R-107-H SUPERELEVATION AND PAVEMENT CROWNS MICHIGAN DEPARTMENT OF TRANSPORTATION SUPERELEVATED FINISHED SECTION LEGEND HIGH SIDE SHOULDER CHART RAMPS
|
|
|
- Morgan Henry
- 5 years ago
- Views:
Transcription
1 PLNE OF UPERELEVTION HOULER LOPE EQUL THE RTE OF UPERELEVTION OR THE NORML HOULER LOPE HIHEVER I GRETER ITH EPTH ON INIE OF URVE EQUL NORML ITH EPTH PLU ITH OF PVEMENT N HOULER INIE THE POINT OF ROTTION TIME RTE OF UPERELEVTION OR ELO N UE, HIHEVER I GRETER HOULER PVEMENT ITH \ PLN GRE N POINT OF ROTTION HOULER HOULER LOPE (EE HIGH IE HOULER HRT) ITH EPTH ON OUTIE OF URVE EQUL NORML ITH EPTH MINU ITH OF PVEMENT N HOULER OUTIE THE POINT OF ROTTION TIME RTE OF UPERELEVTION OR ELO N UE, HIHEVER I GRETER PLN GRE PLN GRE RTE OF UPERELEVTION RTE OF UPERELEVTION (MORE THN ) (HEN RTE OF UPERELEVTION OR LE) EPTH HON ON PLN NOTE: UGRE RINGE HLL E HON ON PLN TYPIL RO ETION UPERELEVTE FINIHE ETION (TO-Y HON) = RMP ITH LEGEN HIGH IE HOULER HRT PLN GRE (NORML) = NORML RON RTE = ITE IN FEET FROM POINT OF ROTTION TO FRTHET OUTIE EGE = x HEN RTE OF FULL UPERELEVTION I FROM TO HOULER LOPE T FULL UPERELEVTION EQUL RTE OF UPERELEVTION MINU NORML HOULER LOPE = RMP ITH UPERELEVTION e = RTE OF UPERELEVTION = x e = RON RUNOUT / TNGENT RUNOUT (VERE RON REMOVE) TO N ILUING RTE OF UPERELEVTION HOULER PLN GRE N POINT OF ROTTION (UPERELEVTE) L = TRNITION LENGTH OR UPERELEVTION RUNOFF OF INIE OR OUTIE EGE OF PVEMENT OVER RTE OF UPERELEVTION RMP = UPERELEVTION TRNITION LOPE OF PVEMENT EGE HOULER NOTE: THE RON POINT N POINT OF ROTTION ILL NORMLLY E T THE ENTER OF TO-LNE N FOUR-LNE UNIVIE PVEMENT N T THE EGE OF N INIE LNE OF FIVE-LNE UNIVIE PVEMENT. THE POINT OF ROTTION ILL NORMLLY E T THE INIE EGE OF IVIE PVEMENT. THE RON I TO E REMOVE IN UPERELEVTION ETION. ON URN ERVIE RO N URN FREE E TRUNKLINE URVE HERE RIVEY RE PREVLENT, N HERE NORML UPERELEVTION NNOT E OTINE, MINIMUM OF. TO UPERELEVTION IN THE IRETION OF THE URVE MY E UE TO REMOVE THE VERE RON. EIGN MOIFITION OF TRNITION, POINT OF ROTTION, N RON MY E NEERY TO IMPROVE RIING QULITY N PPERE. THE LOTION, LENGTH OF UPERELEVTION TRNITION, RON RUNOFF LENGTH, UPERELEVTION RTE, N POINT OF ROTTION ILL E PEIFIE ON THE PLN. PIRL LENGTH ILL E EQUL TO OR LONGER THN TRNITION LOPE LENGTH. PIRL TRNITION HOUL E UE ON NE LIGNMENT, E ON THE EIGN PEE OF THE URVE N THE RIU HON IN THE TLE. THE TLE GIVE THE MXIMUM RIU IN HIH PIRL HOUL E UE. EGIN THE HIGH IE HOULER TRNITION T THE PVEMENT RON RUN OUT POINT (RON REMOVE). TRNITION THE HOULER IN THE ITE "L" TO THE HOULER LOPE RTE REQUIRE T FULL PVEMENT UPERELEVTION. IF THE RTE OF FULL PVEMENT UPERELEVTION I GRETER THN THE NORML HOULER LOPE, EGIN THE LO IE HOULER TRNITION HEN THE PVEMENT REHE THE ME PLNE N LOPE RTE THE NORML HOULER. HEN TRNITIONING THE HOULER LOPE TO/FROM RIGE ETION, LULTE THE TRNITION ITE UING THE UPERELEVTION TRNITION LOPE ( ) REQUIRE FOR THE URVE, OR IN TNGENT ETION, UE THE MINIMUM VLUE FOR UPERELEVTION TRNITION LOPE ( ) GIVEN IN THE TLE, IN THE OLUMN FOR THE PEE OF THE ROY. (TRNITION ITE = HOULER ITH x (RTE OF RIGE HOULER UPERELEVTION MINU RTE OF RO HOULER UPERELEVTION) x 00 / ) EPRTMENT IRETOR Kirk T. teudle MIHIGN EPRTMENT OF TRNPORTTION UREU OF HIGHY EVELOPMENT TNR PLN FOR Michigan epartment of Transportation PREPRE Y PPROVE Y: ENGINEER OF ELIVERY UPERELEVTION N PVEMENT RON EIGN IVIION RN Y: HEKE Y:.L.T..K.P. PPROVE Y: ENGINEER OF EVELOPMENT F.H... PPROVL PLN TE R-0-H HEET OF
2 RTE OF UPERELEVTION N UPERELEVTION TRNITION LOPE URN RIU (FEET) 0 MPH MPH 0 MPH MPH 0 MPH MPH 0 MPH MPH FREEY FREEY N URN RMP 0 MPH MPH 0 MPH e e e e e e e e e e e R MIN.= R MIN.= R MIN.= R MIN.= R MIN.= R MIN.= NOTE: R MIN.= 9 LOOP RMP HLL HVE RTE OF UPERELEVTION R MIN.= THE RTE OF UPERELEVTION FOR URVE PPROHING RMP TERMINL (TOPPING ONITION) HOUL E LIMITE TO MX R MIN.= IF ELT VLUE FROM THE HRT NNOT E OTINE FOR THE EIGN RIU, UE THE MXIMUM ELT VLUE FOR THE ORREPONING PEE R MIN.= FOR RII LE THN THOE TULTE, (UT NOT LE THN R MIN.), UE e max. MXIMUM UPERELEVTION FOR URN FREEY N URN RMP (ITH 0 MPH EIGN PEE) I, OTHERIE maxe = R MIN.= MIHIGN EPRTMENT OF TRNPORTTION UREU OF HIGHY EVELOPMENT TNR PLN FOR UPERELEVTION N PVEMENT RON F.H... PPROVL PLN TE R-0-H HEET OF NOTE: THI PLN I NOT LEGL ENGINEERING OUMENT UT N ELETRONI UPLITE. THE ORIGINL IGNE OPY PPROVE FOR PULITION, I KEPT ON FILE T THE MIHIGN EPRTMENT OF TRNPORTTION.
3 REVITION FOR PIRLE RMP N ROY: T.. = TNGENT TO PIRL.T. = PIRL TO TNGENT.. = URVE TO PIRL P ITE FROM P IN FT. = RON.. = PIRL TO URVE P = RON POINT PIRL URVE TRNITION EIGN PEE (MPH) MXIMUM RIU (FEET) EIGN PEE (MPH) MXIMUM RIU (FEET) = (00) L = (00) L = (00) (UE ONLY FOR ETERMINING P/PT) PLN GRE N POINT OF ROTTION NO - (00) TRNITION TUL TRNITION PLN GRE N POINT OF ROTTION ETION T ETION T ETION T ETION T ETION T ETION T ETION T ETION T UNPIRLE RMP (RON VERE TO UPER) UNPIRLE RMP (RON ME IRETION UPER) = (00) L = (00) PLN GRE N POINT OF ROTTION ETION T ETION T ETION T ETION T UNPIRLE TO-Y ROY MIHIGN EPRTMENT OF TRNPORTTION UREU OF HIGHY EVELOPMENT TNR PLN FOR UPERELEVTION N PVEMENT RON F.H... PPROVL PLN TE R-0-H HEET OF
4 / = (00) - / L = (00) LEFT ROY / / / RIGHT ROY / PLN GRE OR POINT OF ROTTION / / / ETION T ETION T ETION T ETION T UNPIRLE FOUR LNE IVIE ROY OUTIE = (00) - L OUTIE = (00) OUTIE ETION T LEFT ROY RIGHT ROY PLN GRE N POINT OF ROTTION INIE = (00) - L INIE = (00) INIE E ETION T ETION T ETION T ETION T E UNPIRLE IX LNE IVIE ROY MIHIGN EPRTMENT OF TRNPORTTION UREU OF HIGHY EVELOPMENT TNR PLN FOR UPERELEVTION N PVEMENT RON F.H... PPROVL PLN TE R-0-H HEET OF
5 = (00) L = (00) L = (00) T.. OR.T... OR.. T.. OR.T... OR.. PLN GRE OR POINT OF ROTTION NO - (00) TRNITION TUL TRNITION PLN GRE OR POINT OF ROTTION ETION T ETION T ETION T ETION T ETION T ETION T ETION T ETION T PIRLE RMP (RON VERE TO UPER) PIRLE RMP (RON ME IRETION UPER) = (00) L = (00) T.. OR.T.. OR.. PLN GRE N POINT OF ROTTION ETION T ETION T ETION T ETION T PIRLE TO-Y ROY MIHIGN EPRTMENT OF TRNPORTTION UREU OF HIGHY EVELOPMENT TNR PLN FOR UPERELEVTION N PVEMENT RON F.H... PPROVL PLN TE R-0-H HEET OF
6 / = (00) - / L = (00) T.. OR.T.. OR.. LEFT ROY / / / RIGHT ROY / PLN GRE OR POINT OF ROTTION / / / ETION T ETION T ETION T ETION T PIRLE FOUR LNE IVIE ROY = (00) OUTIE T.. OR.T. - L OUTIE = (00). OR.. ETION T LEFT ROY RIGHT ROY T.. OR.T. PLN GRE N POINT OF ROTTION INIE = (00) - L INIE = (00). OR.. E ETION T ETION T ETION T ETION T E PIRLE IX LNE IVIE ROY MIHIGN EPRTMENT OF TRNPORTTION UREU OF HIGHY EVELOPMENT TNR PLN FOR UPERELEVTION N PVEMENT RON F.H... PPROVL PLN TE R-0-H HEET OF
7 = (00) L = (00) Z VLUE FOR UNPIRLE TO Y ROY ITH N O NUMER OF LNE Z Ḋ ETION T Z Ḋ ETION T Z. ETION T - (00) ETION T UNPIRLE TO Y ROY ITH O NUMER OF LNE = (00) L = (00) Z. (FRTHET EGE ON LO IE) NUMER OF LNE Z / / - (00) Z Ḋ ETION T ETION T ETION T ETION T UNPIRLE TO Y ROY ITH O NUMER OF LNE (FRTHET EGE ON HIGH IE) MIHIGN EPRTMENT OF TRNPORTTION UREU OF HIGHY EVELOPMENT TNR PLN FOR UPERELEVTION N PVEMENT RON F.H... PPROVL PLN TE R-0-H HEET OF
for all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx
![for all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx](/thumbs/74/70408252.jpg "for all x in [a,b], then the area of the region bounded by the graphs of f and g and the vertical lines x = a and x = b is b [ ( ) ( )] A= f x g x dx")
Applitions of Integrtion Are of Region Between Two Curves Ojetive: Fin the re of region etween two urves using integrtion. Fin the re of region etween interseting urves using integrtion. Desrie integrtion
Approximation of continuous-time systems with discrete-time systems
Approximtion of continuou-time ytem with icrete-time ytem he continuou-time ytem re replce by icrete-time ytem even for the proceing of continuou-time ignl.. Impule invrince metho 2. Step invrince metho
UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION. B.Sc. Mathematics. (2011 Admn.) Semester Core Course VECTOR CALCULUS
Shool of Dtne Eution UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION B.S. Mthemt 2011 Amn. V Semester Core Course VECTOR CALCULUS Question Bnk & Answer Key 1. The Components of the vetor with initil
I 3 2 = I I 4 = 2A
ECE 210 Eletril Ciruit Anlysis University of llinois t Chigo 2.13 We re ske to use KCL to fin urrents 1 4. The key point in pplying KCL in this prolem is to strt with noe where only one of the urrents
FINAL CONSTRUCTION PLANS FOR COUNTRY HILLS OFFICE CAMPUS LOT 4A
FINL ONTRUTION PLN FOR OUNTRY HILL OFFIE MPU LOT GENY ONTT LIT ENTUR HELTH () 67-98 88 INVERNE R W # TTN: OTT ROOK ENGLEWOO, OLORO 8 ERMN 7TH TREET () 8- ENVER, OLORO 8 TTN: ERIK HNEN ITY OF THORNTON ()
Electronic Circuits I Revision after midterm
Eletroni Ciruits I Revision fter miterm Dr. Ahme ElShfee, ACU : Fll 2018, Eletroni Ciruits I -1 / 14 - MCQ1 # Question If the frequeny of the input voltge in Figure 2 36 is inrese, the output voltge will
50 AMC Lectures Problem Book 2 (36) Substitution Method
0 AMC Letures Prolem Book Sustitution Metho PROBLEMS Prolem : Solve for rel : 9 + 99 + 9 = Prolem : Solve for rel : 0 9 8 8 Prolem : Show tht if 8 Prolem : Show tht + + if rel numers,, n stisf + + = Prolem
Eigenvectors and Eigenvalues
MTB 050 1 ORIGIN 1 Eigenvets n Eigenvlues This wksheet esries the lger use to lulte "prinipl" "hrteristi" iretions lle Eigenvets n the "prinipl" "hrteristi" vlues lle Eigenvlues ssoite with these iretions.
PHYSICS 211 MIDTERM I 22 October 2003
PHYSICS MIDTERM I October 3 Exm i cloed book, cloed note. Ue onl our formul heet. Write ll work nd nwer in exm booklet. The bck of pge will not be grded unle ou o requet on the front of the pge. Show ll
C (6) DOORS TYPICAL, ALL SAME SIZE ENCLOSURE, CUSTOM 6 DOOR REVISION HISTORY ZONE REV DESCRIPTION DATE APPROVED 0.01 RELEASE FOR QUOTE 11/16/12 PH
REVISION HISTORY ZONE REV ESRIPTION TE PPROVE 0.0 RELESE FOR QUOTE /6/2 PH 0.02 E ITONL ETL FOR PGO HOO, SE N OORS. RELESE FOR PROUTION 2/4/3 PH 0.03 INRESE OVERLL OF ENLOUSRE 2/8/3 PH 0.04 REVISE OOR
A Primer on Continuous-time Economic Dynamics
Eonomis 205A Fll 2008 K Kletzer A Primer on Continuous-time Eonomi Dnmis A Liner Differentil Eqution Sstems (i) Simplest se We egin with the simple liner first-orer ifferentil eqution The generl solution
FOUR SCORE, LLC 144 STURBRIDGE ROAD CHARLTON, MA, PROJECT: PROJECT TEAM MECHANICAL
matthew@ 40.25.0749 c rebecca@ 40.25.0869 c HRLTON, M, 020 PROJET TEM OPE ONER: THE OPE I GENERLLY EFINE THE INTERIOR REONFIGURTION OF ITING INGLE TORY INUTRIL PE INTO ULTIVTION FILITY. INIENTL ETERIOR
Solids of Revolution
Solis of Revolution Solis of revolution re rete tking n re n revolving it roun n is of rottion. There re two methos to etermine the volume of the soli of revolution: the isk metho n the shell metho. Disk
CSCI565 - Compiler Design
CSCI565 - Compiler Deign Spring 6 Due Dte: Fe. 5, 6 t : PM in Cl Prolem [ point]: Regulr Expreion nd Finite Automt Develop regulr expreion (RE) tht detet the longet tring over the lphet {-} with the following
( ) Same as above but m = f x = f x - symmetric to y-axis. find where f ( x) Relative: Find where f ( x) x a + lim exists ( lim f exists.
AP Clculus Finl Review Sheet solutions When you see the words This is wht you think of doing Find the zeros Set function =, fctor or use qudrtic eqution if qudrtic, grph to find zeros on clcultor Find
20-JUNE-14 SCHEMATIC HSC REV. DRAWING NO.
THI RWING I THE PROPERTY OF NLOG EVIE IN. IT I NOT TO E REPROUE OR OPIE, IN WHOLE OR IN PRT, OR UE IN FURNIHING INFORMTION TO OTHER, OR FOR NY OTHER PURPOE ETRIMTL TO THE INTERET OF NLOG EVIE. THE EQUIPMT
Section 2.3. Matrix Inverses
Mtri lger Mtri nverses Setion.. Mtri nverses hree si opertions on mtries, ition, multiplition, n sutrtion, re nlogues for mtries of the sme opertions for numers. n this setion we introue the mtri nlogue
Solving Radical Equations
Solving dil Equtions Equtions with dils: A rdil eqution is n eqution in whih vrible ppers in one or more rdinds. Some emples o rdil equtions re: Solution o dil Eqution: The solution o rdil eqution is the
2 D 4X ( 9.81) SHOWN WITH CAM LEVER AND SPACER IN LOADED POSTION APPLICABLE COMPONENTS (FOR REFERENCE ONLY) NOMINAL TERMINAL SIZE
THIS RWING IS UNPULISHE. OPYRIGHT Y RELESE FOR PULITION LL RIGHTS RESERVE. P LTR ESRIPTION TE WN PV G REVISE PER EO0 JUL L M G REVISE PER EO00 MY L M G REVISE PER EO0 0OT L M. PRINT FOR PRT NUMER (SEE
STRUNET CONCRETE DESIGN AIDS
Introtion to Conrete Bem Deign Flow Chrt The onrete em eign low hrt re the ollowing jet: For retnglr em with given imenion: Anlzing the em etion to etere it moment trength n th eining the em etion to e
Linear Inequalities. Work Sheet 1
Work Sheet 1 Liner Inequlities Rent--Hep, cr rentl compny,chrges $ 15 per week plus $ 0.0 per mile to rent one of their crs. Suppose you re limited y how much money you cn spend for the week : You cn spend
Lecture 6: Coding theory
Leture 6: Coing theory Biology 429 Crl Bergstrom Ferury 4, 2008 Soures: This leture loosely follows Cover n Thoms Chpter 5 n Yeung Chpter 3. As usul, some of the text n equtions re tken iretly from those
Continuous 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
2.1 ANGLES AND THEIR MEASURE. y I
.1 ANGLES AND THEIR MEASURE Given two interseting lines or line segments, the mount of rottion out the point of intersetion (the vertex) required to ring one into orrespondene with the other is lled the
Vector Integration. Line integral: Let F ( x y,
Vetor Integrtion Thi hpter tret integrtion in vetor field. It i the mthemti tht engineer nd phiit ue to deribe fluid flow, deign underwter trnmiion ble, eplin the flow of het in tr, nd put tellite in orbit.
The Stirling Engine: The Heat Engine
Memoril University of Newfounln Deprtment of Physis n Physil Oenogrphy Physis 2053 Lortory he Stirling Engine: he Het Engine Do not ttempt to operte the engine without supervision. Introution Het engines
AP Calculus BC Chapter 8: Integration Techniques, L Hopital s Rule and Improper Integrals
AP Clulus BC Chpter 8: Integrtion Tehniques, L Hopitl s Rule nd Improper Integrls 8. Bsi Integrtion Rules In this setion we will review vrious integrtion strtegies. Strtegies: I. Seprte the integrnd into
VTU NOTES QUESTION PAPERS NEWS RESULTS FORUMS Vector Integration
www.boopr.om VTU NOTES QUESTION PAPERS NEWS RESULTS FORUMS Vetor Integrtion Thi hpter tret integrtion in vetor field. It i the mthemti tht engineer nd phiit ue to deribe fluid flow, deign underwter trnmiion
Minnesota 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.
EE Control Systems LECTURE 8
Coyright F.L. Lewi 999 All right reerved Udted: Sundy, Ferury, 999 EE 44 - Control Sytem LECTURE 8 REALIZATION AND CANONICAL FORMS A liner time-invrint (LTI) ytem cn e rereented in mny wy, including: differentil
Calculate the efficiency associated with one rotation of the axle
We cn clculte the efficiency of one rottion of the xle by exining the work one. k Mx Your Rie: Workheet hi ctivity will tke you through the tep neee to optiize the work ue in your ouetrp cr. ollow thi
Edexcel GCE Core Mathematics (C2) Required Knowledge Information Sheet. Daniel Hammocks
Edexcel GCE Core Mthemtics (C) Required Knowledge Informtion Sheet C Formule Given in Mthemticl Formule nd Sttisticl Tles Booklet Cosine Rule o = + c c cosine (A) Binomil Series o ( + ) n = n + n 1 n 1
Probability. b a b. a b 32.
Proility If n event n hppen in '' wys nd fil in '' wys, nd eh of these wys is eqully likely, then proility or the hne, or its hppening is, nd tht of its filing is eg, If in lottery there re prizes nd lnks,
Statistics in medicine
Sttistis in meiine Workshop 1: Sreening n ignosti test evlution Septemer 22, 2016 10:00 AM to 11:50 AM Hope 110 Ftm Shel, MD, MS, MPH, PhD Assistnt Professor Chroni Epiemiology Deprtment Yle Shool of Puli
AP Physics C: Electricity & Magnetism 1999 Free-Response Questions
AP Physics C: Electricity & Mgnetism 1999 Free-esponse Questions The mterils included in these files re intended for non-commercil use by AP techers for course nd exm preprtion; permission for ny other
SCHEMATIC REV. DRAWING NO RELAY CONTROL CHART A A DE N V C L O REVISIONS
THI RWIN I THE PROPERTY OF NLO EVIE IN. IT I NOT TO E REPROUE OR OPIE, IN WHOLE OR IN PRT, OR UE IN FURNIHIN INFORMTN TO OTHER, OR FOR NY OTHER PURPOE ETRIMENTL TO THE INTERET OF NLO EVIE. THE EQUIPMENT
Now we must transform the original model so we can use the new parameters. = S max. Recruits
MODEL FOR VARIABLE RECRUITMENT (ontinue) Alterntive Prmeteriztions of the pwner-reruit Moels We n write ny moel in numerous ifferent ut equivlent forms. Uner ertin irumstnes it is onvenient to work with
Comparing the Pre-image and Image of a Dilation
hpter Summry Key Terms Postultes nd Theorems similr tringles (.1) inluded ngle (.2) inluded side (.2) geometri men (.) indiret mesurement (.6) ngle-ngle Similrity Theorem (.2) Side-Side-Side Similrity
Ch 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,
Math 2142 Homework 2 Solutions. Problem 1. Prove the following formulas for Laplace transforms for s > 0. a s 2 + a 2 L{cos at} = e st.
Mth 2142 Homework 2 Solution Problem 1. Prove the following formul for Lplce trnform for >. L{1} = 1 L{t} = 1 2 L{in t} = 2 + 2 L{co t} = 2 + 2 Solution. For the firt Lplce trnform, we need to clculte:
is the cut off frequency in rads.
0 ELETRIAL IRUITS 9. HIGH RDER ATIVE FILTERS (With Tle) Introdution Thi development explin how to deign Butterworth (Mximlly Flt) or heyhev (Equl Ripple) Low P, High P or Bnd P tive filter. Thi tretment
Farey Fractions. Rickard Fernström. U.U.D.M. Project Report 2017:24. Department of Mathematics Uppsala University
U.U.D.M. Project Report 07:4 Frey Frctions Rickrd Fernström Exmensrete i mtemtik, 5 hp Hledre: Andres Strömergsson Exmintor: Jörgen Östensson Juni 07 Deprtment of Mthemtics Uppsl University Frey Frctions
Applied. Grade 9 Assessment of Mathematics. Multiple-Choice Items. Winter 2005
Applie Gre 9 Assessment of Mthemtis Multiple-Choie Items Winter 2005 Plese note: The formt of these ooklets is slightly ifferent from tht use for the ssessment. The items themselves remin the sme. . Multiple-Choie
QUADRATIC EQUATION. Contents
QUADRATIC EQUATION Contents Topi Pge No. Theory 0-04 Exerise - 05-09 Exerise - 09-3 Exerise - 3 4-5 Exerise - 4 6 Answer Key 7-8 Syllus Qudrti equtions with rel oeffiients, reltions etween roots nd oeffiients,
20.2. The Transform and its Inverse. Introduction. Prerequisites. Learning Outcomes
The Trnform nd it Invere 2.2 Introduction In thi Section we formlly introduce the Lplce trnform. The trnform i only pplied to cul function which were introduced in Section 2.1. We find the Lplce trnform
Practice 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
1 This question is about mean bond enthalpies and their use in the calculation of enthalpy changes.
1 This question is out men ond enthlpies nd their use in the lultion of enthlpy hnges. Define men ond enthlpy s pplied to hlorine. Explin why the enthlpy of tomistion of hlorine is extly hlf the men ond
Design a reinforced concrete retaining wall for the following conditions. f'c = 3000 psi fy = 60 ksi
CE 4 Fall 005 Retag all Deign Example / 8 Deign a reore onrete retag all or the ollog onition. 000 pi 0 i rharge q 400 p Fill: φ o Unit t 00 p H 8 t toe t tem Natral Soil: φ o alloable bearg prere 5000p
f (x)dx = f(b) f(a). a b f (x)dx is the limit of sums
Green s Theorem If f is funtion of one vrible x with derivtive f x) or df dx to the Fundmentl Theorem of lulus, nd [, b] is given intervl then, ording This is not trivil result, onsidering tht b b f x)dx
Location: 229 T y S n - Hμ Néi Code: Eurocode 4 Member: Beams Category: Podium
Projet: ipe Toer Lotion: 9 T S n - Hμ Néi Code: Euroode 4 ember: Bem Ctegor: Podium I - DESIGN DT 1. teril: 1.1 Conrete Compoite bem Conrete grde: 400 (TCVN 5574-1991 C5/30 (Euroode 4) Chrteriti ompreion
Numbers and indices. 1.1 Fractions. GCSE C Example 1. Handy hint. Key point
GCSE C Emple 7 Work out 9 Give your nswer in its simplest form Numers n inies Reiprote mens invert or turn upsie own The reiprol of is 9 9 Mke sure you only invert the frtion you re iviing y 7 You multiply
1. If y 2 2x 2y + 5 = 0 is (A) a circle with centre (1, 1) (B) a parabola with vertex (1, 2) 9 (A) 0, (B) 4, (C) (4, 4) (D) a (C) c = am m.
SET I. If y x y + 5 = 0 is (A) circle with centre (, ) (B) prbol with vertex (, ) (C) prbol with directrix x = 3. The focus of the prbol x 8x + y + 7 = 0 is (D) prbol with directrix x = 9 9 (A) 0, (B)
v v at 1 2 d vit at v v 2a d
SPH3UW Unt. Accelerton n One Denon Pge o 9 Note Phyc Inventory Accelerton the rte o chnge o velocty. Averge ccelerton, ve the chnge n velocty dvded by the te ntervl, v v v ve. t t v dv Intntneou ccelerton
4. UNBALANCED 3 FAULTS
4. UNBALANCED AULTS So fr: we hve tudied lned fult ut unlned fult re more ommon. Need: to nlye unlned ytem. Could: nlye three-wire ytem V n V n V n Mot ommon fult type = ingle-phe to ground i.e. write
CS3510 Design & Analysis of Algorithms Fall 2017 Section A. Test 3 Solutions. Instructor: Richard Peng In class, Wednesday, Nov 15, 2017
Uer ID (NOT he 9 igi numer): gurell4 CS351 Deign & Anlyi of Algorihm Fll 17 Seion A Te 3 Soluion Inruor: Rihr Peng In l, Weney, Nov 15, 17 Do no open hi quiz ookle unil you re iree o o o. Re ll he inruion
Set 6 Paper 2. Set 6 Paper 2. 1 Pearson Education Asia Limited 2017
Set 6 Pper Set 6 Pper. C. C. A. D. B 6. D 7. D 8. A 9. D 0. A. B. B. A. B. B 6. B 7. D 8. C 9. D 0. D. A. A. B. B. C 6. C 7. A 8. B 9. A 0. A. C. D. B. B. B 6. A 7. D 8. A 9. C 0. C. C. D. C. C. D Section
I1 = 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
GRAND PLAN. Visualizing Quaternions. I: Fundamentals of Quaternions. Andrew J. Hanson. II: Visualizing Quaternion Geometry. III: Quaternion Frames
Visuliing Quternions Andrew J. Hnson Computer Siene Deprtment Indin Universit Siggrph Tutoril GRAND PLAN I: Fundmentls of Quternions II: Visuliing Quternion Geometr III: Quternion Frmes IV: Clifford Algers
Expectation and Variance
Expecttion nd Vrince : sum of two die rolls P(= P(= = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 P(=2) = 1/36 P(=3) = 1/18 P(=4) = 1/12 P(=5) = 1/9 P(=7) = 1/6 P(=13) =? 2 1/36 3 1/18 4 1/12 5 1/9 6 5/36 7 1/6
DEPARTMENT OF WATER ENVIRONMENT PROTECTION ONONDAGA COUNTY, NEW YORK
EPRTMENT OF WTER ENVIRONMENT PROTETION ONONG OUNTY, NEW YORK FERURY 0 OK ORHR WSTEWTER TRETMENT PLNT LGOON LENING N REHILITTION PROJET ONTRT NO. GENERL ONONG OUNTY RWING INE SHT. NO. ESRIPTION NEW YORK
CS 2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2014
S 224 DIGITAL LOGI & STATE MAHINE DESIGN SPRING 214 DUE : Mrh 27, 214 HOMEWORK III READ : Relte portions of hpters VII n VIII ASSIGNMENT : There re three questions. Solve ll homework n exm prolems s shown
Polynomials and Division Theory
Higher Checklist (Unit ) Higher Checklist (Unit ) Polynomils nd Division Theory Skill Achieved? Know tht polynomil (expression) is of the form: n x + n x n + n x n + + n x + x + 0 where the i R re the
User's Guide of the Inter-Batch Physico-Chemical Variability Calculator
User's Guide of the Inter-Btch Physico-Chemicl Vribility Clcultor Scope The Inter-Btch Physico-Chemicl Vribility (IBPCV) Clcultor enbles to test if the beteenbtch vribility of the physico-chemicl chrcteristics
Formula for Trapezoid estimate using Left and Right estimates: Trap( n) If the graph of f is decreasing on [a, b], then f ( x ) dx
![Formula for Trapezoid estimate using Left and Right estimates: Trap( n) If the graph of f is decreasing on [a, b], then f ( x ) dx](/thumbs/79/79316452.jpg "Formula for Trapezoid estimate using Left and Right estimates: Trap( n) If the graph of f is decreasing on [a, b], then f ( x ) dx")
Fill in the Blnks for the Big Topis in Chpter 5: The Definite Integrl Estimting n integrl using Riemnn sum:. The Left rule uses the left endpoint of eh suintervl.. The Right rule uses the right endpoint
微波電路講義. eff concept, conformal mapping solution, electrostatic solution 3.11 Summary of transmission lines and waveguides 3-1
Chpte 3 Tnsmissin Lines n Wveguies 3. Genel slutins f TEM, TE n TM wves peues, 3.5 Cxil line (TEM line) TEM me, highe e me et 3.7 Stipline (TEM line) nfml mpping slutin, eletstti slutin 3.8 Mistip (qusi-tem
Artificial Intelligence Markov Decision Problems
rtificil Intelligence Mrkov eciion Problem ilon - briefly mentioned in hpter Ruell nd orvig - hpter 7 Mrkov eciion Problem; pge of Mrkov eciion Problem; pge of exmple: probbilitic blockworld ction outcome
F / x everywhere in some domain containing R. Then, + ). (10.4.1)
0.4 Green's theorem in the plne Double integrls over plne region my be trnsforme into line integrls over the bounry of the region n onversely. This is of prtil interest beuse it my simplify the evlution
ECE 274 Digital Logic RTL Design: Introduction. Digital Design. RTL Design: Capture Behavior, Convert to Circuit. Introduction.
i ni e z ECE 274 igitl ogi T eign: ntroution (Vhi): Ch. 5.1 5.2 Chpter 5: egiter-trnfer evel (T) eign lie to ompny the textbook, Firt Eition, by, John Wiley n on Publiher, 2007. http://www.vhi.om Copyright
Mid-Term Examination - Spring 2014 Mathematical Programming with Applications to Economics Total Score: 45; Time: 3 hours
Mi-Term Exmintion - Spring 0 Mthemtil Progrmming with Applitions to Eonomis Totl Sore: 5; Time: hours. Let G = (N, E) e irete grph. Define the inegree of vertex i N s the numer of eges tht re oming into
SOME COPLANAR POINTS IN TETRAHEDRON
Journl of Pure n Applie Mthemtis: Avnes n Applitions Volume 16, Numer 2, 2016, Pges 109-114 Aville t http://sientifivnes.o.in DOI: http://x.oi.org/10.18642/jpm_7100121752 SOME COPLANAR POINTS IN TETRAHEDRON
( ) as a fraction. Determine location of the highest
AB/ Clulus Exm Review Sheet Solutions A Prelulus Type prolems A1 A A3 A4 A5 A6 A7 This is wht you think of doing Find the zeros of f( x) Set funtion equl to Ftor or use qudrti eqution if qudrti Grph to
Partial 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
AP Calculus AB Unit 4 Assessment
Clss: Dte: 0-04 AP Clulus AB Unit 4 Assessment Multiple Choie Identify the hoie tht best ompletes the sttement or nswers the question. A lultor my NOT be used on this prt of the exm. (6 minutes). The slope
Table of Content. c 1 / 5
Tehnil Informtion - t nd t Temperture for Controlger 03-2018 en Tble of Content Introdution....................................................................... 2 Definitions for t nd t..............................................................
AP Physics 1. Slide 1 / 71. Slide 2 / 71. Slide 3 / 71. Circular Motion. Topics of Uniform Circular Motion (UCM)
Slide 1 / 71 Slide 2 / 71 P Physics 1 irculr Motion 2015-12-02 www.njctl.org Topics of Uniform irculr Motion (UM) Slide 3 / 71 Kinemtics of UM lick on the topic to go to tht section Period, Frequency,
2. The Laplace Transform
. The Lplce Trnform. Review of Lplce Trnform Theory Pierre Simon Mrqui de Lplce (749-87 French tronomer, mthemticin nd politicin, Miniter of Interior for 6 wee under Npoleon, Preident of Acdemie Frncie
PRACTICE EXAM 2 SOLUTIONS
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Deprtment of Phyic Phyic 8.01x Fll Term 00 PRACTICE EXAM SOLUTIONS Proble: Thi i reltively trihtforwrd Newton Second Lw problem. We et up coordinte ytem which i poitive
ERT 316: REACTION ENGINEERING CHAPTER 3 RATE LAWS & STOICHIOMETRY
ER 316: REIO EGIEERIG HER 3 RE LWS & SOIHIOMERY 1 OULIE R 1: Rte Lws Reltive Rtes of Retion Retion Orer & Rte Lw Retion Rte onstnt, k R 2: Stoihiometry th System Stoihiometri le low System Stoihiometri
Restoration Design for RC Slab Bridges by AASHTO LRFD
プレストレストコンクリート工学会第 1 回シンポジウム論文集 (01 年 10 月 ) Retortion Deign or RC Slb Brige b AASHTO LRFD Yokoh Ntionl Univerit, Grute Stuent Abrh G. TAREKEGN Yokoh Ntionl Univerit, Meber o JPCI Ttu TSUBAKI Abtrt: Mot
10 Vector Integral Calculus
Vector Integrl lculus Vector integrl clculus extends integrls s known from clculus to integrls over curves ("line integrls"), surfces ("surfce integrls") nd solids ("volume integrls"). These integrls hve
Amphenol Canada Corp.
HET SINK OPTION = PIN STYLE HET SINK (NIKEL PLTE) N LIP (H=.mm; SN HEIGHT) = PIN STYLE HET SINK (NIKEL PLTE) N LIP (H=.mm; PI HEIGHT) = PIN STYLE HET SINK (NIKEL PLTE) N LIP (H=.mm; TLL) = PIN-FIN HET
Unit 2 Exponents Study Guide
Unit Eponents Stud Guide 7. Integer Eponents Prt : Zero Eponents Algeric Definition: 0 where cn e n non-zero vlue 0 ecuse 0 rised to n power less thn or equl to zero is n undefined vlue. Eple: 0 If ou
5: The Definite Integral
5: The Definite Integrl 5.: Estimting with Finite Sums Consider moving oject its velocity (meters per second) t ny time (seconds) is given y v t = t+. Cn we use this informtion to determine the distnce
PYTHAGORAS THEOREM,TRIGONOMETRY,BEARINGS AND THREE DIMENSIONAL PROBLEMS
PYTHGORS THEOREM,TRIGONOMETRY,ERINGS ND THREE DIMENSIONL PROLEMS 1.1 PYTHGORS THEOREM: 1. The Pythgors Theorem sttes tht the squre of the hypotenuse is equl to the sum of the squres of the other two sides
MATH Final Review
MATH 1591 - Finl Review November 20, 2005 1 Evlution of Limits 1. the ε δ definition of limit. 2. properties of limits. 3. how to use the diret substitution to find limit. 4. how to use the dividing out
SKEW-NORMAL CORRECTION TO GEODETIC DIRECTIONS ON AN ELLIPSOID
Geoptil Science SKEW-NORMAL CORRECTION TO GEODETIC DIRECTIONS ON AN ELLIPSOID In Figure, n re two point t height n h bove n ellipoi of P h emi-mjor xi, n flttening f. The norml n PH (piercing the PH ellipoi
Solutions to assignment 3
D Sruure n Algorihm FR 6. Informik Sner, Telikeplli WS 03/04 hp://www.mpi-.mpg.e/~ner/oure/lg03/inex.hml Soluion o ignmen 3 Exerie Arirge i he ue of irepnie in urreny exhnge re o rnform one uni of urreny
Identify graphs of linear inequalities on a number line.
COMPETENCY 1.0 KNOWLEDGE OF ALGEBRA SKILL 1.1 Identify grphs of liner inequlities on number line. - When grphing first-degree eqution, solve for the vrible. The grph of this solution will be single point
( ) where f ( x ) is a. AB/BC Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x).
AB/ Clculus Exm Review Sheet A. Preclculus Type prolems A1 Find the zeros of f ( x). This is wht you think of doing A2 Find the intersection of f ( x) nd g( x). A3 Show tht f ( x) is even. A4 Show tht
SIDESWAY MAGNIFICATION FACTORS FOR STEEL MOMENT FRAMES WITH VARIOUS TYPES OF COLUMN BASES
Advned Steel Constrution Vol., No., pp. 7-88 () 7 SIDESWAY MAGNIFICATION FACTORS FOR STEEL MOMENT FRAMES WIT VARIOUS TYPES OF COLUMN BASES J. ent sio Assoite Professor, Deprtment of Civil nd Environmentl
MATH 122, Final Exam
MATH, Finl Exm Winter Nme: Setion: You must show ll of your work on the exm pper, legily n in etil, to reeive reit. A formul sheet is tthe.. (7 pts eh) Evlute the following integrls. () 3x + x x Solution.
Calculus 2: Integration. Differentiation. Integration
Clculus 2: Integrtion The reverse process to differentition is known s integrtion. Differentition f() f () Integrtion As it is the opposite of finding the derivtive, the function obtined b integrtion is
CHAPTER 10 PARAMETRIC, VECTOR, AND POLAR FUNCTIONS. dy dx
CHAPTER 0 PARAMETRIC, VECTOR, AND POLAR FUNCTIONS 0.. PARAMETRIC FUNCTIONS A) Recll tht for prmetric equtions,. B) If the equtions x f(t), nd y g(t) define y s twice-differentile function of x, then t
APPENDIX 2 LAPLACE TRANSFORMS
APPENDIX LAPLACE TRANSFORMS Thi ppendix preent hort introduction to Lplce trnform, the bic tool ued in nlyzing continuou ytem in the frequency domin. The Lplce trnform convert liner ordinry differentil
C REVISED PER ECR DEC2015 T.S E.T $ D/C MATING CONNECTOR PART NUMBER WEIGHT. (g)
THIS RWING IS UNPULISHE. OPYRIGHT 00 Y RELESE FOR PULITION LL RIGHTS RESERVE. 00 ISIONS P LTR ESRIPTION TE WN PV 0.7 ISE PER ER0800 E0 T.S E.T 0.7 MTERIL HOUSING:POLYESTER OF GLSS FILLE THERMO PLSTI(UL9V0),
Problems (Show your work!)
Prctice Midter Multiple Choice 1. A. C 3. D 4. D 5. D 6. E 7. D 8. A 9. C 9. In word, 3.5*10 11 i E. 350 billion (I nubered 9 twice by itke!) 10. D 11. B 1. D 13. E 14. A 15. C 16. B 17. A 18. A 19. E
LONG-TERM EROSION DOWNSTREAM REGULATOR STRUCTURE
Sixth Interntionl Wter Tehnology Conferene, IWTC 1, Alexnri, Egypt LONG-TERM EROSION DOWNSTREAM REGULATOR STRUCTURE K. S. El-Alfy 1, M. N. Hmme, A. M. Tlt, n A. F. Yuoif 3 1 Ait Prof., Irrigtion & Hyruli,
EMI SPRINGS OUTER LIGHT PIPES , SCALE 5:1 REVERSED OUTER LIGHT PIPES , SCALE 5:1
THIS RWING IS UNPULISHE. OPYRIGHT Y RELESE FOR PULITION LL RIGHTS RESERVE. LO IST P LTR ESRIPTION TE WN PV RELESE PER EO1400878 13JUN14 JV PR REVISE PER EO1010819 10UG1 PP SH GE SSEMLY GSKET FLNGE EMI
( dg. ) 2 dt. + dt. dt j + dh. + dt. r(t) dt. Comparing this equation with the one listed above for the length of see that
Arc Length of Curves in Three Dimensionl Spce If the vector function r(t) f(t) i + g(t) j + h(t) k trces out the curve C s t vries, we cn mesure distnces long C using formul nerly identicl to one tht we
Appendix A: HVAC Equipment Efficiency Tables
Appenix A: HVAC Equipment Effiieny Tles Figure A.1 Resientil Centrl Air Conitioner FEMP Effiieny Reommention Prout Type Reommene Level Best Aville 11.0 or more EER 14.6 EER Split Systems 13.0 or more SEER