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it would take 3 hours assuming that they painted at the same paces. This is because the three women can paint three fences per 3 hours so divide that by 3 and you get 1 fence per 3 hours. It may seem confusing i am not excellent at explanations. Here is another. The women together can paint one fence per hour, this means each woman can paint 1/3 of a fence each hour, which means a woman would need 3 hours to paint it. That explanation was better. Hope this helps.

-G

Thanks Alan! Now, I get this mumbo-jumbo!.

Note that the prime factorisation of 10^10 is 2^10*5^10

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 lcm(8*512, 10^10) = 40 000 000 000

 lcm(512, 10^10) = 10 000 000 000

I think 8m is meant to be interpreted as 8*m, not 8000+m.

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LCM[8,512, 10^10] =1,330,000,000,000 according to mighty Wolfram/Alpha!. Where does 4 fit in???

"If m is a 3-digit positive integer such that , then what is the value of m?"

512

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What's there to answer ???.................

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1/4(a + 10) =2a -4         multiply both sides by 4 to clear the fraction on the left

a + 10  = 8a - 16          subtract a from both sides and add 16 to both sides

26 = 7a      divide both sides by 7

26 / 7   =   a

The PRIME factors of 2004=2^2 x 3 x 167=4+3+167=174

The product of positive integers x, y and z equals 2004. What is the minimum possible value of the sum x+y+z?

The  divisors of 2004 are  1 | 2 | 3 | 4 | 6 | 12 | 167 | 334 | 501 | 668 | 1002 | 2004

The minimum sum will come from the factors of the middle two divisors, 12 and 167

167 is prime....it will be included in the sum.......the divisors of 12   are 1 | 2 | 3 | 4 | 6 | 12.......

The remaining two integers involved in minimizing the sum will come from the middle two divisors of 12, i.e, 3 and 4

So....the minumum sum is given when  the three integers x, y and z  are   3 , 4 and 167   ....the sum  =  174

cos (theta)  =  [ u (dot) v] /  [ ll u ll * ll v ll ]

u (dot) v  = -1*3 + 4 * -4   =  -19

ll u ll = sqrt [ (-1)^2 + 4^2 ] = sqrt (17)

ll v ll  = sqrt [ (3)^2 + (-4)^2  ]   = 5

So

cos (theta)  =  -19 / [ 5 sqrt (17)]      so using the cosine inverse to find theta, we have

arccos (  -19 / [ 5 sqrt (17)] )  = theta = about 157.166° ......   "e"   is correct

1,000,000,000,000,000     =    "one quadrillion "

We can find the angle thusly :

cos θ   = [ u (dot) v ] / [ ll u ll * ll v ll  ]

u (dot) v  = 1*-1  + 4 * 2 =   7

ll u ll =  √[  1*2 + 4^2 ] = √17

ll v ll  = √ [(-1)^2 + 2^2]  = √5

So   ll u ll *  ll v ll   = √[17 * 5 ]  = √85

So

cos θ   =   7 /  √85    and we can find θ  using the cosine inverse

arccos [  7 /  √85 ] =  θ   =   40.6°

actually sorry guys my bad... it should have been   " (2001^2 - 1999^2) / (2003^2 - 1997^2) = ? "

i coulnt notice the "a^2 - b^2" fact, thanks for the answer Alan and who tried to help me :)

with the a^2 - b^2 fact i easily found the answer of my question it is 1/3 :) 

and im really sory for my mistake, thank you all for helping out :)

Good thinking Alan :)

Here is another way - I used the calculator.  LOL

(2001^2 - 1992^2) / (2003^2 - 1997^2) = 1.497375

Use the fact that a^2 - b^2 = (a+b)(a-b) so we have:  (2001+1992)*9/[(2003+1997)*6]

or 3993*9/(4000*6) ≈ 1.497

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I have never seen a root written like that before but I would say that you are both correct :)

I am not sure how it should be represented but I'd just say   1.05v

the revenue would become     1.05vu = \(1.05*\begin{pmatrix} 1800,\;\; 1200 \end{pmatrix}* \begin{pmatrix} 94300\\ 5200 \end{pmatrix}\)

Find the angle between vectors u and v if u= i + 4j and v= -i+2j. a. 40.60 degrees b. 41.56 degrees c. 39.36 degrees d. 42.01 degrees e. 38.67 degrees

u is in the first quadrant.    Angle with pos x axis is  atan(4/1)

v is in the second quadrant  Angle with pos x axis = 180-atan(2)

angle between them = 180-atan(2)-atan(4)

180-atan(2)-atan(4) = 40.601294645004                     40.60 degrees

However I do not understand why there is an i and a j.  

\(\dfrac{2.981 \times 10^{20}}{3.25\times 10^3}\\=\dfrac{29.81\times10^{19}}{3.25\times10^3}\\=\dfrac{29.81}{3.25}\times\dfrac{10^{19}}{10^3}\\= \dfrac{2981}{325}\times 10^{16}\\\approx 9.1723\times 10^{16}\)

15.5563492 × (cos 135° + i sin 135°) according to the great Wolfram Alpha.

So it's A?

Guys thanks for answering, but I was wrong it must be f(x)=4x²+3x-2. If you can solve it for me thanks in advance but if no it's okay 'cause I knew how to solve it because of you guys 

2016300

\(\text{I am going to go through the 2 possibilities of what this question means.(5^x-3 and 5^(x-3))}\)

\(5^x-3=10\\ 5^x=13\\ x = log_513\\\text{Which is about 1.59}\)

\(5^{x-3}=10\\ x= log_510 + 3\\\text{Which is about 4.43}\)