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kobe (m)
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I see what you're getting at but that's not qutie the problem. The statement is a valid one.
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
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kobe (m)
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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.
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kobe (m)
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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?
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donchichi
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I see what you're getting at but that's not qutie the problem.
The statement is a valid one.
I beg to differ, which means u have to prove to me that it is indeed valid. According to the commutative property of real numbers a + b = b + a if a = x, then x must be equal to a (x = a) and if a+a = x +a, then x + x = a+ x. therefore; as 2a = x+a, then 2x = a+x. Sorry, are u saying my statement is valid or your statement is valid? if its your, just prove it please  |
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donchichi
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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.
lets assign the value x and x+1 to the length and breadth respectively. Area, A = x(x+1) 90 = x(x+1) = x 2 + x moving 90 to the RHS gives x 2 + 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. 10 2 +9 2 = diagonal 2diagonal is sqrt of 181 which gives 13.45cm |
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kobe (m)
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The proof is fine, with the exception of the final step. 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. 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!  |
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kobe (m)
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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?
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kobe (m)
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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?
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donchichi
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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?
Lemme try. Picture this, We draw a triangle with the base line measuring 500ft to represent the distance between the two men and base angles 50 and 45 degrees on the right and left base angles respectively. To measure the height of the plane, we draw a perpendicular divide down to the base line. With that done, we have to triangles. we must imagine that the perpendicular line divides the base line also but not into half, lets say it divides it into x and 500 - x for left and right respectively. we can lable the length of the perpendicular line as y. By rules of trigonometry y/(500-x) = tan 45 (this is for the right triangle which happens to be right angled) y = 500 -x (because tan 45 = 1. we call this equation 1) y/x = tan 50 (this is for the left triangle which also happens to be right angled) y = 1.19x (tan 50 = 1.19. we call this eqn 2) by equating 1 and 2 1.19x = 500 - x x = 228.31 Therefore, y which is 500 - x from eqn 1 gives 271.69ft whachu think? |
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kobe (m)
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Very good. that's correct. Go through the others and see if you're able to solve them, good luck!
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donchichi
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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.
Let the number of dimes be x and quaters be y. Let us also work in cents. Using that; 10x + 25y = 1160 ----------------------- 1 Since there are 32 more dimes than quaters; x = y + 32 --------------------------------- 2 By substituting for x in eqn 1 10(y+32) + 25y = 1160 10y +320 +25y = 1160 35y = 840 y = 24Putting y in eqn 2 gives x = 24 + 32 = 56So there are 56 dimes and 24 quaters. |
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dinozzo
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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?
lets assume the lawn was mowed x times in a month and the laundry y times in a month. the laundry was done 6 more times than the lawn which means y=6x he was paid $12.75 for the month which basically means: for the x times he did the lawn and 6x times he did the laundry he was paid $12.75. in mathematical terms: 0.5(6x) + 1.25x = $12.75, simplifying will give; 4.25x = 12.75; x=3 therefore he mowed the lawn thrice  |
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donchichi
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lets assume the lawn was mowed x times in a month and the laundry y times in a month. the laundry was done 6 more times than the lawn which means y=6x he was paid $12.75 for the month which basically means: for the x times he did the lawn and 6x times he did the laundry he was paid $12.75. in mathematical terms: 0.5(6x) + 1.25x = $12.75, simplifying will give; 4.25x = 12.75; x=3 therefore he mowed the lawn thrice I beg to differ. The questions says he does the laundry 6 more times than he mows the lawn and not he does the laundry 6 times more than he mows the lawn. i think it should be 6 + x. |
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kobe (m)
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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. |
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kobe (m)
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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 |
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kobe (m)
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point (2,2) is sqrt(26) away from the point (3,p). What does p equal?
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bawomolo (m)
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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. x(x+1)=90 x^2+x-90=0 proceeds to cheat using calculator (x+10)(x-9)=0 x=9 or x=-10 length=9 while width=10 tan(theta)=9/10 theta=42 degrees length of diagonal=9/sin(42)= 13.45 |
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bawomolo (m)
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point (2,2) is sqrt(26) away from the point (3,p). What does p equal?
distance = sqrt((2-3)^2+(2-p)^2)
26=(2-3)^2 + (2-p)^2
25=(2-p)^2
(2-p)2-25=0
2-p=5
p=-3 or p=7
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bawomolo (m)
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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? (x+20)*.5= .10x + 20*.6 .5x+10-.10x=12 .4x=2 x=5liters |
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bawomolo (m)
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the area of a trapezoid is less than or equal to 87cm^2.
the base(b1) of the trapezoid is 3cm less than the base(b2) of the trapezoid. the height(h) of the trapezoid is 6cm. what is the maximum value of b1 that can be achieved.
hint- b1 is between 10 and 15
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mama orga (f)
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see talent for nairaland,
na wa oooooooooooooo
make one of una volunteer to be my teacher oooooooooooo
i will be writing series of aptitude tests soon ooo
in my quest for a job
i want to pass them
am serious
someone please help me out
thanks
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mama orga (f)
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see talent for nairaland,
na wa oooooooooooooo
make one of una volunteer to be my teacher oooooooooooo
i will be writing series of aptitude tests soon ooo
in my quest for a job
i want to pass them
am serious
someone please help me out
thanks
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4Him (m)
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I beg to differ. The questions says he does the laundry 6 more times than he mows the lawn and not he does the laundry 6 times more than he mows the lawn. i think it should be 6 + x.
If you use this equation you don't get a round figure. He can't have mowed the lawn 5.6 times. |
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dinozzo
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I beg to differ. The questions says he does the laundry 6 more times than he mows the lawn and not he does the laundry 6 times more than he mows the lawn. i think it should be 6 + x.
ok, if I'm to go with that I'll have 0.5(6+x) + 1.25x = 12.75 1.75x=9.75 x=5.57, I don't know doesn't look like a good answer, maybe the analogy i'm using is all wrong then @kobe whats the answer, I can't think of any other way to solve it  exactly 4Him |
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4Him (m)
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the area of a trapezoid is less than or equal to 87cm^2.
the base(b1) of the trapezoid is 3cm less than the base(b2) of the trapezoid. the height(h) of the trapezoid is 6cm. what is the maximum value of b1 that can be achieved.
hint- b1 is between 10 and 15
Area of trapezoid = h {(b1+b2)/2} Since b1 is 3cm less than b2 - b2 = b1 + 3 Substitute into equation . . . 6{(b1+b1+3)/2} <= 87 6b1 + 9 <= 87 Solving for b1 . . . maximum value = 13 |
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4Him (m)
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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 Since a = x therefore 2(a-x) = 0 a-x = 0 Therefore you can't get 2=1, what you have is 0=0 |
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dinozzo
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Area of trapezoid = h {(b1+b2)/2}
Since b1 is 3cm less than b2 - b2 = b1 + 3
Substitute into equation . . .
6{(b1+b1+3)/2} <= 87
6b1 + 9 <= 87
Solving for b1 . . . maximum value = 13
yeah thats it |
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bawomolo (m)
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correct.
find the magnitude for the zeros of the equation x^2 -10x + 34.
this thread is fun, keep it going
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4Him (m)
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correct.
find the magnitude for the zeros of the equation x^2 -10x + 34.
this thread is fun, keep it going
I'm stuck . . . is the answer x = 5 +/- 3i I'm having to find the square root of a negative number. |
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Bblak (f)
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This is obviously one of the best threads on nairaland  . Hmmmmm, i can see some real brains in here.Keep it up guys.BRB |
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dinozzo
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I'm stuck . . . is the answer x = 5 +/- 3i
I'm having to find the square root of a negative number.
i think thats the answer using the quadratic formula |
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bawomolo (m)
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the zeroes to the equation is 5+/- 3i but u have to find the magnitude of the complex number to get the answer. the magnitude of both zeroes are the same.
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