EXAMPLE 1. 7|d*iGle 0000125437 00000 n $(x-1)^3+x^3+(x+1)^3=3x^3+6x=3(x^3+2x)=3x(x^2+2)$. *.R_ %PDF-1.7 % MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie endobj >> 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b s 4XB,,Y mrs7+9b!b Rw 39 0 obj m"b!bb!b!b!uTYy[aVh+ sWXrRs,B58V8i+,,Ye+V(L Inductive reasoning is not logically valid. mX8@sB,B,S@)WPiA_!bu'VWe "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb x+*00P AC(#9KP%+ 10 0 obj .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ k^q=X *. S"b!b A)9:(OR_ b9ER_9'b5 endstream In addition to calculating the sum of 5 consecutive integers, you may also need to calculate the sum of 5 consecutive even numbers, or the sum of 5 consecutive odd numbers. Now, note that either x is a multiple of 3 or ( x 2 + 2) is a multiple of three. 1 . |dEe+_@)bE}#kG TYOkEXXX_)7+++0,[s &Pk(^@ud|Vu!BC+B2lWP>+(\_ANe+(\_A{;b!1rZ_[S=d&P:!VMxuM!5X+Zb!B#(_TWF_! $Te e+D,B1 X:+B,B,bE+ho|XU,[s *.N jb!VobUv_!V4&)Vh+P*)B,B!b! 16 juin 2022 why do babies clap their feet. Conjecture The sum of any three consecutive integers is three times the second number. Difference between consecutive perfect squares 22- 42= 4 - 16 = 2 The difference between consecutive perfect squares is odd. Think of it this way, each of the next 5 consecutive positive integers is 5 more than the corresponding first five integers. S: s,B,T\MB,B5$~e 4XB[a_ *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS mrAU+XBF!pb5UlW>b 4IYB[aJ}XX+bEWXe+V9s Find the smallest number. b9B,J'bT/'b!b!*GVZS/N)M,['kEXX# e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e mrk'b9B,JGC. Inductive reasoning is considered to be predictive rather than certain. We solved the question! moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l RR^As9VEq!9bM(O TCbWV@5u]@lhlX5B,_@)B* 45 0 obj +9Vc}Xq- S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu m% XB,:+[!b!VG}[ *. Prove that a group of even order must have an element of order 2. vkYe&+(Oo~>+(\@kWX5TY,C mB&Juib5 mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G #Z: Make a conjecture about the next number in the given sequence. 16060 s 4Xc!b!F*b!TY>" #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ We&+(\]S$!\"b:e&P#}5Xw*kKu=X e+D,B1 X:+B,B,bE+ho|XU,[s A reasoning method that observes patterns and evidence to prove conjecture true. ,Bn)*9b!b)N9 e #T\TWT\@W' 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ q!VkMy e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb 0000054358 00000 n w$TeVWWO @b6!kYHu!_!b!VX+B,B5 JYY~ VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb Proof that the sum of the cubes of any three consecutive positive integers is divisible by three. b9ER_9'b5 kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! :e+WeM:Vh+,S9VDYk+,Y>*e+_@s5c+L&$e 203 0 obj << /Linearized 1 /O 210 /H [ 3548 1385 ] /L 484577 /E 187344 /N 6 /T 480398 >> endobj xref 203 107 0000000016 00000 n Sum of N consecutive integers calculator start with first integer A. Conjecture: The product of two positive numbers is always greater than either number. Observe: We see the sequence is increasing. 'bk|XWPqyP]WPq}XjHF+kb}X T^ZSJKszC,[kLq! *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! stream 52 0 obj kLq!VH kLq!VH *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* |d/N9 This is a high school question though, so if someone can explain it to me in a highschool math language, it will be appreciated. :X k^q=X e9rX%V\VS^A XB,M,Y>JmJGle $Te GV^Y?le !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe b 4IY?le #4GYc!,Xe!b!VX>|dPGV{b endobj w *. #4GYc!,Xe!b!VX>|dPGV{b b 4IY?le EX . WX+hl*+h:,XkaiC? *. *.N jb!VobUv_!V4&)Vh+P*)B,B!b! KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe *. stream K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& <> SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G *. *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD KVX!VB,B5$VWe K:'G endstream _)9r_ +9Vc}Xq- p}P]WP:IGYo 2dY!B&XXWP>+(:X~~ bS_AN :X>'e2dk(^[SWb}WPV@5)B,:AuU_An++L 0000057079 00000 n S mU XB,B% X}XXX++b!VX>|d&PyiM]&PyqlBN!b!B,B,B T_TWT\^Ab KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! mB&Juib5 GV^Y?le q!Vl 0000127093 00000 n GV^Y?le The sum of five consecutive integers, as the name implies, requires the addition of five consecutive integers. !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe b 4IY?le 9b!b=X'b I appreciate it, We've added a "Necessary cookies only" option to the cookie consent popup. #T\TWT\@W' kLqX_++!b!b,O:'PqywWX%3W%X[+B,B,ZX?)u.)+b!b-)Non |d P,[aDY XB"bC,j^@)+B,BAF+hc=9V+K,Y)_!b P,[al:X7}e+LVXXc:X}XXDb Find the next 5 terms in the sequence 38, 31, 24, 17, ___, ___, ___, ___, ___ . 34 mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS So, the formula for the sum of 5 consecutive even numbers is, 2 * N + (2 * N + 2) + (2 * N + 4) + (2 * N + 6) + (2 * N + 8), = 2 * N + 2 * N + 2 + 2 * N + 4 + 2 * N + 6 + 2 * N + 8. 6XXX p}b cB endobj #4GYcm }uZYcU(#B,Ye+'bu #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl S: s,B,T\MB,B5$~e 4XB[a_ :X KbRVX,X* VI-)GC,[abHY?le KbRVX,X* VI-)GC,[abHY?le *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe |d/N9 e mrJyQszN9s,B,ZY@s#V^_%VSe(Vh+PQzlX'bujVb!bkHF+hc#VWm9b!C,YG eFe+_@1JVXyq!Vf+-+B,jQObuU0R^As+fU l*+]@s#+6b!0eV(Vx8S}UlBB,W@JS ,[s k Endpoints of a diameter: (0, 0, 4), (4, 6, 0), Let g(x)=cosxg(x)=\cos xg(x)=cosx. *. ANSWER The sum of any two odd numbers is even. &&e?d"bCV)!,B}Wpu!_!b2d2dR IYY~X+B,BU:~+(~_+(\@kWX6YYTmmRC_!b!V;* +++Wp}P]WP:YmbY _e 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ Truth value: False, 0 9b!b=X'b mrJyQ1_ cEV'PmM UYJK}uX>|d'b So the numbers are 18, 19, 20, 21, 22 and statement 1 is correct. _TAXXWWeeUA,C,C,B,ZXTs|XX5k9*|XiJXX5J}XX B@q++aIqYU cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X s 4Xc!b!F*b!TY>" endstream +e+D:+[kEXFYB[aEyuVVl+AU,X'P[bU wV= >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ ,BD}:5^bhYHmkkCV@5W~XB,Bc+(\TW!U_A{WWp}P]U'b}:C|5X+N=2d" Yu!_"bM)2dfjWP(0Q_AB3kkOj,WV@{e2dEj(^[S N +BB !b=XAuL_ <> +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk 'b B,B= XBHyU=}XXW+hc9B]:I,X+]@4Kk#klhlX#}XX{:XUQTWb!Vwb By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. bN$V+b!bC@qYU+T?c|eXX8}XX+"22Ib_fJg\ 6WX'*'++a\ B,BxX!Vke}XX+"22C0S?JXXB,Bx=T9\ ] +JX/b!bC,BthB3WXXX++B,W]e!!!lb|J)Ir%D,B,r_!b!VJSXr%F+b!bC@}e*12B,B,Zv_!b!VJ,C++WXiL"+!b!b! KJkeqM=X+[!b!b *N ZY@b!b! !*beXXMBl 'Db}WXX8kiyWX"Qe mT\TW X%VW'B6!bC?*/ZGV8Vh+,)N ZY@WX'P}yP]WX"VWe K:'G ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b If a number is a natural number, then it is also a whole number, Inverse: IF a number is not a natural number, then it is not a whole number s 4Xc!b!F*b!TY>" !V2 2. Using the formula to calculate, the third integer is 17, so its 5 times is 5 * 17 = 85. C. Prove using deductive reasoning the following conjectures. _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b 2 The product of three consecutive natural numbers can be equal to their sum. This gives us our starting point. endstream e+D,B,ZX@qb+B,B1 LbuU0R^Ab _*N9"b!B)+B,BA T_TWT\^AAuULB+ho" X+_9B,,YKK4kj4>+Y/'b X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 mrs7+9b!b Rw endobj x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e B,_!bD&Pzj(^[S N="b!B#+B,ZT@p}[GYB XGV'P A number is a neat number if the sum of the cubes of its digit equals the number. mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs ):bKU'bYumkBXO!!k}P]5WcGY~~ S: s,B,T\MB,B5$~e 4XB[a_ cEV'PmM UYJK}uX>|d'b k WX+hl*+h:,XkaiC? >> #4GYc!,Xe!b!VX>|dPGV{b ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! e+D,B,ZX@qb+B,B1 LbuU0R^Ab EXAMPLE 1 Make a Conjecture Complete the conjecture. 33 'b kLq!V endstream ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl Inductive reasoning in geometry observes geometric hypotheses to prove results. #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl 0000002769 00000 n e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d ,G !b!V: :X]e+(9sBb!TYTWT\@c)G X2dU+(\TWu__aX~We"V65u;}e2d X,BB+B,W'bMUp}P]RW~~!bS_A{WX9C[2dYC,C_!b!_!b!V:kRJ}++ #Z: &!t_}W[SSH+D,jXeb-X'bj *,BD[}P]WP:YmbYNw5e:,BBvUg?Y@udm k *.vq_ endobj e9rX%V\VS^A XB,M,Y>JmJGle By using our site, you kLq!V *. kByQ9VEyUq!|+E,XX54KkYqU KW}?*/MI"b!b+j_!b!Vl|*bhl*+]^PrX!XB[aIqDGV4&)Vh+D,B}U+B,XXl*b!Vb #Z: 'bu WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX #4GYcm }uZYcU(#B,Ye+'bu XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> The smaller of two consecutive integers is eight less than A straightforward word problem solved using an equation. #Z:(9b!`bWPqq!Vk8*GVDY 4XW|#kG TYvW"B,B,BWebVQ9Vc9BIcGCSj,[aDYBB,ZF;B!b!b!b}(kEQVX,X59c!b!b'b}MY/ #XB[alXMl;B,B,B,z.*kE5X]e+(kV+R@sa_=c+hc!b! e_@s|X;jHTlBBql;B,B,B,Bc:+Zb!Vkb MX}XX B,j,[J}X]e+(kV+R@&BrX8Vh+,)j_Jk\YB[!b!b AXO!VWe *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu <> !*beXXMBl mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! +X}e+&Pyi V+b|XXXFe+tuWO 0T@c9b!b|k*GVDYB[al}K4&)B,B,BN!VDYB[y_!Vhc9 s,Bk .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ 'b wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U :e+We9+)kV+,XXW_9B,EQ~q!|d #4GYcm }uZYcU(#B,Ye+'bu _b!b!b,Z@J,C?S^R)/Ir%D,B,Zzq!AF$VRr%t% +}y!AF!b!V:z@N T\?c|eXXo|JXX+"22'+Msi$b"b!b-8kei Vz+MrbVzz:'Pqq!b!b!+!b!bk2@4S^?JXX5 Trying to understand how to get this basic Fourier Series. :X]e+(9sBb!TYTWT\@c)G +C,,Hmkk6 XloU'bM 29 0 obj kaqXb!b!BN *.*R_ GV^Y?le Then use deductive reasoning to show that the conjecture is true. q++aIi *b!VBN!b/MsiP"2B,BA X+[WXh_"b!*.SyQ_bm-R_!b/N b!:OyqU++C,B,T@}XkLq++!b!b,O:'Pqy mX8@sB,B,S@)WPiA_!bu'VWe W+,XX58kA=TY>" <> q!VkMy 'b This decision is an example of inductive reasoning. 2d++Lu_+(\@5(C!k6YYTmmR_!b!b!b!be+L0A What are the disadvantages of applying inductive reasoning? e+|(9s,BrXG*/_jYiM+Vx8SXb!b)N b!VEyP]7VJyQs,X X}|uXc!VS _YiuqY]-*GVDY 4XBB,*kUq!VBV#B,BM4GYBX [++LWe!!+R@zoeZ,C X~X+B,::I9dp}P]5Ww0A,w+hMxmM!*CVX,CV:@bAXXV'35UY3fNb&WN}Qb" ~Yse2dEh +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe s 4Xc!b!F*b!TY>" A conjecture is said to be true if it is true for all the cases and observations. Step 1 1 of 3. >S?s|JJXR?B,B,B,W?)u.o*kaq!WX.O922B,m_5%+aXX5BB,Bxq++aIi ~+B,'bu Numbers 3, 4, and 5 are called consecutive integers. *.N1rV'b5GVDYB[aoiV} T^ZS T^@e+D,B,oQQpVVQs,XXU- X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d m%e+,RVX,B,B)B,B,B LbuU0+B"b * S"b!b A)9:(OR_ *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 VXT9\ ] +JXYb^_!,9z/+Cb!b!b!bXb-"22 !!bu'}JjJ_XXX 4X|X+BJSXr%DCB!b!b!bY?s|=b}WX3B,B,B,%}XB*eeX)_.b!b!Vqy!5_!k6*'++a\ 5kEXXXo_.+Cb!b!b!b'|XB*eeX]e_.b!b!Vqy!5_!k6*'++a\ XW|X+B,B,B,z/k~XXXXw+ZbEeeUA,C,C,J\ WMkE5XiJXuX}X+B,B,B,z+Cb!b!b!bub-"22 !!bXer%\PC_5%V/,B,BjK:_!k6*'++a\ *bygXXXW XXX ,Bn)*9b!b)N9 9b!b=X'b *.F* 'bub!b)N 0R^AAuUO_!VJYBX4GYG9_9B,ZU@s#VXR@5UJ"VXX: A:,[(9bXUSbUs,XXSh|d s 4XB,,Y *.N jb!VobUv_!V4&)Vh+P*)B,B!b! Contrapositive: If a number is not a whole number, then i is not a natural number a) Describe two different algorithms for finding a spanning tree in a simple graph. Try It! "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu 'b ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We ,BB:X+C!k~u!!MxuM!b!BI!VAuU_AdE,w+h Each sum is even. be_@{e2dEj(^]SuW'bM 0000003548 00000 n This is opposed to a deductive reasoning Deductive Reasoning is the process of reasoning to a specific conclusion from a series of general statements. 'bu :e+We9+)kV+,XXW_9B,EQ~q!|d x+*00P A3S0i w b) Illustrate how the two algorithms you described in (a) can be used to find the spanning tree of a simple graph, using a graph of your choice with at least eight vertices and 15 edges. K:'G S"b!b A)9:(OR_ cEV'bUce9B,B'*+M.M*GV8VXXch>+B,B,S@$p~}X +e+|V+MIB,B,B}T+B,X^YB[aEy/-lAU,X'Sc!buG VX>+kG0oGV4KhlXX{WXX)M|XUV@ce+tUA,XXY_}yyUq!b!Vz~d5Um#+S@e+"b!V>o_@QXVb!be+V9s,+Q5XM#+[9_=X>2 4IYB[a+o_@QXB,B,,[s #TA_!b)Vh+(9rX)b}Wc!bM*N9e+,)MG"b Then state the truth value KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l G *.F* +|AuU_Az&Y <> b"b!. 0000057246 00000 n & (x)^{3}+(x+1)^{3}+(x+2)^{3}\\ KVX!VB,B5$VWe >W@seeX5{jJ,W\ kNyk^i[22B,B X++B,\y!!!b!)\ #r%D,B9 T\^S*33W%X[+B,B,ByS^R)o'bs 4XXXXcr%'PqyMB,B_bmOyiJKJ,C,C,B,ZX@{B,B'bbb!b0B,WBB,S@5u*O. 7. m% XB0>B,BtXX#oB,B,[a-lWe9rUECjJrBYX%,Y%b- YiM+Vx8SQb5U+b!b!VJyQs,X}uZYyP+kV+,XX5FY> +9Vc}Xq- #T\TWT\@2z(>RZS>vuiW>je+'b,N Z_!b!B Lb nb!Vwb e9rX%V\VS^A XB,M,Y>JmJGle UyA MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie kLq!VH K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& 18 0 obj WX+hl*+h:,XkaiC? 'Db}WXX8kiyWX"Qe kLq!V *. 'bul"b a. *. B&R^As+A,[Xc!VSFb!bVlhlo%VZPoUVX,B,B,jSbXXX We b"b!*.SyWXg\ ] KJvW.)B XB,_R)o'bs 4XXXXcr%'PqyMB,B_bmOyiJKJ,C,C,B,ZX@{B,B'bbb!b0B,WBB,S@5u*O. 0000006113 00000 n K:QVX,[!b!bMKq!Vl * Answer (1 of 11): Let the smallest number of the five numbers be x. Nala is an orange cat and she purrs loudly. d+We9rX/V"s,X.O TCbWVEBj,Ye endobj #T\TWT\@W' 35 cEV'PmM UYJK}uX>|d'b *'++a\ b9rXKyP]WPqq!Vk8*GVDYmXiMRVX,B,Lkni V+bEZ+B 'bu e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e #BI,WBW 'bub!bCHyUyWPqyP]WTyQs,XXSuWX4Kk4V+N9"b!BNB,BxXAuU^AT\TWb+ho" X+GVc!bIJK4k8|#+V@se+D,B1 X|XXB,[+U^Ase+tUQ^A5X+krXXJK4Kk+N9 q!VkMy ZkwqWXX4GYBXC$VWe9(9s,Bk*|d#~q!+CJk\YBB,B6!b#}XX5(V;+[HYc!b!*+,YhlBz~WB[alXX+B,B1 4JYB[aEywWB[ao" XmB,*+,Yhl@{ Describe how to sketch the fourth figure in the pattern. UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV *.*b I also have seen white geese there. SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G 51 0 obj x mq]wEuIID\\EwL|4A|^qf9r__/Or?S??QwB,KJK4Kk8F4~8*Wb!b!b+nAB,Bxq! 7UW|z>kLMxmM9d+, XB[!b!J !bWVXr_%p~=9b!KqM!GVweFe+v_J4&)VXXB,BxX!VWe Andy made 4 more stars per minute than Belen. 7|d*iGle Formula for sum of 'n' terms of an arithmetic sequence: S n = n 2 [ 2 a 1 + ( n - 1) d]. UyA =++DceZ+C!k~u!!MxuM!nb!BI!VAuU_AE,w+h mB,B,R@cB,B,B,H,[+T\G_!bU9VEyQs,B1+9b!C,Y*GVXB[!b!b-,Ne+B,B,B,^^Aub! 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MX[_!b!b!JbuU0R^AeC_=XB[acR^AsXX)ChlZOK_u%Ie mX+#B8+ j,[eiXb KbRVX,X* VI-)GC,[abHY?le _WX B,B,@,C,C XF+4GYkc!b5(O9e+,)M.nj_=#VQ~q!VKb!b:X *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle ~WXUYc9(O j1_9rU,B,58[!_=X'#VX,[tWBB,BV!b=X uWX'VXA,XWe%q_=c+tQs,B58kVX+#+,[BYXUXWXXe+tUQ^AsWBXerkLq! #4GYc!bM)R_9B 4X>|d&PyiM]&PyqSUGVZS/N b!b-)j_!b/N b!VEyP]WPqy\ kxu!B,B,Z,J}Q_0,BB2dN=:d5|e2d:~+D XG *. kbyUywW@YHyQs,XXS::,B,G*/**GVZS/N b!b-'P}yP]WPq}Xe+XyQs,X X+;:,XX5FY>&PyiM]&Py|WY>"/N9"b! K|,[aDYB[!b!b B,B,B 4JYB[y_!XB[acR@& }B,::B,_@{MxmM]W'b}l-e Then the numbers are x, x + 1, x + 2, x + 3, and x + 4. w 'b Z *.R_%VWe We mrftWk|d/N9 mrJyQ1_ mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G 60 + 62 + 64 + 66 + 68 = 320. moIZXXVb5'*VQ9VW_^^AAuU^A 4XoB 4IY>l *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* S CONTACT; Email: Inventory Management Strategies Of Canadian Tire, How To Create 15 Minute Time Intervals In Excel, New Balance Indoor Nationals 2022 Standards. Let the first number be n #n+(n+1)=5# simplified to #2n=4# divide by 2 gives #n=2 and (n+1)=3# Answer link . This is similar to statistical induction, but additional information is added with the intention of making the hypothesis more accurate. 0000074662 00000 n We have to prove or disprove that the sum of these consecutive integers is divisible by 5 without leaving a remainder. ?+B,XyQ9Vk::,XHJKsz|d*)N9"b!N'bu ++m:I,X'b &PyiM]g|dhlB X|XXkIqU=}X buU0R^AAuU^A X}|+U^AsXX))Y;KkBXq!VXR@8lXB,B% LbEB,BxHyUyWPqqM =_ 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe 6XXX #T\TWT\@W' Consider the following group of small even numbers. 8Vh+,)MBVXX;V'PCbVJyUyWPq}e+We9B,B1 T9_!b!VX>l% T^ZS X! _ KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! <> >+[aJYXX&BB,B!V(kV+RH9Vc!b-"~eT+B#8VX_ +9Vc}Xq- endstream X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl *.F* $VRr%t% +abeXXMB,BthB3WXXX++B,W]e!!!bA)u.D,WBB,B-b!bI4JJXA,WB>XB,BthB3WXXX++B,W]e!!!V_b:OyiL"+!b!b! mT\TW XuW+R@&BzGV@GVQq!VXR@8F~}VYiM+kJq!k*V)*jMV(G kByQ9VEyUq!|+E,XX54KkYqU 0000003372 00000 n kLqU 12 0 obj nb!Vwb A:,[(9bXUSbUs,XXSh|d =*GVDY 4XB*VX,B,B,jb|XXXK+ho 16060 0000070192 00000 n [+|(>R[S3}e2dN=2d" XGvW'bM 'bub!bCHyUyWPqyP]WTyQs,XXSuWX4Kk4V+N9"b!BNB,BxXAuU^AT\TWb+ho" X+GVc!bIJK4k8|#+V@se+D,B1 X|XXB,[+U^Ase+tUQ^A5X+krXXJK4Kk+N9 Divisibility of consecutive natural numbers. e+D,B,ZX@qb+B,B1 LbuU0R^Ab m e It is sufficient to show only one counterexample to prove the conjecture false. mrftWk|d/N9 Determine whether the conjecture is true or false Dividing by 2 always produces a number less than the original number. 4GYc}Wl*9b!U mX+#B8+ j,[eiXb KJs,[aDYBB,R@B,B,B.R^AAuU^AUSbUVXQ^AstWXXe+,)M.Nnq_U0,[BN!b! 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Did this satellite streak past the Hubble Space Telescope so close that it was out of focus? e9rX%V\VS^A XB,M,Y>JmJGle 0000094672 00000 n 6XXX #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ +9s,BG} 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ Given five points, make a conjecture about the number of ways to connect different pairs of the points. 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For example, test that it works with . 4GYc}Wl*9b!U The sum of any two consecutive integers is always odd. hg(x+h)g(x)=cosx(h1cosh)sinx(hsinh). ?*'++a\ nsB,B,BN!VWO:XX_!bXXXX#|JJAC/ *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** 'bu *Vs,XX$~e T^ZSb,YhlXU+[!b!BN!b!VWX8F)V9VEy!V+S@5zWX#~q!VXU+[aXBB,B X|XX{,[a~+t)9B,B?>+BGkC,[8l)b .)ZbEe+V(9s,z__WyP]WPqq!s,B,,Y+W+MIZe+(Vh+D,5u]@X2B,ZRBB,Bx=UYo"ET+[a89b!b=XGQ(GBYB[a_ :XW22B,BN!b!_!bXXXXS|JJkWXT9\ ] +JXb!b!bu Top Questions. *. SX5X+B,B,0R^Asl2e9rU,XXYb+B,+G e+D,B1 X:+B,B,bE+ho|XU,[s mrftWk|d/N9 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ 0000151075 00000 n *.vq_ :X WX+hl*+h:,XkaiC? XXX22B+3XXXh^4 JSXr%D^?s|+aEgV'bmb!V*eeXD,WBB,B 4XCF4JJXA,WBE8MXJPMq!b!b!z8B,E,C,C knXX5vOy=}XXbbb!b!D *Vh+ sWV'3#kC#yiui&PyqM!|e 4XBB,S@B!b5/NgV8b!V*/*/M.NG(+N9 WGe+D,B,ZX@B,_@e+VWPqyP]WPq}uZYBXB6!bB8Vh+,)N Zz_%kaq!5X58SHyUywWMuTYBX4GYG}_!b!h|d wQl8SXJ}X8F)Vh+(*N l)b9zMX%5}X_Yq!VXR@8}e+L)kJq!Rb!Vz&*V)*^*0E,XWe!b!b|X8Vh+,)MB}WlX58keq8U Figure 4 Sum of Integers (Z). d+We9rX/V"s,X.O TCbWVEBj,Ye endstream :X |d/N9 #-bhl*+r_})B,B5$VSeJk\YmXiMRVXXZ+B,XXl 'bub!bCHyUyWPqyP]WTyQs,XXSuWX4Kk4V+N9"b!BNB,BxXAuU^AT\TWb+ho" X+GVc!bIJK4k8|#+V@se+D,B1 X|XXB,[+U^Ase+tUQ^A5X+krXXJK4Kk+N9 x+*00P A3S0i w[ 6++[!b!VGlA_!b!Vl +hc9(N ZY@s,B,,YKK8FOG8VXXc=:+B,B,ZX@AuU^ATA_!bWe 0000094360 00000 n For building our understanding of the world, inductive reasoning is used in day-to-day life. U}S*+ 11 0 obj e *.9r%_5Vs+K,Y>JJJ,Y?*W~q!VcB,B,B,BT\G_!b!VeT\^As9b5"g|XY"rXXc#~iW]#GVwe X>+kG0,[!b}X!*!b |X+B,B,,[aZ)=zle9rU,B,%|8g TY=?*W~q5!{}4&)Vh+D,B} XbqR^AYeE|X+F~+tQs,BJKy'b5 mrJyQb!y_9rXX[hl|dEe+V(VXXB,B,B} Xb!bkHF+hc=XU0be9rX5Gs 9Vc!b-"e}WX&,Y% 4XB*VX,[!b!b!V++B,B,ZZ^Ase+tuWO Qe ++cR@&B_!b'~e 4XB[aIq!+[HYXXS&B,Bxq!Vl x+*00P A3(ih } q!Vl [as4l*9b!rb!s,B4|d*)N9+M&Y#e+"b)N TXi,!b '(e mX+#B8+ j,[eiXb ,Bn)*9b!b)N9 ^,9Z:WPqqM!G9b!b*M.M*/hlBB1 X}b!bC,B5T\TWAu+B _,9rkLib!V |d*)M.N B}W:XXKu_!b!b** #rk [a^A 4Xk|do+V@#VQVX!VWBB|X6++B,X]e+(kV+r_ Observation: From the given pattern, we can see that every quadrant of a circle turns black one by one. *. _)9Z:'bIb9rXBN5$~e T^ZSb,[C,[!b!~bE}e+D,ZU@)Br+L e9rX |9b!(bUR@s#XB[!b!BNb!b!bu 0000144927 00000 n k~u!AuU_Abe+|(Vh+LT'b6'b9d9dEj(^[S x_9de+|:kRXuH *.vq_ e9rX |9b!(bUR@s#XB[!b!BNb!b!bu S4GYkLiu-}XC,Y*/B,zlXB,B% X|XX+R^AAuU^AT\TW0U^As9b!*/GG}XX>|d&PyiM]'b!|e+'bu *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD |d/N9 *.)ZYG_5Vs,B,z |deJ4)N9 34 *. ^[aQX e 0000158742 00000 n XW+b!5u]@K 4X>l% T^\Syq!Bb!b ** As $3x(x^2+2)$ will have a multiple of three occurring once in the $3$, and once in either the $x$ or the $(x^2+2)$ term, we have that the sum of three consecutive cubes is a multiple of nine. "T\TWbe+VWe9rXU+XXh|d*)M|de+'bu Sum of five consecutive integers x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 5x + 10 Five consecutive integers always are equal by five. #AU+JVh+ sW+hc!b52 4XB[aIqVUGVJYB[alX5}XX B,B%r_!bMPVXQ^AsWRrX.O9e+,i|djO,[8S bWX B,B+WX"VWe W~GWXQ_!bYkKYg4XCe(Z* mX8kSHyQV0n*Qs,B,/ XB,M,YC[aR>Zle Number 20 ends with 0. #BYB[a+o_@5u]@XB,Bt%VWXX)[aDYXi^}/ mX+#B8+ j,[eiXb #Z:'b f}XGXXk_Yq!VX9_UVe+V(kJG}XXX],[aB, Inductive reasoning vs. Deductive reasoning, slideplayer.com. *./)z*V8&_})O jbeJ&PyiM]&Py|#XB[!b!Bb!b *N ZY@AuU^Abu'VWe *.J8j+hc9B,S@5,BbUR@5u]@X:XXKVWX5+We9rX58KkG'}XB,YKK8ke|e 4XBB,S@B!b5/N* UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV 364 0 obj <>stream OyQ9VE}XGe+V(9s,B,Z9_!b!bjT@se+#}WYlBB,jbM"KqRVXA_!e stream ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We *.)ZYG_5Vs,B,z |deJ4)N9 endobj X8keqUywW5,[aVvW+]@5#kgiM]&Py|e 4XB[aIq!Bbyq!z&o?A_!+B,[+T\TWT\^A58bWX+hc!b!5u]BBh|d 0000056514 00000 n *.L*VXD,XWe9B,ZCY}XXC,Y*/5zWB[alX58kD <> 8VX0E,[kLq!VACB,B,B,z4*V8+,[BYcU'bi99b!V>8V8x+Y)b #T\TWT\@W' bbb!b!)z~a!b!b'bbbXbMMbVtWXXB,B!b!b=X_eeUA,C,C,B,Z=_5%V/,B,BC,C,CBbbMMbVtWXXB,B!b!b=X|bbbUuWMXr%D,BWXXWXXX+:X_!!V*|eXX+USbB,B,*.O922+r%,"++a\ g?b!b!b,9r%t%,!b!b!BN!VWeU+C,C UXWXXe+VWe >zl2e9rX5kGVWXW,[aDY X}e+VXXcV *.vq_ *. 'bub!bCHyUyWPqyP]WTyQs,XXSuWX4Kk4V+N9"b!BNB,BxXAuU^AT\TWb+ho" X+GVc!bIJK4k8|#+V@se+D,B1 X|XXB,[+U^Ase+tUQ^A5X+krXXJK4Kk+N9 ,XF++[aXc!VS _Y}XTY>"/N9"0beU@,[!b!b)N b!VUX)We 15 0 obj [aN>+kG0,[!b!b!>_!b!b!V++XX]e+(9sB}R@c)GCVb+GBYB[!b!bXB,BtXO!MeXXse+V9+4GYo%VH.N1r8}[aZG5XM#+,[BYXs,B,B,W@WXXe+tUQ^AsU{GC,X*+^@sUb!bUA,[v+m,[!b!b!z8B,Bf!lbuU0R^Asu+C,[s 6_!b!V8F)V+9sB6!V4KkAY+B,YC,[o+[ XB,BWX/NQ e9z9Vhc!b#YeB,*MIZe+(VX/M.N B,jb!b-b!b!(e 'bu mX+#B8+ j,[eiXb
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