Documents

Mathematics

Description
Modern Mathematics
Categories
Published
of 10
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
  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(

Physics Rotation

Jul 23, 2017

WED Exclusives

Jul 23, 2017
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks