Chpter 6 Opener Try It Yourelf (p. 9). Becue 0 i equl to,.0 i equl to.. 0 So,.0.. i le thn. Becue 8 So,. <.. 7,. i le thn... Becue π. i le thn., π i le thn.. So, π <... Smple nwer: Any deciml greter thn or equl to 0.0 will mke the entence true. So, three deciml re 0.009, 0.00, nd 0.0.. Smple nwer: Any deciml le thn.7 will mke the entence true. So, three deciml re.7,.7, nd.7. 6. Smple nwer: Any deciml le thn or equl to 0.7 will mke the entence true. So, three deciml re 0.7, 0.7, nd 0.7. 7 7 60 7 7 60 9 7 60 9 7. 8. 8 + 0 6 9 8 + 0 6 6 8 + 80 + 80 8 Section 6. 6. Activity (pp. 0 ).. 8 9 yd Check: 9 9 8 c. 8 cm Check: 8 8 80 d. 6 9 mi Check: 9 9 7 90 6 e..89.7 in. Check:.7.7 9 70.89 f... m Check:.. 0. g. ft 9 Check: 9 9. + ( 6 ) + ( ()) + + 0 + 00 99 Copyright Big Ide Lerning, LLC All right reerved. Big Ide Mth Blue Worked-Out Solution 9
. L T..00 T..00.()..96 T..96.(.).. T...(.8).98.00 T..00...8 T..8.(.). 6. T. 6..(.).7 7.9 T. 7.9.(.7).97 7.8 T. 7.8.(.8).08 9.00 T. 9.00.(). L.. 0 0 00 0 0 00 So, the qure root of 00 re 0 nd 0. So, the qure root of re nd.. Becue,.. Becue, ± ± nd. T 8 Period of Pendulum 6. Becue..,.... 7. () The function i not liner ecue it grph i not line.. The re of qure i the ide length qured. So, if you re given the re of qure, find the qure root of the re; tht i, find numer whoe qure i the re. Smple nwer: The ide length of qure with n re of qure feet i feet. You cn check thi y multiplying. 0 6. On Your Own (pp. ). Period (econd) 7 6 0 0 6 7 8 9 L Length (feet) 6 6 6 6 6 6 So, the qure root of 6 re 6 nd 6. 8. 8.... 7 + + + 9. ( 9 0) ( 7 0) ( ) 0. A πr 86.r 900 r 900 r 0 r The rdiu of the circle i out 0 feet. 6. Eercie (pp. ) Voculry nd Concept Check. no; The qure root of 6 i not n integer.. no; The qure of negtive integer i poitive, nd the qure of poitive integer i poitive.. 6 repreent the poitive qure root of 6 ecue it doe not contin negtive ign or plu minu ign in front of the rdicl ign. Prctice nd Prolem Solving. cm Check: 0 60 Big Ide Mth Blue Worked-Out Solution Copyright Big Ide Lerning, LLC All right reerved.
..69. km Check:.. 9 0.69 6. 7. 8. 9. 0. yd 6 6 Check: 6 6 6 6 6 9 9 So, the qure root of 9 re nd. 8 8 6 8 8 6 So, the qure root of 6 re 8 nd 8. So, the qure root of re nd. So, the qure root of re nd.. Becue 6, 6. 9 9. Becue,. 0 00 00 0 0. Becue, ± ± 96 96 nd.. Becue.7 7.9,. Becue..8, nd.. 7.9.7.7. ±.8 ±.. 8. 6 7 9. 0 0 0 9 6 0. 6.76 +..6 +. 8. 8 8. +.8 8(.9) +.8. +.8 80. ( 6 ) 7. + ( 9 + ). A 9 9 7+ 0 0 One ide of the e of the notepd i inche.. In the contet of the prolem, negtive rdiu doe not mke ene. So, there i only one nwer for the rdiu of the utton. 6. 8 9 nd 9 > 8 So, 8 > 8. 7. 0. 0. 8. So, 0. 0.. nd < So, <. 6. Becue 9 6, 6 9 9. 7. ± repreent oth the poitive nd negtive qure root. So, ± ± nd. Copyright Big Ide Lerning, LLC All right reerved. Big Ide Mth Blue Worked-Out Solution 6
9. A h 0 h 8 h 8 h 8 h 9 h The height of the il i 9 feet. 0. ye; Smple nwer: Conider the perfect qure, nd. Their product cn e written.. v K v 6 v 6 v 8 v The pple i trveling t rte of 8 meter per econd... The two wtch fce re imilr, o the rtio of their re i equl to the qure of the rtio of their correponding rdii. Are of mll rdiu of mll Are of lrge rdiu of lrge 6 rdiu of mll rdiu of lrge 6 rdiu of mll rdiu of lrge rdiu of mll rdiu of lrge The rtio of the rdiu of the mller wtch fce to the rdiu of the lrger wtch fce i.. Let r e the rdiu of the mller wtch fce nd R e the rdiu of the lrger wtch fce. Solve the proportion for R. r R R 0 R, or. C n + 7 80 n n + 7 900 n 900 n 0 n The length in inche i 0. Convert to feet uing the fct tht foot inche. ft 0 in.. ft in. So, the length of the window i. feet. 7 + 0 + 8 A h ( )( 7)( 0) h 7 0 0.h. P ()() 7 0.h 706 0.h 8 0.h 8 h The height of the tringle i 8 centimeter. Fir Gme Review. + 9 + 6 6. 8 + 6 + 89 7. 69 8. 6 76 9 9. B; The tringle h one right ngle. So, the tringle i right. Section 6. 6. Activity (pp. 6 7). e. The reltionhip i + c. 6 The rdiu of the lrger wtch fce i or. centimeter. Big Ide Mth Blue Worked-Out Solution Copyright Big Ide Lerning, LLC All right reerved.
.. + c 9 + 6 c c c c The length of the hypotenue i.. 0 + c 00 + 76 c 676 c 676 c 6 c The length of the hypotenue i 6. c. + + 9 6 9 + 6 6 6 6 6 c c c c c c The length of the hypotenue i. 6 d. ( 0.6) + ( 0.8) c 0.6 + 0.6 c c c c The length of the hypotenue i... + 6 0 + 6 00 The length of the leg i.. ( 0.) + ( 0.) 0.076 + 0.6 0.0 0.0 0. The length of the leg i 0... In right tringle the um of the qure of the length of the leg i equl to the qure of the length of the hypotenue. Smple nwer: 6 + 8 0 6 + 6 00 00 00 6. On Your Own (pp. 8 9). 8 + c 6 + c 89 c 89 7 c c The length of the hypotenue i 7 feet.. + 0 c 9 + 00 c 6 9 + 00 00 c c 00 00 c 0 c c 8 0 The length of the hypotenue i inch. 6 Copyright Big Ide Lerning, LLC All right reerved. Big Ide Mth Blue Worked-Out Solution 6
6 + + 900. 6 6 900 0 The length of the leg i 0 yrd. + 9.6 0. + 9.6 08.6 6. 6 The length of the leg i meter. 9 + 8 +. The ditnce etween the group of hiker i + 0 kilometer. 6. Eercie (pp. 0 ) Voculry nd Concept Check. The leg of right tringle re the two ide tht form the right ngle. The hypotenue i the ide oppoite the right ngle. Alo, the hypotenue i the longet ide nd the leg re the other two ide.. The third quetion i different ecue it k which ide i leg, where the other three quetion ll k which ide i the hypotenue. nd re the leg, nd c i the hypotenue. Prctice nd Prolem Solving. + c 0 + 6 00 + 676 76 76 The length of the leg i centimeter. + 0 c + 00 c 8 c. 8 c 9 c The length of the hypotenue i 9 kilometer. +.6 0.6 +.6.6 8. 8 9 The length of the leg i 9 inche. 9 + + 6. 8 The length of the leg i millimeter. 7. + 9.6 c.8 + 9.6 c c 7. c c The length of the hypotenue i feet. 8. + 7 + 6 69 + 6 9 9 9, or The length of the leg i yrd. 6 Big Ide Mth Blue Worked-Out Solution Copyright Big Ide Lerning, LLC All right reerved.
9. i the hypotenue, not leg. 7 + 9 + 6 76 76 The length of the leg i feet..6 +. c.6 + 0.89 c. c 0.. c 6. c The wire i 6. feet long. + 0 + 6. 00 6 6 So, 6 centimeter. + + 69 + c + + 69. 69 7 So, 7 millimeter.. ye; + d 76 + 0 d 600 d 600 d 0 d The length of the televiion digonl i 0 inche. So, it i on le. +.8 + 7.6. 6.6 7.6. The wingpn of the utterfly i. 8.centimeter. + 80 8 +,00,76 6 6. 6 9 The ll i 9 yrd from the hole. Ue the fct tht yrd feet to convert to feet. ft 9 yd 7 ft yd So, the ll i 7 feet from the hole. 7.. Smple nwer: y 0 0 0 0 0 6 Friend 0 0 You. 0 feet ecue the two e of the tringle re equivlent nd the height re lo equivlent. So, the hypotenue of ech tringle re equivlent. Copyright Big Ide Lerning, LLC All right reerved. Big Ide Mth Blue Worked-Out Solution 6
8.. 0 00 + + c c 6 c 6 c c + c + c + c 00 c 00 c 6 6 0 c The length of your friend throw i repreented y c + c. So, the length i + 0 feet. 8 + 78 + 9 9 7 So, 7. Fir Gme Review 9. Becue 6 6, ± 6 ± 6 6 nd 6. 0. Becue,.. Becue 69, 69.. Becue,.. C; All ngle in n equingulr tringle nd n equilterl tringle meure 60. A right tringle h one ngle meuring 90, o the other two ngle mut dd up to 90. So, right tringle cnnot hve n otue ngle. An iocele tringle h two congruent ngle. It i poile for the third ngle to e otue. Study Help (p. ) Aville t BigIdeMth.com. Quiz 6. 6. (p. ). 96 96 So, the qure root of 96 re nd... 7 7 9 7 7 9 So, the qure root of 9 re 7 nd 7. 0 0 00 0 0 00 So, the qure root of 00 re 0 nd 0.. Becue, 6. Becue,. 6. 6. Becue. 6., ± 6. ±.. nd.. 7. 9 + ( 7) + + 6 8. 0 6 0 0 6 6 9. + 00 + + 0 + 9 + 0 c 8 + 600 c 68 c 0. 68 c c The length of the hypotenue i feet. + + 0 809 78. 78 8 The length of the leg i 8 inche. 66 Big Ide Mth Blue Worked-Out Solution Copyright Big Ide Lerning, LLC All right reerved.
.6 + 6. + 9.69..6. 9.69 6. The length of the leg i 6. centimeter.. 0 + c 9 + 00 9 6 + 00 00 c c c 00 00 c 0 c c The length of the hypotenue i yrd.. A πr.r 00 r 00 r 0 r The dimeter of the pool cover i 0 0 feet.. A,000,000,000,000 000 The length of one ide of the prcel i 000 feet. 6. Ue the fct tht yrd feet nd foot inche to convert yrd to inche. ft in. yd yd yd ft in. in. 8 + c 78 + 0 c 809 c 809 c c The length of the digonl i inche. Section 6. 6. Activity (pp. ) c yd.. no; i n irrtionl numer, nd 6 nd 780 re rtionl numer. An irrtionl numer cnnot equl rtionl numer.. no; The numer given y the clcultor i n pproimtion. c. Smple nwer: Archimede my hve ued Gue, Check, nd Revie to pproimte. He could hve done thi y quring the frction nd eeing if he w cloe, then rewriting frction nd chnging them lightly. AC + BC AB. d. + ( BC) + ( BC) ( BC) ( BC) BC 8 in. e. The length of egment BC i out 7 grid qure, or out.7 unit. So,.7. Copyright Big Ide Lerning, LLC All right reerved. Big Ide Mth Blue Worked-Out Solution 67
. D 6. 90 69 96 B Becue 90 i cloer to 96 thn to 69, to thn to. So, 90. 90 i cloer 7. 6 9 7 Becue 7 i cloer to 9 thn to, 7 i cloer to thn to. So, 7. ( AC) + ( BC) ( AB) + ( BC) + ( BC) ( BC) ( BC) 9 BC.. To find deciml pproimtion of qure root tht re irrtionl, ue clcultor or find qure root of perfect qure neret to the rdicnd nd determine which qure root i cloet to the rdicnd. 6. On Your Own (pp. 6 8). The numer 0. neither terminte nor repet. So, it i irrtionl.. Becue 96, 96 i perfect qure. So, 96 i rtionl.. The numer i not perfect qure. So, i irrtionl... C 6 6 6 9 7 Becue i cloer to 6 thn to, 6 thn to. So, 6. 8 i cloer to 6 8 8 9 00 0 A Scle: of unit 0 8. 9. 0.. i to the right of. So, i greter. 0 i to the right of ecue 0 i poitive nd i negtive. So, 0 i greter. 9 i to the right of. So, i greter. A 6 9 Becue. 9 6 6 6 9 0 9 6 i cloer to thn to 6, to thn to. So, the rdiu i out inche. i cloer..7 h.7 0.70 Becue.70 i le thn, you cnnot ee frther thn nuticl mile. 6. Eercie (pp. 9 ) Voculry nd Concept Check. A rtionl numer i numer tht cn e written the rtio of two integer. An irrtionl numer cnnot e written the rtio of two integer. 0 6 6 6 0 Becue 8 i cloer to 8 thn to 00, 9 thn to 0. So, 8 9. 8 i cloer to. Becue i etween the perfect qure nd 6, ut i cloer to 6, 6. 68 Big Ide Mth Blue Worked-Out Solution Copyright Big Ide Lerning, LLC All right reerved.
. Rel numer re the et of rtionl nd irrtionl numer. Smple nwer:,, nd 7 re rel 8 numer.. 8 doe not elong ecue it i n irrtionl numer. The other three numer re rtionl numer. Prctice nd Prolem Solving. ye; Uing clcultor, 9.6 0 nd.6067977. So, the rtionl numer i reonle pproimtion of the qure root. 6. no; Uing clcultor, 0.08 0 nd.6679. So, the rtionl numer i not reonle pproimtion of the qure root. 7. no; Uing clcultor, 678.7 0 nd 8.906. So, the rtionl numer i not reonle pproimtion of the qure root. 8. ye; Uing clcultor, 677 6.708 0 nd 6.70809. So, the rtionl numer i reonle pproimtion of the qure root. 6. no; + c + 6 c 6 + 6 c c c c The length of the hypotenue i inche. Becue i not perfect qure, the length of the hypotenue i not rtionl numer. 7.. Becue your ge i non-negtive integer, it i nturl numer.. Becue prime numer i diviile only y nd itelf, it i not perfect qure. So, the qure root of prime numer i irrtionl. 8. c. circumference πd π dimeter d Becue π neither terminte nor repet, the rtio of the circumference of circle to it dimeter i irrtionl. 9 6 6 6 Becue i cloer to thn to 6, i cloer to thn to. So,. 9. The numer.666666 repet. So, it i rtionl. π 0. The numer 0. neither terminte nor repet. 6 So, it i irrtionl.. The numer 7 i not perfect qure. So, 7 irrtionl.. The numer. terminte. So, it i rtionl.. The numer 8 cn e written the rtio of 9 9 i 9. 0. Becue 68 i cloer to 676 thn to 79, to 6 thn to 7. So, 68 6. 6 676 6 8 9 68 6 6 8 79 7 78 8 68 i cloer Becue 6 i cloer to 6 thn to 9, 6 i cloer to 8 thn to 7. So, 6 8. 9 7 6 6 two integer. So, it i rtionl.. 0. The numer i not perfect qure. So, i irrtionl.. Becue, the numer i perfect qure. So, i rtionl.. 00 0 Becue 0 i cloer to 00 thn to, 0 i cloer to 0 thn to. So, 0 0. Becue 7 6.7 i cloer to 9 thn to, 7 i 7 cloer to thn to. So,. 8 9 9 6 7 Copyright Big Ide Lerning, LLC All right reerved. Big Ide Mth Blue Worked-Out Solution 69
. 9. 0. 0. 0. Becue 67. i cloer to 69 thn to, i cloer to thn to. So,.. A. 6. 7. 8. 96 Becue i cloer to 6 thn to 9, i cloer to thn to. So, nd. The ide length of qure on the checkerord i out centimeter. The ide of the checkerord contin 8 qure ech. So, the length of ide of the 8 centimeter. checkerord i P 8 The perimeter of the checkerord i out 8 centimeter. 0 69 0 i to the right of 0. So, 0 i greter. i to the right of. ecue i poitive nd. i negtive. So, i greter. i to the right of 0. So, i greter. i to the right of 6. 8 So, i greter. 9 6 6 6 6 9 7 6 8 8 9 00 0. 6 0 6 0 0.7 00 0 69 6 8 9 0 0. 0. i to the right of 0.. So, 0. i greter. 8 i to the right of 9. So, 8 i greter.. A 66 66 66 Becue 66 i cloer to 6 thn to 8, 66 i cloer to 8 thn to 9. So, one of the ide of the court i out 8 feet... h.,000 8. The mimum ditnce i out 8. nuticl mile.. Smple nwer: Becue 8 9 nd 00 0, nd re ny numer etween 8 nd 00, nd >. So, one nwer i 8 nd 97... 6. Becue 0.9 i cloer to 0.6 thn to 0.9, cloer to 0.6 thn to 0.7. So, 0.9 0.6. Becue.9 i cloer to. thn to, to. thn to. So,.9.. Becue. i cloer to. thn to.69, cloer to. thn to.. So,... 7. v r 0 9 8 96 66 69 0.9 i.9 i cloer. i 6 6 6.76 00.8 0. The velocity of cr going round the loop i out 0. meter per econd. 9 7 6 8 8 9 00 0 0. 0. 0.8 0.9 0.9.... 0.6 0.6 0.9 0.7 0.6 0.8.9......69..96. 70 Big Ide Mth Blue Worked-Out Solution Copyright Big Ide Lerning, LLC All right reerved.
8. ye; Becue, i rtionl numer. i perfect qure. So, no; Becue 6 i not perfect qure, i not 6 rtionl numer. d 9. t.7.9.9 It tke the lloon out.7 econd to fll to the ground. 0.. lwy; The product of two rtionl numer cn e written the rtio of two integer. So, the product i rtionl. Smple nwer: 0. ometime; The product of non-zero rtionl numer nd n irrtionl numer cnnot e written the rtio of two integer. However, the product of 0 nd n irrtionl numer i 0, which i rtionl. Smple nwer: π π i irrtionl, ut 0 π 0 i rtionl. c. ometime; The product of two irrtionl numer cn e written or cnnot e written the rtio of two integer. Smple nwer: π i rtionl, ut π π π i irrtionl. Fir Gme Review. + y + y + y π + 8 t π t π + 8t 8π t π 8π + 8t t π + t.. 7k 9 + k 7k + k 9 0k 9 ide length of red tringle. D; ide length of lue tringle 0 The rtio i :. Leon 6. Prctice (pp. A B). So, the cue root of i.. 6 So, the cue root of 6 i.. ( ) ( ) So, the cue root of i.. 0 0 0 0 So, the cue root of 0 i 0.. 6 6 6 6 So, the cue root of 6 i 6. 6. 7 ( 7) ( 7) 7. So, the cue root of i 7. 0 0 0 000 So, the cue root of i. 000 0 8. 0. ( 0.) ( 0.) 0.008 So, the cue root of 0.008 i 0.. 9. Ue the formul for the volume of cue to find the ide length. V 8 The ide length i 8 centimeter. Ue formul to find the urfce re of the cue. S 6 () 68 8 The urfce re of the cue i 8 qure centimeter. Copyright Big Ide Lerning, LLC All right reerved. Big Ide Mth Blue Worked-Out Solution 7
0. Step : Mke tle of numer whoe qure re cloe to the rdicnd,. 7 Numer Squre of Numer 9 6 The tle how tht i not perfect qure. It i etween the perfect qure nd 9. 9 6 So, i etween nd. Step : Mke tle of numer etween nd whoe qure re cloe to. Numer.... Squre of Numer..8.9.76 Becue i cloer to.8 thn to.9,. thn to....8.9.76.... So,.. Big Ide Mth Blue Worked-Out Solution i cloer to. Step : Mke tle of numer whoe qure re cloe to the rdicnd,. Numer Squre of Numer 9 6 The tle how tht i not perfect qure. It i etween the perfect qure 9 nd 6. 9 6 So, i etween nd. Step : Mke tle of numer etween nd whoe qure re cloe to. Numer..6.7.8 Squre of Numer..96.69. Becue i cloer to.96 thn to.69 nd i the oppoite of, i cloer to.6 thn to.7...69.96..8.7.6. So,.6.. Step : Mke tle of numer whoe qure re cloe to the rdicnd,. Numer 6 Squre of Numer 9 6 6 The tle how tht i not perfect qure. It i etween the perfect qure 6 nd. 9 6 6 6 So, i etween nd. Step : Mke tle of numer etween nd whoe qure re cloe to. Numer.6.7.8.9 Squre of Numer.6.09.0.0 Becue i cloer to.0 thn to.0 nd i the oppoite of, i cloer to.9 thn to.8..0.0.09.6.9.8.7.6 So,.9.. Step : Mke tle of numer whoe qure re cloe to the rdicnd, 0. Numer 9 0 Squre of Numer 8 00 The tle how tht 0 i not perfect qure. It i etween the perfect qure 00 nd. 0 8 00 9 0 So, 0 i etween 0 nd. Step : Mke tle of numer etween 0 nd whoe qure re cloe to 0. Numer 0. 0. 0. 0.6 Squre of Numer Becue 0 i cloer to 0. thn to 08.6, cloer to 0. thn to 0.. So, 0 0.. 06.09 08.6 0..6 06.09 08.6 0 0..6 0. 0. 0. 0.6 0 i Copyright Big Ide Lerning, LLC All right reerved.
. To etimte 7 to the neret hundredth, crete tle of numer etween 8. nd 8. whoe qure re cloe to 7, nd then determine which qure i cloet to 7.. To etimte cue root to the neret tenth, crete tle of integer whoe cue re cloe to the rdicnd. Determine which two integer the cue root i etween. Then crete nother tle of numer etween thoe two integer whoe cue re cloe to the rdicnd. Determine which cue i cloet to the rdicnd. Step : Mke tle of numer whoe cue re cloe to the rdicnd,. Numer Cue of numer 8 7 6 The tle how tht i not perfect cue. It i etween the perfect cue 8 nd 7. 8 7 6 So, i etween nd. Step : Mke tle of numer etween nd whoe cue re cloe to. Numer....6 Cue of numer Becue i cloer to.8 thn to.6, i cloer to. thn to.. So,.. 6. 9 i poitive numer nd 87 numer. So, 9 > 87. i negtive 7. 6 i etween the perfect qure nd 9. 0 i etween the perfect qure 6 nd. So, 6 < 0. 8. i etween the perfect qure 9 nd 6. So, i etween nd. i etween. nd.. π. So, π <..67.8.6 7.76.67.8.6 7.76....6 Numer.... Squre of numer 0. 0.89.6. 9. i etween the perfect qure 6 nd. So, i etween nd. Numer...6.7 Squre of numer 9.6 0..6.09 i etween. nd.6. So,.6 nd.. i etween 8 i etween the perfect cue nd 6. So, 8 i etween nd. Numer.... Cue of numer 8 i etween. nd.. So, < 8. Section 6. 6. Activity (pp. ). c. + ( CD) + ( CD) ( CD) CD f. +.6 9. 8.8 79.07 7.088 ( CD). Anwer hould include, ut i not limited to: Student will meure the indicted ody prt length nd record the meurement in tle. They will then clculte the indicted rtio nd compre them to the golden rtio. The tle hould e net nd the clcultion ccurte. Meurement will e different for different tudent, ut rtio hould e pproimtely.68.. The golden rtio i +. Anwer hould include, ut i not limited to: Student will lit emple of the golden rtio in rt nd rchitecture. Student hould provide ource for their emple. 6. On Your Own (pp. ). + ( + ). 6 0 + 0 ( 6 + ) 0 0 0 Copyright Big Ide Lerning, LLC All right reerved. Big Ide Mth Blue Worked-Out Solution 7
. 7 7 ( ) 7 7. 6 6 6. 9 9 6. 98 9 9 7 7 7 + + + 7. ( 7 ) + + + 8. ( ) 9. + ( + ) 6 7. 8. 9. 6 6 6 0. 6 7 7 ( 6 ) 7 7. + + 8. 6 6 ( ) 6 6.. 9. (. 9.) 7.7 0. V Bh ( 0)( 8) 0 8 00 0 The volume i 0 cuic meter. 6. Eercie (pp. 6 7) Voculry nd Concept Check. Adding nd utrcting qure root i imilr to comining like term ecue you cn think of like rdicnd like vrile term.. The Product Property of Squre Root nd the Quotient Property of Squre Root re imilr in tht oth propertie re ued to implify qure root y tking qure root of numer inide the rdicl. Prctice nd Prolem Solving..6 66 The rtio of the ide length i out.6, which i cloe to the golden rtio...6 The rtio of the ide length i out.6, which i cloe to the golden rtio.. 0. The rtio of the ide length i out., which i not cloe to the golden rtio.. 7 7 + + 0 8 8 8 8 8. When dding qure root, you do not dd rdicnd. + ( + ) 7 6. 8 9 9 7. 00 00 00 0 8. 9. 8 6 6 0.... 6.. 6 6 8 6 6 6 7 7 7 9 9 7. c c c Length + + + + 0 in. 9 9 0 0 + + + 9 9 9 9 6. ( ) 7 Big Ide Mth Blue Worked-Out Solution Copyright Big Ide Lerning, LLC All right reerved.
7. + 6 6 + 6 6 + 6 6 + 6 ( + ) 6 6 6 8. 7 + 8 7 + 7 7 + 7 7 + 7 + 7 0 7 9. 0. V.. Bh ( 0) 0,00 0 The volume i 0 cuic feet. ± ± So, or. P + w + 0 68 + 0 68 + 0 88 The perimeter i 88 feet, or out. feet.. A w 0 ( 0) 0 0 0 680 The re i 680 qure feet.. V π π π 9 7π πr r h 7 r.8 7 r 7 r r r r The rdiu i kilometer, or out 9.6 kilometer... r r r r r r 98 98. r 9 7 The minimum rdiu needed i 7 inche. Fir Gme Review. + c 76 + 0 c 600 c 600 c 0 c. 0 + 6 00 676 + 76 76 The length of the The length of the leg i hypotenue i 0 meter. inche. 6. + + 8 8 9 The length of the leg i 9 centimeter. Copyright Big Ide Lerning, LLC All right reerved. Big Ide Mth Blue Worked-Out Solution 7
7. C; Becue 00 0 nd, you know tht 0 i etween 0 nd on numer line. Section 6. 6. Activity (pp. 8 9).. Let d e the ditnce from econd e to home plte. d 90 90 90 + 90 d 800 + 800 d 6,00 d 6,00 d 800 d 800 d 90 d 7. d The plyer throw the ll out 7. feet. One deciml point of ccurcy i reonle, ecue it give the ditnce ccurte to out n inch.. From prt () you know tht the ditnce from third e to firt e i 90 feet. The ditnce etween the pitcher mound to firt e i hlf thi ditnce, or 90 feet. Ue the known vlue to check if they tify the Pythgoren Theorem. 60. + 90 660. + 800 660. + 0 800 660. + 0 800 0 660. + 0 800 660. + 0 800 660. + 00 800 770. 800 The vlue do not tify the Pythgoren Theorem. So, the ditnce from the pitcher mound to home plte doe not form right tringle with firt e. 00 0 8 9. + 8 0 + 78,00,6,6 89 89 89 06. The ldder will rech out 06. + 8. feet high on the uilding... 6 + c 6 + 6 c c c c c c P 6 + + 0 + 7. The perimeter i out 7. feet. You need to ue the Pythgoren Theorem to find the hypotenue of the tringle. + + 9. The height of the trpezoid i inche. P + + + 9 +. The perimeter i out. inche. You need to ue the Pythgoren Theorem to find the height of the trpezoid. + c 9 + c c c. c c The ide length of the prllelogrm i P + 0 + 7. centimeter. The perimeter i out 7. centimeter. You need to ue the Pythgoren Theorem to find the ide length of the prllelogrm. 76 Big Ide Mth Blue Worked-Out Solution Copyright Big Ide Lerning, LLC All right reerved.
.. Ue the Pythgoren Theorem to find the height of the tringle in term of. 6. Smple nwer: You wnt to know if you cn fit 7-foot-dimeter circulr tle with folding leg through doorwy tht i inche wide nd 6 feet 8 inche tll. You cn ue the Pythgoren Theorem to help you decide. h. h + h + h h h A h A formul for the re of n equilterl tringle with ide length i A ( 0) A. 00. The re i out. qure inche.. Smple nwer: The Pythgoren Theorem cn e ued to find ditnce nd to find re of polygon. in. + c + 80 6 + 600 76 76 889 889 889 86.9 Becue the tle i 7 feet 8 inche wide, it will proly fit through the doorwy on n ngle, if the tle top i not too thick. 6. On Your Own (pp. 60 6). + c + 9 c c c.6 c N School c Home W Pot Office O E S 6 ft 8 in. 80 in. Your home i out.6 mile from your chool. Copyright Big Ide Lerning, LLC All right reerved. Big Ide Mth Blue Worked-Out Solution 77
Chpter 6. The firt et of numer doen t elong ecue it i the. + 00 0 only et tht i not Pythgoren triple. + c + 90,000,00,00 + c + 6 8 6 + 8 0,00 6 + 6 00 9 + 6 6 80. 00 00 9 6 8 + c + 7 + + 69 0 m 9 + 76 6 69 69 9 6 6 9 Prctice nd Prolem Solving. 6 + 0 c 00 m. m + c 6 + 00 c Not drwn to cle 6 c The height of the firework i out 80. +. 8.8 meter.. + c 6 + 7 + 0 8 + 00 78 8 78 The tringle i right tringle. The tringle i not right tringle. The length of the hypotenue i meter. 8 + + 6 8 8 The tringle i not right tringle. 6. The perimeter i out 7.7 meter. + c 6 + c 6 + c 0 c 0 c 0 c 0 c 0 c + c + (0.7) (.) P 6 + 0 + 6 + 7.7. + c c c 96 + 79 0 0 0 9. c c + c. 6 + 0.6.6.6.6 9 The tringle i right tringle. 6. Eercie (pp. 6 6) Voculry nd Concept Check The ide length of the prllelogrm i 0 feet. ( ) P 0 + ( + 9) 0 + () 0 +.6 The perimeter i out.6 feet.. You cn ue the Pythgoren Theorem to find ditnce in coordinte plne y forming right tringle with the unknown ditnce the hypotenue. 78 Big Ide Mth Blue Worked-Out Solution Copyright Big Ide Lerning, LLC All right reerved.
. + c + c 8 c 8 c c c c The ide length of the qure i yrd. P 8. The perimeter i out. yrd. 6. 6 + d 6 + 9 d d d 6.7 d y 6 d 6 6 7 The ditnce i out 6.7 unit. 7. + 6 d 6 + 6 d d d 7. d y 6 d 6 6 7 The ditnce i out 7. unit. Copyright Big Ide Lerning, LLC All right reerved. + d + d 9 d 8. 9 d. d The ditnce i out. unit. + 0 + 900 76 9. 0. 6 76 7. The height i out 7. feet. + 0 60 + 00 600 00 00. The height i out. yrd. + 6 + 6 89. y 6 7 89.7 The height i out.7 +.. meter. 60 + 00 c 600 + 0,000 c,600 c. d,600 c 6.6 c The length of the hortcut i out 6.6 meter. Big Ide Mth Blue Worked-Out Solution 79
. + 8 7 + 6 89 89 89 The tringle i right tringle.. + c 9 + 0 ( 9.) + (.6) 0 68.6 +.6 00 00 00 The tringle i right tringle.. + c 8 + 8.. 6 + 7.. 6.. The tringle i not right tringle. 6. + 9 96 + 6 9 7 9 The tringle i not right tringle. 7. 9 + 0 8 + 00 The tringle i right tringle. 8.. +.8.96 +.0 The tringle i right tringle. 9. 8 + 0 c 6 + 00 c 6 c 6 c.8 c The ditnce i out (.8).6 inche. Ue the fct tht inche foot to convert to feet. ft.6 in..8 ft in. So, the ditnce from point A to point B i out.8 feet. 0. Convert feet to kilometer. 0,000 ft ft y ft m.8 ft 0,000 ft km km km 000 m 8,000 ft 0,000 km.8 000 0,000 km 80 6. km 8000 ft m km 8000 km.8 ft 000 m.8 000 8000 km 80. km Plne A: + c 6. + 7. + 6. 6. 7.9 Plne A i out 7.9 kilometer from the tower. Plne B: + c. + 7 y.76 + 9.76 y y.76 y 7. y Plne B i out 7. kilometer from the tower. So, Plne B i lightly cloer. 80 Big Ide Mth Blue Worked-Out Solution Copyright Big Ide Lerning, LLC All right reerved.
. Anwer hould include, ut i not limited to: Student will find mll o nd ccurtely meure it dimenion. They will then ue the Pythgoren Theorem to find length BC nd length AB. They will check their work uing tring nd ruler. + d 9 + 9 d 8 d 8 d 8 d + c + e + e 0 e 0 e 0 e + c 8 + f 6 + 68 f f. 68 68 8 e f O d f y f The length of the three ide re 8, 0, nd 68. Ue the Convere of the Pythgoren Theorem to determine if the tringle i right tringle. + c d + e f ( 8) + ( 0) ( 68 ) 8 8 + 0 0 68 68 8 + 0 68 8 + 0 68 68 68 So, the tringle i right tringle. Fir Gme Review + 9 + 7 + + + 78. men 6 6 The men i. The dt in order i 9,,,,, 7. + medin. The medin i.. The vlue occur mot often. So, the mode i.. + + 6 + 7 + + 9 + 0 men 7 7 7 The men i. The dt in order i 0, 6, 9,,, 7,. The middle vlue i. So, the medin i. All dt vlue occur once. So, there i no mode. 67 + 9 + + 7 + 9 90. men 8 The men i 8. The dt in order i, 9, 9, 67, 7. The middle vlue i 9. So, the medin i 9. The vlue 9 occur mot often. So, the mode i 9. 80 8 80 6 80 080 6. B; S ( n ) The um of the ngle meure of n octgon i 080. Quiz 6. 6. (p. 6). Becue, i perfect qure nd i rtionl.. Becue cn e written 9 0, i rtionl. 9 9. Becue i not perfect qure, i irrtionl... 6 6 9 7 6 8 Becue 8 i cloer to 6 thn to 9, 8 i cloer to 6 thn to 7. So, 8 6. 99 Becue 99 i cloer to 00 thn to 8, 99 to 0 thn to 9. So, 99 0. 8 00 0 8 9 6 8 i cloer Copyright Big Ide Lerning, LLC All right reerved. Big Ide Mth Blue Worked-Out Solution 8
6. 7. 8. Becue 7 i cloer to 69 thn to 96, to thn to. So, 7. i to the right of. So, i greter. 7 i cloer. i to the right of.8. So,. i greter. 9. + ( + ) 0. 7 ( 7)... V 6 6 6 Bh. The volume i out. cuic inche. V 69 Bh ( 0.)( 0.6) 0. 0.6 0.6 0.6 The volume i 0.6 cuic centimeter. + c + 9 c c. c.8 c 7 96 9 6.8 The cin i out.8 kilometer from the pek..6.. 0 9 y Cin 6 c Pek 6 7 7 + c 9 + c 7 c. 7 c 8.6 c The fire tower i out 8.6 kilometer from the lke. + c + c 0 c 6. 0 c 7. c The lke i out 7. kilometer from the pek. 6 + 0 c 6 + 00 c 6 c 6 c.7 c 7. You re out.7 kilometer from the lke. 8. 6 + 8 6 + 78 809 900 809 The tringle i not right tringle. 9.. +..7. +..69.69.69 The tringle i right tringle. Chpter 6 Review (pp. 6 67).. 6 6 So, the qure root of 6 re nd. 0 0 900 0 0 900 y 8 Fire Tower 7 7 Lke O 6 7 So, the qure root of 900 re 0 nd 0. 6 c y Lke O 6 7 c Pek 6 7 O You y 0 7 Lke c 6 8 Big Ide Mth Blue Worked-Out Solution Copyright Big Ide Lerning, LLC All right reerved.
. 0 0 00 0 0 00 So, the qure root of 00 re 0 nd 0.. Becue, 9. Becue, 6. Becue..96, nd... 9. ±.96 ±.. 7. 6 6 8. + 9 + +, or 6 9. 0( 8 ) 0( 9 ) 0( ) 0 0.. + c + c 69 c 69 7 c c The length of the hypotenue i 7 inche. + c 0. + 0. + 0.6 0.09 0. 0.6 0. The length of the leg i 0. centimeter... Becue 7 i cloer to 69 thn to 96, to thn to. So, 7. 99 99 00 00 9 0 9 0 0 6. 96 6 6 6 6 6 7. 7 8. 69 + + 6 0 0. The height i out. feet. 77 + 8 + 96 9. 99 7 96 6 The height i 6 feet. 7 96 7 i cloer. 9 6 Chpter 6 Tet (p. 68). Becue 0 600, 600 0 0.. Becue i cloer to 6 thn to 9, thn to. So,. 90 Becue 90 i cloer to 8 thn to 00, 9 thn to 0. So, 90 9. i cloer to 6 8 8 9 00 0 90 i cloer to. Becue, 7 9. 9 7 7 0 00 00 0 0. Becue, ± ± 9 9 0 nd.. + 8 6 + 8 + Copyright Big Ide Lerning, LLC All right reerved. Big Ide Mth Blue Worked-Out Solution 8
7. + + 6 + 6 6, or + 6 + 76 676 00 6. 00 0 The length of the leg i 0 inche. 7. The deciml form of 6π neither terminte nor repet. So, 6π i irrtionl. 8. 9 i perfect qure. So, 9 9. 0. i rtionl. i to the right of 0.6. So, i greter. i to the right of 6.. So, i greter.. 6 + ( 6 + ). 0 0 0 0. 9 + 80 89 + 600 79 79 79 The tringle i right tringle. + 7 + 9 6 76. 76 0.6 0. 0. 0 6. 6 6 9 7 6 8 The height of the root i meter. + 6 + 7 600. 600 60 The ltitude of the lloon i 60 + 6 66 feet. Chpter 6 Stndrdized Tet Prctice (pp. 69 7). D; T L.... The period i. econd.. H; To write liner eqution in lope-intercept form, you mut olve the eqution for y. So, Pt hould utrct from oth ide of the eqution nd divide every term y 6. 6y 6y + y 6. A; Numer of home equl numer of home uilt ech yer An eqution i n 8y + 60.. G; Becue the domin i finite numer of vlue, the domin i dicrete.. Ue the Pythgoren Theorem. 0 + 0 c 600 +,00 c 6,000 c 6,000 c 6. c time numer of yer plu numer of home t trt Vrile: Let n e the numer of home nd y e the numer of yer n 8 y + 60 c 0 yd 0 yd The ditnce etween oppoite corner i out 6. yrd. 8 Big Ide Mth Blue Worked-Out Solution Copyright Big Ide Lerning, LLC All right reerved.
6. 0h + 0 60 0h 600 h The conultnt worked hour. 7. B; S 80( n ) S 80n 60 S + 60 80n S 60 + n 80 80 S + n 80 8. I; To get the y-vlue in the tle, multiply the -vlue y, then dd 6. So, the liner function y + 6 relte y nd in the tle. 9. C; + c + 7 + 9 6 76 76 The vlue of i centimeter.. + 6 d 089 + 6 d d d 6 d N (, 6) (0, 6) Airplne 0 0 6 d 0 0 0 Strting Point W S 0 0 0 0 E The irplne i 6 mile from it trting point.. F; The grph of the line y h lope of nd pe through ( 0, ). 0. I; Let h e the height of the tree. 6 h. 0 6 0.h 80.h 0 h The height of the tree i 0 feet.. C; 6 6 6 6. F; The um of two complementry ngle i 90. So, the meure of n ngle whoe complement i degree 90. i. B; g 8.h 8.h.h 6 h After out 6.0 hour, you will fill up gin. Copyright Big Ide Lerning, LLC All right reerved. Big Ide Mth Blue Worked-Out Solution 8