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The Cambridge Diet supplies .8 g of calcium per day, in

Linear Algebra and Its Applications | 4th Edition | ISBN: 9780321385178 | Authors: David C. Lay ISBN: 9780321385178 62

Solution for problem 4E Chapter 1.10

Linear Algebra and Its Applications | 4th Edition

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Linear Algebra and Its Applications | 4th Edition | ISBN: 9780321385178 | Authors: David C. Lay

Linear Algebra and Its Applications | 4th Edition

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Problem 4E

Problem 4E

The Cambridge Diet supplies .8 g of calcium per day, in addition to the nutrients listed in the Table 1 for Example 1. The amounts of calcium per unit (100 g) supplied by the three ingredients in the Cambridge Diet are as follows: 1.26 g from nonfat milk, .19 g from soy flour, and .8 g from whey. Another ingredient in the diet mixture is isolated soy protein, which provides the following nutrients in each unit: 80 g of protein, 0 g of carbohydrate, 3.4 g of fat, and .18 g of calcium.

a. Set up a matrix equation whose solution determines the amounts of nonfat milk, soy flour, whey, and isolated soy protein necessary to supply the precise amounts of protein, carbohydrate, fat, and calcium in the Cambridge Diet. State what the variables in the equation represent.

b. [M] Solve the equation in (a) and discuss your answer.

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Geo 101 – The Dynamic Earth Exam 4 Study Guide THIS IS NOT ALL INCLUSIVE – especially if you don’t fill it out fully.  What are the types of fossilization that we covered and how do they work o Frozen or Dried o Amber or Tar  Sticky sap on a tree, tar is when oil has seeped to the surface looking like a drinking hole o Preserved or replaced o Permineralization o Carbonization o Molds and Casts (Replica or original) o Trace Fossils o Extraordinary fossils (DNA)  What are evolution and natural selection o Evolution  Both fact and theory  Change in a population over a succession of generations, due to the transfer of inheritable characteristics o Natural Selection  Is theory that explains fact  Organisms are different  Same differences are advantages  More advantages = more offspring  Population of organisms are always changing to adapt to their environment  What are some the many pieces of evidence that help us understand how organisms evolve o Anatomy­ skeletons, teeth, anything left behind  Fossils  Modern o Vestigial organ  Organ that no longer functions in the same way that it did o Embryology  Way bone develops o Genetics  PNAS  Phylogenic relationships among the major cetartiodactly subgroups o Biogeography o Homology  The sameness  How anatomy looks the same in different creatures  What causes extinction o Climate change o Tectonic activity  Causes sea level to rise  Habitat changes o Asteroid or comet impact o New Predators  You must know the definitions of the relative dating techniques we covered in class and be able to use them like we did during the class activity. o Original Horizontality  How sediment is deposited  Fairly horizontal o Superposition  Applies to  Sedimentary only  Undeformed  Older on bottom  Can get tricky o Lateral Continuity  Sediments are deposited in continuous layers  Can be distributed later o Cross cutting relationships  Formations in relation to each other  Baked contact  Inclusions  What do unconformities tell us o Abrupt transitions in a stratigraphic column  Missing time  Non deposition  Erosion  How do geologists use fossils for dating o Principle of Fossil Succession  Fossils are found in limited strata  Found in a definable order (amphibians, mammals, etc.)  Don’t reappear o How we use fossil  Index fossils Trilobites  Well dated  Widespread  Short lived  How was the geologic column created o Represents entire Earths History o Graphic representation of the layers of rock that make up the earths crust o Divided into segments each of which represents a specific time interval  How does a radioactive isotope give us a numerical age o Decay and Half Life  Unstable atoms eject particles predictably  Become more stable atom (14C – 14 N)  Parent isotope  Daughter Isotope o Half Life  Time it takes for half of the population to decay  Cannot predict when single atom will decay  What characteristics does an object need in order to be dated with radio­isotopes o Carbon dating  What can be dated with radioactive methods  What other methods can you use to determine a numerical age o Igeneous rocks o Metamorphic  Sometimes, depends on temperature and mineral type  What did we date to determine the age of the earth o 4.5 Billion Years old  Know the major events in each eon or era that we covered in class: names of supercontinents, big geological events, types of life that first appeared. (Use the handouts – they will make studying so much easier!!) Hadean Eon ­ 4.55 Ga formation of Earth ­ 4.5 Ga differentiation o Dense materials sink ­ 4.5 Ga formation of moon ­ Before 4.4 Ga o Molten tock surface o Non oxygen atmosphere o No water ­ After 4.4 Ga (Australian zircon) o Maybe solid rock o Non oxygen atmosphere o Some water ­ 4 Ga Meteor o Destroyed existing surface o Surface reformed  small volcanic islands ­ End of Hadean Eon o No life o Very little land o Acidic ocean not made out of water Archean ­ Paleogeography o 80% of continental area ­ Seas and Atmosphere o Liquid water to create seas o Not much oxygen in atmosphere ­ First Life o Earliest fossil  3.5 Ga  Single cell  Carbon isotopes  Stromatolites  Algae mats  Photosynthesis (creates oxygen)  2.95 Ga  Helped increase oxygen Proterozoic Eon Start Paleography ­ 90% of continental crust that we have today ­ This is growing throughout the entire eon Supercontinents ­ Large land masses­ nearly all continents ­ Constant splitting and reassembling ­ Profound affect on climate Rodinia – first supercontinent Pannotia­ reverse of rodinia Atmosphere ­ Amount of oxygen increases so much ­ Algae is causing the leap of oxygen ­ How do we know this o BIF­ bandit iron formation  Cannot form unless a certain amount of oxygen is in the air o This changes chemistry of ocean Life ­ Eukaryotic evidence = 2.7 Ga ­ First fossils from 2.1 Ga ­ Symbiotic relationship Life Plants ­ Ocean – algae ­ Land­ algae o Fungi fossil­ 650 to 544 Ma o Molecular clock= 1.3 Ga Ediacaran Fauna – soft bodied – very unlikely we have the fossils for them ­ 565 Ma (million years) ­ Worms, jellyfish ­ No shells ­ Underwater Soft bodied fossils Snowball Earth – glaciers everywhere ­ Glaciers on land ­ Possible frozen ocean ­ Mass extinction ends eon End of the Proterozoic o Paleozoic Era  Early o Break Up of Pannotia o Epic Continental seas o Taconic Orogeny o New England o Ends in glaciation  Life o Cambrian Explosion  Massive diversification of life  Plants o Ocean  Algae  Seaweed o Land  Simple Fungi  Algae  Liverwort  Animal o Diverse shelled animals o Triobites o Sponges o Corals o Echinoderms o First Vertebrate  Jawless Fish  Middle  Paleogeography o Climate warmed and sea level rose  Reefs o Progenies  Plants o Vascular plants  Woody tissue, seeds, veins  Could grow larger o Large swampy forests (mosses and ferns)  Animals o Diverse shelled animals o Fish: Jawed, lobe fin, ray fin o Spiders and insects o 1 amphibians  Tiktaalik o Cross between fish and tetrapod o Fish  Fins  Scales  Gills o Tetrapod­ anything that has these four appendages  Flat head  Ribs  Neck  Fins support weight  Late  Paleogeography o Global cooling  Sea level drop o Pangaea forms o Alleghanian Orogeny  Appalachians  Ancestral Rockies  Plants o Gymnosperms  Conifer  Cycads (palm like)  Ginkgo  Animals o Amphibians Diversify st o 1 reptiles  eggs with shells  End  Giant extinction event at 248 million o 96% of marine species o 70% of terrestrial species o largest in history Mesozoic Early Paleography  Break up of Pangaea  North Atlantic Ocean  Inland seas Plants  Gymnosperms diversify Animals  1 swimming and flying reptiles  1 turtles  Coral Dinosaurs!  Warm­blooded  Huge sauropods  Feathered birds­ last dinosaurs Mammals  Very small  Not like modern Late Paleography  Pangaea broken o India  Warming and sea level rise o Inland seas  Laramide orogeny Plants  1 flowering plants  Flowering plants and hardwoods take over Animals  Modern fish  Dinosaurs diversify  Mammals diversify End of Mesozoic  K­T boundary extinction event o Meteor o Dinosaurs (except birds) o 75% plant life Cenozoic Paleogeography  Himalaya formation  Atlantic and Pacific separated Climate  Cooler climate o Grasslands  Ice age: o Creates land bridge Plants  Flowering plants and gymnosperms diversify st  1 grasses Animals  Mammals diversify and flourished o Giant mammals at first  What is the extremely general history of human evolution (What did the graph on the slide look like)  How do the various fossil fuels form o Sun  Solar energy  Plant Matter  Fossil Fuel  Wind o Gravity  Tides  Falling Water o Chemical Reactions o Nuclear Fission o Geothermal – happens in the center of the Earth o Oil and Natural Gas  Hydrocarbon compounds  Remains of marine algae and plankton  In what geological formations do different fossil fuels get trapped o Anticline o Fault o Salt Dome o Stratigraphic  What methods do we use to extract fossil fuels o Tar Sands  Viscious oil in sand  Cannot Pump  Mined then heated  Heated then pumped  Very expensive o Oil Shale  Has not reached oil window  Mined then heated  Very expensive o Fracking  Hydraulic Fracturing  Extracting natural gas  Increases well production  Drawbacks  Groundwater contamination  Land use issues o Extracting Oil and Natural Gas  Drilling  Puncture the seal rock  Pumping  Brings oil to the surface o Refining Oil  Crude oil is distilled  Process depends on grade  Sulfur content  Specific gravity  Are we running out of oil What are the various answers to this question o Other sources exist  Liquidfied coal  Oil shade  Tar Sands  Methane hydrate o Not economically viable at current prices and technology o Will we run out  Geologists  Soon  Economists  Will stop using it first  What are the drawbacks of fossil fuel use o Air Pollutions  Particles and gases  Acid Rain o Carbon Dioxide  Greenhouse gas o Byproducts  Mine runoff o Spills  Groundwater  Ocean o Fatalities in mines  A lot  What are the types of alternative energy we covered What are their advantages and drawbacks o Nuclear Power  Energy release when nucleus is split (fission)  Drawback  Controlling nuclear reactions o Lot of work and planning o Potential meltdown  Nuclear waste  Damaging to living organisms  Long time decay (decades­ centuries) o Wind  Must have steady breeze  Clean  Drawback  Noisy  Ugly  Hazard to Wildlife o Solar  Sunlight converted to electricity  Clean  Drawbacks  Not efficient  Not cost effective o Hydroelectric  Two Kinds  River o No pollutants o Drawbacks  Damns  Tidal o No pollutants o Drawbacks  Construction o Geothermal  Use the earths eternal heat where it come near the surface  Used in two ways  Water  Steam to turn turbines  Drawbacks  Conditions limited Extra office hours for exam prep: Monday, April 11 from 12:00­2:00pm (if these don’t work, email for an appointment)

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Chapter 1.10, Problem 4E is Solved
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Textbook: Linear Algebra and Its Applications
Edition: 4
Author: David C. Lay
ISBN: 9780321385178

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The Cambridge Diet supplies .8 g of calcium per day, in