₦airaland Forum

hmmmm.

see math scholars abeg .

busy solving with passion , greets you all guys



@ jackpot sorry couldn't post solutions, but am glad. guys are already doing so ,

really gat tight schedules with school tinz & other engagements .



Nice solving

#shalom

jackpot:
@Maths generals,

Please help meeeeeee


A combat-ready soldier on a level ground, wants to toss a grenade from a height of 1.8 meters off the ground, to a stationary enemy target, on the edge of a cliff of height 50metres. The horizontal distance of the soldier from the foot of the cliff is 20metres.

(a) If he intends tossing at an angle of 75degrees, what is the least initial velocity of his projection?

(b)If he intends tossing with an initial velocity of 70m/s, what is the least angle of projection if his missile will hit the target at the shortest possible time?

(take g=9.8m/s², ignore spin, drag force, air resistance)



Tags: agentofchange1, doubleDx, Laplacian, AlphaMaximus, STENON, AmazingAngel, Richiez, rhydex247, montty, CalculusFx, thankyouJesus, calculus3e, all maths generals, sergeants

OK , on bed now without writing stuffs , maybe 2maro b4 nw..

benji93:
you tried bro,but maybe you should try it this way
sin(2x) =2sinxcosx
(1/2)sin(2x) =sinxcosx
dy = sinxcosx dx= (1/2)sin(2x) dx
y=(-1/24)cos(2x)

let's differentiate his answer & see if we could get back the integrand

d(-cos^2 x/2) /dx = -(-2) cosxsinx /2 = cosxsinx = sinxcosx..............(as expected)



now let's check yours

dy/dx = -(-2)/24 sin2x = 1/12 sin2x = 2/12 * sinxcosx

=1/6 sinxcosx =/= sinxcosx ??.

so what can you say now ?.

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Congratulations to the new President elect.!!
(General ) Mohammad BUHARI, God give you
grace & strength to do better than the outgoing
President ,
great tributes to my ever humble , diligent &
sagacious president Dr. Good luck Ebele
Jonathan . you really displayed high level of
rationality & integrity , so unfortunate you
couldn't make it , all the same , God knows best
.
A better Nigeria is what we all hope for.
# it .IS.WELL!!!!!

how awkward , our fear of either Gej or Gmb. emerging winner all boils down to a selfish / sentimental base . haba .

seriously , am less concern about who wins or lose , but my ultimate concern is that I sleep/ wake , have the basic stuff of life , stay happy with family & loved ones .
you think Gmb or Gej can give that ,? . what we need to be doing now is not lamenting or being pessimistic , rather to accept the new incumbent in good fate & continue loving one another & pray for peace then do our best to be good patriotic citizens of Nigeria.


God keep us all

one people , one country .


#shalom.

Laplacian:
Find the differential equation corresponding to;
y=Ae^3x+Be^x.............(1)

Solution:
since there are two unknown constants (A & B), we need two differential equations.
y'=3Ae^3x+Be^x..............(2.)

y"=9Ae^3x+Be^x................(3.)

if, from eqn(1), we substitute for Be^x in (2) and (3) we get;
y'=2Ae^3x+y...................(4)

y"=8Ae^3x+y...................(5)

now, y"-4*eqn(4) gives
y"-4y'+3y=0

nice1 .prof.

how about using determinant , ? which is better ?.

miniyi:
Will be expecting.. Thanks

sorry , didn't reply u all dix while .

set x+1=3sinhx. instead

that's it

woow!! I love this ...

just the kind of wife I need

hmm

I know my prayer will be answered soon.

keep it up dearie ,

All.the.best my angel.


#team.maths.

Buhari's Child Zara Is Paying Over £40,000/ #
12millionNaira as School FeesDeveloping Her
Future & Career,Jonathan's Children av been
moved
2 London 4 Studies 2residence whiledeveloping
their career & living In Affluence.....*Atiku
Abubakar's Children Ar Abroad Schooling....*T
inubu's Children Ar Abroad Schooling & Living
inAffluence, dey Ar All Developing & Investing In
their Children2 Continue 2 Rule Us After dey Ar
Gone.... U ar there As AJobless Graduate Wearing
APC &PDP Customized Vest & Polo, Chanting
"Change" HoldingBrooms & Carrying Umbrellas
Chanting "Transformation"Killing urself,
Fermenting
Trouble & Constituting a Nuisance2 d Society
because of Peanuts that can't make ua better
person......Even If u av No Paying Jobs, Why Not
Do
Apprentice Orlearn a Skill that will make u more
Productive 2day in dSociety. Why Not Do
Volunteering Jobs Instead Of LookingFor Big Pay
Jobs!!!!Stop Being A Disgrace 2 ur Discipline, Stop
Wearing APCVest & Carrying PDP Umbrellas
Because That is d Wish ofPoliticians 4 u...Dey
Know
If u av a Good Job, dey Can't Use u As A Thug /
Propaganda agent If Buhari will Not Bring All His
TenChildren 2 d Street 4 Campaign & Jonathan
Will
not Bringhis Children & Blood Brothers 2 d Street
4
Campaign, Then uar a Disgrace 2 ur Family If u
Dnt
Stop Masquerading urselfAs PDP & APC
Agents.Up
Till Now, I av Never Seen Buhari 's Children OnD
Street Wearing APC Vest & Holding Brooms,
Neither
av Iseen Jonathan'sChildren Carrying d PDP
Umbrella Even On Social Media LetAlone In d
Street....A Word Is Enough 4 d Wise..

Buhari's Child Zara Is Paying Over £40,000/ #
12millionNaira as School FeesDeveloping Her
Future & Career,Jonathan's Children av been
moved
2 London 4 Studies 2residence whiledeveloping
their career & living In Affluence.....*Atiku
Abubakar's Children Ar Abroad Schooling....*T
inubu's Children Ar Abroad Schooling & Living
inAffluence, dey Ar All Developing & Investing In
their Children2 Continue 2 Rule Us After dey Ar
Gone.... U ar there As AJobless Graduate Wearing
APC &PDP Customized Vest & Polo, Chanting
"Change" HoldingBrooms & Carrying Umbrellas
Chanting "Transformation"Killing urself,
Fermenting
Trouble & Constituting a Nuisance2 d Society
because of Peanuts that can't make ua better
person......Even If u av No Paying Jobs, Why Not
Do
Apprentice Orlearn a Skill that will make u more
Productive 2day in dSociety. Why Not Do
Volunteering Jobs Instead Of LookingFor Big Pay
Jobs!!!!Stop Being A Disgrace 2 ur Discipline, Stop
Wearing APCVest & Carrying PDP Umbrellas
Because That is d Wish ofPoliticians 4 u...Dey
Know
If u av a Good Job, dey Can't Use u As A Thug /
Propaganda agent If Buhari will Not Bring All His
TenChildren 2 d Street 4 Campaign & Jonathan
Will
not Bringhis Children & Blood Brothers 2 d Street
4
Campaign, Then uar a Disgrace 2 ur Family If u
Dnt
Stop Masquerading urselfAs PDP & APC
Agents.Up
Till Now, I av Never Seen Buhari 's Children OnD
Street Wearing APC Vest & Holding Brooms,
Neither
av Iseen Jonathan'sChildren Carrying d PDP
Umbrella Even On Social Media LetAlone In d
Street....A Word Is Enough 4 d Wise..

miniyi:
thanks

oo my bad, it just dawn on me , there was a mistake in the substitution

i will post the correction later . chai ..

[quote author=miniyi post=31903394]thanks [/quote


Don't mention

its fun solving but not fun typing ..



its well.

miniyi:
pls I need the solution to an integral..
Integral of (x+3)/((x^2+2x+10)^1/2) thanks

OK

+++++++++++++solution +++++++++++

let's consider content of the denominator

x² +2x +10

complete the square we. get

x² +2x +1-1+10

=(x+1)² +9

we now have

$(x+3)dx /√((x+1)² +3²)

set x+1=3tan¢ .........(*)

dx=3sec² ¢ d¢

thus we have

$ (x+3)/√(9(tan²¢ +1) * 3sec²¢ d¢

simplifies to

$(x+3)sec¢d¢

recall from (*),
x+1=3tan¢ , => x= 3tan¢-1

=> $(3tan¢ +2)sec¢ d¢

=> 3$sin¢ d¢ /cos² ¢ +2$sec¢ d¢

now computing using substitution ,

we get

3sec¢ +2In(sec¢ + tan¢ ) + k


where sec¢ & tan¢ = √((x+1)² +9 )/3

& (x+1)/3. respectively.

deduce & reduce further

that's it man ,


hope u get ?

Emdee590:
Thank you sir

UWC. sir.

here

bolkay47:
exactly sir... That's what I get too

nice.

Emdee590:
So that is the solving and you Have just gotten it as the answer . How do I thank you and the gurus here ? Either way I remain loyal , thank you and may God almighty keep you fit so to continue solving our questions for us . That question above na 200 level question ooo and we for we class nobody fit get that question right ... Once again thank you

its OK bro , to God be glory , we learn daily , put more effort , practice daily with determination , don't always rush to post questions here or give some1 else without you actually trying exhaustively & extensively to obtain valid solution . only after which still didn't get it , then you could seek for help from others
that's how you learn / develop/ improve. your mathematical prowess .

bolkay47:
y=(sinx)^x^3 find dy/dx

here

take natural logarithm of both sides

=> lny=x^3 ln(sinx)

differentiating implicitly we have ,

=> y'/y = 3x^2 ln(sinx) + x^3cosx/sinx

=> y' =dy/dx =y(3x^2ln(sinx) +x^3cotx )

or dy/dx = x^2[ xcotx + 3ln(sinx) ] * (sinx)^(x^3)

that's it man.

Emdee590:
It is +3

OK here

Emdee590:
Let B=[1 3
5 3] i.e a 2*2 matrix , if f(x)=2x^2-4x 3 , what is f(B)?

N/B the options are also in matrix form . Please solve it vividly for me thank you

OK


check the ur f(x) d last part is it +3. or -3 ?

doubleDx:
Yes you're right!

The options are all wrong!

α = 4 and α + 1 = 5

Which makes the equation => x² + 9x + 20

And K = 20

yes boss , thought as much

welcome back prof.

its me benbuks. ur boy.

where hast thou bin sir ?.

Emdee590:
[color=#990000][/color]
The roots of the equation x^2+9x+k=0 are a (i.e alpha ) and a+1(i.e. Alpha + 1); The value of K is : (a) 9 (b) 10 (c) 11 (d) 12



Please gurus help as na ma test be that

OK recheck the question/options.

sure its correct ?

cus. m getting k=20 .

Videx1:
thanks

UWC man.

joywendy:
lol...haba no....i used to follow the thread silently back in the day been long i ve been here.

yea ..miss/Mrs. joy . I know that , just kidding .

thankyouJesus:
yeah, thank you. How come?

1 (first derivative) , 2 ( second derivative) . . . e.t.c up to nth derivative .


try get college maths vol. 2 or engineering math by h.k dass o r surf the net 4 more understanding .

joywendy:
so this thread is still alive?

sure! , u want it dead .?