Enhancing Botanical Composition and Wildlife Habitat of Pastures in South Central Iowa through Soil Disturbance by Mob-grazing of Beef Cattle
|
|
- George Singleton
- 5 years ago
- Views:
Transcription
1 Animl Industry Report AS 66 ASL R Enhncing Botnicl Composition nd Wildlife Hitt of Pstures in South Centrl Iow through Soil Disturnce y Mo-grzing of Beef Cttle Justin J. Bisinger Iow Stte University, equus146@istte.edu Jmes R. Russell Iow Stte University, jrussell@istte.edu Dougls Allen Ber Iow Stte University, morricl@istte.edu Joe Sellers Iow Stte University Helg Offenurger Iow Deprtment of Nturl Resources Recommended Cittion Bisinger, Justin J.; Russell, Jmes R.; Ber, Dougls Allen; Sellers, Joe; nd Offenurger, Helg (214) "Enhncing Botnicl Composition nd Wildlife Hitt of Pstures in South Centrl Iow through Soil Disturnce y Mo-grzing of Beef Cttle," Animl Industry Report: AS 66, ASL R2888. DOI: Aville t: This Environment is rought to you for free nd open ccess y the Animl Science Reserch Reports t Iow Stte University Digitl Repository. It hs een ccepted for inclusion in Animl Industry Report y n uthorized editor of Iow Stte University Digitl Repository. For more informtion, plese contct digirep@istte.edu.
2 Iow Stte University Animl Industry Report 214 Enhncing Botnicl Composition nd Wildlife Hitt of Pstures in South Centrl Iow through Soil Disturnce y Mo-grzing of Beef Cttle A.S. Leflet R2888 Justin Bisinger, Grdute Assistnt; Jim Russell, Professor, Deprtment of Animl Science; Dn Morricl, Professor, Deprtment of Animl Science; Joe Sellers, Livestock Specilist; Helg Offenurger, Iow DNR Summry nd Implictions South centrl Iow grsslnds re dominted y cool seson grss species with low productivity nd little plnt diversity which limits the forge yield nd qulity for grzing nimls nd hitt for ntive grsslnd wildlife. Strtegic spring mo-grzing my reduce competition from cool-seson grss species llowing erly successionl species, legumes, nd ntive plnts to estlish while improving soil chrcteristics. Two locks of three replicted pstures were divided into 5 equl-sized pddocks to determine the effects of erly spring mo-grzing on psture forge nd soil chrcteristics. In ech psture, one pddock ws not grzed (NG) nd 4 were strip- (S; moved once per dy with ck fence) or mo- (M; moved 4 times per dy with ck fence) grzed eginning in My of 211 (BL1) nd 212 (BL2) y 1 cows t live forge DM llownce of 2% BW/d. Susequently, one mo (MR) nd strip (SR) pddock in ech psture ws rottionlly stocked to remove 5% of the live forge with 35-d rest periods eginning 6 d fter spring grzing in yr 1 of ech lock. Mesurements included psture otnicl composition determined y the line trnsect method, soil penetrtion resistnce determined with penetrometer, wter infiltrtion determined with doule ring infiltrometers, soil ulk density, nd ground nesting ird hitt mesured s visul ostruction to 3.3x 3.3 ft ord y imge nlysis of digitl photos. In BL1 nd BL2 fter mo- or strip- grzing, the proportion of re ground ws greter (P<.5) in rottionlly grzed pddocks thn NG pddocks in most months. The proportion of nnul grsses ws greter (P<.5) in grzed thn NG pddocks in July 211 in BL1. In 212, the proportion of legumes ws greter (P<.5) thn NG pddocks in M, MR, nd SR pddocks in My, M nd SR pddocks in July, nd ll grzed pddocks in BL 1 in Octoer. But in 213, the proportion of legumes ws greter in MR nd S pddocks in My nd MR pddocks in Octoer thn NG pddocks. The proportion of wrm seson grsses in BL2 ws less (P<.5) in MR nd SR pddocks thn NG nd M pddocks in August 213. In BL1, penetrtion resistnce ws greter (P<.5) in rottionlly stocked pddocks compred to NG pddocks in My nd Octoer of 212 nd 213, however reductions (P<.5) in wter infiltrtion rtes occurred in rottionlly stocked pddocks only in Octoer 212 nd 213. In BL1, visul ostruction ws less (P<.5) in M pddocks thn S nd NG pddocks to 15.7 inches high in Octoer 211. However in BL2, no differences in visul ostruction occurred in Octoer 212. A single mo- or strip-grzing event of grsslnd in the spring my improve the nutritionl vlue of the forge for grzing livestock nd hitt for wildlife. However, the extent nd longevity of these responses re relted to soil moisture t the time of grzing nd susequent mngement nd climtic conditions. Introduction Overgrzing from continuous stocking of southern Iow pstures llows cool seson grsses like tll fescue to dominte other forge species nd decrese persistence of legumes. Even with nitrogen inputs, production of these pstures re limited, resulting in reduced vegettive cover nd incresed soil erosion in precipittion runoff. Furthermore, the low productivity nd nutritionl vlue of overgrzed pstures provides little incentive to deter producers from converting psturelnd into croplnd or selling it for recretionl uses like hunting. Typiclly fter psturelnd is sold for recretionl uses such s hunting, cttle re removed. However, without the disturnce nd defolition provided y grzing of perennil grsslnds, tree cover increses nd cool seson grsses ecome dominnt resulting in poor hitt for some wildlife species including owhite quil. Reducing competition from cool seson grsses through disturnce y grzing llow legumes nd other plnt species to estlish which increse sesonl productivity, resilience to wether disruptions, nd wildlife hitt. The nitrogen-fixing cpilities nd high protein concentrtions of legumes improves productivity nd nutritionl qulity of forges for grzing livestock. Incresed plnt diversity increses root mss nd this long with forge incorported into the soil through disturnce increses soil orgnic mtter which my increse soil cron sequestrtion, nd wter infiltrtion rtes. These fctors will, in turn, increse resilience to environmentl stress nd decrese soil erosion in grsslnds. In ddition, incresed plnt species diversity in grsslnd ecosystems will increse feed sources nd hitt structure for wildlife. The improvement of wildlife hitt from grzing my crete llinces etween cow/clf producers needing more grzing lnd nd lndowners wnting to estlish or improve wildlife hitt.
3 Iow Stte University Animl Industry Report 214 Strtegic grzing t high stocking densities for short periods of time followed y long rest periods, known s mo-grzing, my reduce competition from cool seson grss species nd provide the soil disturnce necessry to estlish more diverse plnt communities while providing other ecosystem enefits in psture nd grsslnds. The ojective of this study ws to evlute the effectiveness of strtegic spring mo-grzing to improve otnicl composition of forge for grzing, wildlife hitt, nd soil qulity under the soil nd climtic conditions prevlent in south centrl Iow. Mterils nd Methods Two locks of three replicted pstures contining mixtures of cool seson grsses nd legumes without (BL1) or with (BL2) wrm seson grsses were divided into 5 equl-sized pddocks (BL1, 1 cre; BL2,.5 cre) to determine the effects of single erly spring mo-grzing event on susequent plnt species diversity nd soil chrcteristics in grsslnds. In ech psture, one pddock ws not grzed (NG) nd 4 were strip (S; moved once per dy with ck fence) or mo (M; moved 4 times per dy with ck fence) grzed eginning in My of 211 (BL1) nd 212 (BL2) y 1 August-clving cows (men ody weight; 1291[BL1] nd 1416 [BL2] l) t live forge llownce of 2% BW/d. Susequently, one mo (MR) nd strip (SR) pddock in ech psture ws rottionlly stocked with 35-d rest periods eginning 6 d fter spring mogrzing in the first yer of ech lock nd in erly My of ech susequent yer. When grzing y rottionl stocking, cttle were stocked to remove 5% of the live forge mesured with flling plte meter (8.8 l/yd 2 ). Dominnt vegettive cover or plnt species including re soil, ded plnt residue, perennil cool nd wrm seson grsses, nnul grsses, legumes, nd rodlef weeds were identified t 1 eqully spced sites on 5 ft string t 1 sites per pddock in spring, summer, nd fll of ech yer. The numer of sites with perennil cool or wrm seson grsses, nnul grsses, rodlef weeds, sedge, nd legumes were summed s the numer of sites with live forge nd the proportion of sites with ech plnt clss ws expressed s percentge of sites with live forge. Wter infiltrtion ws determined t three rndomly selected sites in ech pddock in My nd Octoer y dding wter to doule ring infiltrometers to mintin ponding depth etween 2 nd 1 inches over 9 minutes. Wter infiltrtion ws clculted s the verge of the mount nd time of the lst three dditions of wter to the infiltrometers. Compction ws mesured to depth of 6 inches with field scout SC 9 penetrometer with.5 inch dimeter cone tip t 1 sites in ech pddock in My nd Octoer of ech yer. Soil ulk density nd totl cron were determined with soil smples to depth of 3 inches from 6 sites in ech pddock. Ground nesting ird hitt ws mesured s visul ostruction in digitl photos of 3.3x3.3 foot ord t distnce of 13.2 feet nd height of 3.3 feet in July nd Octoer of ech yer. Digitl photos were cropped nd visul ostruction determined with Sigm Scn Pro 5 t 3.8 inch intervls mrked on the visul ostruction ord. Dt were nlyzed y month with the MIXED procedure of SAS within BL1 nd BL2. Differences etween mens with significnt tretment effects were determined y the PDIFF procedure of SAS. Results nd Discussion Stocking densities for mo- nd strip-grzed pddocks during erly spring mo grzing were 53, nd 147, ls/cre in BL1 nd 47, nd 18, ls/cre in BL2, respectively. In BL1, re ground ws greter (P<.5) in S thn MR nd SR pddocks in July 211. Following July 211, the proportion of re ground ws (P<.5) greter in MR pddocks thn NG pddocks in ll smpling months, ut only greter in SR thn NG pddocks through My 212. Ded plnt residue ws greter (P<.8) in Octoer in pddocks grzed y either the M or S systems thn NG pddocks fter mo-grzing in 211.The proportion of coolseson grsses (fig. 1A) ws less (P <.5) in pddocks grzed y either the M, S, MR, or SR systems in July 211 nd My 212 thn NG pddocks. Following My 212, lower (P <.5) proportions of cool seson grsses were oserved in MR nd SR pddocks thn NG pddocks. Annul grsses s proportion of live forge were greter (P<.5) in July 211. The proportion of nnul grsses in the live species did not differ etween tretments in Octoer 211, 212, nd My 213. However, in August nd Octoer 213 the proportion of nnul grsses ws greter in MR nd SR thn NG, M, nd S pddocks. Conversely, in 212, legumes (fig. 1B) s proportion of live forge were greter (P<.5) in M, MR, nd S in My, M nd S in July, nd ll grzed pddocks in Octoer thn NG pddocks. Susequently, in 213, greter (P<.7) proportions of legumes still occurred in MR nd S in My, nd MR pddocks in Octoer thn NG pddocks. This result implies tht the increse in the proportion of legumes ws etter mintined in mo-grzed pddocks tht were susequently rottionlly stocked. The proportion of re ground ws greter (P <.5) in MR nd SR pddocks thn NG pddocks in ll smpling months fter My 212. While M or S grzing hd little effect on the proportions of cool seson grsses in the live forge immeditely fter grzing, the proportion of cool seson grsses (fig. 2A) ws less (P<.5) in M nd S thn NG pddocks in Octoer 212. In comprison to NG pddocks, the proportion of wrm seson grsses ws (P<.5) lower in MR nd SR pddocks in August 213, ut did not differ in other months. No differences in the proportion of nnul grsses etween tretments occurred in the yer tht pddocks in BL2 were mo- or strip-grzed (212). However, while there continued to e no difference in the proportion of nnul grsses in the NG, M, nd S pddocks in My 213, the proportion of nnul grsses in MR nd SR pddocks were greter (P <.5) thn M, S,
4 Iow Stte University Animl Industry Report 214 nd NG pddocks in July nd Octoer 213. Conversely, the proportions of legumes in the live forge were greter (P<.5) in S nd M pddocks thn NG pddocks in Octoer 212 nd My 213, respectively (fig. 2B). No differences in penetrtion resistnce t ny depth were oserved etween tretments fter tretments were pplied in BL1 in 211. However, compred to NG pddocks in BL1, penetrtion resistnce ws greter (P<.5) t depth of 2 inches in pddocks grzed y ny tretment in My 212 nd 213 nd in MR nd SR pddocks in Octoer 212 nd 213 (fig. 3A). In ddition, greter (P<.5) penetrtion resistnce in pddocks grzed y ny tretment thn NG pddocks occurred t depth of 5 nd 6 inches in Octoer 212 nd My 213. In BL2, penetrtion resistnce t depth of 2 inches ws greter (P <.5) in MR nd SR pddocks thn NG, M, nd S pddocks in Octoer 213 (fig. 3B). In 212 nd My 213 there were few significnt differences t other depths. However in Octoer 213, penetrtion resistnce in rottionlly stocked pddocks ws greter thn NG pddocks to depth of 4 inches. Unlike BL1, in BL2 there were no significnt differences in penetrtion resistnce elow 4 inches etween tretments. Soil ulk density in BL1 ws greter (P<.5) in MR nd S pddocks in Octoer 211 nd ll grzed pddocks in Octoer 212 thn NG pddocks. However, unlike penetrtion resistnce, there ws no difference in soil ulk density etween tretments in BL1 in Octoer 213. In BL2, soil ulk density ws greter (P<.5) in SR pddocks thn NG pddocks in Octoer 213. As result of the differences in soil compction, wter infiltrtion rte ws greter (P<.5) in NG, M, nd S pddocks in Octoer 212 nd NG pddocks in Octoer 213 thn MR nd SR pddocks in BL1. In BL2, infiltrtion rtes in pddocks grzed y ny of the systems were greter (P<.5) thn NG pddocks in Octoer 212. However, no differences in infiltrtion rtes etween tretments in BL2 occurred in ny other month. In BL1, M nd S pddocks provided less (P<.5) visul ostruction up to 39.4 inches thn forge in NG pddocks in July 211 which ws immeditely fter the tretments were pplied. In Octoer 211, visul ostruction to height of 15.7 inches in M pddocks ws less (P<.5) thn NG nd S pddocks (fig. 4A). In ddition, ove 15.7 inches, visul ostruction ws lower (P<.5) in M nd S pddocks thn NG pddocks. In July 212, no differences occurred in visul ostruction etween tretments. But in Octoer 212, there ws less (P<.5) visul ostruction t 3.9 to 7.9 inches in S thn M pddocks. In BL2, visul ostruction ws less (P<.5) up to 39.4 inches in M nd S pddocks thn NG pddocks in July 212 immeditely fter the tretments were pplied. In Octoer 212, there were no differences in visul ostruction in BL2 (fig. 4B). Becuse of the differences in the responses of plnt communities nd soil qulity to grzing tretments in BL1 nd BL2, this study indictes the effects of mo- nd stripgrzing on plnt species nd soil properties re likely influenced y more fctors thn stocking density. The species succession which occurred in BL1 with incresed levels of nnul grsses, did not occur in BL2. Furthermore increses in penetrtion resistnce which occurred in ll grzed pddocks in BL1 only occurred in pddocks tht were rottionlly grzed in BL2. Differences etween locks my hve een relted to rinfll during mo- nd strip-grzing which were.55 nd.5 inches in BL1 in 211 nd BL2 in 212, respectively. Results from BL1 indicte mo- or strip-grzing cn e used to reduce competition from cool seson grsses nd llow nnul grsses nd eventully legumes to estlish if rinfll mounts re enough to llow significnt soil disturnce. These effects my lso e ltered y greter stocking densities or lengths of the grzing period. The increse in nnul grsses nd legumes resulting from mo- nd stripgrzing in BL1 my e eneficil to ground nesting irds nd other wildlife. However within 2 yers, the plnt community egn to resemle pddocks with no grzing which lcked qulity wildlife hitt. In oth locks re ground incresed with rottionl grzing nd ws most persistent in MR pddocks. This effect could increse the risks of soil erosion in pstures, ut re ground is needed in grsslnds mnged for owhite quil hitt. Furthermore, the incresed legume popultions in rottionlly stocked pddocks in BL1 lsted longer in mogrzed thn strip-grzed pddocks possily resulting from more soil disturnce. Although soil penetrtion resistnce nd ulk density re sometimes relted to wter infiltrtion rtes, in this project correltion coefficients were not greter thn.25. Further nlysis on the impct of soil moisture on the chnge in plnt species nd soil chrcteristics following mo- nd strip-grzing is needed to determine environmentl conditions most likely to produce the desired chnge in plnt species while improving soil qulity chrcteristics. Acknowledgements The uthors would like to thnk Kevin Mher nd the other personnel t the McNy Reserch Frm for ssistnce with mngement of the cttle; grdute students Mrgret Dunn nd Lur Dniels; nd undergrdute students Dve Mstolek, Kelsey Mrtin, Brin Nyheim, nd Quinton Normn tht hve helped with the dt collection nd nlysis in this experiment. This mteril is sed upon work supported y the Leopold Center for Sustinle Agriculture.
5 Iow Stte University Animl Industry Report 214 Figure 1. The Effects of Strip or Mo-grzing with or without Susequent Rottionl Grzing on the Proportion of Cool Seson Grsses (A) nd Legumes (B) s Percentge of Totl Psture Are in BL1 pddocks not grzed (NG), Mo-grzed (M), Mo-grzed with 6 Dys Rest Followed y Rottionl Grzing (MR), Strip-grzed (S), Stripgrzed with 6 Dys Rest Followed y Rottionl Grzing (SR). %, live forge (A; Cool Seson Grsses) c c c c %, live forge (B; Legumes) My, 211 July, 211 Octoer, 211 My, 212 July, 212 Octoer, 212 NG M MR S SR c c My, 213 August, 213 Octoer, 213 -c Differences etween tretment (NG, M, MR, S, SR) mens within month with different superscripts re significnt (P<.5) Figure 2. The Effects of Strip or Mo-grzing with or without Susequent Rottionl Grzing on the Proportion of Cool Seson Grsses (A) nd Legumes (B) s Percentge of Totl Live Forge in BL2 pddocks not grzed (NG), Mo-grzed (M), Mo-grzed with 6 Dys Rest Followed y Rottionl Grzing (MR), Strip-grzed (S), Stripgrzed with 6 Dys Rest Followed y Rottionl Grzing (SR). %, live forge (A; Cool Seson Grsses) c c %, live forge (B; Legumes) My, 212 July, 212 Octoer, 212 My, 213 August, 213 Octoer, 213 NG M MR S SR -c Differences etween tretment (NG, M, MR, S, SR) mens within month with different superscripts re significnt (P<.5)
6 Iow Stte University Animl Industry Report 214 Figure 3. The Effects of Strip or Mo-grzing with or without Susequent Rottionl Grzing on penetrtion resistnce t depth of 2 inches in BL1 (A) nd BL2 (B) pddocks not grzed (NG), Mo-grzed (M), Mo-grzed with 6 Dys Rest Followed y Rottionl Grzing (MR), Strip-grzed (S), Strip-grzed with 6 Dys Rest Followed y Rottionl Grzing (SR). KP KP (A; BL1) c c c My, 211 Octoer, 211 My, 212 Octoer, 212 My, 213 Octoer, 213 (B; BL2) My, 212 Octoer, 212 My, 213 Octoer, 213 -c Differences etween tretment (NG, M, MR, S, SR) mens within month with different superscripts re significnt (P<.5) c c NG M MR S SR NG M MR S SR Figure 4. The Effects of Strip or Mo-grzing with or without Susequent Rottionl Grzing on Visul Ostruction in Octoer 211 in BL1(A) nd Octoer 212 in BL2 (B) t Height Increments of , , , nd inches t Distnce of 13.2 feet in pddocks not grzed (NG), Mo-grzed (M), nd Strip-grzed (S). Visul ostruction, % (A; BL1) Height, inches NG M S Visul ostruction, % (B; BL2) Height, inches NG M S - Differences etween tretment (NG, M, MR, S, SR) mens within month with different superscripts re significnt (P<.5)
Reducing Nonpoint Source Pollution through Effective Ditch Management
Reducing Nonpoint Source Pollution through Effective Ditch Mngement Meliss Huert DNREC Division of Wtershed Stewrdship Dringe Progrm University of Delwre Artificil Dringe in Delwre Engineered system to
More information0.1 THE REAL NUMBER LINE AND ORDER
6000_000.qd //0 :6 AM Pge 0-0- CHAPTER 0 A Preclculus Review 0. THE REAL NUMBER LINE AND ORDER Represent, clssify, nd order rel numers. Use inequlities to represent sets of rel numers. Solve inequlities.
More informationManure Management Rate Effects on Soil Health in SD
Mnure Mngement Rte Effects on Soil Helth in SD Anthony Bly, SDSU Extension, Soils Field Specilist, Sioux Flls Regionl Center 2014 Bord of Regents, South Dkot Stte University Authors nd Collbortors Dr.
More informationInterpreting Integrals and the Fundamental Theorem
Interpreting Integrls nd the Fundmentl Theorem Tody, we go further in interpreting the mening of the definite integrl. Using Units to Aid Interprettion We lredy know tht if f(t) is the rte of chnge of
More informationAlternative Control Strategies for Cabbage Aphids in Fall Crops
Alterntive Control Strtegies for Cge Aphids in Fll Crops By Susn B. Scheufele UMss Extension Vegetle Progrm Cge phids (CA) cn severely reduce yield nd mrketility of rssic crops throughout the yer ut cn
More information7.1 Integral as Net Change and 7.2 Areas in the Plane Calculus
7.1 Integrl s Net Chnge nd 7. Ares in the Plne Clculus 7.1 INTEGRAL AS NET CHANGE Notecrds from 7.1: Displcement vs Totl Distnce, Integrl s Net Chnge We hve lredy seen how the position of n oject cn e
More informationDesigning Information Devices and Systems I Spring 2018 Homework 7
EECS 16A Designing Informtion Devices nd Systems I Spring 2018 omework 7 This homework is due Mrch 12, 2018, t 23:59. Self-grdes re due Mrch 15, 2018, t 23:59. Sumission Formt Your homework sumission should
More informationChapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses
Chpter 9: Inferences bsed on Two smples: Confidence intervls nd tests of hypotheses 9.1 The trget prmeter : difference between two popultion mens : difference between two popultion proportions : rtio of
More informationStream Bank Erosion as a Source of Sediment and Phosphorus in Grazed Gastures of the Rathbun Lake Watershed in Southern Iowa, United States
Nturl Resource Ecology nd Mngement Pulictions Nturl Resource Ecology nd Mngement 11-2012 Strem Bnk Erosion s Source of Sediment nd Phosphorus in Grzed Gstures of the Rthun Lke Wtershed in Southern Iow,
More informationUNIVERSITY OF KWAZULU-NATAL EXAMINATIONS: JUNE 2007
EXAMINATIONS: SUBJECT, COURSE AND CODE: HYDROLOGY 20 DURATION: HOURS TOTAL MARKS: 00 Internl Exminer : Ms ML Wrburton : Prof RE Schulze : Ms KT Chetty : Mr MJC Horn Externl Exminer : Prof PJT Roberts STUDENTS
More informationContinuous Random Variables Class 5, Jeremy Orloff and Jonathan Bloom
Lerning Gols Continuous Rndom Vriles Clss 5, 8.05 Jeremy Orloff nd Jonthn Bloom. Know the definition of continuous rndom vrile. 2. Know the definition of the proility density function (pdf) nd cumultive
More informationList all of the possible rational roots of each equation. Then find all solutions (both real and imaginary) of the equation. 1.
Mth Anlysis CP WS 4.X- Section 4.-4.4 Review Complete ech question without the use of grphing clcultor.. Compre the mening of the words: roots, zeros nd fctors.. Determine whether - is root of 0. Show
More informationThe Fundamental Theorem of Calculus. The Total Change Theorem and the Area Under a Curve.
Clculus Li Vs The Fundmentl Theorem of Clculus. The Totl Chnge Theorem nd the Are Under Curve. Recll the following fct from Clculus course. If continuous function f(x) represents the rte of chnge of F
More informationChapter 9 Definite Integrals
Chpter 9 Definite Integrls In the previous chpter we found how to tke n ntiderivtive nd investigted the indefinite integrl. In this chpter the connection etween ntiderivtives nd definite integrls is estlished
More information5.1 How do we Measure Distance Traveled given Velocity? Student Notes
. How do we Mesure Distnce Trveled given Velocity? Student Notes EX ) The tle contins velocities of moving cr in ft/sec for time t in seconds: time (sec) 3 velocity (ft/sec) 3 A) Lel the x-xis & y-xis
More informationAdvanced Algebra & Trigonometry Midterm Review Packet
Nme Dte Advnced Alger & Trigonometry Midterm Review Pcket The Advnced Alger & Trigonometry midterm em will test your generl knowledge of the mteril we hve covered since the eginning of the school yer.
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: How to identify the leding coefficients nd degrees of polynomils How to dd nd subtrct polynomils How to multiply polynomils
More informationSection 6: Area, Volume, and Average Value
Chpter The Integrl Applied Clculus Section 6: Are, Volume, nd Averge Vlue Are We hve lredy used integrls to find the re etween the grph of function nd the horizontl xis. Integrls cn lso e used to find
More informationStudent Activity 3: Single Factor ANOVA
MATH 40 Student Activity 3: Single Fctor ANOVA Some Bsic Concepts In designed experiment, two or more tretments, or combintions of tretments, is pplied to experimentl units The number of tretments, whether
More information3 x x x 1 3 x a a a 2 7 a Ba 1 NOW TRY EXERCISES 89 AND a 2/ Evaluate each expression.
SECTION. Eponents nd Rdicls 7 B 7 7 7 7 7 7 7 NOW TRY EXERCISES 89 AND 9 7. EXERCISES CONCEPTS. () Using eponentil nottion, we cn write the product s. In the epression 3 4,the numer 3 is clled the, nd
More informationThe 1 th International and The 4 th National Congress on Recycling of Organic Waste in Agriculture April 2012 in Isfahan, Iran
The 1 th Interntionl nd The 4 th Ntionl Congress on The Effect of Prticle Size nd Composting Period on (C/N) Rtio of Dte- Plm Wste Min Mortzvi 1, Ahmd Mohmmdi Ghehsreh 2 nd Mhmoud Klsi 3 1. M.Sc. Student,
More informationSUMMER KNOWHOW STUDY AND LEARNING CENTRE
SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18
More information2 b. , a. area is S= 2π xds. Again, understand where these formulas came from (pages ).
AP Clculus BC Review Chpter 8 Prt nd Chpter 9 Things to Know nd Be Ale to Do Know everything from the first prt of Chpter 8 Given n integrnd figure out how to ntidifferentite it using ny of the following
More informationEFFECTS OF DORMANT SEASON GRAZING ON HERBAGE PRODUCTION AND PLANT GROWTH. Sciences Department, NDSU, Fargo. NDSU, Hettinger, ND
EFFECTS OF DORMANT SEASON GRAZING ON HERBAGE PRODUCTION AND PLANT GROWTH Kristy-Lyne Nelson 1, Kevin Sedivec 1, Jckie Olson 2, Mitch Fulkner 3, Tim Fller 4, Christopher Schuer 4 1 Grdute Student, Stte
More informationThe practical version
Roerto s Notes on Integrl Clculus Chpter 4: Definite integrls nd the FTC Section 7 The Fundmentl Theorem of Clculus: The prcticl version Wht you need to know lredy: The theoreticl version of the FTC. Wht
More informationSilicon Nanowire Based Single-Molecule SERS Sensor
Supporting informtion Silicon Nnowire Bsed Single-Molecule SERS Sensor Hui Wng, Xuemei Hn, Xuemei Ou, Chun-Sing Lee, Xiohong Zhng* nd Shuit-Tong Lee S1, A series of Si nnowires coted with compct ggregtes
More informationMath 116 Final Exam April 26, 2013
Mth 6 Finl Exm April 26, 23 Nme: EXAM SOLUTIONS Instructor: Section:. Do not open this exm until you re told to do so. 2. This exm hs 5 pges including this cover. There re problems. Note tht the problems
More informationMinnesota State University, Mankato 44 th Annual High School Mathematics Contest April 12, 2017
Minnesot Stte University, Mnkto 44 th Annul High School Mthemtics Contest April, 07. A 5 ft. ldder is plced ginst verticl wll of uilding. The foot of the ldder rests on the floor nd is 7 ft. from the wll.
More informationMA 15910, Lessons 2a and 2b Introduction to Functions Algebra: Sections 3.5 and 7.4 Calculus: Sections 1.2 and 2.1
MA 15910, Lessons nd Introduction to Functions Alger: Sections 3.5 nd 7.4 Clculus: Sections 1. nd.1 Representing n Intervl Set of Numers Inequlity Symol Numer Line Grph Intervl Nottion ) (, ) ( (, ) ]
More informationCHAPTER 20: Second Law of Thermodynamics
CHAER 0: Second Lw of hermodynmics Responses to Questions 3. kg of liquid iron will hve greter entropy, since it is less ordered thn solid iron nd its molecules hve more therml motion. In ddition, het
More information7.1 Integral as Net Change Calculus. What is the total distance traveled? What is the total displacement?
7.1 Integrl s Net Chnge Clculus 7.1 INTEGRAL AS NET CHANGE Distnce versus Displcement We hve lredy seen how the position of n oject cn e found y finding the integrl of the velocity function. The chnge
More informationI1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3
2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is
More informationAn Overview of Integration
An Overview of Integrtion S. F. Ellermeyer July 26, 2 The Definite Integrl of Function f Over n Intervl, Suppose tht f is continuous function defined on n intervl,. The definite integrl of f from to is
More information12.1 Introduction to Rational Expressions
. Introduction to Rtionl Epressions A rtionl epression is rtio of polynomils; tht is, frction tht hs polynomil s numertor nd/or denomintor. Smple rtionl epressions: 0 EVALUATING RATIONAL EXPRESSIONS To
More informationDesigning Information Devices and Systems I Discussion 8B
Lst Updted: 2018-10-17 19:40 1 EECS 16A Fll 2018 Designing Informtion Devices nd Systems I Discussion 8B 1. Why Bother With Thévenin Anywy? () Find Thévenin eqiuvlent for the circuit shown elow. 2kΩ 5V
More informationThe Fundamental Theorem of Calculus, Particle Motion, and Average Value
The Fundmentl Theorem of Clculus, Prticle Motion, nd Averge Vlue b Three Things to Alwys Keep In Mind: (1) v( dt p( b) p( ), where v( represents the velocity nd p( represents the position. b (2) v ( dt
More informationPhysics 202H - Introductory Quantum Physics I Homework #08 - Solutions Fall 2004 Due 5:01 PM, Monday 2004/11/15
Physics H - Introductory Quntum Physics I Homework #8 - Solutions Fll 4 Due 5:1 PM, Mondy 4/11/15 [55 points totl] Journl questions. Briefly shre your thoughts on the following questions: Of the mteril
More informationImprovement of chilling efficiency and product quality of broiler carcasses using sub-zero saline solutions
Improvement of chilling efficiency nd product qulity of roiler crcsses using su-zero sline solutions I. Kng*, M.M. Metheny*, nd PhD, H.C. Lee*, PhD, D. Bennett *, PhD, S. Hurley, PhD, Animl Science*/Agriusiness
More informationName Solutions to Test 3 November 8, 2017
Nme Solutions to Test 3 November 8, 07 This test consists of three prts. Plese note tht in prts II nd III, you cn skip one question of those offered. Some possibly useful formuls cn be found below. Brrier
More informationChapter 6 Continuous Random Variables and Distributions
Chpter 6 Continuous Rndom Vriles nd Distriutions Mny economic nd usiness mesures such s sles investment consumption nd cost cn hve the continuous numericl vlues so tht they cn not e represented y discrete
More informationp-adic Egyptian Fractions
p-adic Egyptin Frctions Contents 1 Introduction 1 2 Trditionl Egyptin Frctions nd Greedy Algorithm 2 3 Set-up 3 4 p-greedy Algorithm 5 5 p-egyptin Trditionl 10 6 Conclusion 1 Introduction An Egyptin frction
More informationPrecalculus Spring 2017
Preclculus Spring 2017 Exm 3 Summry (Section 4.1 through 5.2, nd 9.4) Section P.5 Find domins of lgebric expressions Simplify rtionl expressions Add, subtrct, multiply, & divide rtionl expressions Simplify
More informationPHYS Summer Professor Caillault Homework Solutions. Chapter 2
PHYS 1111 - Summer 2007 - Professor Cillult Homework Solutions Chpter 2 5. Picture the Problem: The runner moves long the ovl trck. Strtegy: The distnce is the totl length of trvel, nd the displcement
More informationSection 4: Integration ECO4112F 2011
Reding: Ching Chpter Section : Integrtion ECOF Note: These notes do not fully cover the mteril in Ching, ut re ment to supplement your reding in Ching. Thus fr the optimistion you hve covered hs een sttic
More informationExample. Have precipitation and streamflow data, need to estimate losses
Excess Rinfll Excess rinfll Rinfll tht is neither retined on the lnd surfce nor infiltrted into the soil Grph of excess rinfll versus time is clled excess rinfll hyetogrph Direct runoff = observed stremflow
More informationSection 4.8. D v(t j 1 ) t. (4.8.1) j=1
Difference Equtions to Differentil Equtions Section.8 Distnce, Position, nd the Length of Curves Although we motivted the definition of the definite integrl with the notion of re, there re mny pplictions
More information2.4 Linear Inequalities and Interval Notation
.4 Liner Inequlities nd Intervl Nottion We wnt to solve equtions tht hve n inequlity symol insted of n equl sign. There re four inequlity symols tht we will look t: Less thn , Less thn or
More informationMatching patterns of line segments by eigenvector decomposition
Title Mtching ptterns of line segments y eigenvector decomposition Author(s) Chn, BHB; Hung, YS Cittion The 5th IEEE Southwest Symposium on Imge Anlysis nd Interprettion Proceedings, Snte Fe, NM., 7-9
More informationTrigonometric Functions
Exercise. Degrees nd Rdins Chpter Trigonometric Functions EXERCISE. Degrees nd Rdins 4. Since 45 corresponds to rdin mesure of π/4 rd, we hve: 90 = 45 corresponds to π/4 or π/ rd. 5 = 7 45 corresponds
More informationMath 8 Winter 2015 Applications of Integration
Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl
More informationContinuous Random Variable X:
Continuous Rndom Vrile : The continuous rndom vrile hs its vlues in n intervl, nd it hs proility distriution unction or proility density unction p.d. stisies:, 0 & d Which does men tht the totl re under
More information4.1 One-to-One Functions; Inverse Functions. EX) Find the inverse of the following functions. State if the inverse also forms a function or not.
4.1 One-to-One Functions; Inverse Functions Finding Inverses of Functions To find the inverse of function simply switch nd y vlues. Input becomes Output nd Output becomes Input. EX) Find the inverse of
More information13.4 Work done by Constant Forces
13.4 Work done by Constnt Forces We will begin our discussion of the concept of work by nlyzing the motion of n object in one dimension cted on by constnt forces. Let s consider the following exmple: push
More informationEnergy (kcal mol -1 ) Force (kcal mol -1 Å -1 ) Pore axis (Å) Mixed Mo-only S-only Graphene
Force (kcl mol -1 Å -1 ) Energy (kcl mol -1 ) 3 1-1 - -3 Mixed Mo-only S-only Grphene 6 5 3 1 Mixed Mo-only S-only Grphene - -1-1 1 Pore xis (Å) -1 1 Pore xis (Å) Supplementry Figure 1 Energy Brriers.
More information200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes
PHYSICS 132 Smple Finl 200 points 5 Problems on 4 Pges nd 20 Multiple Choice/Short Answer Questions on 5 pges 1 hour, 48 minutes Student Nme: Recittion Instructor (circle one): nme1 nme2 nme3 nme4 Write
More informationSatellite Retrieval Data Assimilation
tellite etrievl Dt Assimiltion odgers C. D. Inverse Methods for Atmospheric ounding: Theor nd Prctice World cientific Pu. Co. Hckensck N.J. 2000 Chpter 3 nd Chpter 8 Dve uhl Artist depiction of NAA terr
More informationCh AP Problems
Ch. 7.-7. AP Prolems. Willy nd his friends decided to rce ech other one fternoon. Willy volunteered to rce first. His position is descried y the function f(t). Joe, his friend from school, rced ginst him,
More informationROB EBY Blinn College Mathematics Department
ROB EBY Blinn College Mthemtics Deprtment Mthemtics Deprtment 5.1, 5.2 Are, Definite Integrls MATH 2413 Rob Eby-Fll 26 Weknowthtwhengiventhedistncefunction, wecnfindthevelocitytnypointbyfindingthederivtiveorinstntneous
More informationSpatial Distribution of Spartina pectinata Transplants to Restore Wet Prairie
Sptil Distriution of Sprtin pectint Trnsplnts to Restore Wet Pririe lexndr Frser 1 nd Kelly Kindscher 2,3 strct Restortion of wet pririe in the centrl midwestern United Sttes should include Pririe cordgrss
More informationDesigning Information Devices and Systems I Anant Sahai, Ali Niknejad. This homework is due October 19, 2015, at Noon.
EECS 16A Designing Informtion Devices nd Systems I Fll 2015 Annt Shi, Ali Niknejd Homework 7 This homework is due Octoer 19, 2015, t Noon. 1. Circuits with cpcitors nd resistors () Find the voltges cross
More informationPractice Final. Name: Problem 1. Show all of your work, label your answers clearly, and do not use a calculator.
Nme: MATH 2250 Clculus Eric Perkerson Dte: December 11, 2015 Prctice Finl Show ll of your work, lbel your nswers clerly, nd do not use clcultor. Problem 1 Compute the following limits, showing pproprite
More informationThe Trapezoidal Rule
_.qd // : PM Pge 9 SECTION. Numericl Integrtion 9 f Section. The re of the region cn e pproimted using four trpezoids. Figure. = f( ) f( ) n The re of the first trpezoid is f f n. Figure. = Numericl Integrtion
More information3.1 Exponential Functions and Their Graphs
. Eponentil Functions nd Their Grphs Sllbus Objective: 9. The student will sketch the grph of eponentil, logistic, or logrithmic function. 9. The student will evlute eponentil or logrithmic epressions.
More informationProperties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives
Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn
More informationRole of Endophytic Fungi in Forage Production of Tall Fescue, Festuca arundinacea
Proceedings of The Fourth Interntionl Irn & Russi Conference 327 Role of Endophytic Fungi in Forge Production of Tll Fescue, Festuc rundince 1 2 Mohmmd Rez Szlin, Rez Mohmmdi nd AghFkhr Mirlohi 1, 2, 3-Deprtment
More informationMA123, Chapter 10: Formulas for integrals: integrals, antiderivatives, and the Fundamental Theorem of Calculus (pp.
MA123, Chpter 1: Formuls for integrls: integrls, ntiderivtives, nd the Fundmentl Theorem of Clculus (pp. 27-233, Gootmn) Chpter Gols: Assignments: Understnd the sttement of the Fundmentl Theorem of Clculus.
More informationAlgebra Readiness PLACEMENT 1 Fraction Basics 2 Percent Basics 3. Algebra Basics 9. CRS Algebra 1
Algebr Rediness PLACEMENT Frction Bsics Percent Bsics Algebr Bsics CRS Algebr CRS - Algebr Comprehensive Pre-Post Assessment CRS - Algebr Comprehensive Midterm Assessment Algebr Bsics CRS - Algebr Quik-Piks
More informationSection 5.1 #7, 10, 16, 21, 25; Section 5.2 #8, 9, 15, 20, 27, 30; Section 5.3 #4, 6, 9, 13, 16, 28, 31; Section 5.4 #7, 18, 21, 23, 25, 29, 40
Mth B Prof. Audrey Terrs HW # Solutions by Alex Eustis Due Tuesdy, Oct. 9 Section 5. #7,, 6,, 5; Section 5. #8, 9, 5,, 7, 3; Section 5.3 #4, 6, 9, 3, 6, 8, 3; Section 5.4 #7, 8,, 3, 5, 9, 4 5..7 Since
More information: IPREM/LCABIE, UMR VNRS Université de Pau et des Pays de l Adour (UPPA), F Pau Cedex 09 b. : CEA, DAM, DIF, F Arpajon, Cedex.
Are polytomic interferences, cross contmintion, mixing-effect, etc., ostcles for use of Lser ltion - ICP-MS coupling s n opertionl technique for urnium isotope rtio prticle nlysis? Arine DONARD,, Fien
More information(i) b b. (ii) (iii) (vi) b. P a g e Exponential Functions 1. Properties of Exponents: Ex1. Solve the following equation
P g e 30 4.2 Eponentil Functions 1. Properties of Eponents: (i) (iii) (iv) (v) (vi) 1 If 1, 0 1, nd 1, then E1. Solve the following eqution 4 3. 1 2 89 8(2 ) 7 Definition: The eponentil function with se
More informationChanges in ph and microbial composition in the ruminal and reticular fluids of SARA cattle
66 th EAAP Annul Meeting (Wrsw, 215) Chnges in ph nd microil composition in the ruminl nd reticulr fluids of SARA cttle Shigeru SATO Coopertive Deprtment of Veterinry Medicine, Fculty of Agriculture, Iwte
More informationdy ky, dt where proportionality constant k may be positive or negative
Section 1.2 Autonomous DEs of the form 0 The DE y is mthemticl model for wide vriety of pplictions. Some of the pplictions re descried y sying the rte of chnge of y(t) is proportionl to the mount present.
More informationLesson 5.3 Graph General Rational Functions
Copright Houghton Mifflin Hrcourt Publishing Compn. All rights reserved. Averge cost ($) C 8 6 4 O 4 6 8 Number of people number of hits.. number of times t bt.5 n n 4 b. 4.5 4.5.5; No, btting verge of.5
More informationRoadmap. Tropical seagrasses: natural & anthropogenic impacts 5/15/2015
Rodmp Tropicl segrsses: nturl & nthropogenic impcts Mrine Botny 5.14.15 Angel L Quiros Introduction to tropicl segrsses Threts to segrsses My thesis: Lnd to se impcts on segrsses The Mechnism : A field
More informationTopics. Topics. Minecto Pro 1/25/2016. Medicating onions for thrips infestations: New remedies to consider
// Medicting onions for thrips infesttions: New remedies to consider Jnury, I. Performnce of II. Evluting s for Exirel Brin A. Nult Professor Deprtment of Entomology III. Compring thrips control erly in
More informationSESSION 2 Exponential and Logarithmic Functions. Math 30-1 R 3. (Revisit, Review and Revive)
Mth 0-1 R (Revisit, Review nd Revive) SESSION Eponentil nd Logrithmic Functions 1 Eponentil nd Logrithmic Functions Key Concepts The Eponent Lws m n 1 n n m m n m n m mn m m m m mn m m m b n b b b Simplify
More informationValidation of APHRODITE Precipitation Data for Humid and Sub Humid Regions of Pakistan
Pkistn Journl of Meteorology Vol.9, Issue 17: July 2012 Vlidtion of APHRODITE Precipittion Dt for Humid nd Su Humid Regions of Pkistn Ali, G. 1, 2, G. Rsul 2, T. Mhmood 2, Q. Zmn 2, S. B. Cheem 2 Astrct
More informationLecture 2: January 27
CS 684: Algorithmic Gme Theory Spring 217 Lecturer: Év Trdos Lecture 2: Jnury 27 Scrie: Alert Julius Liu 2.1 Logistics Scrie notes must e sumitted within 24 hours of the corresponding lecture for full
More informationHints for Exercise 1 on: Current and Resistance
Hints for Exercise 1 on: Current nd Resistnce Review the concepts of: electric current, conventionl current flow direction, current density, crrier drift velocity, crrier numer density, Ohm s lw, electric
More information8Similarity UNCORRECTED PAGE PROOFS. 8.1 Kick off with CAS 8.2 Similar objects 8.3 Linear scale factors. 8.4 Area and volume scale factors 8.
8.1 Kick off with S 8. Similr ojects 8. Liner scle fctors 8Similrity 8. re nd volume scle fctors 8. Review U N O R R E TE D P G E PR O O FS 8.1 Kick off with S Plese refer to the Resources t in the Prelims
More informationAPPROXIMATE INTEGRATION
APPROXIMATE INTEGRATION. Introduction We hve seen tht there re functions whose nti-derivtives cnnot be expressed in closed form. For these resons ny definite integrl involving these integrnds cnnot be
More informationAPPENDIX. Precalculus Review D.1. Real Numbers and the Real Number Line
APPENDIX D Preclculus Review APPENDIX D.1 Rel Numers n the Rel Numer Line Rel Numers n the Rel Numer Line Orer n Inequlities Asolute Vlue n Distnce Rel Numers n the Rel Numer Line Rel numers cn e represente
More informationIntermediate Math Circles Wednesday, November 14, 2018 Finite Automata II. Nickolas Rollick a b b. a b 4
Intermedite Mth Circles Wednesdy, Novemer 14, 2018 Finite Automt II Nickols Rollick nrollick@uwterloo.c Regulr Lnguges Lst time, we were introduced to the ide of DFA (deterministic finite utomton), one
More informationCS103B Handout 18 Winter 2007 February 28, 2007 Finite Automata
CS103B ndout 18 Winter 2007 Ferury 28, 2007 Finite Automt Initil text y Mggie Johnson. Introduction Severl childrens gmes fit the following description: Pieces re set up on plying ord; dice re thrown or
More information1 Probability Density Functions
Lis Yn CS 9 Continuous Distributions Lecture Notes #9 July 6, 28 Bsed on chpter by Chris Piech So fr, ll rndom vribles we hve seen hve been discrete. In ll the cses we hve seen in CS 9, this ment tht our
More informationSupplementary material
10.1071/FP11237_AC CSIRO 2012 Accessory Puliction: Functionl Plnt Biology 2012, 39(5), 379 393. Supplementry mteril Tle S1. Effect of wter regime nd genotype on different growth prmeters: spike dry mtter
More informationChapter 3 Exponential and Logarithmic Functions Section 3.1
Chpter 3 Eponentil nd Logrithmic Functions Section 3. EXPONENTIAL FUNCTIONS AND THEIR GRAPHS Eponentil Functions Eponentil functions re non-lgebric functions. The re clled trnscendentl functions. The eponentil
More informationMath 31S. Rumbos Fall Solutions to Assignment #16
Mth 31S. Rumbos Fll 2016 1 Solutions to Assignment #16 1. Logistic Growth 1. Suppose tht the growth of certin niml popultion is governed by the differentil eqution 1000 dn N dt = 100 N, (1) where N(t)
More informationLINEAR ALGEBRA APPLIED
5.5 Applictions of Inner Product Spces 5.5 Applictions of Inner Product Spces 7 Find the cross product of two vectors in R. Find the liner or qudrtic lest squres pproimtion of function. Find the nth-order
More informationPartial Derivatives. Limits. For a single variable function f (x), the limit lim
Limits Prtil Derivtives For single vrible function f (x), the limit lim x f (x) exists only if the right-hnd side limit equls to the left-hnd side limit, i.e., lim f (x) = lim f (x). x x + For two vribles
More informationDesigning Information Devices and Systems I Spring 2018 Homework 8
EECS 16A Designing Informtion Devices nd Systems I Spring 2018 Homework 8 This homework is due Mrch 19, 2018, t 23:59. Self-grdes re due Mrch 22, 2018, t 23:59. Sumission Formt Your homework sumission
More information( ) 1. Algebra 2: Final Exam Review. y e + e e ) 4 x 10 = 10,000 = 9) Name
Algebr : Finl Exm Review Nme Chpter 6 Grph ech function. Determine if the function represents exponentil growth or decy. Determine the eqution of the symptote, the domin nd the rnge of the function. )
More informationChapter 5 1. = on [ 1, 2] 1. Let gx ( ) e x. . The derivative of g is g ( x) e 1
Chpter 5. Let g ( e. on [, ]. The derivtive of g is g ( e ( Write the slope intercept form of the eqution of the tngent line to the grph of g t. (b Determine the -coordinte of ech criticl vlue of g. Show
More information( ) as a fraction. Determine location of the highest
AB Clculus Exm Review Sheet - Solutions A. Preclculus Type prolems A1 A2 A3 A4 A5 A6 A7 This is wht you think of doing Find the zeros of f ( x). Set function equl to 0. Fctor or use qudrtic eqution if
More informationu( t) + K 2 ( ) = 1 t > 0 Analyzing Damped Oscillations Problem (Meador, example 2-18, pp 44-48): Determine the equation of the following graph.
nlyzing Dmped Oscilltions Prolem (Medor, exmple 2-18, pp 44-48): Determine the eqution of the following grph. The eqution is ssumed to e of the following form f ( t) = K 1 u( t) + K 2 e!"t sin (#t + $
More informationMotion. Acceleration. Part 2: Constant Acceleration. October Lab Phyiscs. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration.
Motion ccelertion Prt : Constnt ccelertion ccelertion ccelertion ccelertion is the rte of chnge of elocity. = - o t = Δ Δt ccelertion = = - o t chnge of elocity elpsed time ccelertion is ector, lthough
More informationThe area under the graph of f and above the x-axis between a and b is denoted by. f(x) dx. π O
1 Section 5. The Definite Integrl Suppose tht function f is continuous nd positive over n intervl [, ]. y = f(x) x The re under the grph of f nd ove the x-xis etween nd is denoted y f(x) dx nd clled the
More informationFirst Semester Review Calculus BC
First Semester Review lculus. Wht is the coordinte of the point of inflection on the grph of Multiple hoice: No lcultor y 3 3 5 4? 5 0 0 3 5 0. The grph of piecewise-liner function f, for 4, is shown below.
More informationfractions Let s Learn to
5 simple lgebric frctions corne lens pupil retin Norml vision light focused on the retin concve lens Shortsightedness (myopi) light focused in front of the retin Corrected myopi light focused on the retin
More informationSample Problems for the Final of Math 121, Fall, 2005
Smple Problems for the Finl of Mth, Fll, 5 The following is collection of vrious types of smple problems covering sections.8,.,.5, nd.8 6.5 of the text which constitute only prt of the common Mth Finl.
More information