# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

2 Pages

### team hw 10HW12#44

Course: MATH 115, Fall 2006
School: Michigan
Rating:

Word Count: 527

#### Document Preview

4 Chapter Review #44 (a) The mouse changes direction at approximately t=17, 23, 27. To determine this, we look at where the graph changes from positive to negative, or vice versa. At t=17, the graph goes from positive to negative, or in terms of position, the mouse changes from moving right to moving left. At t=23, the mouse changes from moving left to moving right, and at t=27, the mouse changes from moving...

Register Now

#### Unformatted Document Excerpt

Coursehero >> Michigan >> Michigan >> MATH 115

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
4 Chapter Review #44 (a) The mouse changes direction at approximately t=17, 23, 27. To determine this, we look at where the graph changes from positive to negative, or vice versa. At t=17, the graph goes from positive to negative, or in terms of position, the mouse changes from moving right to moving left. At t=23, the mouse changes from moving left to moving right, and at t=27, the mouse changes from moving right to moving left. (b) The mouse is moving most rapidly to the right where there is a maximum on the graph, so at approximately t=10. He is moving most rapidly to the left where there is a minimum, so around t=40. (c) From looking at the graph, we can determine when the mouse is farthest to the right of center where the area under the curve is the greatest positive value. In this case the greatest area under the curve is found on the interval (0,17), so the greatest area occurs when t=17. Therefore at t=17, the mouse is the farthest to the right of center. To find the time at which the mouse is farthest to the left of center, we must find where the greatest negative area under the curve occurs. Since this is found on the interval (27,40), the greatest area occurs at t=40, which means mouse is farthest to the left of center at t=40. (d) (10,17), (20,23), (24,27) ??? (e) To estimate where the mouse is at the center of the tunnel, we had to find the area under the curve to determine at what time the mouse's displacement was zero. We started by taking the left and right approximations at n=2.5 intervals. At each interval, we averaged the right and left value. We then added them together and multiplied our sum by our interval 2.5 to yield an of answer -138.75. We then worked backwards, adding the intervals back to find an estimate what values of t a displacement of 0 fell between. At t=35, the displacement was 1.25 and at t=37.5, it equaled -67.5. From this we could determine that was in this interval, but closer to 35. So we narrowed our interval in increments, by cutting each interval and each approximation in half, until we reached a very small interval of (35.078125, 35.0390625). Table of Values! t (in seconds) 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25 approximation 3.5 10 15.5 19 19 14 1.5 -13.5 -13.5 0 27.5 30 32.5 35 37.5 40 2 -10 -21 -26 -27.5 -28.5 If the displacement (area under the curve) at t=35 is 1.25, we needed a smaller interval to give us an area closer to 0. We did this by added smaller and smaller rectangles to 1.25 to narrow it down substantially. We took smaller increments, starting at t=35.625 which we determined to have an average approximation of -27.5. We then added 1.25 and .625(-27.5) to get a total area under the curve of -15.93. From this we repeatedly divided the number after the decimal by 2. So t=35.3125, 35.15625 and so on and did the same to -27.5 to yield -27.125, -27.0625, etc. We finally narrowed down our interval to 35.0390625<t<35.078125. At t=35.625~ -27.5 1.25 + (.625)(-27.5)~ -15.93 At t=35.3125~ -27.125 1.25 + (.3125)(-27.125)~ -7.22 At t=35.15625~ -27.0625 1.25 + (.15625)(-27.0625)~ -2.97 At t=35.078125~ -27.03125 1.25 + (.078125)( -27.03125)~ -.86182 At t=35.0390625~ -27.015625 1.25 + (.0390625)( -27.015625)~ .193 (getting closer...) So, the area under the curve is zero somewhere on the interval of 35.0390625<t<35.078125.
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Michigan - SPANISH - 275
Espaol 275Silabeo: Ejercicio 1Dividir las palabras a continuacin en slabas. 1. p r e o c u p a d o 2. p a d r e 3. c a r r o 4. e m p e z a r 5. t o 6. s i g l o 7. c o m b i n a c i n 8. e s t e r e o t i p o 9. a p r o p i a d o 10. c a r a c
Michigan - SPANISH - 275
1 SER/ESTAR- Dilemas Escoja entre ser y estar y conjugue el verbo. 1. Yo (1) soy aficionado a la msica clsica. (2) Estoy muy contento porquetengo dos entradas para un concierto de la orquesta sinfnica de la universidad. (3) _Estoy loco por verla.!
Michigan - BIOMEDE - 221
1 Christie Donahue 92337669 Homework #1 September 19, 2007 1. Review Lecture 01 &quot;Motivation / Biomimetics&quot;, available in the folder &quot;Resources&quot; on Ctools This lecture was intriguing and provoked a new interest in the subject of biomimetics. Prior to
Michigan - BIOMEDE - 221
Christie Donahue 92337669 Homework #2 September 26, 20071) 1.11 A sample of methane of mass 4.5 g (4.5g(1mol/16.04g)=.2804mol) occupies 12.7 L at 310K. a) Calculate work done when the gas expands isothermally (delta T=0) against a constant external
Michigan - BIOMEDE - 221
BME 221 Homework #3, Sept 20, 20071) Read pages 49-72 in the Atkins DePaula book 2) Answer the following problems from Atkins, DePaula: 1.26 3) 4) 5) 6) 7) 1.27 1.30 1.31 1.34 1.368) You have been asked to investigate the thermodynamic properties
E. Michigan - ASTRO - 205
Ben Milkovich Astronomy 205 Feb 19 2008 Radiation 2) Define each of these Period this is the time it takes for an entire wave to pass by an area. An entire wave consists of one trough and one crest, usually measured from trough to trough, or crest t
E. Michigan - ASTRO - 205
Ben Milkovich Astro 205 Joe Lowry 4) Asteroid of Pd = 2.0 AU and Ad = 4.0 Au. Find (A)semimajor axis, (B)eccentricity, and (C)period. 2.0 AU 4.0 AU (a) 3.0 AU = semimaor axis 2 Pd a 2 3 1 (b)Pd = a(1 e) e eccentricity a 3 3 (c) P 2a3 P a3 27 years =
E. Michigan - HIST - 103
Ben Milkovich History 103 1-30-08 Project #1 WrightIn my opinion the passage about the Wright brothers' first recorded flight was very interesting. At first this descriptive article seemed to go nowhere other than a descriptive article. It wasn't u
E. Michigan - HIST - 103
Reading 13.1, Chamberlain is clearly worried about entering a war to protect another nation. I feel seeing what happened to his native country entering world war one to protect France, and living with the repercussions of it, chamberlain did not want
Rochester College - ESSC - 104
Ben Milkovich Instruments 1-a 2-a 3-a Ground Deformations 1-c 2-c 3-c Earthquakes 1-a 2-b 3-b
Michigan - PHYSICS - 260
Quiz #5(Turn in on Monday)260-F07Name_We have seen that when a dielectric is inserted into a parallel plate capacitor it is sucked into the gap if the capacitor has first been disconnected from the battery that charged it. The energy U stored
Michigan - PHYSICS - 260
P260 F07Quiz # 6NAME_More on the velocity selector. Suppose we have set up the crossed E and B fields throughout a region E of space so that v , where v is the velocity of a + charged particle projected to the right and B moving perpendicular t
Michigan - PHYSICS - 260
P260 F07Quiz #7Name_A bit more on Potential Theory. We saw for electrostatics that, in the spirit of Helmholtz's theorem (a vector field is completely specified by its divergence and curl), E and E 0. The zero-curl equation is important in
Wyoming - FIN - 4900
ADDITIONAL RECIPES AND FORMULAS FOR EXAM 2Short-cuts for Cobb-Douglas production functions q = AL K Average product of labor: APL = AK L1- since APL = q AL K AK = = 1- L L LAverage product of capital: APK = AL K 1- since APK = q AL K AL = =
Grand Valley State - BUS - 101
Binford Career Exploration Assignment #1 Job: Advertisement Team President for America's Dairy Farmer The job that I decided to explore is one of great importance. We have all seen those milk advertisements everywhere. They read &quot;Got Milk?' on them,
Grand Valley State - BUS - 101
Career: Website Designer and Manager The job I chose to look at is a Website designer and manager and their job is very important to the Internet industry. The Internet is the fastest growing zone for consumers in this modern age and more and more we
Grand Valley State - BUS - 101
BUS 1012/14/07Kyle BinfordCareer Exploration The job I chose to do is an advertising &amp; marketing research director and there are so many job openings for this position in the US right now. The A&amp;M Research Director has many responsibilities tha
Grand Valley State - BUS - 101
Career Exploration: Financial Advisor Everyday more and more business are losing money and losing customers due to poor choices in their financial decisions. That is where a good financial advisor comes into play. Their job is basically to analyze an
Michigan State University - GLG - 201
Chapter 1: An Introduction to GeologyGeology: science that pursues an understanding of planet Earth A) Physical geology: the materials composing earth and seeks to understand the processes that operate beneath and upon its surface B) Historical geol
Michigan State University - GLG - 201
Chapter 22: Planetary GeologyTwo types of planets: A) Terrestrial planets (Earth-like): Mercury, Venus, Earth, Mars 1) Called the inner planets 2) Densities are 5x greater than water a) Consists mostly of rocky and metallic substances b) Minor amoun
Michigan State University - GLG - 201
Chapter 2: Plate TectonicsContinental drift: A) Pangaea: single supercontinent once existed B) Began to fragment into smaller continents which gradually &quot;drifted&quot; to their current positions C) Evidence: 1) Fit of South America and Africa a) Not perf
Michigan State University - GLG - 201
Chapter 5: Volcanoes and Other Igneous ActivityVolcanoes can either extrude magma violently or gently A) depending on: 1) Composition 2) Temperature 3) Amount of dissolved gases B) All factors influence viscosity (magma's mobility) 1) More viscous=g
Michigan State University - GLG - 201
Chapter 6: Weathering and SoilExternal processes: occur at or near earth's surface and are powered by Sun's energy A) Responsible for transforming solid rock into sediment B) Include: 1) Weathering: physical breakdown and chemical alteration of a ro
Michigan State University - GLG - 201
Chapter 7: Sedimentary RocksSedimentary rocks: made of sediments that are from weathering A) Constituent 5% by volume of earth's outer 16km B) At the surface about 75% is sedimentary rocks C) Comprises a relatively thin and discontinuous layer in up
Michigan State University - MATH - 202
Definitions Collinear: three points that all lie on a single line Rotation of rays: the collection of all possible rays emanating from a single point Midpoint: divides the line segment into two equal parts Complementary: the sum of two angles is
Michigan State University - STT - 200
Frequency table: class width=(highest value)-(lowest value)/# of classes Scattergram: direction, form, strength, unusual features Mode The value that occurs most frequently or the frequency class with the highest frequency. A data set may be unimodal
Michigan State University - GEO - 203
Chapter Two-Energy: Warming the Earth and the AtmosphereEnergy: ability or capacity to do work on some form of matter A) Terms: 1) Matter: anything that has mass and occupies space 2) Work is done on matter when matter is either pushed, pulled, or l
Michigan State University - GEO - 203
Chapter 8: PrecipitationI) Cloud droplets grow larger A) Ordinary cloud droplet has a diameter of 20m 1) 100x smaller than a typical raindrop 2) When in equilibrium size of droplet does not change a) Total number of vapor molecules around the drople
Michigan State University - GEO - 203
Chapter Eleven: Wind-Global SystemsI) General circulation of the atmosphere: when winds throughout the world are averaged for a long period and local wind patterns diminish A) Underlying cause is unequal heating of the earth's surface B) Energy bala
Michigan State University - GEO - 203
Chapter 5: Atmospheric MoistureWater is only compound that occurs naturally as a solid, liquid, and gas A) Gas: it moves freely, mixing well with neighboring atoms and molecules 1) When neighboring molecules of oxygen and nitrogen collide they bounc
Michigan State University - GEO - 203
Chapter 9: The Atmosphere in MotionI) Air pressure: mass of air above a given level A) Always decreases with increasing height 1) Most of our atmosphere is crowded close to the earth's surface 2) causes air pressure to decrease with height, rapidly
Michigan State University - GEO - 203
Chapter 19: Climate ChangeI) II) Both heats and colds are becoming more moderate Evidence only gives us a little understanding of what climate was like in the past. Types of evidence: A) Samples taken from the ocean floor sediments and ice from Gree
Michigan State University - GEO - 203
Chapter One: The Earth and Its AtmosphereStars: hot, glowing balls of gas that generate energy by converting hydrogen into helium near their centers II) Sun is average size star A) Earth is an average distance of nearly 150 million km from the sun B
Michigan State University - GEO - 203
Chapter 7: Stability and Cloud DevelopmentI.
Michigan State University - GEO - 203
I)Dew: tiny visible specks of water that condense on twigs, leaves, blades of grass A) Cause 1) Clear, calm nights objects near earth's surface cool rapidly by emitting infrared radiation, become colder than surrounding air 2) Air that comes in con
Michigan State University - GEO - 203
Chapter 10: Wind-Small Scale and Local SystemsI) Scales of motion: hierarchy of motion arranged according to their size A) Microscale: diameters of few meters or less 1) Eddies: spinning globs of air that have a life history of their own 2) Disperse
Michigan State University - GEO - 203
Chapter Three: Seasonal and Daily TemperaturesThe earth revolves around the sun and spins on its own axis A) Spins on its own axis 1) One spin/24 hours 2) Direction is counterclockwise 3) Earth is tilted 23.5 on its own axis 4) Half of globe is alwa
Michigan State University - GEO - 203
Chapter 12: Air Masses and FrontsAir mass: large body of air whose properties of temperature and humidity are fairly similar in any horizontal direction at any given latitude A) Source regions: regions where air masses originate 1) Good source regio
Michigan State University - PHY - 231
Chapter 8: Rotational Equilibrium and Rotational DynamicsTorques () cause angular acceleration A) If a force is applied to a door three factors determine the effectiveness of the force: 1) Magnitude of the force 2) Position of application of the for
Michigan State University - PHY - 231
Chapter 11: Energy in Thermal ProcessesI) Internal energy (U): the energy associated with the microscopic components of a system, includes the kinetic and potential energy associated with the random translational, rotational, and vibrational motion
Michigan State University - PHY - 231
Chapter Five: EnergyI) Work: displacement of an object due to an applied force A) W = Fx B) Scalar quantity C) Measured in Newton-meter or Joule D) The force can be split into two components, but only the component parallel to the direction of displ
Michigan State University - PHY - 231
Chapter Four: The Laws of MotionI) Force: push or pull on some object A) Vector quantity: can control magnitude and direction of an applied force B) Types of forces 1) Contact forces: result from physical contact b/t two objects 2) Field forces: an
Michigan State University - PHY - 231
Chapter 14: SoundSound waves have their source in a vibrating object A) Tuning fork: common device for producing pure musical notes 1) Two metal prongs (tines) that vibrate when struck 2) Vibration disturbs the air near them 3) Compression: When a t
Michigan State University - PHY - 231
Chapter 9: Solids and FluidsI) Types of Matter A) Solids: definite volume and shape 1) Atoms help together by electrical forces 2) Atoms located at specific positions with respect to one another and can vibrate in their positions a) Low temperature:
Michigan State University - PHY - 231
Chapter One: IntroductionI. Dimension: physical nature of a quantity A. Length, mass, time, etc. B. Brackets often used to denote dimensions of physical quantity C. Dimensional analysis: procedure to derive a mathematical expression or equation or c
Michigan State University - PHY - 231
Chapter 7: Rotational Motion and the Law of GravityI) Angular position: the angle measured in radians A) = s/r B) 2 radians = 360o II) Angular displacement: the difference in its final and initial angles ( ) III) Angular speed () A) Each point on
Michigan State University - PHY - 231
Chapter Six: Momentum and CollisionsI) Linear momentum (p): p = mv A) Vector quantity B) Can be broken down into its components C) More momentum an object has the more force that has to be applied to stop it in a given time II) The net force acting
Michigan State University - PHY - 231
Chapter 10: Thermal PhysicsI) II) Thermal physics: the study of temperature, heat, and how they affect matter Thermodynamics A) Thermal contact: if energy can be exchanged b/t two objects B) Thermal equilibrium: if two objects are in thermal contact
Michigan State University - PHY - 231
Chapter 13: Vibrations and WavesI) II) Periodic vibrations can cause disturbances that move through a medium in the form of waves Simple harmonic motion: when the net force along the direction of motion obeys Hooke's law (F=-kx), when the net force
Michigan State University - PHY - 231
Chapter Three: Vectors and Two-Dimensional MotionI) Vectors A) Two vectors are equal if they have the same magnitude and the same direction. B) Components of vectors 1) A = Ax + Ay 2) Ax = A cos 3) Ay = A sin 4) A = (Ax2 + Ay2) 5) tan = Ay / Ax C) A
Michigan State University - PHY - 231
Chapter 12: The Laws of ThermodynamicsEnergy can be transferred to a system by heat and by work done on the system A) The work done on a gas at constant pressure (isobaric process) is : 1) W=-PV 2) Work done by the gas on its environment is the nega
Michigan State University - PHY - 231
Chapter Two: Motion in One DimensionI) Dynamics A) Study of motion and of physical concepts such as force and mass B) Kinematics: part of dynamics that describes motion without regard to its causes II) Earth and the universe A) Geocentric model: Ear
Michigan State University - PHY - 232
Constants: Ke = 9.0x109N-m2/C2 0= 1/(4Ke) = 8.85x10-12 C2/N-m2 1ev=1.60x10-19C-V=1.60x10-19J 1kWh=3.60x105J melectron=9.109x10-31kg mproton=1.672x10-27kg qelectron=-1.60219x10-19C o=4*10-7Tm/A Field lines: positivenegative F=Ke |q1|q2|/r2 = qE E= Ke
Michigan State University - PSL - 250
Thalamus o GNRH-necessary for onset of puberty. Increases release of FSH and LH from anterior pituitary Posterior pituitary o Vasopressin-BP osmolarity/concentration, increases water reabsoprtion by inserting aquaporins o Oxytocin-important in r
Michigan State University - PSL - 250
Test 1 Material Molecules-assembly of atoms, major ones: carbs, proteins, lipids, nucleic acids (smallest) Cells-basic unit of life, carry out life processes, uses energy, has metabolism, removes waste o Endoplasmic reticiulum (ER)-organelle, compl
Michigan State University - PSL - 250
Test 2 Material Cerebellum-structure on back of brainstem that controls coordinated movements and learned movements. Frontal lobe decides what, cerebellum does it o Balance-maintains balance and controls eye movements o Coordination-connected to mot
Michigan State University - PSL - 250
Test 3 Material Physical factors for blood vessels-some factors constant like length, others are variable. Flow=pressure/resistance o Vessel radius-most important variable factor because resistance=1/radius4 so a small constriction causes a large in
Michigan State University - PSL - 250
Test 4 MaterialUrination Nephron-functional unit of the kidney with a vascular and a filtration system. Everything but cells and proteins in the blood can be filtered through pores, most of it is reabsorbed Inulin-a large fructose polymer that is
Grand Valley State - BUS - 101
Exam 2 Study GuideWhat is a joint venture? -They allow companies to share risks, costs, profits, and management responsibilities with one or more host country nationals What is an acquisition? -A procedure in which one firm purchases the property an
Grand Valley State - BUS - 101
Introduction To Business Exam 3 Study GuideWhat is the definition of management? Management is the process of achieving organizational objectives through people and other resources. What are the types of skills a manager should have? Planning, Organ
Grand Valley State - GPY - 235
My Hometown: Northville, MI By Kyle BinfordMy Hometown: Northville, MI Northville, Michigan was originally created in 1867 and officially became a city in 1955. The Northville area is just 2.2 sq miles and is about 30 minutes east of Detroit. The a