₦airaland Forum

echibuzor: A population of Ikamudu (yoruba : an insect that smells horribly when you step on it) exhibits logistic growth. If the carrying
capacity is 500 butterflies and r = 0.1 individuals/(individuals x month), what is the
maximum population growth rate for the population? (Hint: maximum population growth
rate occurs when N = K/2).

factorial1: *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 - xy = 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: ...d sum of two non-zero integers is equal to their product...find d numbers....

echibuzor: One-Half is 0.5, Its different from saying One and a Half which is 1.5;

statusnet: One half is clearly 0.5 ,check google

factorial1: 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

Laplacian: observe that;
cosx+1=2cos^2(x/2)
so
(cosx+1)^-1=1/2*sec^2(x/2)

y=(cosx+1)^-2=1/4*sec^4(x/2)

integration by part gives;

y=1/4*[2sec^2(x/2)tan(x/2)-
§2sec^2(x/2)tan^2(x/2)dx]

or
y=1/4*[2sec^2(x/2)tan(x/2)-
§2sec^2(x/2){sec^2(x/2)-1}dx]

or
y=1/4*[2sec^2(x/2)tan(x/2)-
8y+4tan(x/2)]

or by collecting 'y' together,
3y=1/4*[2sec^2(x/2)tan(x/2)+4tan(x/2)]
the required integration is therefore
y=1/12*[2sec^2(x/2)+4]*tan(x/2)
or
y=[6tan(x/2)+2tan^3(x/2)]/12+C

smurfy: One-half means 1.5, not 0.5. Dr Gboy was right. The question is faulty. Most of the participants didn't notice it because we we're all suffering from hot-seat syndrome then.

benbuks: Find the anti-derivative of (cosx +1)^-2

smurfy: The answer is 5627 ~ 5600 bullets.

No. 2

Amazing Angel: Wats d name of d topic to d question alpha maximum posted d other tym abt handshakes?

smurfy: The only way I could solve this is by using numbers.

Here goes...

Let True Radius = 20cm
Let Error Radius = 18cm.
PE = (TR - ER)/TR * 100%
This gives 10% (My P is therefore 10. Now let's find PE for the circumference. Whatever I get is directly compared with the value of P above.)

Now, C = 2 * pi * r
True C = 2 * pi * 20
= 40 * pi cm
Error C = 2 * pi * 18
= 36 * pi cm
PE = (TC - EC)/TC * 100%.
This gives (4pi/40pi) * 100% = 10%.

This shows that if there's a 10% error in the measurement of the radius of a circle, there'll be a 10% corresponding error in the measurement of its circumference. Hence, the correct answer is P%.

The issue is whether this can be solved neatly, algebraically without using this primary school method. That, I'd like to know.

smurfy: If the above is your answer, then it's wrong. The options are

A. (1/2)P%
B. P%
C. (3/2)P%
D. 2P%

Note: Clear working ll be appreciated.

factorial1: explain hw you arrived @that bro...?

smurfy: An error of P% is made in measuring the radius of a circle. Calculate the approximate percentage error in the measurement of the circumference.

Alpha Maximus: .... This is an elimination round where half of you will be evicted at the end of the day! I can't post simple questions. We aim to seperate the masters from the novices(no offence meant to anybody) . Besides the solution was quite easy, I haven't even started setting hard questions. Goodluck

Alpha Maximus: Pls don't give any clues.

busuyem: Sorry, I think ur solution is wrong because u made use of 50 as the universal set when universal set is 2000. 50 is just the number of those that do not partake in the three food (Beans, Rice and Dodo). Check ur workings again.

Richiez: 2Sin²x - 3Sinx + 1 = 0

find x

don't panic time just started counting

remember to send answers to sfadeshola@yahoo.com and richobiagba@gmail.com

akpos4uall: I just modified my previous post. Check it for the correction.

6 ate Dodo and Rice

22 took Beans only

3 ate Beans,Rice and Dodo

5 ate beans and Rice,

Mbahchiboy: PLZ I'M I TOO LATE TO B A PARTAKER?

Mbahchiboy: plz u guys should help solve dis using "d citizen" approach.i tried doing it but i dont know my mistake.
(1)if 4^x=8x find x.
(2) find x if (4/x)^x=2x