Log in to StudySoup
Get Full Access to A First Course In Differential Equations With Modeling Applications - 10 Edition - Chapter 5.r - Problem 26e
Join StudySoup for FREE
Get Full Access to A First Course In Differential Equations With Modeling Applications - 10 Edition - Chapter 5.r - Problem 26e

Already have an account? Login here
Reset your password

Suppose the mass m on the flat, dry, frictionless surface

A First Course in Differential Equations with Modeling Applications | 10th Edition | ISBN: 9781111827052 | Authors: Dennis G. Zill ISBN: 9781111827052 44

Solution for problem 26E Chapter 5.R

A First Course in Differential Equations with Modeling Applications | 10th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
A First Course in Differential Equations with Modeling Applications | 10th Edition | ISBN: 9781111827052 | Authors: Dennis G. Zill

A First Course in Differential Equations with Modeling Applications | 10th Edition

4 5 1 321 Reviews
Problem 26E

Problem 26E

Suppose the mass m on the flat, dry, frictionless surface in Problem 25 is attached to two springs as shown Figure 5.R.4. If the spring constants are  determine a differential equation for the displacement of the freely sliding mass.

Step-by-Step Solution:
Step 1 of 3

Chapter 6 Proteins Overview of Protein - Body is made up of thousands of proteins - Contains nitrogen, carbon, hydrogen, and oxygen - General functions • Regulates and maintains body functions • Provides essential form of nitrogen (in the form of amino acids) Proteins - In the developed world: • Diet is typically rich in protein - In the developing world: • Protein is a deficiency is an issue • Important to focus on protein in diet planning - Aside from water, protein makes up the major part of the lean body tissue - About 17% of body weight Protein Structure - Amino acids are the building blocks of proteins - Amino acids contain nitrogen bonded to carbon • makes them unique from carbohydrates and fats AminoAcids - The proteins in our bodies are made up of 20 different amino acids • 9 are essentials • Some are limiting • 11 are nonessential • New category • Conditionally or acquired indispensable • Infants or disease states AminoAcid Structure - Central carbon - Acid group - Amino group - Side group - Hydrogen - Side group for each different amino acid is different • This gives each amino acid its own characteristics Peptide Bond - Amino acids are connected together by a peptide bond - 2 amino acids-dipeptide, 3 amino acids - tripeptide, etc. - Many amino acids-polypeptide - Some proteins contain multiple polypeptide chains Protein Structure - The sequence of amino acids is called the protein primary structure - Primary structure leads to the protein higher order structure - The higher order structure causes the protein to get into a specific shape (native conformation) - This shape is necessary for the protein to work properly Disruption of Normal Structure - Denaturation • Heat • Strong acids • Bases • Heavy metals - Protein unfolds - Can’t work properly Protein Primary Structure - The protein’s primary structure is determined by the genes (DNA). DNAis kept in the cell’s nucleus - The information of the protein’s primary structure gets transcribed into messenger RNA (mRNA) - mRNAleaves the nucleus and goes to the ribosome (rough ER) where the protein gets translated (made) Protein Synthesis - DNAcontains coded instructions - Copies of codes • transferred to the cytoplasm (via mRNA) - Amino acids added one at a time • With aid of transfer RNA(tRNA) - Requires energy Central Dogma of Biology DNA<> RNA> Protein How to Change Protein Structure - Genetic alterations - Can change the protein’s primary structure - Sometimes this is no big deal - Sometimes it is • It can lead to genetic diseases Sickle CellAnemia - Asingle base substitution • causes one amino acid to be changed in the polypeptide of the hemoglobin protein - Alters the higher order structure of the protein - The protein doesn't work as efficiently - Hemoglobin binds oxygen in red blood cells - With sickle cell anemia, RBC become sickle shapes instead of biconcave Digestion of Proteins - Pre-digestion—cooking • heat denatures proteins, softens food - Digestion begins in stomach 1.Acid (HCL) denatures proteins 2. Pepsin (enzyme) breaks peptide bonds of proteins resulting in protein fragments - Pepsin released by cells in stomach & activates by the acidic environment - What controls pepsin/stomach acid • gastrin: hormone • released in response to think about food, chewing, and digesting food - In the stomach is partially digested protein and other nutrients—chyme - gluten:protein (wheat), makes dough elasticity Movement to SI - Release of CCK (hormone)—chyme stimulates - CCK causes pancreas to release proteolytic enzymes (tripsin,chymotrypsin) - pepsin inactivates (elevated PH) - several peptidases (2-3 amino acid in length) & free amino acids absorbed by active transport - any intracellular peptides digested by enzymes within cells AminoAcidAbsorption - Taken up by capillaries & taken to the liver via the portal vein - liver • amino acids used as building blocks to make liver proteins • broken down for energy • released into blood • converted to nonessential amino acids, glucose/fat Gluten Sensitivity: Celiac Disease - incomplete gluten breakdown in SI leaving small peptides & amino acids - Celiac disease, inflammatory response to small peptides & amino acids - Autoimmune response, genetic predisposition - Prevalence in US is 1 in 133 - In people with related symptoms: 1 in 56 Infant Digestion of Proteins - Up to 4-5 months of age • GI tract is somewhat permeable to small proteins (whole proteins can be absorbed) • If breasted, this allows antibodies to be passed from mother to baby - Recommendation: • waiting until infant is 6-12 mo. old before introducing allergy foods Functions of Proteins in body 1. Producing vital body structures - Body is in a state of constant protein turnover • producing proteins and disassembling proteins - what happens with protein inadequacy • protein production slows down • muscles, blood protein, vital organs decrease in size—brain resists 2. Maintaining Fluid Balance - blood proteins attract fluids - What happens with protein inadequacy • fluid shifts into tissues—edema 3. Contributing to acid-base balance - act as buffers—maintain PH within narrow range • keeps blood slightly alkaline 4. Forming hormones/enzymes - hormones: communicate between cells - enzymes: catalyzes reaction in cells 5. Transport and signaling receptors - Transport: bring nutrients into cells - Signaling receptors: communication in cells 6. Contributing to immune function - antibodies production - What happens with protein inadequacy • decrease in immune function 7. Providing energy - When needed • prolonged exercise • calorie restriction - cells use primarily fats and CHO - Why its efficient • it wastes calories to metabolize amino acids for energy 8. Forming glucose - amino acids can be converted to glucose • when glucose is low - What happens with starvation muscle wasting and edema results from protein breakdown • - glycogenic amino acids - nonessential/essential amino acids 9. Contributing to Satiety - proteins provide highest feeling of satisfaction after eating - may contribute to calorie control during weight loss AminoAcids—fate in cells - breakdown results in release of ammonia Protein Need - If you aren't growing - only need enough protein to replace what they lose daily - What are you replacing - normal protein breakdown (protein turnover) - goal is protein balance Protein RDA - Western Diet—70% of dietary protein typically comes from animal sources - water packed tuna=most nutrient dense - Top 5: beef, poultry, milk, white bread, cheese Problem with Increased Protein Diet - typical source of increased protein diet • animal meat - consequence: • likely to be low in fiber, vitamins, phytochemical • high in saturated fat & cholesterol - Red meat (processed) linked with colon cancer - Increased diet associated with calcium losses in urine - Vegetarian: person who abstains from consumption of meat - Semi-vegetarian: similar to a vegetarian but may consume fish or poultry, or something other than meats - Vegan Vegan Diet - complementary proteins - Nutrient Deficiency concerns • Vitamin B12 • Iron Zinc • • Calcium • Omega 3-fatty acid Alternates to typical Increase protein diet - animal proteins tend to be complete proteins • contains all essential amino acids - plant proteins tend to be incomplete proteins low in one or more essential amino acids • Plant Sources - Nuts: grow on trees - Seeds: vegetables/flowering - Legumes: pods that contain single row of seeds Vegetarian Diets - grains/nuts low in amino acid lycines - veggies/legumes low in methionine - Complimentary proteins—2/more proteins to compensate for deficiencies in essential amino acids content of each protein Complete Plant Protein - quinoa: grain like crop - amaranth: seeds ground into flour, leafy greens - soybeans - buckwheat: not a wheat (rhubarb), grain ground into flour (ex. soba noodles) Protein Consumption - Issues • gluten sensitivity • other Food Protein inAllergies - immune system mistakes food protein for harmful invaders - 8 foods account for 90% of food related allergies; soy, peanuts, tree nuts, wheat, milk, eggs, fish and shellfish - Reactions range from mild to fatal - Introducing allergenic foods early may prevent allergies Protein-Calorie Malnutrition - In the developed world • diet typically rich in world • protein deficiency is issue • important to focus on protein in diet planning - somewhat rare in developed countries • seen in certain populations - In developing countries • stunts growth • increased risk of infection Protein-Energy Malnutrition - Marasmus: starvation/insufficient protein and calorie - Kwashiorkor: marginal amount of calorie and insufficient protein - diseases commonly found inAfrica Protein-Energy Malnutrition in US - Hospital Patients - Long term care residents - community dwelling adults - dialysis patients ALL COMMON: older adults > 65 y/o Chapter 8 Vitamins Vitamins - Definiton: organic substances needed in only small amounts for the proper function of our body • essential • non-caloric • Don’t get energy but work together with enzymes to help use the energy Criteria to be classified as a vitamin - The body is unable to synthesize enough of the compound to maintain health - Absence of the compound from the diet for a defined period produces deficiency symptoms - Can be reversed when the compound is resupplied Vitamin classification - Acompound does not qualify as a vitamin merely because the body can not make it Megadoses of Vitamins - Megadose: • Beyond estimates of needs • Or not in a balanced diet • 2-10 times the normal human needs - Increased risk for toxicity symptoms • Proven useful in treating several non-deficiency diseases Niacin and cholesterol • -Issues with megadoses • Over-supplementation can lead to vitamin levels building up over time • Why Vitamins can be stored within the body • • Which vitamins have the potential for reaching toxic levels Fat soluble vitamins – especially vitaminA Vitamin Preservation - The riper the food the more the vitamins - Vitamins lost from time picked to consumed • Locally grown food is likely to have more vitamins Best to eat as soon as possible after harvest • - Water soluble vitamins destroyed by improper storage or excessive cooking • Heat, light, air, cooking in water, alkalinity - Fresh is better than frozen (as close to harvest date and grown closer to you is even better) How to preserve vitamins in foods - Freezing – best method - Blanching – also works Destroys enzymes that degrade vitamins (heat denatures proteins) • • Put it in boiling water for a few seconds and then freeze ▯ Two classes of vitamins 1. Fat-soluble vitamins –A, D, E, and K - - Absorbed in chylomicrons - Stored in liver and fatty tissue Not readily excreted - 2. Water soluble vitamins – C and B vitamins - Absorbed in capillaries - In general, not stored very well in the body Excess (because it is not stored well) excreted in urine - • If you want to take a lot, then you should space out when you’re taking it VitaminA(Retinoids) and Carotenoids Almost all is stored in the liver - - Deficiency or toxicity can cause severe problems • Narrow range of optimal intake - Retinoids Three active forms of vitaminA(preformed): • - Retinol - Retinal - Retinoic acid Exist only in animal products • - Carotenoids • Contained in plant pigments - Phytochemicals – polyphenols By consuming fruits and vegetables you are getting all of the polyphenols in this large class • - Principle pigments for red, orange, yellow, and green colored fruits and vegetables - Some are precursors to vitaminA • Can be turned into vitaminA: pro-vitamin - Beta-carotene • Carotenoid that can be sufficiently absorbed and converted to retinol • Carrots have a lot of beta-carotene Functions of VitaminAand Carotenoids 1. Health of Epithelial Cells and Immune Function - Maintains health of epithelial cells that line the internal and external surfaces • Lungs, intestines, stomach, vagina, urinary tract, bladder, eyes, and skin - Healthy epithelial tissues serve as important barriers to infection 2. Vision - Night blindness: vitaminAdeficiency disorder that results in loss of ability to see under low-light conditions - VitaminAis important for light-dark vision and color vision • And carotenoids are important for vision • Retina consists of rods and cones • Rods detect black and white, night vision Cones respond for color vision • 3. Carotenoids for Vision - Lutein and zeaxanthin in high concentrations in retina • Found in green leafy vegetables Help prevent macular degeneration • • The central focus of your sight is degenerated so you cannot see the center of what you are looking at • Food sources may help decrease risk of cataracts 4. Cardiovascular Disease Prevention - Carotenoids may decrease risk by preventing oxidation of LDL - Recommendation to consume 5 servings per day of fruits and vegetables 5. Growth, Development, and Reproduction - VitaminAbinds to receptors on DNAto increase synthesis or proteins required for growth - Important for the differentiation and maturation of cells in early fetal growth - Deficiency can cause stunted growth in children 6. Cancer Prevention - Potential benefits but also potential risks • Lower risk of skin, lung, bladder and breast cancers - Megadose supplements pose potential risk for toxicity (enough toxicity can cause cancer) Supplementation not recommended • - Carotenoids • Decrease risk of lung and oral cancers, prostate cancer in men VitaminADeficiency - leading cause of blindness worldwide - eye cells affected • inability to adjust to dim light, causes night blindness - Xerophthalmia: hardening of the cornea, drying of surface of eye and results in blindness. - Risk— NorthAmericans are low risk • TypicalAmerican diet contain preformed VitaminA • Worldwide 1/3 of children suffer - Attempts to reduce problem: 1. Promote breast feeding 2. VitaminAmegadose 2x a year 3. Fortification of sugar/margarine Getting Enough Carotenoids & VitaminA - Preformed VitaminA • Liver, fish oils, fortified milk, butter, yogurt, eggs - Carotenoids • Dark green/yellow-orange veggies • cooking improves bioavailability - RDAexpressed in retinol activity equivalents • Takes into account both preformed and carotenoid sources - typicalAmerican diets sufficient • Supplementation unnecessary for most people Avoiding too much - excess links to birthday defects and liver toxicity • Preformed vitaminA - carotenoids in large amounts do not cause toxic effects • Hypercarotinemia: skin turns yellow orange particularly hands and soles • disappears when intake decreases Vitamin D fat soluble - not just a vitamin but also hormone - Require skin, liver, and kidneys - Body can make vitamin D when exposed to UVB light - Exposure time depends on skin color, age, time of the day, season, location Functions of Vitamin D - helps regulate blood calcium levels and bone metabolism (works with paratynoid hormone) • Helps regulate calcium and phosphorus absorption from intestine • Regulates deposition of calcium in bone • Regulates calcium excretion from kidney - helps in development and can decrease risk of cancer and skin, colon, prostate, ovary, breasts Deficiency of vitamin D - in children causes rickets • Bow legs, and large head, joints, rib cage, deformed pelvis - adults causing Osteomalacia • Softening of bones • Leads to fracture of hips and other bones Vitamin D toxicity - UL-50 micrograms per day - Too much can cause calcium deposits and soft tissues - Can't develop vitamin D toxicity because of too much sunlight Vitamin D foods - fatty fish, fortified milk, yogurt, some breakfast cereal Vitamin E fat soluble - Family of compounds called Tocopherols - Alpha Tocopherol: main form in body - Gamma Tocopherol: foods - Acts as a fat soluble antioxidant - Resides in cell membrane Vitamin E antioxidant rule - oxidizing agent seeking electrons - Example: double bonds of unsaturated fatty acid and phospholipids - Oxidizing agents can create free radicals - As an antioxidant, vitamin E has electrons it can get up as agents - Result: protects compounds of cell (phospholipids) Deficiency of vitamin E - cause cell membrane to break down - Particularly true in RBC, breaking of RBC is called hemolysis • leads to hemolytic anemia - premature infants particularly at risk - smokers Vitamin E toxicity - UL-1000 micrograms per day - Increased doses can interfere with clotting mechanisms and body, leading to hemorrhage - Thus, people at risk are individually taking anticoagulants, high doses of aspirin, or are deficient in vitamin K Vitamin E and foods - plant oils, ready to eat cereals, dry roasted sunflower seeds and almonds, some fruits and vegetables Vitamin K - vital for blood clotting - K in vitamin K comes from danish spelling of coagulation - Vitamin K activates proteins present in bone, muscle, and kidneys to give calcium binding ability to those organs - Poor vitamin K intake is associated with hip fractures in woman - 10% of K is created by bacteria in GI tract - Babies routinely provided with vitamin K supplement at birth to ensure no blood clotting Vitamin K in foods - liver, green leafy foods and vegetables, kale, turnip greens, dark green lettuce, spinach, Brussel sprouts, asparagus, broccoli - oils: soybean, canola Vitamin K toxicity - no risk of toxicity, no upper limit set - Megadoses reduce effectiveness of anti-coagulant meds Water soluble vitamins - vitamin C - B vitamins (function as precursors to enzymes) Thiamin, Riboflavin, Niacin, Biotin, Vitamin B6, Folate, and Vitamin B12 • Vitamin C What is it - compound with antiscorbutic activity Dietary form is ascorbic acid • • similiar structure to glucose • essential - Foods: citrus fruit, green peppers, Brussel sprouts, strawberries, tomatoes, fortified drinks - Stability: rapidly lost by processing and cooking food • It is unstable in the presence of heat, iron, copper, and oxygen Vitamin C Functions - Formation of collagen • Strengthens structural tissues by increasing cross connections between amino acids - Formation of other compounds • Synthesis of carnitine; formation of serotonin and norepinephrine - Antioxidant • Can readily accept or donate electrons B Vitamins - occur in many of same foods - lack of one B vitamin may mean others are also low in diet - B Vitamin deficiency symptoms typically occur in brain, nervous system, skin, and GI tact - Several B Vitamins are in whole grains, but are removed during the milling process - To counter these losses, flour in US in enriched with four B vitamin (thiamin, riboflavin, niacin, folate) Vitamin B6 - Pyridoxine - needed for the activity of many enzymes • CHO, protein, and fat metabolism - particularly important in amino acid metabolism • aids in transferring Nitrogen group • allowing us to make amino acids (nonessential amino acids) - Necessary for the synthesis of neurotransmitters • allows nerve cells to communicate - Important in the synthesis of hemoglobin - Important in the synthesis of WBC - Necessary for conversion of tryptophan to niacin Vitamin B12 - contains mineral cobalt - must bing to intrinsic factor, made by the stomach, in order to be absorbed - defective B12 absorption is common in older people Vitamin B12 in Food - Animal products: meat, milk, poultry, seafood, eggs, ready to eat cereal Vitamin B12 Functions - required to convert folate into active form - maintain the myelin sheaths that insulates neurons • destruction of myelin causes paralysis, and perhaps death Vitamin B12 Deficiency - pernicious anemia— “leading to death - Symptoms: weakness, sore tongue, apathy, tingling in the extremities. - Infants of vegans are at risk Folate - term folate encompasses a variety of forms of vitamin - Folic acid is the synthetic form Folate functions - single carbon supplier/donor - coenzyme helps 1. Form DNA 2. metabolize various amino acids and their derivatives Folate Deficiency - bone marrow produces immature RBC (megaloblasts • megaloblastic anemia - Symptoms • inflamed tongue • mental confusion • depression • problem with nerves - 10% of population has genetic defects in metabolism of folate • as a result they need up to 2x the RDAto compensate - this defect, along with maternal folate deficiency has been linked to neural tube defects in the fetus Neural Tube Defects - affects about 2000 infants a year in the US - Spini bifia to anencephaly - Neural tube closes within first 28 days of pregnancy • a time when many women are not even aware they are pregnant - it is crucial for all women of child bearing age to have an adequate intake of folate Folate in Food - RDA400 micrograms per day - pregnant RDA600 micrograms per day - name folate comes from foliage - green leafy veggies, organic meats, sprouts, other veggies, dried beans, and orange juice - susceptible to destruction by heat Thiamin (B1) - helps release energy from CHO and amino acids - Beriber “I cant, I cant” - related to nervous system Thiamin in foods - no Upper limit - pork products, whole grains, ready to eat cereals, and enriched grains Riboflavin (B2) and Niacin (B3) - both did in energy in metabolism - coenzyme - Riboflavin: flavin adenine dinucleotide - Niacin: nicotinamide adenine dinucleotide Pantothenic acid - energy in metabolism - coenzymes—coenzymeA - deficiency among healthy people who eat varied diet (pan=“all”) Chapter 9 Water and Minerals Water - Life cannot exist without water - Water is the solvent for the chemicals in body, allowing chemical reactions to take place - Makes up 50 to 70% of body's weight - Cannot survive long without water Fluid compartments - intracellular: water inside - Extracellular: water outside of cell - Water can move, diffuse, between compartments Control - ions control movement of water between the intracellular and extracellular compartment - Ions are minerals with an electrical charge also called electrolytes - Movement of water across a semipermeable membrane is called Osmosis Functions - solvent for chemicals and body, alas chemical reactions to take place - Contributes to body temperature regulation, sweat - Helps remove waste products Waste dissolves in water - • cushions and lubricates • Knees, joints, saliva, bile The water balancing act - water is not stored - Precisely regulated by nervous, endocrine, digestive, and urinary system If we don't get enough water - 1 to 2% loss—thirst mechanism occurs how does water converse water - Antidiuretic hormone (ADH) • Released by pituitary • Communicates with kidney to conserve water Aldersterone • • Released form adrenal gland when blood volume decreases • Communicates with kidney to conserve water • Causes salt to be taken up What if thirst is ignored - 4% loss: muscles his strength and endurance - 10 to 12% loss: heat tolerance is decreased - 20% loss: coma and perhaps that Can thirst be ignored - yes - Athletes – weigh before and after - Sick children - older people - Infants Can you consume too much water - too much in a short period time leads to water intoxication or poisoning - Dilute sodium levels: hyponatremia levels of sodium - Symptoms: nausea, mental confusion, vomiting, headache, muscle weakness, convulsions Minerals - major minerals > 100 milligrams per day - Trace minerals < 100 milligrams per day Bioavailability of minerals - bioavailability : how much we take in • Depends on how much is in the food and our ability to absorb it - so, amount in food doesn't generally reflect the bio availability - Minerals from plants • Depends on the soil is grown in • May be bound by dietary fibers and other molecules - minerals from animal sources • Are not as dependent on soil condition • Absorbed better than plant sources fewer binders and dietary fibers • - mineral binders • Oxalates (spinach): binds calcium • Phytate's (grains): binds calcium, iron, zinc and others • Mineral – mineral interactions • Calcium – iron; zinc – copper • Vitamin – mineral interaction • Vitamin C improves iron absorption • Vitamin D improves calcium absorption Mineral Toxicity - minerals can be toxic and high levels, especially trace minerals - not a problem when food is the source, but can be from mineral supplements Major minerals - calcium, phosphorus, potassium - Silver, sodium, chloride, magnesium Calcium (Ca) - most abundant mineral in body - 99% of body calcium in bone • Integral part of bone structure • Storehouse for calcium in blood - adults absorb 25% of the calcium in foods eaten - Increase in infants and during pregnancy (up to 60%) Serum calcium (functions) - regulates transport of ions across cell's membrane (important nerve transmission) - Helps maintain blood pressure - Essential for muscle contractions - Essential for secretion of hormones, enzymes, neurotransmitters - Essential for a blood clotting Positive health benefits Positive links between calcium and tank and risks of: - certain cancers and kidney stones - Hypertension, high blood cholesterol, and obesity Osteoporisis - decreased bone mass related to aging, genetic background, and poor diet - Leads to 1.5 million bone fractures per year in the US - Not just women - Characterized by: Loss of height • • Pain • Kypnosis (hunched over) - bones become brittle Bone density - reaches peek in twenties - Levels off in 30s - Lose after 40 - ** need to build about density when you were young** - How to maintain adequate bone density: 1. adequate amount of calcium and vitamin D in your diet 2. exercise 3. estrogen Calcium in foods - AI 1000-1200 mg per day - Foods: • Dairy (milk, cheese, yogurt) • breads, rolls • Green leafy vegetables, kale, collard, turnips, mustard greens - Calcium fortified products - Supplements calcium based antacids - UL 2500 mg per day (risk of kidney stones) Sodium (Na) - absorb about 100% of sodium consumed - 30 to 40% found in bone - The major positive ion found in extracellular fluid - Functions: fluid balance between compartments, nerve impulse conduction, absorption of glucose Sodium deficiency - rare – excessive perspiration, persistent vomiting, diarrhea. It leads to muscle cramps, nausea, vomiting, dizziness, coma Sodium sensitivity - for most people body will adjust to increased sodium intake by increasing urine output - 10 to 15% of adults are sodium sensitive • Sodium intake leads to increased blood pressure - UL 2300 mg per day Chloride (Cl) - ion of chlorine - Major negative ion for extracellular fluid - used in producing stomach acid and during immune response of white blood cells Potassium (K) - Major positive ion in intracellular fluid compartment 95% of bodies potassium - Like sodium, potassium is important in fluid balance and nerve impulse transmission - Unlike sodium, increased potassium intake is associated with lower blood pressure - Increased risk of deficiency – people on diuretics to treated high blood pressure, alcoholics, eating disorders - Can lead to heart failure - Too much – due to kidney failure, can stop heart Potassium in foods - AI 4700 mg per day - Foods: • Unprocessed foods good source • Rich: potatoes, plums, avocados, bananas, cantaloupe, honeydew melon, raisins • greens Trace Minerals - Iron, Zinc, Selenium, Iodine, Copper, Chromium, Fluoride, Chromium, etc. Iron (Fe) - in every cell of body - Absorb about 18% of that present in food - Most iron associated with hemoglobin (red blood cells) and myoglobin (muscle) – heme iron - Other types called nonheme iron - When red blood cells die, iron recycled, so we lose very little except during bleeding Iron absorption - heme iron more readily absorbed the nonheme iron - Vitamin C 75 mg – enhances absorption of nonheme - Tannins in tea and phytates in grain inhibit iron absorption Iron in foods—heme vs. non-heme - Heme: meat, poultry, shellfish - Non-heme: nuts, eggs, beans, breads, leafy veggies, chocolate Iron Deficiency - Anemia: decreased oxygen carrying capacity of the blood • Lower number of RBCs • Less oxygen to cells 30% of the world population • • 1/2 of which is due to low iron - Neurological dysfunction called Pica • eating weird things (ice, clay, paste, dirt) Anemia Low iron associatedAnemia: - impaired physical and mental activity • fatigue, loss of appetite • decreased learning ability • decreased attention span Iron Toxicity - Hemochromatosis - Genetic disease associated with increase iron absorption - Iron builds up in the liver and blood - If not treated will lead to organ damage, especially in the liver and heart. Avoiding to much Iron - UL 45 mg/day - stomach irritation, toxicity can be life threatening Zinc (Zn) - About 40% of dietary Zn is absorbed - Zinc is a cofactor for up to 200 different enzymes Functions: - growth, wound healing - sexual maturity - taste perception - immune system, indirect antioxidant Zinc-sources - oysters, beefs, seafood in general - high protein diets, rich in animal sources, are high in zinc Zinc deficiency - first recognized in the 1960s in boys from the middle east - diet low in animal protein, exclusive use of unleavened bread Symptoms: - acne-like rash, diarrhea, lack of appetite - delayed wound healing, impaired immunity - reduced sense of taste and smell, hair loss Getting Enough Zinc - RDAmen: 11mg, women: 8mg • Average NorthAmericans consume 10-14 mg/day - Absorption depends on body needs • Phytic acids binds to zinc and limits availability • High calcium intake decreases zinc absorption • Zinc competes with copper and iron for absorption Avoiding Too much Zinc - UL 40 mg • Excess interfered with copper metabolism • Toxicity can occur from supplementation or overconsumption of zinc-fortified foods • Intake >100mg results in diarrhea, cramps, nausea, vomiting, loss of appetite Selenium (Se) - Indirect antioxidant, works with Vitamin E to help protect cell membranes from oxidizing agents - Binds to enzymes—protects against oxidation - May have anticancer properties Selenium Deficiency - found in some areas of china - People developed characteristic muscle and heart problems associated with inadequate selenium intake Selenium Sources - Se in soil (upper midwest) Selenium in foods - RDA55 micrograms/day - UL 400 micrograms/day (hair loss) Foods: - fish, eggs, shellfish, grains and seed grown in soils contain selenium Iodide (I) - Ion of iodide - used in the production of thyroid hormone - Thyroid hormone helps regulate metabolic rate, and promotes growth and development Iodide deficiency - Deficiency: cells of thyroid enlarge in attempt to trap more iodine (goiter). - People are sluggish and gain weight - During pregnancy, deficiency can cause extreme and irreversible mental and physical retardation of developing baby (cretinism) • Can be reversed if corrected within first 6 months of pregnancy Getting enough Iodide - RDAand DV 150 micrograms • 1/2 teaspoon of iodide-fortified salt supplies this amount - amount NorthAmericans consume more than RDA • Iodized salt, dairy products, grain products • sea salt and kosher salt not iodized Avoiding Too much Iodide - UL 1.1 milligrams • High amounts can inhibits thyroid hormone synthesis • may appear in individuals consuming a lot of seaweed Copper (Cu) - 12-75% is absorbed - involved in: 1. the metabolism of iron by functioning in the formation of hemoglobin and transport of iron 2. the formation of connective tissue 3. is a cofactor for antioxidant enzymes Getting Enough copper - Sources include: liver, legumes, seeds, whole grain breads and cereals, cocoa • Form found in supplements not readily absorbed - Absorption highly variable • Higher intakes associated with lower absorption efficiency • Phytates, fiber, excess zinc and iron supplements interfere with absorption -Average Intake: 1 mg women, 1.6 mg men Avoiding too much Coppers - Single dose >10 mg can cause toxicity • symptoms: Gi distress, vomiting blood, tarry feces, damage to liver and kidneys • Toxicity cannot occur with food, only supplements - Wilsons disease • a genetic disorder that results in accumulation of copper in tissues • characterized by damage to the liver, nervous system, and other organs PUB QUIZ 1. What is the central dogma of biology DNA-RNA-Protein 2. What is pepsin where and how activated an enzyme in the stomach and is activated by HCL and gastrin, splits proteinT 3. Where does the digestion of proteins begin Full digestion begins in stomach 4. What makes proteins unique from carbs and fats presence of Nitrogen 5. Trueor False.Asingle amino acid change in the protein hemoglobin is responsible for the diseases sickle cell anemia. 6. Name two ways proteins can be denatured. Heat and pH 7. How do proteins contribute to immune functions They act as antibodies 8. What is different about protein absorption in infants Mother passes on immunity from breast feeding, and the stomach is permeable so it can absorb the whole protein (antibodies) 9. Amino acids are taken up by capillaries and transported to which organ Liver by the portal vein 10. True or False. Proteins are the most efficient source of fuel. 11. How does the body get rid of the nitrogen waste via urea, processed out through the kidneys and passes through the urine 12. What are some uses with a high and low protein consumption High: eating a lot of meat and getting saturated fats, Low: deficiency 13. Methionine is limiting in which foods Lysine is limiting in which foods 14. Which vitamin plays an important role in clotting Vitamin K 15. What vitamins are mostly coenzymes B Vitamins 16. Name one water soluble and one fat soluble vitamin that has antioxidant properties Fat: E, Water: C 17. What is the typical amount of calories found in vitamins zero, noncaloric 18. True or False. Fat soluble vitamins are more susceptible to breakdown (between harvesting and eating). 19. What vitamin requires the skin, liver, and kidney to be functional Vitamin D 20. Are carotenoids a performed VitaminAor the provitamin form Provitamin 21. Trueor False. The heyday for discovery of vitamins was over 50 years ago. 22. Which B vitamins are added to refined flour Why 23. Where are fat soluble vitamins primarily stored adipose tissue, liver 24. The RDAand DV for vitamins is typically in the range of MILLIGRAMS. 25. What is the main form of Vitamin E in the body Tocopherols

Step 2 of 3

Chapter 5.R, Problem 26E is Solved
Step 3 of 3

Textbook: A First Course in Differential Equations with Modeling Applications
Edition: 10
Author: Dennis G. Zill
ISBN: 9781111827052

The answer to “Suppose the mass m on the flat, dry, frictionless surface in is attached to two springs as shown Figure 5.R.4. If the spring constants are determine a differential equation for the displacement of the freely sliding mass.” is broken down into a number of easy to follow steps, and 37 words. The full step-by-step solution to problem: 26E from chapter: 5.R was answered by , our top Calculus solution expert on 07/17/17, 09:41AM. A First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052. This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. Since the solution to 26E from 5.R chapter was answered, more than 283 students have viewed the full step-by-step answer. This full solution covers the following key subjects: mass, freely, determine, Differential, displacement. This expansive textbook survival guide covers 109 chapters, and 4053 solutions.

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Suppose the mass m on the flat, dry, frictionless surface