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Nairaland Mathematics Clinic - Education (209) - Nairaland

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Re: Nairaland Mathematics Clinic by Nobody: 10:13pm On Nov 16, 2015
jackpot:
how do we get the closed form solution? mind showing elaborate steps?
You can also solve it using another identity.
Writing both cos(x) and sin(x) in terms of tan(x).
This is the identity for sin(x) in terms of tan(x)

And that of cos(x) is

Re: Nairaland Mathematics Clinic by agentofchange1(m): 10:44pm On Nov 16, 2015
1
ladokuntlad:

Sowie i need to b precise before solving
1 or 2?
Re: Nairaland Mathematics Clinic by agentofchange1(m): 10:48pm On Nov 16, 2015
1)
find the Fourier transform of sin(nx)cos(nx)
2)
find the domain of convergence of sigma of (-1)n zn /2n for 0,1,2. . . to infinity

asap
Re: Nairaland Mathematics Clinic by Mathemagician1(m): 6:45am On Nov 17, 2015
all4naija:
Find the volume of a cylinder with a diameter of 4xsq - 6x + 2 and a height of 2x + 7.

Here you go

1 Like

Re: Nairaland Mathematics Clinic by Blackeard(m): 7:54am On Nov 17, 2015
Yea.
Madmathecian:



Hmm, are those Olympiad questions really for secondary school pupils? And the exam is four hours no calculator.
Re: Nairaland Mathematics Clinic by michoa(m): 2:04pm On Nov 17, 2015
Hello! good job. Please I'm having problem on how to get all the subset of {a,b,c,d,e}. Kindly help me out pls.
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 4:35pm On Nov 17, 2015
michoa:
Hello! good job. Please I'm having problem on how to get all the subset of {a,b,c,d,e}. Kindly help me out pls.
Dia are 2n subset in any given sets
Where n is the number of elements
Thus urs is 25=32 subsets

{},{a},{b},{c},{d},{e}
{a,b},{a,c},{a,d},{a,e},{b,c},{b,d},{b,e},{c,d},{c,e},{d,e}
{a,b,c},{a,b,d},{a,b,e},{a,c,d},{a,c,e},{a,d,e},{b,c,d},{b,c,e},{b,d,e},{c,d,e}
{a,b,c,d},{a,b,c,e},{a,b,d,e},{a,c,d,e},{b,c,d,e},{a,b,c,d,e}
Makes total of 32

1 Like

Re: Nairaland Mathematics Clinic by GeniusDavid(m): 6:31pm On Nov 17, 2015
Guys please help me solve this.
2 raise to power x = 8x

find x.
(Question is legit, got asked in school today)
Karmanaut, MathsChic and the gangs, your help is needed.
Re: Nairaland Mathematics Clinic by Nobody: 6:56pm On Nov 17, 2015
GeniusDavid:
Guys please help me solve this.
2 raise to power x = 8x

find x.
(Question is legit, got asked in school today)
your help is needed.
The question cannot be solved analytically as there is no closed form.
You can use Numerical methods.
Since the question is in exponential form you can use the Lambert W function
Or you can use any other numerical method.
The graph shows there are two roots: one near 0, and the other near 5.
So if you take your initial root as 0, or 5 you'll converge to the answer.
Using the Newton method, I got x=0.13749962877970117511or x=5.4449075546102070517

Re: Nairaland Mathematics Clinic by ladokuntlad(m): 7:31pm On Nov 17, 2015
GeniusDavid:
Guys please help me solve this.
2 raise to power x = 8x

find x.
(Question is legit, got asked in school today)
Karmanaut, MathsChic and the gangs, your help is needed.
APART FROM GRAPHICAL METHOD
We can also use NEWTON-RAPHSON method i.e
[img]http://web.mit.edu/10.001/Web/Course_Notes/NLAE/equation7.gif[/img]
where Xi denotes first guess or initial number
F(Xi) denotes d solution at Xi
and F'(Xi) denote solution of the derivative at Xi
from either methods, we get
x=0.1375
and
x= 5.4449
Re: Nairaland Mathematics Clinic by Madmathecian(m): 7:36pm On Nov 17, 2015
GeniusDavid:
Guys please help me solve this.
2 raise to power x = 8x

find x.
(Question is legit, got asked in school today)
Karmanaut, MathsChic and the gangs, your help is needed.


Is 8 raised to the power of x also? If yes then raise two to the power of 3 then equate powers.
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 7:37pm On Nov 17, 2015
Madmathecian:



Is 8 raised to the power of x also? If yes then raise two to the power of 3 then equate powers.
no 8 is not raised
2x=8x
Re: Nairaland Mathematics Clinic by petengine(m): 8:21pm On Nov 17, 2015
Pls solve this problems. thanks

Re: Nairaland Mathematics Clinic by Nobody: 8:53pm On Nov 17, 2015
petengine:
Pls solve this problems. thanks
Cc Agentofchange1
Statistics is your bailiwick. cheesy
Re: Nairaland Mathematics Clinic by Nobody: 9:23pm On Nov 17, 2015
Solving the question using the Lambert W function.
Y = Xex = X = W(Y)
2x=8x
Dividing both sides by 2x
1 = 8x/(2xx[/sup])
1 = 8x*e-x ln(2)
1/8 = x*e-x ln (2)
-ln(2)/8 = (-x ln(2))*e(-x ln(2))
I
"Taking W of both sides"
W(-ln(2)/cool = -x ln(2)
x = -W(-ln(2)/cool / ln(2) and x= -W-1 (-ln(2)/cool / ln(2)
Numerically, you have x1 = 0.13749962877970117511and
x2 = 5.4449075546102070517
Which correspond to the answers we got using the Newton-Raphson method.

Drawing separate graphs, you'll see they intersect at the roots of the equation.
The blue line is that of 8x, while the black curve is for 2[sup]x

Re: Nairaland Mathematics Clinic by petengine(m): 9:46pm On Nov 17, 2015
Karmanaut:
Solving the question using the Lambert W function.
Y = Xex = X = W(Y)
2x=8x
Dividing both sides by 2x
1 = 8x/(2xx[/sup])
1 = 8x*e-x ln(2)
1/8 = x*e-x ln (2)
-ln(2)/8 = (-x ln(2))*e(-x ln(2))
I
"Taking W of both sides"
W(-ln(2)/cool = -x ln(2)
x = -W(-ln(2)/cool / ln(2) and x= -W-1 (-ln(2)/cool / ln(2)
Numerically, you have x1 = 0.13749962877970117511and
x2 = 5.4449075546102070517
Which correspond to the answers we got using the Newton-Raphson method.

Drawing separate graphs, you'll see they intersect at the roots of the equation.
The blue line is that of 8x, while the black curve is for 2[sup]x
sorry is this the solution to the problem I posted in to find E given t and N?
Re: Nairaland Mathematics Clinic by Nobody: 9:59pm On Nov 17, 2015
petengine:

sorry is this the solution to the problem I posted in to find E given t and N?
No sir, this is the solution to the 2x = 8x problem given by GeniusDavid.
Your question is under Statistics
, which isn't my forte.
Re: Nairaland Mathematics Clinic by whitecloth: 11:14pm On Nov 17, 2015
This is my first time noticing something like this on NL, you guys are awesome.
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 11:45pm On Nov 17, 2015
whitecloth:
This is my first time noticing something like this on NL, you guys are awesome.
you welcome on-board
Re: Nairaland Mathematics Clinic by Madmathecian(m): 11:38am On Nov 18, 2015
There are n sweets in a bag. Six of the sweets are orange. The rest of the sweets are yellow.
Hannah takes a sweet from the bag. She eats the sweet. Hannah then takes at random another sweet from the bag. She eats the sweet. The probability that Hannah eats two orange sweets is 1/3. Show that n²-n-90=0
Re: Nairaland Mathematics Clinic by Mathemagician1(m): 12:09pm On Nov 18, 2015
Madmathecian:
There are n sweets in a bag. Six of the sweets are orange. The rest of
the sweets are yellow.

Hannah takes a sweet from the bag. She eats the sweet.
Hannah
then takes at random another sweet from the bag. She eats the
sweet.
The probability that Hannah eats two orange sweets is 1/3.
Show
that n²-n-90=0

Re: Nairaland Mathematics Clinic by ladokuntlad(m): 12:11pm On Nov 18, 2015
Madmathecian:
There are n sweets in a bag. Six of the sweets are orange. The rest of
the sweets are yellow.

Hannah takes a sweet from the bag. She eats the sweet.
Hannah
then takes at random another sweet from the bag. She eats the
sweet.
The probability that Hannah eats two orange sweets is 1/3.
Show
that n²-n-90=0

Re: Nairaland Mathematics Clinic by Madmathecian(m): 9:17pm On Nov 18, 2015
Good work my bosses, ladokuntlad and Mathemagician1
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 9:27pm On Nov 18, 2015
Madmathecian:
Good work my bosses, ladokuntlad and Mathemagician1
anytime u need our services boss
Re: Nairaland Mathematics Clinic by Madmathecian(m): 11:40pm On Nov 18, 2015
Let the real numbers a,b,c,d satisfy the relations a+ b+c+ d= 6 and a2 + b2  + c2  + d2 = 12.

Prove that


36 =< 4( a3 +  b3 + c3  + d3 ) - ( a4 +  b4 +  c4 + d4 ) =< 48
Re: Nairaland Mathematics Clinic by petengine(m): 11:58pm On Nov 18, 2015
If X^3 + 3aX^2 + bx + c is a perfect square, show dat b^3=27c^2

Re: Nairaland Mathematics Clinic by jackpot(f): 2:10am On Nov 19, 2015
petengine:
If X^3 + 3aX^2 + bx + c is a perfect square, show dat b^3=27c^2
Sir, perfect square or cube?
Re: Nairaland Mathematics Clinic by petengine(m): 6:45am On Nov 19, 2015
jackpot:
Sir, perfect square or cube?
cube
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 10:32am On Nov 19, 2015
petengine:
If X^3 + 3aX^2 + bx + c is a perfect square, show dat b^3=27c^2
Here u go

Re: Nairaland Mathematics Clinic by petengine(m): 2:16pm On Nov 19, 2015
Thanks.
Re: Nairaland Mathematics Clinic by jackpot(f): 7:47pm On Nov 19, 2015
smiley
Re: Nairaland Mathematics Clinic by ladokuntlad(m): 9:15pm On Nov 19, 2015
ennie123 i site u

welcome on-board

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