratum Basale: o Single layer of stem cells  DO NOT differentiate  Continuous mitotic division  One daughter cell stays in stratum basale for mitosis  The other daughter cell is pushed up to Stratum basale and upward o Pushed upward: continuous mitotic division pushes up the older cells until it reaches stratum corneum o Keratinocyte in stratum spinosum: develop pre-keratin filaments which attach to desmosomes and form networks  Stratum Spinosum: cells appear to have spines o If you compare a stained and unstained sample  Will see spines in stained sample but not the unstained  Keratinocytes shrink with staining but desmosome do not  Stratum granulosum: beginning of keratinization process o Appearance of two types of granules o Granules: membrane bound sac-like structures  Lamellar granules: laminated granules  Performs function in stratum granulosum  Releases glycolipid material contained inside to the outside surface of the plasma membrane of each and every keratinocyte 5 o Significance: due to chemical structure of material  Does not allow water to pass membrane  Epidermal water barrier: prevent loss of water through skin  Keratohyaline granules: DOES NOT perform function in stratum granulosum  Stratum Corneum: releasing of material in keratohyaline granule o Keratohyaline granule: contains protein  Protein released into the inside of keratinocytes  Acts like a glue-like material make pre-keratin filaments together to for bundles of fibrous protein: keratin  Compare keratinocytes from stratum granulosum and stratum corneum:  Stratum corneum: keratinocytes have no organelles or nucleus  Further from stratum granulosum becomes epidermis (epithelium cells avascular: need nourishment from underlying connective tissue)  Keratinocyte in stratum corneum far from dermis, lack proper nutrition o goes through programmed cell death: Apoptosis  Nucleus and organelles degenerates 6  CELL DIES WITHOUT RUPTURING CELL  MAJOR change between keratinocytes in granulosum to corneum layers  Shedding due to friction at stratum corneum  Dandruff: dander-stratum corneum cells being shed  Callus: thickening of stratum corneum due to friction o Stratum Lucidum: (Thick skin ONLY)  Release of keratohyaline granules will start in the lucidum and continues in the corneum  Epidermis: Stratified Squamous Epithelial Tissue o Keratinized stratified squamous epithelial tissue  Dermis: connective tissue o Ground substance, fibers, cellular elements o Keep in mind cellular elements from connective tissue Chapter 4  Especially: macrophages Refer to Figure 5.3 Light micrograph of the dermis (page 154) o Papillary layer: small region right under epidermis  Loose alveolar connective tissue  Dermal papillae: finger-like projecting areas  Usually house different structures: o Blood capillaries o Free nerve endings: pain receptors 7  Sometimes rest on top of a region of dermis naturally higher causing higher epidermal/dermal ridges: friction ridge  Skin markings: o Reticular layer: dense irregular connective tissue  Skin markings: Chapter 5: The Integumentary System Announcements: o Scantrons returned next week  Wednesday labs canceled o All other labs will continue as normal Refer to Figure 5.1 Skin Structures (page 151)  Dermis made of 2 connective tissues o Papillary layer: small region right under epidermis  Loose alveolar connective tissue  All structures of loose alveolar connective tissue present: ground substance, fibers, cellular elements o Fibroblasts, white blood cells, macrophage nd  Macrophage: 2 line of defense st  1 line of defense is Langerhans cells in epidermis  Dermal papillae (any finger-like projection): finger-like projecting areas of dermis  Creates indentation of epidermis 8  Usually house different structures: o Blood capillaries o Free nerve endings: pain receptors o Touch receptor: Tactile or Meissner’s corpuscles (MAKE SURE TO DIFFERENTIATE FROM TACTILE CELLS)  In the thick skin have dermal papillae that are naturally located at higher regions of the dermis: dermal ridges o Sometimes rest on top of a region of dermis naturally higher causing higher epidermal ridges Refer to Figure 5.4 Dermal modifications result in characteristic skin markings (page 155) o Dermal ridges + Epidermal ridges = friction ridges  Thought to enhance the gripping capability of our hands and feet  Have the openings of the ducts of the sweat glands  Film of sweat: fingerprints o unique  Skin markings: dermal and epidermal ridges, friction ridges o Reticular layer: dense irregular connective tissue  Bundles of collagen fibers running in different directions  Skin markings: cleavage (tension lines) 9  Less dense areas or separations of the dense irregular tissue: gaps between fiber bundles o Whitish areas on figure 4.8 (e) page 132  Neck and trunk area cleavage lines run in circles  Make incision parallel to these lines to assist with short healing process o Dermis skin marking: flexure lines  Look at palm of hand: the lines at knuckles  Enfolding of dermis to allow for more free movement  Skin color o 3 pigments associated with skin color  Melanin: most important because synthesized in skin and major pigment of the skin  Synthesized in the melanocyte  Protects from UV rays o Darker pigment due to more exposure to UV rays o Relatively same number of melanocytes in everyone regardless of pigment  Melanin reduces as it moves up the epidermis due to lymphocyte  NOT RANDOM  Variety of colors runs from reddish yellow to brownish black 10  Differences between light and dark pigment: o Difference in kind of melanin o Amount of melanin granules  Tan: fades after 45 days due to continuous mitotic division pushing keratinocyte to surface and then sheds  Carotene: found in carrots  Yellow to orange  Capability to accumulate in stratum corneum o Yellowish pigment of the edges of the palms or soles of feet  Due to high consumption of plants that contain carotene  Associated with vitamin A o Skin and eyes  Hemoglobin  Oxygen binds to hemoglobin causing red color o Oxygenated hemoglobin  Blood vessels in dermis  Reddish pigment in fair pigmented people Refer to Figure 5.6 Skin appendages: structure of a hair and hair follicle (a)  Hair: strands of keratinized epidermal cells- dead cells  2 major regions 11 o Hair shaft (body): portion that projects out of the skin surface o Hair root: (in dermis) (b)  Layers of the wall of the hair: o Regardless if the shaft of the root the hair is made up of 3 concentric layers  Concentric layers: all share the same base  DON’T CONFUSE WALL OF FOLLICLE with hair walls (c)  Medulla: large irregular cells o sometimes contain pigment o Typically contain air bubbles or air spaces  Cortex: surrounds the medulla o Flat elongated cells o Cortical cells in colored hair contain the pigment of the hair  Grey or white hair: cortical cells contain most air bubbles and spaces  Cuticle: single layer of cells o In the deeper portion of root: cells contain nucleus Keep in mind for  Keratinization is still occurring in cells in the root EXAM o In the shaft portion: cells have no nuclei due to apoptosis  Keratinization is complete when cuticle reaches shaft 12  Cells in shaft overlap each other: like roof shingles  Avoids tangling and matting of hair  Structure of the hair follicle: surrounds the root ONLY o Invaginated inward in the dermis  Pulls part of the epidermis and dermis downward  Connective tissue root sheath: outermost layer: made of dermal tissue  Glassy membrane: basal lamina serving as basement membrane 13

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Chapter 6.4, Problem 60 is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 2
Author: William L. Briggs
ISBN: 9780321947345

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The solid formed when the region bounded by y = 2, y = 2x