₦airaland Forum

ladokuntlad:
Sowie i need to b precise before solving
1 or 2?

ladokuntlad:
1st or sedond one?

ladokuntlad:
U mean X^x=10^10[sup]1003[/sup] Or X^x=(10¹⁰)¹⁰⁰³ ??

MathsChic:
Let m = 2015
Let I₁ = sin^m(x)/(sin^m(x)+cos^m(x))

∫sin^m(x)/(sin^m(x)+cos^m(x)) dx, 0<x<2pi

I₁ is a periodic function, and if shifted by pi/2 will give
sin^m(x-pi/2)/(sin^m(x-pi/2)+cos^m(x-pi/2)), and should give the same result when integrated between 0<x<2pi

Let's call it I₂
So, I₂ = cos^m(x)/(cos^m(x)+sin^m(x))

∫I₁, 0<x<2pi =M
∫I₂, 0<x<2pi =M

therefore, 2M = ∫I₁ + ∫I₂
2M = ∫((cos^m(x)+sin^m(x))/(cos^m(x)+sin^m(x)), 0<x<2pi
2M = ∫dx, 0<x<2pi
2M = [x],0,2pi
2M = 2pi

therefore M = pi.

∫I₁ = pi

m can be any value, answer will still be pi.

Soneh:
the bossss!thank you very much

Karmanaut:
Soneh, my boss has solved the rest.
Cheers.

Soneh:
please gurus in the house help me

2.show that if aline L has the equation Ax+By=C, then a line M perpendicular to L has an equation of the form -Bx+Ay=E

Known that a straight line equation has the form

y=mx +c ( m= gradient , c= intercept ) .......(#)

so, lets re-write Ax+By=C as By =-Ax +C

y=-Ax/B +C/B , Comparing with the above ,

thus, m= -A/B ( call it m1)

For two perpendicular lines , m1*m2=-1

it follows that m2 = B/A

we then put this in (#) , we get
y =BX/A + C

Or
-Bx +Ay = AC ( let AC= E , for all E belonging to reals )

hence -BX +Ay =E

the proof. as required


3.IF x²+y²=a², find the value of dy/dx

it can be established that dy/dx = -f_x /f_y

where
f_x = 2x .........( partial derivative wrt. x)
f_y =2y...........( partial derivative wrt y )\

thus, y' = dy/dx = -2x/2y =-x/y


guess that's it man

masperano:
Let me take on this question. I will try to skip the part you do not want to hear: "mathematicians can work anywhere"(even if my trajectory of arguments will spiral through that path).
In our present society mathematics plays an important role in the development of science and technology. This spans over several fields like {medicine, epidemiology, engineering, finance etc}. I usually do not divulge information, but for this question let me make an exception. My second degree was in mathematical modelling in the u.k. Mathematical modelling is the process of capturing real life process into mathematical framework, solving it in the context of using mathematical techniques hence gaining insight to real life process. Let me give you an example for instance if there is an outbreak of a disease, what are the strategies one can implement to try to curb the spread of the disease. should infected people be isolated? the effect of implementing an awareness program? will treatment of the infected people suffice? what is the asymptotic behavior of the disease? . Now these questions can only be answered by knowing the nature of the disease, basic reproduction number(a measure of how the disease spreads) and the asymptotic behavior of the equilibrium states. That's when you hear of the SIR models and so on.

My current work is on Physiology. trying to formulate mathematical model to describe the transport mechanism of the lymphatic vascular system. We hear of elephantiasis(the swelling of the limbs) this as a result of the failure of the lymphatic system. There is no cure for it and one of the problem is that no one adequately understand the transport mechanism. Now this means i have to understand the physiology of the lymphatics to make rational assumptions for my model. So you you see you are covering two sides: i.e. it must make both physiological sense as well mathematical sense.

Also in finance you cannot undermine the power of mathematics. Sorry for the deviation, my aim is for you to see the application of mathematics in your every day life. Having said that, you should know that there is a huge difference between learning mathematics and knowing when to apply them. The problem with our educational sector is that they don't teach us how to think , they just give equations you learn how to solve, or memorize the theorems, go into the exam hall and reproduce it and you get a first class. But when you go to a top tier school in the western world and meet your contemporaries then you realize your weaknesses (don't worry this was exactly what happened to me). My advice to you is for you to keep pushing yourself, and please don't hesitate to learn programs this is very necessary.

Conclusively you can be of immense value to any firm spanning from Finance, medical, Engineering sector. Most firms look for analytical and quantitative minded individuals. I have seen many bright minds in this forum who just need the right guidance. Any one who wants to perhaps go into mathematical biology should contact people like Abba Gumel (i have met him once and he is highly prolific and a named Professor at Arizona state university) or Daniel Okuonghae (got his M.Sc in mathematical modelling from Oxford University presently in Uniben). These are people who will guide you into the trajectory of value in the context of application of mathematics.

Karmanaut:
Turns out it had a series expansion. Maths Chic wrote the answer.
Getting to that, cheers.

Hadampson:
Tanx Karmanaut... D questn z nt complete. Dis is d final questn on dat word problem.. If d time taken for student to walk =35mins... Find d value of v?

Karmanaut:
Yes, boss. There's no series solution.

jackpot:
fine. Hope you're good?

ladokuntlad:
U can assist him naaaa.

Though i av the solutions with me already, jst wanna c if dia ar beta approach

ladokuntlad:
House i av a cowbell question to give

x+y+z=1
x²+y²+z²=35
x³+y³+z³=97

Show workings if x=-1 y=-3 and z=-3

ladokuntlad:
Go meet d Australians dat set d questions. Dey ar secondary school maths oooo

ladokuntlad:
Scroll up maths olympiad questions

ladokuntlad:
Boss u av some of my questions to answer naaa. Oya kindly giv me solutions to it

jackpot:
Hey agentofchange

MathsChic:
See below attachments for the solution. Typically would have loved to type them out here with html, but it'll be cumbersome. Don't know why this site is like that

But a solution can't exist at x=0. I've explained all the details. Please bear with my almost illegible handwriting

Solving normally...
xy'-y-x-1=0
y'-y/x =1+1/x
(x^-1y)'=1/x + 1/x²
(x^-1y) = Inx - 1/x
y=xInx - 1

The power series solution is simply an approximation of the solution curve at x=1, which should give a good solution at that point. Should be desire a solution at any other point, we can do x = x_o. We can't get a solution at x=0 because of the Inx curve. And the first order DE showed it in the coefficients of y' and y, since 1/x is not analytic at x=0.

Karmanaut:
Typo.
It should be 1/1 = 1.