100% found this document useful (4 votes)
329 views12 pages

Unreadable Document with Symbols

The document describes various mathematical equations and relationships. It defines variables such as volume (V), length (L), width (W), height (H), radius (R), and density (d). It then proceeds to derive equations for calculating volume, surface area, mass, and other values based on the given variables. For example, it shows that volume of a rectangular prism can be calculated as V = LWH, and that the surface area of a sphere is 4πR^2. The document appears to be detailing mathematical concepts and formulas for geometric shapes and their properties.

Uploaded by

Ioana Muresan
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
100% found this document useful (4 votes)
329 views12 pages

Unreadable Document with Symbols

The document describes various mathematical equations and relationships. It defines variables such as volume (V), length (L), width (W), height (H), radius (R), and density (d). It then proceeds to derive equations for calculating volume, surface area, mass, and other values based on the given variables. For example, it shows that volume of a rectangular prism can be calculated as V = LWH, and that the surface area of a sphere is 4πR^2. The document appears to be detailing mathematical concepts and formulas for geometric shapes and their properties.

Uploaded by

Ioana Muresan
Copyright
© Attribution Non-Commercial (BY-NC)
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 12

,flir.;..

;,,

,1

cA-

,\i

=-

a>_

D2

--

Y.e>\- &+ !=,

50s-fu

"

=-

't..64r+"r

a6 +";\
\g

-@3\

., I u^

P?o-

= (: ft{\

\\ru* = 2S=@nn. ,
\r \ 'f. L

- l{N"
=-'. A\-"* = -hb\ {se\ '4;;

,-

sl*
:!{.rr

r- h-\
\t: -:t:.-'< )
tftr':

; \' \l :- \5:
l'.i!
? " - xL
{0
Lh''"'t
+
=
*\B= 6\*&
--; li .'v..-'
v:
S,"-,\. - Z3.*\ -0,:' - Z]:''i '
_
- iFD \:i
-:
-_..
"),i '!t;3,-, ) - ,r'\'4: - ;2 )
-Y
Y\*$ =
/-"\r-t.r.

t.1.

-?

!J

v?

! \7-r-

-. _-

J,

l_, {,1 i

t'',:

"-l
,l

L.'

\,-

\'\' 4i:,''

I,l ,)

R-{=
1o.n

+=^$

7_

Nur

\i12,65 P?o
-.- ).)o Efo

\c!,ih"*,'
U+'=A\W , E{
g

te.i$r'col-r^

--0o.

{4';,.
rl\l -- +\fM* e. + {A

Ys*g:cryu

Rd\=

oot

'l

{tr*.S - \J, rnr,n


J": ? +! tOI)
I'
oK
-fli\
:g,
Rdl =--

{\.tr\ =

hd,t{$\.r'trcr}r-s

HJ^t[

$tt=

Z- Par$ ' ir,'


A'

u Nv

KT

{-

6e"A'x+

ns$* > Y\It$,

O ti**

\[*

icr+-{.bd.J:-*-

[t:

(e:.4'- *o*r'^\'l'*
=

tt}-op = ?orrl.!1e
.^\
\1&gn
klt\ Y +?
r\I^
*=Y-

-liil*

ba.b
\i-r''ox *- $^'q- [t t --l b/
L' \tt"
\
\$dt i \ * b<-v>
'{r.*ir." = ',\.
-:-

t-\Nr \

qr a ...{.},
Tuir, > c

Tt\r

6j.r.0r* X.i

| ^,

tY

Tr vl l,JTtl

Dt! a-,' i
)

& k *::::!':j:-o:3::g
*r*4
\)

tt:,htlfr'l

;Cj:i

\"

'ta
tt.i"r't

) i'-

= ?dtGd*
t 'r-.:,r '- 2,1 * -.4L
loo
N

4,, * rvw1
.-.
1' -l^.1: e

4J

di

=-;-i

t? O,,

.'r

+at*,&a-(l_
'

'il

.r "; .,
'P
lLs,U-=,-.l**'O1
(: {
i

?'

..___J

ooLl"nc..c/r-'es*

4,t=

"&

, .-t

rr

.c

Cr

'1
(JJL

,A

i-ti

l/

f,lr::e

ot- )'a'

2*

i. ::..,i

.-:,..,

to

crr0t''L

dg

,ug=*.-.,.=

Oreou-e
'-' '.
,/a:j Eat,)L.-t-4_

,*-c'P-*.uI
()
DJ1!'-Y r

1,.,.

Jp-b','r

(eku?-u-;

c.,l

+r*P;;) *

e;-:;

taou,,)

w-pzc"La,'ea-

-!

r*;'Qa'

/-n'

'fi'tJJ

Q)
____*o"yt2'd/y1--\/__canrt-tf{Y-*
l-

{./
r-L

+F-nj

P'l-ot'-d

',)
o
lTtr
l'l
o
,,'al_t_?

--r

--1 "

| _: -

?,L

i-

.^/

"to-"+u
l---r- '4''o'f'e-r'^- frhLft")
>
,
7_------_.....

1*

',*LJ
,.&,ht
I

/J CL

t+-

ta

.. *\

-=
+r
i+ft.,..i
lrari r I .m
-b
\.

3/tJr

'>" )

L' (l^Ltv1

'

y'^,i.r-.4;.'' le

- d.rt"$

o,4pnt

p.+.7JB C

FiDl ar ?1Y

)'Y i

trfl

o&
2,

=) ?r., = ),. q...,,'-4 -

.'.

?. r.- .

'I

-':., *-

Zsrui,

9,tz+'-r-

.aJ

3,-,
-,
"' -i '";

4J

"-.b-a.xt_bJrg- *:' tz-rrE


lY-

,!-l,L

A\
(- i2.,4:

r
-*. b
r.

tatAiJr'<k"t"

,lLr".J-

to

i,n-n"irg-'-

T-

a
;z t-,'"1

-.-.--*-.-.-'-

- r; .r:
tI,

!,1.,u

Nc= I
e-rrd tna

N. cud + la

- "ala>tLa

o*fr,

oL

f\lJel

U'4vr

2;t^

cae$'u/vL)i
twdlxi/r,afu
J. ."!4"9 o.r
,aJdaa
{"nactia. ynatt-,a}H 6J 21i'i;{&}L
&*a-ae,a.U &
Li )

'4.J= %
b-

e<sL,
1,,

xi_{i.r

rdI

y!"eh"t',
:ilaf,:-o.,

ta,

tr#*

{6tr1-il'

o,,tt*

t,totS'U.zJ"\

c'j

ek"

db
,D

.s
6t, #b
c4Ta

i.n

t
J,
t&Jzc)az:rt

! iF-/ec-

q"tnf

at

ftn4 =

tu+^%'o

+t

CrF-'ld'

l*-'ee{r^&,*:
t

Q**= hr", P",J

'>G!i.u..r^o-

tr*.r'-.,

X f"ttltan

rn^:
t ue.,+
*f*."'-- 3

Vol- pa+er.+
&v*

G*t
J,

I
r,
L\r, l{1" VU$
-47 r\

lulv+= 14t+ .Tr".t4rI

L*,ee-

fLa'd)'4")

#*b:t.,,4 ' *

r"'.&'r,

t-1

t'\1- ia4+Tv,#/,
t'.
)i
,
do
t
'ot=
ae.L,{L,-lj

.[d2
t,
+b=
lL

d.! ewnrrye
ea-l-+

tt**t"=x

t-)

i),,'s.q" ''

i;::,

- r'"j. * \r i,l

i-=^1

a.r
I

CpNTlNA

T:UNb.ftI1i'

\!r) Vtu*ln "n4ehetcl&!'m-"totq22q

A-.t

u)

n>a&ju a&-4etc
al"*,t*
U
-+ dA.$ d-r w f/n&e

deJelrrni.naAeo,

f"{= w
L= I

Ai,$.+"; f,"-,a^4a

4 bo^n
I --

rrn

Fe.u

e+ i
, k _r
Crf= oreN J "

Vol= Nl+

XAr da^d

\d-

f oentt

V =
b.l"n

l=)

'.-d4"";''

b cn;* =

Yu^dpqti
LA&

-'
t
lx"
+

>

L,-

U
v&F

9"

=)

fl
f'l

W;faana

la"

3.=

tg

*.tm =

aan"

o4.hrh. ttJ.nnt:,I

fsf e fa*-

Vd= N + G/
i 1*
=F

|{;^_*\ -/*=..1

{r= B' I r,ni


^

9e

JA

dn\E fe

\e_

2*= f,""*dc,bi

I
)-)
'it

(r1|,el

4o c,rn

eY

t-l

L>

s''

A'

t^
('m

4o t"'n

fuxaarn

*t-

c''?-'u

b >- L2+ loetm

| -l

Pct

lr2tJ.

ir,aNl

\-__L__l-]__.

Vd

**r-L*J.arne

fZe^e

bz

LJTT-

\ ,'+-77x

^f

:)@
ole*,ta.i""a,u".a_

\'u<ftn

^ r 2o.
.___ -a.,

/_

^
F! lmrau , ct*l)
\

t al

rlw;{n*ea-

!
ar'La'-.J OJ:
---'

) {2

&&n

L^n 4c',',crr
--:----*

\.t*v

2 = rz..+-!.
t-'
*ar/' od,",
!

*'I

tx.

lH

D/

,'{

ll=

,-Pv
l-

Po.e,.,o*.^,

^:\

4.*

L-r.o,

4gaadtt^

Hf*'lsl+ r'

'*unaa*;PAz
}

&7

+L'Lt

.1

Pi'J

Pc-

'f=4 W*/ \

w ?+t

4u" I6oar",

Woc!'xn
(}

=\ t= L- t$

lJ*rt_t
*t-

2:urz

2-

,t
@

\ .":)*-*

+a

zfu
"
t-\ ^38

'i1t.tb*:{ tl

@
Q Pnta, 'ryrga*tb".

'gbr'r&;

d{-+cgEr11-..;..n41,rL{6, 6lirt.n<rr4)urr1-i,4t

-ji-mel*j*

f.t z FonI

r1=

t";*'',-

f"u = {^*,.t
= qirca'r"l
ll
h,-, _ /L:

b$L

s).

,..1
t.'4!

+ 6-e,r:.
=>
r

J, A2,

d-Jb!cchd.':a"fda,

n,
4e
_ to

7-

rorJ"

\t tfcrn:
\ -i -

Un' ldt-

aLrwr<7t>-|.

&>

utNn's*t!-<r-,' 4", 5-

+ +e)

(",+

a:"'\

W-)

=)
de-L,*rr".,c"v,

t - Jr^
;-.-v

.
='\

=4,

lLl]_
aJ

a*<r:

&art

ti;

4un.dn*,e-

ir-Jl
t:--*1

? b /,oa,",n

*.1
,,/i

l6,L
')

14

.,

*.,r. <i1,
/!^**^-_._l ^-_.*
,'x--'--------+
5<|l/ ,
i
l,\J
':2_-.___-___--_. -*
I

Ja"

hu=

Q3!"

zd*L uz

SQaa",,^.(e+.1

*u+, = 4o ro-,
*: i1 > 7c ,.r-.,

frt

"*-.nra!*f
2

(*b*o

C,:.,{J,..r,

+Z iA
(_) '

jr.,

> r)o';

le r- >t

r
aq [:,

"

?.i,.

c,
+

!r:n

[Y)C\ U)'J

r'

i-^-

'

,r.'.,'1,

)o, F r

i=_1

_. I

)'-

).-

= -:*,
c.6 _rli
,

T
c...u. !r^.'tllt"rf +)

=\

I
I

.,1.*

,,r.,.,,.

:. L

'-.:ft,'

!\a,\-

(rt:t.-

1\''-.,
i".,"i

-,,

A)'.;er't
j,L

*l-'ea ,/^ tr f ur$)T

+d-larr/;cl:_-F

-. 2-:.i. = Ad.
I, 15 'ir+s-u
., , _. t. u! ,oxd
q7d ** !i n
.' '
!r^d- = t-1+ 4^
ltj

t-i

gJe

Ca= Gq\
+ &v:,ffic'I
My/lA

t"4y+

u! -

'=)

Fy

l4u

ry,

fu+

Q-

= 9,

\/auf;ca*u,

.rt

w
A'

.o
Lgd..

*Y&

4. )

Tu ( 1/+t.

uta =

\.

r'

'Fac,n =
I
'fl

g
1t

Q-r

tt

.o
<bEL

/"-'* 2f 'Lf
-

./

E -

^
t6. ot'

lYt

q,fh

---'\J*

V.l

iax*

\/)

"r9

dBe+

r-li-]
l"e

/?\

(
\A ^,':4tL 'Y1'^ ,/<'e'r.z .=

O1l,'.':rr,h

ln
='t-:\ .t, I

<iur,.,, &_

*J
z-.
\-t2:

u3Ji,^_x.
^-^.,

i,-":

la"Jw,

*.p.*l Tka

'

Lt f>

l:F4-...
f4

o:

L
d",-rrr:e.n

_j
+$f,CL*Z

d**<-2"^

2o

41u.i

i{

o;3F

d!

Qe

.a4'.A8'atza-

U-'2J
,h.* f,:"'

ae-{^.-o" z*oyr*J;

EC'
= 1.,'
r+i/+"2
Fef

Vd

'

-+ =

.:le

4->

4"r

r?-,

-:i,--

r'-'^l

(t1,,.1 tt
t't\+
-_
(;

F=** =

!.r:

p,

t ;.

-0=o
",
,l

.-a

z/*

'7,.,J:

-)

-\
-)

;:r'.

l2 =tJ

:- - -/ -

/,

-t-

:r

Lt,. !. ,...: .
'

=/-:

lttt

..r'
:....i..
\1^ --

1 .t

t.,

\.rl = l-t.:,....i -.
).

lvlyl* ru. ,
t':;1. J .- Iij,
-"l!\i

er"

f\1r'^L

Vc!
L/

I'lva-

-:\

.,-l

"'

-:-.

!!

*i.

)l

,:- [*i t
i4t

You might also like