Chapter 7

Unit Analysis

Activity

Creates an awareness of real-world applications of

measurement formulas.

As a result of this activity thestudent will be able to usemathematical equations or

calculations to solve 'real world'problems.

Used as extra credit on finalexam, done in pairs in class.

C7Al

Forensic Science

Who actually uses this stuff? How many times have you wanted to ask yourinstructor this question? Here is your chance to see how one group ofprofessionals uses formulas.

Forensic Science is a popular subject now with TV shows like CSI andForensic Files. Each case involves people from different areas of expertisesuch as toxicology, anthropology, accident reconstruction, ballistics, etc. Inthe course of analyzing the evidence in a case, several of these experts useformulas.

PatbologylMedicaiExaminer

The time (in hours) since death occurs can be estimated for the first 8 hours by theformula:

T = 37 - 1.5t

where ! = currentbodytemperaturein °C, and t .= time sincedeath.

Many factors ftom the environment can affect the body temperature so other changes inthe body such as rigor mortis and livor mortis can also be used to estimate time of death.

11) A bodytemperaturewastaken 2- hoursafterdeath. Whatwouldyouexpect2

the temperatureof the bodyto be in °C ?

2) Convert your solution to Of.

How can the Medical Examiner calculate how long a body has been dead by using thebody's temperature? To do this, we need to rewrite our formula.

T - 37t =

-1.5

t = time since death T = CWTentbody temperature in °C

~'()3) .Abody is found and the temperature of the body is , C. How long has this person

been dead?

4) The temperature of a body is 78.35 op~ How long has this person been dead?

Anthropology

. When bones are discovered, the stature of the person may help to identify the person. Ifthe entire skeleton is not present, then the long bones (ulna, radius, femur, tibia, fibula) ofthe body can be used to estimate height.

1) Find your height in inches on the wall height chart. in.

2) Have your partner measure your ulna in centimeters. em.

Lower Limit em. Uooer Limit em.

3) Use the fonnulasbelowto findthe lowerandupper limitsfor heightin centimeters.

Black Males Lower Limit 3.26 . ULNA + 79.29 - 4.42UpperLimit 3.26. ULNA + 79.29 + 4.42

WhiteMales LowerLimit 3.70 . ULNA + 74.05 - 4.32Upper Limit 3.70 . ULNA + 74.05 + 4.32

Black_Females LowerLimit 3.31 . ULNA + 75.38 - 4.83

UpperLimit 3.31 . ULNA + 75.38 + 4.83

White Females LowerLimit 4.27 . ULNA + 57.76 - 4.30Upper Limit 4.27 . ULNA + 57.76 + 4.30

4) Use the conversion factor 1 inch = 2.54 centimeten to convert your lower andupper limits ftom centimeters to inches.

Lower Limit inches

UDDer Limit inches

5) Does your height fall within this range?

Info Sheet

A concise place for theconversions used in this chapter.

C711

Matbematlcs Flexible Leamlnl! CenterReference Sbeet

Perimeter is the sum of tbe lengths of the sides.

Area of a rectaagle A" (Length) x (Width)

Mean is the average.

Area ora triaugle A_!(Base) x (Height)2

Order of Operations - farentheslsE,xponeatsMultiply or nlvlde as you see left to rightAdd or ~ubtract as you see left to right

Words to Numben fA Few Common Samnles\

Four times a numberThe sum of twice a number and threeThe difference of three times a number and five

The product of 5 and a number

The quotient of a number and six

Length Is five more than the widthLength Is four leIS tban three times tbe widthTbe sum of a number and elgbtThe difference of a Dumber and sevenSix times the difference of a twice a number and one

Length is twice the width

4a2n+33n-55n.6L-W+53L .. 3W -4n+8n-76(2n- I)L .. 2W

u.s. O' AIUtA

sq.in (in')- l44in' III'sq.lI(ft') 144 inl . I at

-or-1ft' 844in'

sq.yd(yd')- 9ft' .!Itsq.ft(ft') 9 ft' -I yd' Iyd, or 9ft'

43,560ft' 18CICIcres-sq. ft I 8CIC- 43,560 ft'

-or-lacre 43p601I'

.....-sq. 640aaa-lmi'640aaa lmi'

miles(mi') a;;;ror

ACTUAL CONVERSJQNFACTORS. BI!TWI!I!N

'I1fE NB11UC AND U.s. SYS'I1!MSOP MJ!ASUIU!MI!NI"LENGTHincha-- 2.54em lin-or-centimeterS 2.S4cm-' in lin 2.54em

3.28ft 1mfocI__ Im-3.28ft

-or-1m 3.28ft

1.61km 1mmila--kilomclas 1.61km-I mi

-or-1m 1.61km

AREA

sqinches--- .6."Scml. t in'6.45em' lin2

sqccnlimctas -.r.;ror 6.45em'

...meta&-- IJ96 yd' -I...' 1.196r" 1m'sqyanIs 1m or\.I 96yd'

......---hectaRS2.47"".... lha

I ha -2.47 """'"

-or-1ha 2.47_

VOLUME

cubic inclJa..-- 16.39mL- I in'16.39mL lin'

millililCl'S J'j;Ior'i6.39;l

IitI:II-<JUIIII 1.06ql-llilerl.06qt llikiror-lliler 1.06qt

pllons--3.19lilaS - I pi 3.19li_or

lilaS Ipi 3.19litcnWEIGHT

ounces-.. loz28.3,-loz or-

pams 10. 28.3,

kilopams-2.20 I.... I q or

pounds I lea 2.20lb

UNITS 011L NGJ:RIN''I'HR U.s. a-M.

feel (1I)--.indK:s (in) 12in-1 II12in 1ftlii'"or"i2j;

focI-yds (yd) I yd-3ft l!!.or!l!!1)'11 3ft

I mi-5,280ft5.280ft lmi

feel--mita (mi) -or-Imi 5,28011

UNITS 011VOLUMII:IN TIIJI:U.s. SWTEM .

eubic incha (in ')- 1.728in' III'

cubic feel(ft ') I ftJ -1,728 in--or-

1ft' 1.728inl

cubicfeel(ft')- 270' .!l!tcubic yanIs (yd') l)d' -27 ft' -Iyd' or 27ft'

Ouidounces(0 oz)-- \C-80oz800z 'Ie-or-

cup(e) Ie 800z

...--piatI (pC) I pI- 2 c or!l!tpl 2e

(ql) Iqt-2p1 !I!!._Iqt 2p1

q-...... (pi) I pI-4qt .!!!.orIpi 4qt

UNlTSOF.WI!IGHT IN'I1fEU.s. SYSTI!M

ounces (oz)--pounds 160z libIlb-16oz -or-

(Ib) lib 160z

pcIIJIIIIo-Imw(T) IT - 2,000112.ooolb IT--..ror2;OOOjb

NB11UCUNITS OFWEIGHt'

millipams (ms)---pams (&)I.ooo....or---!L

1,-1,00011II I, 1.000....

CCIJIipu (q)--p8uor-!L

1,-100.. 1& 100..

ki'- (ks)-pams 1,000&-Iq1.000&or

Ilea 1.000,

metric_ (I)--tilqpamsI.oooq or---!!-

1,000lea- 11 11 1.000'"

I'ORMULA IN SYMBOLS

1'............110 Cdsi... C _ S(F-32) Sublract 32. multiplyby 5.9 and thcrodivide by9

Cdsi1810 Fabrenheit F..!C+32Multiply byj.... tile odd32-5

M&TIUCUNITSOJI.UNGTH

miUimctcn(mm)- 1.000""" 1m-or-mctas(81) 1,000"""-181 1m I.ooomm

ccntimcIaI(CIII)- 100cm 1m-or-- 100CIII-lm1m 100....cIcci_ (dID)- 10dID 1m-or-meterS 10dID-lm 1m 10dm

decamctaI (dam)- I dam-10m10m ldam

meterS W;;; or;

hcc:Iomacn (hm)- I bin-lOOm100m llan-or-

metas llan 100m

IciICI1Idcn(km)- 1000... IkmI km-I,IIOOtn . -or-

metal Ikm 1000...

METRICUNI1SOF-VOLUME

miUililCn(mL)- I L-I.ooomL 1.000mL IL-or-lilCn(L) IL. looomL

bectoIltas(bL)- 100L-11IL100L IhL-or-

Ii_ IIIL 100L

kilolilaS(kL)-lilcn I.oooL-1 kL1.000L IkL-or-

IkL 1.000L

MDlUC UNITSOFAREA

I an1 -IOOmmJ100mm' Ian'

sq.mm-sq em or lOOmm'

I....' -IOOan'100an' I....'

oq.an--eq dm - h!m' or lOOan'

I m1 .IOOdmJ100dm' 1m'

sq. dm---sq_ 81 "'""1m' or IOOdm'

100m' laaq.m__(I) la- 100m' !;- or 100m'

100. IhlIRS-'-'a (ha) lha-IOO.

-or-lha 1001