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Lê Quốc Trần Anh Coordinator
13/05/2018 at 03:40
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Find the last 2-digit numbers of: \(D=1978^{1986^8}\)


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Emily
01/03/2018 at 07:12
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1
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A motor scooter can go 30 miles per hour. How many feet per second is this? 

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    Jacob 05/03/2018 at 02:37

    a mile = 5280 feets, an hour = 3600 seconds

    30 miles per hour = 30 x 5280 feets per hour = 30 x 5280 / 3600 feets per second = 44 feets per second


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Lê Quốc Trần Anh Coordinator
28/02/2018 at 15:23
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Find the last three-digit numbers of: \(M=2^{2018}\) 

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    Nguyễn Huy Thắng 28/04/2018 at 15:47

    We have: \(2^{2018}=\left(2^{1009}\right)^2=\left(2^{979}\cdot2^{30}\right)^2=\left(\left(2^{11}\right)^{89}\cdot2^{30}\right)^2\)

    \(\equiv\left(48^{89}\cdot824\right)^2\left(mod1000\right)\)\(=\left(48^3\cdot\left(48^2\right)^{43}\cdot824\right)^2\)

    \(\equiv\left(592\cdot304^{43}\cdot824\right)^2\left(mod1000\right)\)

    \(\equiv\left(592\cdot\left(304^5\right)^8\cdot464\cdot824\right)^2\left(mod1000\right)\)

    \(\equiv\left(912\cdot24^8\right)^2\left(mod1000\right)\)

    \(\equiv\left(912\cdot776^2\right)^2\left(mod1000\right)\)

    \(\equiv\left(912\cdot176\right)^2\left(mod1000\right)\)

    \(\equiv512^2\left(mod1000\right)\equiv144\left(mod1000\right)\)

    So the last three-digit numbers of \(M\) is \(144\)

    Lê Quốc Trần Anh selected this answer.
  • ...
    Đỗ Anh 10/05/2018 at 11:00

    Theo bài ra  ta có:  22018= ( 21009)2= ( 2979⋅ 230)2= ( ( 211)89⋅ 230)222018=(21009)2=(2979⋅230)2=((211)89⋅230)2

    ≡ ( 4889⋅ 824 )2( m o d1000 )≡(4889⋅824)2(mod1000)= ( 483⋅ ( 482)43⋅ 824 )2=(483⋅(482)43⋅824)2

    ≡ ( 592 ⋅ 30443⋅ 824 )2( m o d1000 )≡(592⋅30443⋅824)2(mod1000)

    ≡ ( 592 ⋅ ( 3045)số 8⋅ 464 ⋅ 824 )2( m o d1000 )≡(592⋅(3045)số 8⋅464⋅824)2(mod1000)

    ≡ ( 912 ⋅ 24số 8)2( m o d1000 )≡(912⋅24số 8)2(mod1000)

    ≡ ( 912 ⋅ 7762)2( m o d1000 )≡(912⋅7762)2(mod1000)

    ≡ ( 912 ⋅ 176 )2( m o d1000 )≡(912⋅176)2(mod1000)

    ≡ 5122( m o d1000 ) ≡144 ( m o d1000 )≡5122(mod1000)≡144(mod1000)

    Vì vậy, con số ba chữ số cuối cùng của  MM  là  144


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An Duong moderators
27/02/2018 at 07:27
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A 200-pound man and his two sons each weighing 100 pounds want to cross a river, If they have only one boat and it can safely carry only 200 pounds, how can they cross the river?

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    Anna 27/02/2018 at 08:26

    2 sons x and y cross; x returns.

    Father crosses; y returns.

    Two sons cross. 

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    Lê Quốc Trần Anh Coordinator 28/02/2018 at 15:27
    In Anna's second line: father cross, x or y returns
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    ¤« 04/03/2018 at 14:49

    2 sons x and y cross; x returns.

    Father crosses; y returns.

    Two sons cross.


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Emma
27/02/2018 at 09:40
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7
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Of the three figures shown below, which ones can be drawn without going over any lines twice and without crossing any lines? 

undefined

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    I love Math 02/03/2018 at 12:42

    Figure 2

  • ...
    nguyen tuan anh 26/04/2018 at 04:14

    figure twololang

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    nguyen tuan anh 22/04/2018 at 01:11

    figure two


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Anna
27/02/2018 at 07:49
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2
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In the early 1700's the city of Konigsperg, Gemany was connected by seven bridges. Many people in the city at that time were interested in finding if it were possible to walk through the city so as to cross each bridge. exactly once. 

undefined

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    Anna 28/02/2018 at 07:45

    Seven Bridges of Königsberg - Wikipedia

  • ...
    Anna 28/02/2018 at 07:44

    The Seven Bridges of Königsberg - Numberphile - YouTube


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maths is ok
25/02/2018 at 22:27
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4
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In a Province A, 12 people own 7 bicycles, 15 people own 4 cars and 10 people own 3 motorcycles. The total number of vehicles is 18000 more than the total population. What is the total population of A?

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    lehahieu 27/02/2018 at 14:16

    The total population in Province A is :

         18000 - ( 12 x 7 + 15 x 4 + 10 x 3 ) = 17826 ( people )

                  Answer : 17826 people

  • ...
    I love Math 27/02/2018 at 04:40

    The total population in Province A is :

                         18000 - ( 12 x 7 + 15 x 4 + 10 x 3 ) = 17826 ( people )

                                        Answer : 17826 people

  • ...
    ¤« 04/03/2018 at 14:50

    The total population in Province A is :

         18000 - ( 12 x 7 + 15 x 4 + 10 x 3 ) = 17826 ( people )

                  Answer : 17826 people


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Alone
27/12/2017 at 22:20
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With a,b>0 satisfy a+b=2.Find the minimum of A=\(\left(1-\dfrac{4}{a^2}\right)\left(1-\dfrac{4}{b^2}\right)\)

P/s:The exam of the excellent teacher of Duc Tho district 

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    Hà Minh Hiếu 27/02/2018 at 11:09

    A = \(\left(1-\dfrac{4}{a^2}\right)\left(1-\dfrac{4}{b^2}\right)\)

        = \(\dfrac{\left(a-2\right)\left(a+2\right)\left(b-2\right)\left(b+2\right)}{a^2b^2}\) 

        = \(\dfrac{ab\left(a+2\right)\left(b+2\right)}{a^2b^2}\)

       = \(\dfrac{ab+2\left(a+b\right)+4}{ab}\)

      = \(1+\dfrac{8}{ab}\)

     \(\le1+\dfrac{8}{\left(\dfrac{a+b}{2}\right)^2}=1+8=9\)

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    Thanh Nguyen 07/02/2018 at 19:18

    9 . cá 100%

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    Faded 22/01/2018 at 12:33

    A= (1-2a)(1-2b)(1+2a)(1+2b

    )

    A= ( 1-a+ba

    )(1-a+bb)(1+a+ba)(1+a+bb

    )

    A= ba

    .ab.(2+ba)(2+ab

    )

    A= 4 +1 + 2 (ba+ab

    ) >= 5 +2. 2√ba.ab= 5+4 =9


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Cloud moderators
27/12/2017 at 17:33
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Find the domain of the  expression \(\dfrac{2}{3x+2}+\dfrac{2x-1}{x+1}+\dfrac{2}{x}\).


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Cloud moderators
11/12/2017 at 15:36
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A repeating integer is one in which a sequence of digits occurs two or more times to make the entire number. The 4-digit number 4242 is a repeating integer. How many numbers are six-digit repeating integers?


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