# Mathematics

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Modern Mathematics
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Laws of Exponents LawExample x 1 = x 6 1 = 6 x 0 = 1 7 0 = 1 x -1 = 1/x 4 -1 = 1/4 x m x n = x m+n x 2 x 3= x 2+3= x 5 x m  /x n= x m-n x 6  /x 2= x 6-2= x 4 (x m ) n = x mn( x 2)3= x 2×3= x 6 (xy) n = x n y n  (xy) 3 = x 3 y 3  (x/y) n = x n  /y n  (x/y) 2 = x 2  /y 2  x -n = 1/x n x -3 = 1/x 3   fractional exponents : Laws of Loga!t ms Example : y=log 4 (1/4). Find y   4 y = 4 #og4(0\$25)  % s!n&e 4 #og4(0\$25) = '4 y = 4 -1 y = -1 Properties of logarithm : 1. log a (mn) = log a m + log a n   the log of a multiplication  is the sum of the logs   2. log a (m/n) = log a m - log a n   the log of a division  is the difference of the logs   3. log a (1/n) = log a 1 – log a nsine #og a (1) = 0 = -log a n4. log a (m !  ) = ! ( log a m) the log of m with an exponent r is r times the log of m    ones!on *a&tos 1. ength#mpe!ial \$nit%et!i \$nit1 inh 2.54 cm  o! 25.4 mm 1 &oot==' 12 inch (12  2.4) m = 3.5 cm 1 ya!d ==' 3 foot  (3  3*.) m ! 1.5 cm 1   m!#e ==' 1#\$ %ard  (*.1  1,*) m = 1\$1 m ! 1.6 km 1 nat!&a# m!#e   1\$,5 m1 #eage ==' 3 mile 4\$, m  %et!i \$nit #mpe!ial \$nit 1 mete1\$1 ya. 2. %ass#mpe!ial \$nit%et!i \$nit1 one2.3 g%et!i \$nit #mpe!ial \$nit1 0g2.2 pond3. ime1 minte ==' * seond1 ho! ==' * minte = (* *) se. = 3** seonds1 day ==' 24 ho! = (24  *) min. = 144* mintes4. empe!at!eelsisFah!enheit (m#t!p#y /5 + 32) == pefom &a#&#at!on !n t e o.e of m#t!p#y y /5 t en a.. w!t 32 (onstant)Fah!enheitelsis ( - 32 multiply 5/9) ==> pefom &a#&#at!on !n t e o.e of m!ns 32 (onstant)  t en m#t!p#y y 5/   elsis to Fah!enheit (  /) + 32 = F Fah!enheit to elsis(F - 32) x / =  e#s!s to *a en e!t   1. + 32 = F *a en e!t to e#s!s (F - 32) / 1. = elsis5el6in(add 2,3) =='  + 2,3 = 5el6in7 55el6in elsis(mins 2,3) ==' 5 – 2,3 =    Fah!enheit5el6in(on6e!t to elsis &i!st7 then + 2,3) ==' (F - 32) / 1. =  =='  + 2,3 = 5el6in7 55el6in Fah!enheit(on6e!t to elsis &i!st7 then on6e!t to Fah!enheit)==' 5 – 2,3 =  =='   1. + 32 = F(mins 2,3) (  1. + 32 = F)  . 8!ea#mpe!ial \$nit%et!i \$nit 1 inh  1 inh(2.4 m  2.4 m) 1 s&uare inch '1 in 2   ( (.4) m 2 = \$.45 cm 2  1 &oot  1 &oot(*.3* m  *.3* m)1 s9a!e &oot (1 &t 2  )*.*3 m 2   1 mile  1 mile1. 0m  1.0m1 s9a!e mile (1 mile 2 )2. 0m 2 %et!i \$nit #mpe!ial \$nit1 met!e  1 met!e1.1 ya!d  1.1 ya!d1 s9a!e met!e (1 m 2 )1.21 ya!d 2 . olme#mpe!ial \$nit%et!i \$nit1 ;i inh (in 3 )(2.4 m  2.4 m  2.4 m)= 1.3 m 3   1 ga##on4\$55 #!te %et!i \$nit #mpe!ial \$nit1 ;i met!e (1.1 ya!d  1.1 ya!d  1.1ya!d)= 1.33 ya!d 3  1 lit!e= *.**1 m 3  = 1 dm 3 = 1*** m 3 1 #!te1\$76 p!nt ,. <peedon <# \$nit<# nit5not = (natial mile/ ho!)(1. 0m/ho!)===========================================================================================Example: on6e!t 1 ;i ya!d into ;i &eet. nswe   ee ae 27 &!& feet !n a &!& ya.\$    !mp#e geomet!&a# &onst&t!ons 1. !iangle- has th!ee sides and th!ee angles--- >ight 8ngle !iangle ---????ame o& !iangleE9ilate!al !iangle<alene !ight angled t!iangle #soseles !ight angled t!iangle <hape o& !iangle @es!iptiona A Bhih has : - three equal angles   o&   60 -  and three equal sides a A Bhih has :- one !ight angle - tBo nea# angles-all th!ee sides ha6e di&&e!entlengths (no e9al sides) a A Bhih has :- one !ight angle- tBo equal angles  o& 45- and tBo equal sides   (tBo sides e9al in length)ame o& !iangle8te !iangle>ight angled t!iangle C;tse t!iangle <hape o& !iangle @es!iptiona A Bhih has : - a ll angles that a!e less than )   a A Bhih has :- a !ight angle (*) a A Bhih has :- an angle more than )  *rea  *rea of +riangle ! , - ase - height 'measured at right angles to the ase(

Jul 23, 2017

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Jul 23, 2017
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