₦airaland Forum

badmus45:
find dy/dx at point (2,3) on the curve 3x^2+2y^2+xy^2+x-7=0 show full workings

F(x,y)=3x² +2y² +xy²+x-7

y'=dy/dx = -Fx/Fy

F_x=6x +y² +1. ( derivative wrt .x)

F_y=4y+2xy ...(derivative wrt . y)

Now dy/dx = -(6x+y² +1)/(4y+2xy)

thus @ (x,y)=(2,3) (I.e dy/dx |(2,3)

=> -[6(2) +(3)² +1 ] /[4(3) +2(2)(3)

=-(12+9+1)/(12+12) =-22/24 =-11/12

that's it .

naturalwaves:
Well, I got. "-140" as my answer. If that is wrong, then, I must have made a mistake in the calculation. See my solution below,

seems or right ....leme verify something . sha ..




BTW:still expecting my airtime ooo.

naturalwaves:
Infact, over correct dey worry your solution. Thumbs up man. That's the answer. Send a PM to get your gift. Your approach was even totally different from mine but we got the same answer. That's the beauty of mathemtics. See mine below;

hmmm.OK. sir .

naturalwaves:
Hmmm.

Solution

let's pick √(25+10√6)

put √p +√q =√(25+10√6)

taking square of both sides , we have

p+q +2√(pq) =25 +10√6

compare both sides to have

p+q =25 ....... B

& √(pq)=5√6......E

take square again from E

=>pq=150.....N

from N, p=150/q

put in B

=>q² -25q +150=0

solve to obtain q = 10 ,15

=> p =15..(when q=10)
& p=10....(when q=15)

thus , √(25+10√6)= √15+√10

similarly if we pick √(25-10√6 ) we have √15-√10

hence √(25+10√6)+√(25-10√6)=√15+√10+√15-√10=2√15

that's. it man


guess am right

naturalwaves:
Is this a 5*5 matrix and do you want us to find the determinant?

yes. sir

naturalwaves:
Hahaha benbucks, I knowingly didn't mention the maths gurus in the house. The prize is just a recharge card token if it is correct.

OK

its. 2√15



solution loading

for how much ?

I have the solution here .

tohero:
Battle of the Titans!


They made me thought if I ever sat in a mathematics class.

no be small tin oo

Evaluate

|5 1 0 0 0|
|1 4 0 1 2|
|3 2 1 4 0|
|0 1 2 1 0|
|1 2 0 1 2|

hmmm. think am enjoying this. drama. as long it doesn't leads to something else .

hmm ride profs .


na wa ooo. Differential equations sha ..


^^hay guys those are. mathematical models that assume a real life phenomenon , why not use both model to solve a problem let's see what happens .?

just a suggestion sha ..


## just passing by


c.ya lera .


1luv

greetings .....


happy new year

please help out with this. integral of ln(sinx) dx = ?

Laplacian:
It Is a NON-LINEAR, SECOND DEGREE, THIRD ORDER differential equation

PROOF;

given; sin(y'')+y'=0 or

sin(y'') = -y'............(1.)

first we differentiate the above

using function of a function to get;

d[sin(y" )]/dy" x dy"/dt + d(y')/dt=0 where we take t as the independent variable; we obtain

cos(y" ) x y'" + y"=0 or

cos(y" ) = -y"/y'" ..............(2.)

square (1.) and (2.) and add;

sin²(y'' ) + cos²(y'' )= (y')² + (y"/y'" )²=1 or

[1-(y')²] x (y'" )²-(y" )²=0

Q.E.D

if u doubt that the two differential equations are inequivalent, solve the first one (since it is easier) and show that it satisfies the second.

hay man , the prof. himself. .

but seems its of a non-existence /infinite degree since even after every successive derivatives we obtain different D.E ......we employ your approach for P.S ( power series solutions) .

hope you get the gist ..?

you're great man !!

jackpot:
Please, help Me with this


Does the differential equation y"+sin(y')=0 has a degree?

If Yes, what is the degree?

If No, explain why.


tags: benbuks=, agentofchange1, tohero, doubleDx, Laplacian, dejt4u,
tohero, efficiencie, all math generals and
sergeants.

hay. my angel its me ben. I've deactivated the benbuks account ...

its a second order. non-linear D.E .... with degree 1

AlphaMaximus:
I hail you Sir Ben....

yes. boss ....nice job..

how far you na ?

scholag:
my kid sister, a student of SLT came home with these questions that I should solve. I'm not good with Mathematics and I must be a big sister by helping her get the solutions. Hence, I'm pleading to the conscience of great Mathematicians here to please help a sister!!!
I uploaded a picture of the questions oooo! Yeee! Have mercy nlanders plzz

Q8.

///// SOLUTIONS \\\\\\\

solve for x
a) 2^2x+1 - 5(2^x ) +2 =0

let's rewrite the equation as

2(2^x )² -5 (2^x) +2=0

set 2^x = v
we thus have

2v² -5v +2=0

solving the quadratic equation ,

=> v=0.5 or 2

since v=2^x
when v=0.5=2^-1

=>2^x= 2^-1
=>. x=-1

also , for v=2

2^x=2¹

=> x=1

hence x=1. ( true solution for the given equation)

b)using logarithm to solve

5. 4^x+3*8 .2^2x-1 =4
.8^3x

re-writing we have

5.4^x.4³.8 .2^2x . 2^-1=4 .8^3x

taking log of both sides , we have

brb...

waleadex:
Airtime sent....

wow...confirmed.!!

tnx
...sir..

waleadex:
Though you got the answer but I have a different approach to solving the problem. Send your number so I credit your phone ASAP.

OK. boss..


07064396712


thanks ..let's see your approach .

waleadex:
Solve this maths question and win a prize. Inspection method is not allowed, but you must show your work by snapping and uploading the image here.

*******Solution******


taking ratio with 4^x throughout,

we have

(3/4)^x + 1= (5/4)^x

=>(0.75)^x -( 1.25)^x+1

=(1-0.25)^x -(1+0.25)^x +1

Now by. binomials, (1+r)^p=1+pr + 0.5p(p-1)r² +. . .

we thus have

1-0.25x -1-0.25x +1 =0

=> x=1/0.5

hence x=2

guess am right.

@ PatEinstEin ( m ), AlphaMaximus

this's. benbuks. speaking ...

greet thee. men & brethren..

happy solving...

lantessy:
Do you mean integral of In (sinx) dx from 0 to π?

No just the indefinite integral. sir .


good luck ...

jamace:
This was the answer my maths 101 lecturer gave me when I asked same question. But I have not seen where differentiation and integration have been used to solve real life problems. The mathematics I have seen even the engineers using is elementary mathematics like the ones we did in primary and secondary schools. Integration and differentiation ends in the 4 walls of the university. Am I wrong?

hmmm, oh.. my dear brother, maybe you need proper orientation. on mathematic(especially calculus ) , you see ,we live in dynamic cosmos of complexities & uncertainties for which we implore same basic principles of mathematics & thus far the world has drastically revolutionised which of course calculus & other. branch of math played key roles .

Now

calculus is a mathematical study of how entities changes , the rate at which it occurred & the. variable(s) involved for such changes .

when talk of differentiation or integration is not just about say " find dy/dx of. y=2x^2 thus =4x or taking the integral of the differentiated function to obtain back 2x^2 + k ( for any 'k' being an arbitrary scalar ) . it goes beyond that , you need to understand. the interpretation of that " quote anywhere calculus has vast application (real life) in almost all disciplines .

though I get some point you where trying to project you as an engineer may not do integration or differentiation in your office during work , wait a minute , am not sure. if you've ever heard of. Differential equations ( O.d.e,s p.d.e's or S.d.e's ) for your information young man , mathematical model are being developed to solve so many. diseases , population problem or even economic crisis & lots more all with the knowledge of my dear friend "Mr calculus " .

its a pity our Nigerian education system is greatly flawed cause they teach you the 'how' but not the 'why' . so bro . re-arrange your philosophy..


#team.math.


yours BENBUKS.

--shalom--

try this. guys



integral of. ln(sinx) dx .


good luck..

similar ambition ....guys....I intend studying Mathematics. in either. Cambridge, Princeton , or MlT


hmmmm ...so help me. God .

fr3do:
X + X^3/3! + X^5/5! + X^7/7! + ...

Op, what function is this?

the nth term = x^(2n-1) /(2n-1) !

you what function is this ?

1-x-x^2 -x^3 - . . .

phemolisti:
1. Integral of x(tan^2 x - sec^2x)dx with lower and upper limit =pi

2. Sqr rt of x (x^2 +3x-2)^2. note d sqr rt covers only x

3.if usin integration by parts, show that if ln= integral of sin^(-n) xdx, then pi ln=-cosxsin^(n-1)x +(n-1) hence ,evaluate integral of sin^(-s)xdx

Q1.

From Pythagorean identities ,

1 + tan²x = sec²x

=> tan² - sec²x =-1

we thus have

integral (-x)dx = -x²/ 2

now input your limits

from what to pi ?

for Q2 & Q3 .. re-check & write well.

akpos4uall: ^^^
Instead of those plenty plenty wahalai above for problem 3, we can just state that the (r + 1)th term in the expression (1 + x)ⁿ is ⁿC_r * x^r
Where r = 0, 1, 2, ... n
ⁿC_r = n!/(r! * (n - r)!)
:. The (r + 1)th term of x²ⁿ(1 + x^-2)²ⁿ = ²ⁿC_r * x^-2r * x²ⁿ
= ²ⁿC_r * x^{2n - 2r}
From here we can arrive at the right answer as posted earlier.

..

great job master....ur d man...

hmmm.