₦airaland Forum

Given x² - y² = 77 and x + y = 11 find x?

A boot that costs x dollars is marked down by 20 percent off its original price on Monday, then an additional 10 percent on Tuesday. What is the price of the jacket, in terms of x?

good ke. all of you guys are just too good. even you sister imani, i'm amazed at your superpower.

I gotta post more problems.

huxley:
What is the product of:

(x-a)(x-b)(x-c)(x-d) . . . . (x-z)

Product of (x-a)(x-b)(x-c)(x-d) . . . . (x-z)
= (x-a)(x-b)(x-c)(x-d) . . . (x-x), (x-z)
= (x-a)(x-b)(x-c)(x-d) . . . .(0), . (x-z)
=0*(x-a)(x-b)(x-c)(x-d) . . . . (x-z)
= 0

I don't understand what you mean by in powers of X up to 3, but

Expansion of (2X+4)⁶ using the binomial theorem is:

Coefficients are : 1 6 15 20 15 6 1

1(2x)⁶4⁰+6(2x)⁵4¹+15(2x)⁴4²+20(2x)³4³+15(2x)²4⁴+6(2x)¹4⁵+1(2x)⁰4⁶

Simplifies to:
64x⁶+768x⁵+3840x⁴+10240x³+15360x²+12288x+4096

integral of xlnx using int by parts = uv-integral (vdu)
u = lnx dv = x
du = 1/xdx
v = integral of dv = x²/2

applying formula.

uv = x²/2lnx
integral vdu = integral (x²/2 * 1/x dx) = x/2

integral xlnx = x²/2lnx - 1/4x² + C

Rasheed can mow his mother's lawn in 6 minutes. His brother Peter can mow it in 9 minutes. How long will it take them to do it together, if each has his own lawnmower.

t(rasheed) = 6 minutes
t(peter) = 9 minutes

Rasheed mows one lawn over 6 minutes
Peter mows one lawn over 9 minutes
Rate of work for Rasheed = L/6
Rate of work for Peter = L/9

Now we want to mow one lawn when both are doing it together.
Time it takes to mow one lawn
amount of work done = rate at which the work is done multiplied by the time they worked.
So we want time.
1L= (L/6 + L/9)t
t = L/(L/6+L/9) = 54/15mins

point (2,2) is sqrt(26) away from the point (3,p). What does p equal?

I was able to balance a weightless beam, ten meters long, on a fulcrum by putting a 6 kg mass on one end, and an unknown mass on the other end. To balance this, I had to place the fulcrum 1.5 meters from the 6kg mass. What is the unknown mass?

Let Fulcrum point be pivot axis.
Basically, for balance we want the moment M about this pivot to be 0.
Moment = M = L*F = lever arm multiplied by the force.
Force is proportional to mass, so we can just neglect the acceleration of gravity in thsi problem.

6kg will create a moment in one direction, where M1 = 6 * 1.5
8kg will create a moment in the other direction where its moment M2 = 8 * L, where L is our unknown.

For balance, M1 = M2, so 9 = 8L, and L = 9m/8

kobe:
A sink can be filled in 3 mins by the cold water faucet and in 5 mins by the hot water faucet. The drain can empty the sink in 6 mins. If the drain is open, how long will it take to fill the sink with both the faucets open?

delta_v (change in volume) = dv = Vf - Vi = Vsink = V
dv1 = dv2 = V = -dv3

Let x = dv1/dt1
let y = dv2/dt2
let z = dv3/dt3 (<0, sink is draining)
dv1 = xdt1, x = v/3
dv2 = ydt2, y = v/5
dv3 = zdt3, z = -v/6

total action:
dV = (x+y-z)dt , dt = V/(x+y-z) = v/11v/30 = 30/11minutes.

My question is based on the highlighted portion of your posts.

So would you still call that being ignorantas deduced from the 1st paragraph of your statement above?

If we're addressing the question of : would you date from a different religion?  I don't think the answer is automatically "no" as some on this thread have assumed it to be.
I think the phrase: "don't knock it until you try it," works well in this scenario.  Obviously cultural practices have a profound effect on relationships, that's why people generally tend to choose partners they can ultimately relate to ethnically, lingually, and culturally.  It makes things easier but it's not undoable if they choose to explore another route.  It could turn out that both partners are actually compatible to the extent where the religion is a non-issue in their r-ship.

But, if we're addressing the question of: would you end a beautiful relationship over religious differences?
It's like saying, "I love my wife but she's igbo" or "I'm a chelsea fan, I love my wife, and I have a beautiful relationship, but she's a manchester united fan."
That said, if said person chooses to end a "beautiful" relationship over religious differences, then the question becomes "why would you end a beautiful relationship?" .  Ultimately, I'd be forced to disagree with his profession of the relationship as "beautiful", because often when you romanticize a relationship as "beautiful", people would automatifally assume things are "cinderella".
In his experience it's no cinderella.  Religion is an issue to him and it's up to him to decide if he can handle the differences between himself and his partner.


If you have someone with an "Ndipe-esque" extremist religious view, he'd automatically look past anyone not from his religious background, namely he'll be ignorant to a certain other group of people.

This is why it's all subjective.  Preference matters. Context matters.

Its simply myopia (short-sightedness) and utter ignorance that makes people think difference in religion cannot lead to beautiful and lasting marital union, if both parties understand that religion is about you having a relationship with your creator.

The problem here is not the religion, but peopleNigerians that have to take things to the extreme

I agree with this part of jjay1's quote.

Very good. that's correct. Go through the others and see if you're able to solve them, good luck!

A plane is spotted by 2 men who are 500 feet apart. As the plane passes over the line joining them, each man takes a sighting of the angle of elevation to the plane. The man on the far right measures an angle to be 45 degrees and the man on the far left measures an angle to be 50 degrees. How high is the plane?

A sink can be filled in 3 mins by the cold water faucet and in 5 mins by the hot water faucet. The drain can empty the sink in 6 mins. If the drain is open, how long will it take to fill the sink with both the faucets open?

The proof is fine, with the exception of the final step.

kobe:
The following is invalid, explain why.

a = x
a+a = a+x
2a = a+x
2a-2x = a+x-2x
2(a-x) = a+x-2x
2(a-x) = a-x
2 = 1

The step 2(a-x) = a-x is where it's prone to go wrong.
Dividing by a-x on both sides means you're dividing by zero. (You can not divide by zero).
a-x = 0, because a = x, therefore x-x =0.

donchichi:
lets assign the value x and x+1 to the length and breadth respectively.

Area, A = x(x+1)

90 = x(x+1) = x² + x

moving 90 to the RHS gives

x² + x - 90 = 0
(x+10)(x-9) = 0
x is either -10 or 9. -10 is impossible because its negative so x is 9cm. which means the other dimension(x+1) is 10cm

the diagonal can be gotten by pythagoras theorem. 10² +9² = diagonal²
diagonal is sqrt of 181 which gives

Yes, Bravo!

Justin's parents pay him $0.50 to do the laundry and $1.25 to mow the lawn. In one month, he does the laundry 6 more times than he mows the lawn. If his parents pay him $12.75 that month, how many times did he mow the lawn?

The length and the width of a rectange are given by consecutive integers. The area of the rectangle is 90 cm squared . Find the length of a diagonal of the rectange.

I see what you're getting at but that's not qutie the problem.
The statement is a valid one.

donchichi:
if we reverse the eqn from the start;

x = a
x+x = x+a
2x = x+a

Now referring to your equation at exactly

2a-2x = a+x-2x

if we substititute the value fro 2x on the RHS, we get

a+x-(x+a) which gives 0

the 2x in the equation is a not a single entity but a sum of two entities

The following is invalid, explain why.

a = x
a+a = a+x
2a = a+x
2a-2x = a+x-2x
2(a-x) = a+x-2x
2(a-x) = a-x
2 = 1

Rasheed can mow his mother's lawn in 6 minutes. His brother Peter can mow it in 9 minutes. How long will it take them to do it together, if each has his own lawnmower.

I was able to balance a weightless beam, ten meters long, on a fulcrum by putting a 6 kg mass on one end, and an unknown mass on the other end. To balance this, I had to place the fulcrum 1.5 meters from the 6kg mass. What is the unknown mass?

I have $11.60, all dimes and quarters, in my pocket. I have 32 more dimes than quarters. How many dimes, and how many quarters, do I have?

For non-Americans, a dime is $0.10 and a quarter is $0.25.

How many liters of a 10% solution of acid should be added to 20 liters of a 60% solution of acid to obtain a 50% solution?

4Him:
i think this is 6 P 2 = 30

should be 15.

woohoo, you guys are getting them all right.

If the positive integer y leaves a remainder of 2 when divided by 8, what will the remainder be when y + 9 is divided by 8?

Let the function f be defined by f(x) = x² - 7x + 10 and f(t + 1) = 0, what is one possible value of t?

Of the 6 courses offered by the music department at her college, Kay must choose exactly 2 of them. How many different combinations of 2 courses are possible for Kay if there are no restrictions on which 2 courses she can choose?

A number P is divisible by 2, 3, and 15. Find a number P, such that P + 30 is also divisible by 2, 3, and 15.
Show your work.

A special lottery is to be held to select the student who will live in the only deluxe room in a dormitory. There are 100 seniors, 150 juniors, and 200 sophomores who applied. Each senior's name is placed in the lottery 3 times; each junior's name, 2 times; and each sophomore's name, 1 time. What is the probability that a senior's name will be chosen?

Wow good job guys. you've certainly more than met expectations, way to go. I'll post more below.

Enjoy

4Him:
I don't think so . . . its all fun. Seriously half of those who insult others on Nairaland can't dare do that in real life.
I for one would like to see troOe stand on her toes and call me a bald head in real life.  

Hmm!  I agree wholeheartedly 4him.  The best remedy for the usual balderdash that occurs online ( as with most everything else in life) is to just "let it go".  It is that simple.  Once you close "X" out this window, it is as if those you were getting worked-up over never actually existed.

almondjoy:
That should teach you never to stay away from Nairaland for more than 12 hours! Who is going to feel you in with the "numerous" historical events that have occurred since last year.  The best you could have done is to sit with those ghosts in the "45,000" online guests while observing the goings-on of the "200" registered members to keep you posted!

On Nairaland. . . .you snooze, you loose!  There are somethings you can never recapture.  You have to see them to believe them!

Imani:
Remember my elips are sealed

stillwater:
You are not the only one. Wish I was here then

I didn't even realize I had been away for that long. Time flies when you're heavily involed in a time-consuming process. Keeping busy keeps me too busy to commit myself to cyber posting.
Imani I thought we were best friends? You can't even re-hash old wounds and let a brutha know what's up?