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Re: Nairaland Mathematics Clinic by Richiez(m): 7:36am On Apr 20, 2013
2nioshine: Really impresed wsh i could remain always on d tread lyk wen it was newly opend............bt sku strez keeps........@Ric,echibuzor,biola,gh.guru and all who az contributd 'RESPECT'....Where iz my man Double dx @?
respect too man! hmmm double dx hasn't been on for a while now, i don't know the reason sha
Re: Nairaland Mathematics Clinic by Nobody: 10:38am On Apr 21, 2013
2nioshine: Really impresed wsh i could remain always on d tread lyk wen it was newly opend............bt sku strez keeps........@Ric,echibuzor,biola,gh.guru and all who az contributd 'RESPECT'....Where iz my man Double dx @?

I'm here Chief 2nioshine, how have you been bruv? it's been a while.... respek mi bredda!

Richiez: respect too man! hmmm double dx hasn't been on for a while now, i don't know the reason sha

General Richiez, salutations sire! I have been a little busy lately....will be contributing from time to time. Trust you are doing good. Keep up the good work bruv!
Re: Nairaland Mathematics Clinic by biolabee(m): 12:13pm On Apr 21, 2013
2nioshine: Really impresed wsh i could remain always on d tread lyk wen it was newly opend............bt sku strez keeps........@Ric,echibuzor,biola,gh.guru and all who az contributd 'RESPECT'....Where iz my man Double dx @?

kudos and nutin do u, a good idea is good because when others rest, others help to keep it up
Re: Nairaland Mathematics Clinic by johnpaul1101(m): 2:14pm On Apr 22, 2013
Please someone should help me out with this: solve cos345 without the use of calculator or table
Re: Nairaland Mathematics Clinic by echibuzor: 3:39pm On Apr 22, 2013
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Re: Nairaland Mathematics Clinic by echibuzor: 3:40pm On Apr 22, 2013
johnpaul1101: Please someone should help me out with this: solve cos345 without the use of calculator or table

That's Cos 15 in the fourth quadrant.... Solution Loading


cos 2x = 2cos^2 15 - 1
2cos^2x = cos2x + 1 ... x = 15

2cos^2 (15) = cos 30 + 1 .... Cos 30 = (√3)/2

2cos^2 (15) = [(√3)/2] + 1

cos^2 (15) = ([(√3)/2] + 1) /2

2cos^2 15 = [(√3) + 2] /2

cos^2 15 = [(√3) + 2] /4

Square root both sides...
cos15 = ±√([(√3) + 2] /4)

cos15 = (√[(√3) + 2])/2

and that, my friend, is cos 345 = cos 15 = (√[(√3) + 2])/2...

Did u notice that i removed the ± in the final answer? That's because Cos is always positive in the fourth quadrant....

At first I was solving for sin15 before i looked at the question again... But, Hey, U might need it too someday right?

So, Here goes, Its quite lengthy and questions about further explanations are welcomed... Lets go there....
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Sin (2y) = 2sinycosy ------ (by putting y=15)
Sin30 = 2sin15cos15 ------(ii) (cos^2 (y) = 1 – sin^2 (y))
Hence, cosy = √(1 – sin^ (y))
By putting this into eq (ii) we have;
Sin30 =2sin15 * √1-sin^2 (15)
Square both sides…
Sin^2 (30) = 4sin^2 (15) (1 – Sin^2 (15))
Open Bracket to give…
Sin^2 (30) = 4sin^2 (15) – 4sin^4 (15)
Remember that Sin ^2 (30) = Sin30 * Sin30 and Sin 30 = ½ (abi?)
So: ½ * ½ = 4Sin^2 (15) - 4Sin^4 (15)
¼ = 4Sin^2 (15) - 4Sin^4 (15)
Cross Multiply…..
1 = 16Sin^2 (15) – 16Sin^4 (15) =>>> 16Sin^4 (15) -16Sin^2 (15) +1 = 0
What we have here is a quadratic equation of the Sin^2 form
Let Sin^2 (15) = x
Our new equation becomes…..
16x2 – 16x + 1 = 0
Using Quadratic Formulae (Popularly known as Almighty Fomular)
x = [-(-16) ± √162 - 64 ] /32
==>> [16±√256 – 64] /32
==>> [16 ± √192] /32 ==>> [16 ± √64 * √3] / 32
==>> [16 ± 8√3] /32 …… By Simplifying with a common factor (cool
==>> [2 ± √3] /4 ]
Sin^2 (15) = [2 ± √3] /4]
Sqrt both sides….
Sin15 = ± (√[2± √3] /4 )
This is where the logic comes in… Remember that I said Sin345 is Sin 15 in the fourth Quadrant (Fourth Quadrant is angles between 2710 and 3600) and any Sine in the Fourth Quadrant gives a negative answer… This point eliminates + √[2± √3] /4 from being a valid answer, which gives us with -√[2± √3] /4… Also (√2+√3) / 4 gives a value too extreme to be relevant… Hence, we are left with
-√[2 - √3] /4 as our answer for sin15
To have a more simplified answer… -√[2 - √3] /4 is also the same as [√(2 - √3)] / √4 which gives -[√(2 - √3)] /2 …….. That is your answer… Confirm with a calculator… Questionand request on further explanations are welcome…

Chibuzor..

1 Like

Re: Nairaland Mathematics Clinic by Nobody: 4:35pm On Apr 22, 2013
hi pls can some teach me how to find domain and range of a function?..pls i nid to knw dis
Re: Nairaland Mathematics Clinic by oluebubesyd(m): 7:08am On Apr 23, 2013
required to prove:
(cosec A)^2- cosecA= [cotA]^2/(1 + sinA)
Re: Nairaland Mathematics Clinic by MEILYN(m): 12:04pm On Apr 23, 2013
@ Richiez can we meet pls?
Re: Nairaland Mathematics Clinic by Richiez(m): 4:25pm On Apr 23, 2013
MEILYN: @ Richiez can we meet pls?
sure! anytime u'r ready

1 Like

Re: Nairaland Mathematics Clinic by Richiez(m): 11:40am On Apr 25, 2013
Jasboi: hi pls can some teach me how to find domain and range of a function?..pls i nid to knw dis
post a question on dis topic (mapping), the solution wud help u understand better
Re: Nairaland Mathematics Clinic by Richiez(m): 11:44am On Apr 25, 2013
oluebubesyd: required to prove: (cosec A)^2- cosecA= [cotA]^2/(1 + sinA)
solution loading...
Re: Nairaland Mathematics Clinic by spircy: 1:25pm On Apr 25, 2013
pls,i need questions and solution on stability(3 by 3 of linearsystem and non linear system)hear from any one soon.thanks
Re: Nairaland Mathematics Clinic by solgee(m): 1:31pm On Apr 25, 2013
Expand (4X+5)^8
Thank You
Re: Nairaland Mathematics Clinic by Itulah(m): 7:40pm On Apr 25, 2013
All the gurus in the house, abeg help me with this?

1)The equation of the motion of a body performing damped forced vibration is
d2x/dt2+5dx/dt+6x=cost,
solve this equation given that x=0.1 and dx/dt=0, when t=0.
Write the steady state solution in the form ksin(t+a)

2) Use Laplace transform to solve the following equation:
a)3f`(t)+2f(t)=t where f(0)=-2
b) f``(t)-4f(t)=sin2t where f(0)=1 and f`(0)=-2

Please help....
Re: Nairaland Mathematics Clinic by Nobody: 10:58am On Apr 27, 2013
Richiez: sure! anytime u'r ready

gringringrin
Re: Nairaland Mathematics Clinic by fazbuk(m): 10:35pm On Apr 28, 2013
Pls solve: Solve d 2nd oda differential equation (d^u/dt^2 - 4u=24sin2t; given dat @ t =0,u =3 and du/dt =4
Re: Nairaland Mathematics Clinic by Nobody: 3:05pm On May 02, 2013
oluebubesyd: required to prove:
(cosec A)2- cosecA= [cotA]2/(1 + sinA)

Solution

(Cosec A)2 - Cosec A= [CotA]2/(1 + SinA)

From the RHS

We know that CotA = CosA/SinA and Cos2A + Sin2A = 1

:. Cos2A/Sin2A(1 + sinA)=>>>

= Cos2A/(Sin2A)(1 + SinA)
Since we are proving towards CosecA which is an inverse of SinA, let's replace Cos2A with "1 - Sin2A" ===>>>

= (1 - Sin2A)/[Sin2A(1 + Sin A)]
Since =>> A2 - B2 = (A - B)(A + B):.12 - Sin2A = (1 - Sin A)(1 + Sin A), substituting yields=>>
= (1 - Sin A)(1 + Sin A)/[Sin2A (1 + Sin A)]
= (1 - Sin A)(1 + Sin A)/[Sin2A (1 + Sin A)]
= (1 - Sin A)/Sin2A
= 1/Sin2A - Sin A/Sin2A
= Cosec2A - 1/SinA
= Cosec2A - CosecA

Hence RHS = LHS, proved.

5 Likes

Re: Nairaland Mathematics Clinic by Nobody: 8:32pm On May 03, 2013
Big baws for the great mathematicians over here......pls, am an undergraduate, i want u guys to recommend texbook(s) on real analysis, mathematical method,ODEs,PDEs, complex analysis,abstract algebra,mathematical modelling ASAP aside from both ordinary engineering mathematics and advanced enginnering mathematics by KA stroud and Dexter J. Booth....i would prefer one that comprises of most them
Re: Nairaland Mathematics Clinic by Nobody: 10:37pm On May 03, 2013
Youngsage:
x + y =5 -------- eqn i.
x^x + y^y=31 ----- eqn ii.
From equatns i & ii, take the log of both sides
(xlog^x + ylog^y) = log 31------ eqn iii.
log(x+y) = log 5 ------------ eqn iv.
xylogxy= log 31 -------- eqn v.
log xy = log 5 --------- eqn vi.
(Using elimination method);
xylog5 = log31
xy = log 31/log 5 =6.2 approx. 6.

Recall, from eqn i, x + y = 5.
So x = 6/y or y = 6/x.
Therefore x=2 when y=3.
ans: x=2, and y=3.
dats so wrong,ow on earth did u arrive @ equ v?...wondering y d 29likes!
Re: Nairaland Mathematics Clinic by Nobody: 10:48pm On May 03, 2013
Richiez:

nice try bro, although you made some some mistakes especially at the point where you took log of both sides. e.g it ought to be log(x+y)= log5 and not logx + logy = log5. but i must admit, you did a very good job.

here's another approach;

x + y = 5.......(1)
x^x + y^y =31.......(2)

from eqn(1), x=5-y, hence we substitute this value for x in eqn(2).
(5-y)^(5-y) + y^y = 31.......(3)
now, we have reduced the problem to what value of y that must be inserted in eqn (3) to obtain 31.

a thorough look at eqns (1) & (2) shows that the values of x & y must be positive integers within the range 0<x<5 and 0<y<5
clearly, y=3
i.e (5-3)^(5-3) + 3^3
2^2 + 27
4+27=31
now that we have established that y=3, we shall substitute the value of y in eqn(1) to get x
recall that x+y=5
therefore; x+3=5 or x=5-3=2
hence, x=2 when y=3
dat range of value,is infinite,mreova no theory justify the required value as an integer,dat a guesswrk would require infinite trial...d only method applicable is numerical method.
Re: Nairaland Mathematics Clinic by Nobody: 11:16pm On May 03, 2013
solomon111: The fifth equation follows the principle/laws of logarithm.
E.g
1)logx +logy =logxy
2)alogx +blogy=ablogxy.
3)logx-logy=logx/logy
law 2 nd 3 aint it...
Re: Nairaland Mathematics Clinic by Nobody: 11:24pm On May 03, 2013
ultranet: pls can u solve dis question: 3^x=9x...(interested in d working)
answer bein 3 cnt b algebraically proven bt numerically!
Re: Nairaland Mathematics Clinic by cnnamoko(m): 3:13am On May 04, 2013
for over 10,000 research papers, term papers, essays visit http://nairaproject.com
Re: Nairaland Mathematics Clinic by personal59: 9:21am On May 04, 2013
Richiez: This thread is the meeting point for nairaland maths gurus...i dare you all to ask me a question in mathematics without me having an answer to them, LETS START
pls help me to solve this ordinary differential equation (2x-4y+5)dy/dx+x-2y+3 equal 0 pls d calculation (steps) is needed for self understanding thanks.
Re: Nairaland Mathematics Clinic by Nobody: 11:43am On May 04, 2013
O'steve:
pls awos help me wit dis question: An interview was conducted among some ICAN staff working in examinations,accounts and administrative departments. The interview reveals dt some staff hv served in more dan one of dese departments, during d period investigated. In d interview,42 said dey hv served in at least 2departs,49 said dey hv served in exams,63 said dey hv served in accnts while 10claimed dey hv served only in admin dept. It was discovered dt 35 hv served in xactly 2depts while 23served in exam dept only and 25 served in accnts dept only. (a)Draw Euler-venn diagram to illustrate d above info. (b) Determine d no of staff who hv served in d depts of : i. Exams and Admin ii.Exams and accnts iii.Accnts and admin iv. Admin v. Exams,accnts and admin. (c) How many staff were involved in the interview? Thank u for ur anticipated co-operation.
...
(A)No tool 2 draw.
B(i)11
(ii)22
(iii)23
(iv)37
(v)7
(c)122
Re: Nairaland Mathematics Clinic by personal59: 11:05pm On May 04, 2013
Pls help m with the ODE is a must assignment pls am begging pls
Re: Nairaland Mathematics Clinic by Richiez(m): 7:34am On May 05, 2013
@doubledx thanks alot for your contribution, you are truly a great man1

1 Like

Re: Nairaland Mathematics Clinic by Richiez(m): 7:40am On May 05, 2013
@echibuzor, ur contributions simply proves that u'r outstanding

1 Like

Re: Nairaland Mathematics Clinic by Richiez(m): 7:46am On May 05, 2013
@hilaomo, hmmm seems we have a new guru in d house. good work bro, but next time u make corrections or criticisms, back them up with detailed solution. welcome bro!
Re: Nairaland Mathematics Clinic by Richiez(m): 9:36am On May 05, 2013
fazbuk: Pls solve: Solve d 2nd oda differential equation
(d^u/dt^2 - 4u=24sin2t; given dat @ t =0,u =3 and du/dt =4
solution loading...
check back by 2pm
Re: Nairaland Mathematics Clinic by Richiez(m): 9:38am On May 05, 2013
solgee: Expand (4X+5)^8
Thank You
solution loading...
check back by 2pm

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