₦airaland Forum

When 'll d final round commence?

Yup!

echibuzor: 2. Volume of cylinder = ^r²h, d/dx (^r²h) = 2^rh
put in the correct measurement into this to get 80^
Multiply the result above with (4.02 - 4.00) => 0.02
Approximate increase = 0.02 * 80^ = 5.02655 cm

echibuzor: The man said non-zero

0 and 0 too

smurfy: The numbers are integers, so only 2 and 2 qualify as answers.

factorial1: oops, could'nt notice that though, guess I've to think of another method to use. thanks brov

Dane17: . u manipulated . I don't get dis part (Therefore, add eqn (ii) and
(iii)...(i.e x + y) together and equate it
with their product(i.e xy), x + y = xy, xy - x
+ xy - x y = xy, which is equal to 2xy - 2x
= xy,). how did u arrive at 2xy-2x=xy. Finally d answer to his question is not just 2 and 2 . they are many values like 3 and 1.5 which gives 4.5 . look at my previous solving carefully and u will understand

factorial1: oops, could'nt notice that though, guess I've to think of another method to use. thanks brov

noticed!

Nice one brah CORRECT...waiting for others qts to be solved. Qt2 and 4 to be precise.

echibuzor: All these questions are from one problem. Linear Approximation.. I ll tackle them later, I am on my way to work..
*****************************************************
1. The Surface Area of the sphere at correct measurement is 4*^r² = 4*3.142*100 = 8800/7 = 1257.14
Surface Area with error input 4*3.142*10.1² = 1281.90
Approximate increase = 1281.90 - 1257.14 = 24.76.
Now, if we are dealing with a complex function. You go by the linear approximation technique, the derivative of the surface area(without error) multiplied by the error in measurement. i.e d/dx (4^r²) = 8^r = 8 * 3.142 * 10 => 251.43 multiplied by (10.1 - 10);
25.143
(2, 3) Apply the second approach and you should get your answers faster...
Its pretty straight-forward though...

oops, could'nt notice that though, guess I've to think of another method to use. thanks brov

echibuzor: **Clears throat**
Your head is there, but ehm... that bolded part should be 2xy-x-y

Brov, u aint told to do try and error, laplacian asked for a proof, and I've done that. #Cheers

Dane17: . x+y=xy ; x=xy-y ; x=y(x-1) ; y=x/x-1 ; therefore if x=2 ; y= 2/1 ; if x=3 ;y=3/2 if x=4 ; y=4/3 and so on.

Alright, will work on that too.... Thanks for the enlightment brov, bravo! Hope this's correct...? @smurfy. [quote author=Calculusf(x)]hmmm ,for numbers greater than 4000(it can be 4,5 or 6 digits)if 4digits,we can see 4 and 5,and for the number to end with even,any of 0,2 or 4 must end the number,also note that the number must not be repeated,then we do it like this,make hole,4 for four digits,5 for five digits etc
4 DIGITS STARTING WITH 5
it can end with 0,2 or 4,then the fourth hole will have 3,it starts with 5,the first hole with have 1,don't forget there are six numbers in all,the last and the first are known therefore it gives 1*4*3*3=36
4 DIGITS STARTING WITH 4
since repeatition is not allowed,then it can end with 0 or 2,then the holes will have 1*4*3*2=24
total=36+24=60
5 DIGITS
it can end with 0,2 or 4.but note that 0 cannot be in the first hole so as not to make the number 4digits again(then only 4 digits can occupy the first hole)...then the holes are 4*4*3*2*3=288...
6 DIGITS
Same as 5 digits...it can end with 0,2 or 4,then 3 can occupy the last hole,and can start with 4 in the first hole coz 0 cannot start the digit...then 4*4*3*2*1*3=288...
TOTAL=288+288+60=636ways[/quote]

*clears throat*
let's go,
firstly, let the two numbers be 'x' and 'y'. From the qt, it can be infered dhat the sum of this non-zero integers is equal to their product: the mathematical representation is x + y = xy.....(i)
Now, from equation (i), make x the subject of the relation/formulae, the result is x = xy - y.....(ii), also, make y the subject of the relation from eqn (i), the result is y = xy - x....(iii). Therefore, add eqn (ii) and (iii)...(i.e x + y) together and equate it with their product(i.e xy), x + y = xy, xy - x + xy - x = xy, which is equal to 2xy - 2x = xy, collecting the like terms, we have 2xy - xy = 2x, xy(2 - 1) = 2x, therefore xy = 2x, divide both side by x, we have xy/x = 2x=x, from there....y = 2. So, subitutute y=2 into any of the above equation. I use eqn (i) which is x + y = xy, x + 2 = 2x, collecting the like terms x - 2x = -2, -x = -2. Note: minus cancelled out, therefor x = 2. With this...I think u are satisfied sir? The two non-zero integers in which their sum is equal to their product is/are ''2'' and ''2''. Thanks

Laplacian: dats d correct answer but i want 2 c ur proof...

Ok, here is the solution

If all six digits are used and the number is to be even, the last(right hand) digits must be either 0, 2 or 4 which gives 3 choices. When this's is done, there are 4 choices for the first digit, 3 for the 2nd, 2 for the third and 1 for the forth digit. So, we av 4 x 3 x 2 x 1 x3 = 62 even numbers using all five digits. Now, if all five digits are used and the number is to be even, the last digit cannot be 1, and either 0, 2 or 4 has already been used: therefore, der are 2 choices for the first, for the 2nd digits der are now 2 choices, 1 for d third n' 1 4 the forth= 2 x 2 x 1 x 1=4. Therefore the total num. of even numbers is 4+ 62= 66. Hope I'm correct sha...? coz the qt is somhw confusing to me seeing 0(zero) der

smurfy: How many even numbers greater than 4000 can be formed using the digits 0, 1, 2, 3, 4, 5? [Note: A digit can be used only once.]

Oh! Sorry 4 dat, that's wat I actually wanted to du now(to ans. ur qt)
Note: I'm nt dah less busy, I'll try to be contributing too...

smurfy: @factorial1

We not only ask questions on this thread. We ATTEMPT to answer posted questions, too.
I'm yet to see you attempt any.

Sometimes, my solution can be completely wrong, but I trust Masters Laplacian, Maximus, Richiez, Jackpot, Ortarico, DoubleDx, Benbuks, etc. to put me through.

I must confess that I've learnt a lot on this thread. I now visit this thread more than I do Yahoo News, Punchng.com, BBC, CNN, etc.

I'd like to see you attempt a question or two soonest.

Lest I forget, thanks for your last set of questions. I'm eagerly following the solution provided by the masters.

The numbers are 2 and 2. [quote author=Laplacian][/quote]

I think u should check dah qt1 and qt2 again bro. qt3 ans.(9%) is correct though. I asked 5 qts bro, what of qt4, u mistakingly omitted it by answering qt5 as qt4. #Cheers.

Ortarico: Hmmmmm. . . . Let's go:

1. Let A = 4r2 be the surface area of the sphere in cm2 . Then dA = 8r. The small dr change in A when the radius changes from 10cm to 10.1cm is then given by small change in A dA (small change in r) dr r=10 = 8 10 0.1 = 8. Thus the increase in the surface area is approximately 8 cm2


2. The volume of the cylinder (in cm2 ) is given by V = r2 h where h is the height and r is the radius (in cm). Thus dV = 2rh. Hence the change in V when the radius changes dr from 4cm to 4.02cm and the height is 10cm is given by change in V dV (change in r) dr r=4 = 2 4 h 0.02 = 2 4 10 0.02 40 = . 25 Thus the volume increases by 40 25 cm3

3. For a sphere, the volume V = (4/3) pi r^3
Take log, log V = 3 log r + log[(4/3) pi]
Differentiate both sides
dV/V = 3 dr/r
If dr/r = 0.03 = 3%, the dV/V is 0.09 or 9%.
You may also find it arithmetically.
Error in V,
eV = abs(V-V0)/V0 = abs( r^3/r0^3 – 1) = abs[(1+- 0.03)^3 -1 ]
Take 1+0.03, then eV = 1.03^3 – 1 = 0.093 = 9.3%
Take 1-0.03, then eV = 1 – 0.97^3 = 0.087 = 8.7%

4. x = tan(y)
y = arctan(x)
dy/dx = 1/(x² + 1)

Same here, been busy too, dat's y I posted it yesterday night.

Ortarico: I've been too busy these days, but I'll see what I can do before then, even if 5 Sir.

.

Play with the questions below:
1. If the radius of a sphere is increased from 10cm to 10.1cm, what is the approximate increase in the surface area?

2. The height of a cylinder is 10cm and its radius is 4cm. Find the approximate increase in volume when the radius increases to 4.02cm

3. An error of 3% is made in measuring the radius of a sphere. Find the percentage error in volume?

4. The side of a square is 5cm. How much will the area of the square increase when the side expands by 0.01cm? And lastly

5. If x=tany; find dy/dx?

It's correct bro

Laplacian: pls recheck ur solution

@bolded sir, eachother is used for two person, while one another is used for more than two person, I think one another suits the statement bro. No one is perfect sir. Take note. #Shalom

Boll2010: I mean I was so surprised! People find it cool to write!

Am-to ask questions
I'm-means you
Been-to a place
Being-how do I explain this(like you),I don't know how to really explain it,
There-refer to a place
Their-refer to people

I'm not being trying to act like a professor,just felt we should help eachother

thanks brov. bravo!

smurfy: @factorial1

Congrats for being able to make it to the grand finale.

Please don't let your phone or any other thing hinder you from participating fully this time.

Again, I say, congrats.

eshe oga mi sir. I'll try my possible best bro. [quote author=Dr.Gboy]Hey bro, don't lose hope yet. I won't be chanced to participate in the finals coz I got some issues to attend to. Richiez said the next eligible contestant will be substituted. You should definitely be the one. Best of luck [/quote]

#yimu.... thanks brov.

aysuccess99: Yes,it's true o...congrats to the great mathematigician who made it to the final..it's great having people like FACTORIAL in the competition. LUCK PLAYED A GOOD PART ON HIM. I'm really happy that he was given the opportunity to compete in the finals(thanks to DR. GBOY---->THE GREAT PHILANTROPIST,SUPER OPERATOR,MATHS GURU)...
BEST OF LUCK TO ALL FINALISTS. I Doff My Cap For U Guys O...U All Did A Great Job...
Factorial1 Congrats To You........IWE FACTORIAL.

*sigh*
.
.
Morning y'all, I congratulates the FINALISTS, though...It was'nt expected of me to miss out the last round of this great competition...buh, der's nothing I could do to ascertain that. I thank God! As per yesterday, I thank you all for ur concern(either +ve or -ve). Though, I tried my possible best to participate fully but all were to no avail. Albeit, I've really learnt alot since the commencement of this quiz so to say, and has indeed gladdens my heart seeing we(Nigerian students) performing utmostly and outstandingly GREAT. I pray God help us in Jesus name(Amen). Kudos y'all. #Cheers.

GOD BLESS NIGERIA.

I omitted nothing der, the qt is correct n' accurate!

Mbahchiboy: BEFORE I START PLZ cross check d ques i think u omitted d value of y

#yimu... finally ba3 low! factorial this way >>^

aysuccess99: u dat u are through wit d qstns...

O boi....c hw guyz dey observe...same here o!

hmm, 1 bar tinx here, keeping mute for a while...

wer's Dr.Gboy n' co..?

Absent!

Richiez: It's the turn of participant no4:::Logodwhiz:::

please choose a number quickly or we'll help you

Choi, I no be lion na, why devour...? nice one!

Fynestboi: Richiez what are we waiting for?



Please let stop the chit chat, and be at alert to devour the questions. Thanks.

hehe.... wen denniece dey der(observing as usual, silent killer, maths himself), u, kendyzma...n' odas'! Novice ni mi

aysuccess99: Oga mi oga mi...me gen2 o...i hail all of u o.....@jaryeh,smurfy,kendzyma,amazing angel,logodwhiz..........@factorial and smurfy, i don dey watch both of u since o...u guys no dey lowkey at all o...u guys don solve maths die....d final is urz my ogas....

@kendyzma, lowkey tinx abi...;? Iyen na make sence boss


Note: 3 questions r all what we'll be question'd on for 2day, to know those who are qualified for the FINAL, won't I run sha...? I no fit face my ogas'....

#Cheers