Pre-calculas

In oceanography the density of the sea is a very important value need to be defined . The density of the sea water depends on the temperature salinity and pressure . Usually , the researcher operates with another value denoted as ?0 which is defined in the following manner (1

is the density of sea water

At atmospheric pressure and at temperature of 0 ?C the density is a function of the salinity only , or , as a simple relationship exists between salinity and chlorinity , the density can be considered a function of chlorinity . The International

Commission , which determined the relation between salinity and chlorinity and developed the standard technique for determinations of chlorinity by titration , also determined the density of sea water at 0 ? with a high degree of accuracy , using pycnometers . From these determinations the following empirical data were collected 180 446

190 484

200 546 The relation between ?0 and chlorinity was derived from these data (2

Where Cl is the chlorinity expressed as o /oo . Hence ?0 is the third-power polynomial on chlorinity . The empirical data along with the polynomial function are presented below

The information was retrieved from the site

HYPERLINK "http /content .cdlib .org /xtf /view ?docId kt167nb66r chunk .id d3_3_ch03 t oc .id ch03 brand eschol http /content .cdlib .org /xtf /view ?docId kt167nb66r chunk .id d3_3_ch03 to c .id ch03 brand eschol

One of the problems in which the necessity to apply rational function arises is the following . We need to find out whether a person can lift up a big concrete plate with the weight of 400 kg with the help of a board 2 m long that will serve as a lever as it is shown in the figure below . And how much should such person weight in to be able to lift that plate

The experiment shows that the smallest weight of a person who can lift that plate depends on the distance from the plate at which the support for the board will be placed . The experimental data are set out below

x , m m , kg

0 ,31 72 ,8

0 ,33 78 ,7

0 ,35 84

0 ,36 88 ,4

0 ,39 97 ,7

0 ,4 100

0 ,28 64 ,6

0 ,32 75

0 ,37 89 ,7 However , the equation of mechanics helps to derive exact weight of a person who would be able to lift up the plate . For this purpose momental equation is used (3

Here M 400kg , l 2m , g 9 .81H /kg , x is the distance between the plate and support

From this equation we can solve for person 's weight (4

In our particular case (5

Thus , the weight of a person is a rational function of x . The figure below shows the results of the experiment together with the graph (5 m , kg

x , m

W

D

F

a

D

TZ

SH

o

r

yu .a

o

r

tz

yu

yu

kdG

b

the adult person who weights 70kg can lift up the...