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Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Nobody: 1:02pm On Nov 14, 2013 |
Richiez: Question 2 is by Quiz master Doubledx ========================== Solution to Question 2. ========================== Since Sec(x) = 1/Cos(x), Statement 1 is true... Statement 2, Sec(x) = 1/{2cos2(x/2) - 1} In this case we check it from the denominator of the expression => 1/Cos(x) Cos(x) = Cos(x/2 + x/2) Applying trig identities for cos(A + B) = CosACosB - SinASinB, We have => cos(x) = Cos(x/2)Cos(x/2) - sin(x/2)sin(x/2) Cos(x) = cos2(x/2) - sin2(x/2).....(1) But from trig identities=> sin2(A) + Cos2(A) = 1 Similarly=> sin2(x/2) + cos2(x/2) = 1 Thus=> sin2(x/2) = 1 - cos2(x/2)....(2) Now, substituting (2) in (1) yields => Cos(x) = cos2(x/2) - [1 - cos2(x/2)] Cos(x) = cos2(x/2) - 1 + cos2(x/2) Colecting like terms yields => Cos(x) = 2cos2(x/2) - 1, Now, since cosx = the denominator of statement 2 it means that it is true for Sec(x) = 1/Cos(x) = 2cos2(x/2) - 1 Now, to statement 3. the relationship is the same, it's only that this time we MUST solve in terms of sin(x) since the denominator is => {1 - 2sin2(x/2)} Now we have to show that cos(x) = {1 - 2sin2(x/2)} to prove that the statement f(x) = sec(x) = 1/{1 - 2sin2(x/2)} is true. Since from (1) above we know that => Cos(x) = cos2(x/2) - sin2(x/2).....(1) And from trig identities sin2(x/2) = 1 - cos2(x/2)....(2) In this case we have to make cos2(x/2) the subject of the formula Thus => cos2(x/2) = 1 - sin2(x/2)....(3) which when you substitute (3) into (1) will yield=> cos(x) = 1 - sin2(x/2) - sin2(x/2) cos(x) = 1 - 2sin2(x/2) Therefore since the denominator of statement 3 equals cos(x), it means... 1, 2 and 3 are all true, hence the solution. C is the correct Answer! Note, this is not supposed to be this long but I had to explain for the benefit of other viewers! |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Richiez(m): 1:03pm On Nov 14, 2013 |
SCORE CARD FOR ROUND 3 1st Question 1. :::JARYEH::: 10pts 2. :::DENNIECE1::: 10pts 3. :::IDENYIJOSHUA::: 8pts 4. :::PAPINDINHO::: 2pts 5. :::DR.GBOY::: 8pts 6. :::FACTORIAL1::: 8pts 7. :::AYSUCCESS99::: 10pts 8. :::MIRACY::: 2pts 9. :::KENDZYMA::: 10pts 10. :::LOGODWHIZ::: 8pts 11. [url=https://www.nairaland.com/amazing%20angel]:::AMAZING ANGEL:::[/url] 10pts 12. :::SMURFY::: 8pts 13. :::MOZARINIA::: 2pts 14. :::TOIDEVE::: 4pts 15. :::CASHIO::: 2pts 16. :::DYSHOW::: 4pts |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Richiez(m): 1:04pm On Nov 14, 2013 |
participants should note that they are not allowed to post an answer twice....henceforth, double post will attract minus 1 mark |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Nobody: 1:04pm On Nov 14, 2013 |
Alpha Maximus: Please post your answers to both Doubledx and me. And no double-answering please; cross-check before sending. Yeah. No double answers, but remember option c was initially wrong. |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Richiez(m): 1:05pm On Nov 14, 2013 |
get ready for Question 4 chosen by Busuyem |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Richiez(m): 1:07pm On Nov 14, 2013 |
Question 4 ...still by Quiz master Doubledx If the roots of the quadratic expression x^2 + Qx + 24 = 0 are α and ß respectively and the sum of their squares is 73, which of the following MUST be true about the values of x? 1. (x^2 + 3) > 10 2. (2x - 3) < 0 3. x^2 > 120 (remember, more than one option may be the correct answer) just 10 mins!!! time is ticking |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Nobody: 1:08pm On Nov 14, 2013 |
Richiez: participants should note that they are not allowed to post an answer twice....henceforth, double post will attract minus 1 mark What!!!! I got the question! All the options are correct. The initial question I opened on my phone had error for option c |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by AlphaMaximus(m): 1:15pm On Nov 14, 2013 |
smurfy:option I only,option I and II only and option I, II and III are three entirely different choices. When either of the first two options are chosen by a participant, the consequence is that he/she is implying that that option II or III is wrong and the chosen are the only correct options , whichever the case may be |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by denniece1(m): 1:18pm On Nov 14, 2013 |
Sent!....choi |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Richiez(m): 1:19pm On Nov 14, 2013 |
Time is Up!!! Quiz master Doubledx will now post the correct solution Quiz masters Alphamaximus and Doubledx will send me the names and I will post the new score card |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by denniece1(m): 1:21pm On Nov 14, 2013 |
Doubledx na wa 4 ur question o |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by DrGboy(m): 1:22pm On Nov 14, 2013 |
hope u've received it? |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by busuyem: 1:23pm On Nov 14, 2013 |
throw question 10 to the floor |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by AmazingAngel(f): 1:23pm On Nov 14, 2013 |
Hope it doesn't matter if I send the same answer 2tyms,my mail is doing sumhow 1 Like |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Nobody: 1:23pm On Nov 14, 2013 |
sent! @doubledx, hope u saw my mail...dis question is dem hard...chai...i fear 4 here o... |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Nobody: 1:24pm On Nov 14, 2013 |
Alpha Maximus: option I only,option I and II only and option I, II and III are three entirely different choices. When either of the first two options are chosen by a participant, the consequence is that he/she is implying that that option II or III is wrong and the chosen are the only correct options , whichever the case may be No Maximus. You don't understand. When Richiez first posted the question, the multiple choice I only, II and III only etc. wasn't included. Ask Richiez. Only the answers I, II and III were there. Then option III had a typo. That's why I didn't pick it. I submitted my answer, refreshed the page only to see A, B, C, etc. and correction to option III |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Idenyijoshua(m): 1:24pm On Nov 14, 2013 |
denniece1: Doubledx na wa 4 ur question od question na war and with limited time |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Nobody: 1:25pm On Nov 14, 2013 |
busuyem: throw question 10 to the floormy chairman, i beg easy o, ur choice of qstns are damn hard,#biko,ogini,please,ejo#....am begging o...easy does things. |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Richiez(m): 1:26pm On Nov 14, 2013 |
Amazing Angel: Hope it doesn't matter if I send the same answer 2tyms,my mail is doing sumhowif it's same answer, you won't be penalized |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by AmazingAngel(f): 1:26pm On Nov 14, 2013 |
D question was not hard,it depend on ♓☺Ϟ•̸ fast Ʊя̲̅ mind thinks |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by busuyem: 1:27pm On Nov 14, 2013 |
aysuccess99: Lolz. U dey fear? |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by AmazingAngel(f): 1:28pm On Nov 14, 2013 |
Richiez:tank God |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Richiez(m): 1:29pm On Nov 14, 2013 |
smurfy: when a quiz master posts the solution, it will come with the full question in objectives. but for this round I will personally remove all objective answers and allow the participants derive the correct answers themselves |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by factorial1(m): 1:29pm On Nov 14, 2013 |
mi o she mo, *running out* limited time...busy tinx, O boi, na guessing sure pass. Hope to see some questions that does'nt require more calculation. #Shalom |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Nobody: 1:29pm On Nov 14, 2013 |
@Richiez Please read my comment above and affirm that option c initially had a typo. There was something like and all over the place for option c before the correction. I sent the corrected solution in time. Please adjust the scoreboard for me accordingly. Thanks. |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Idenyijoshua(m): 1:32pm On Nov 14, 2013 |
Jst got a better understanding of d question now. ;( |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Nobody: 1:32pm On Nov 14, 2013 |
Richiez: No problem. Please give me my mark. It's such a cheap half-angle formula question. |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by jaryeh(m): 1:32pm On Nov 14, 2013 |
How many questions are we gonna answer today |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Richiez(m): 1:33pm On Nov 14, 2013 |
@smurfy, I will do so if the quiz masters confirms your statement...hold on |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Nobody: 1:33pm On Nov 14, 2013 |
smurfy: @Richiez The typo was sin^(x/2) instead of sin^2(x/2), it was something that was easy to understand... Well, @ richiez I think you should give him the mark! |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Richiez(m): 1:34pm On Nov 14, 2013 |
jaryeh:it depends on time....quiz stops by 3:30pm |
Re: Nairaland Math Quiz Winner l::::::JARYEH::::::l by Nobody: 1:34pm On Nov 14, 2013 |
Option III had the letter b inside square brackets in two places |
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