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Vui Ghét Nét
06/03/2019 at 23:48
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Compact

A = \(\left(a+b+c\right)^2+\left(a+b-c\right)^2-2\left(a-b\right)^2\)


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Asta Cache
06/03/2019 at 13:51
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Write the letter to send for your best friend.

nônno

  • ...
    Nguyễn Thị Linh 06/03/2019 at 23:32

    No, The letter math


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Lê Anh Duy
04/03/2019 at 15:28
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32) Solve the equation (And you will know the surprising age of Tran Anh):

\(\sqrt{x-89}+\sqrt{91-x}=x^2-180x+8102\)

(P/s: Please do this math problem by yourself, step-to-step, and don't try to copy from the Internet, please)

 

Equation

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    FacuFeri 06/03/2019 at 05:13

    We have : \(x^2-180x+8102=\left(x^2-180x+8100\right)+2=\left(x-90\right)^2+2\ge2\forall x\left(1\right)\)

    Applying the Bunhiacopxki inequality , we have : 

    \(\left(\sqrt{x-89}+\sqrt{91-x}\right)^2\le\left(1+1\right)\left(x-89+91-x\right)\)

    \(\Rightarrow\left(\sqrt{x-89}+\sqrt{91-x}\right)^2\le2.2=4\)

    \(\Rightarrow\sqrt{x-89}+\sqrt{91-x}\le2\left(2\right)\)

    Because \(\sqrt{x-89}+\sqrt{91-x}=x^2-180x+8102\)

    So ( 1 ) ; ( 2 ) ; we have : \(\sqrt{x-89}+\sqrt{91-x}=x^2-180x+8102=2\)

    Equal sign occurs \(\Leftrightarrow\sqrt{x-89}=\sqrt{91-x};x-90=0\left(3\right)\)

    We have : \(\sqrt{x-89}=\sqrt{91-x}\)  \(\Leftrightarrow x-89=91-x\Leftrightarrow x=90\left(4\right)\)

     ( 3 ) ; ( 4 ) \(\Rightarrow x=90\) is the result of the equation

    Lê Anh Duy selected this answer.
  • ...
    Huy Toàn 8A (TL) 06/03/2019 at 13:14

    Đk : \(89\le x\le91\)

    Applying the Bunhiacopxki inequality

    We have : VT \(=1.\sqrt{x-89}+1.\sqrt{91-x}\le\sqrt{\left(1+1\right)\left(x-89+91-x\right)=2}\)

    => VT \(\le2\)

    And VP = \(x^2-2.x.90+90^2+2=\left(x-90\right)^2+2\ge2\)

    => VP  \(\ge2\ge\) VT

    The sign "=" occurs when and only when: 

    \(\left\{{}\begin{matrix}\sqrt{x-89}=\sqrt{91-x}\\x-90=0\end{matrix}\right.\) => \(x=90\)(satisfy)

    The answer is 90

  • ...
    FacuFeri 05/03/2019 at 05:10

    Tran Anh ??? Le Quoc Tran Anh ??? 


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El matadora
03/03/2019 at 09:11
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Ai là người Việt nam ko

Trả lời m đi 

  • ...
    Huy Toàn 8A (TL) 03/03/2019 at 13:37

    El matodora : The Spam question

    You should write the real question in English


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Quoc Tran Anh Le Coordinator
02/03/2019 at 13:22
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A speed of 60 miles per hour is equal to 88 feet per second. If the speed limit in a school zone is 15 miles per hour, what is the speed limit in this zone in feet per second?

 

Mathcounts

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    Alone 03/03/2019 at 15:25

    The speed limit in this zone in feet per second is:
        88:60 x 15==22(feet)

    Quoc Tran Anh Le selected this answer.
  • ...
    nguyễn kim tuyen 14/04/2019 at 02:40

    22 feet


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Quoc Tran Anh Le Coordinator
02/03/2019 at 13:21
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In the figure, two regular pentagons have been attached to a regular hexagon to create a 12-gon. If each regular polygon has side length 3 feet, what is the perimeter of the resulting 12-gon?

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Quoc Tran Anh Le Coordinator
02/03/2019 at 13:19
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If the value of x is 10, what is the value of 3x + 4x + 5x ? Solve in many ways.

 

Mathcounts

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    Huy Toàn 8A (TL) 02/03/2019 at 13:29

    C1:  We have : 3x + 4x + 5x = x (3 + 4 + 5)

    Replace x = 10 <=> 10 ( 3 + 4 + 5) = 10 . 12 = 120

    C2 : 3x + 4x + 5x <=> 3 . 10 + 4 . 10 + 5 . 10 = 30 + 40 + 50 = 120

    Quoc Tran Anh Le selected this answer.

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Quoc Tran Anh Le Coordinator
02/03/2019 at 13:19
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Of 1000 people surveyed, one-third of the 630 people who reported owning a cat also own a dog. If each person surveyed owns a cat, a dog or both, how many own a dog?

 

Mathcounts


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Quoc Tran Anh Le Coordinator
28/02/2019 at 15:14
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What is the quotient when 1,000,000,000 is divided by 28 × 57?

 

Mathcounts

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    Huy Toàn 8A (TL) 01/03/2019 at 04:01

    We have 

    \(\dfrac{2}{8}.\dfrac{5}{7}=256.78125=20000000\)

    \(=>1000000000:\left(\dfrac{2}{8}.\dfrac{5}{7}\right)=1000000000:20000000=50\)

    The answer is 50

    Quoc Tran Anh Le selected this answer.
  • ...
    Thanh Hải Đặng 16/03/2019 at 05:26

    1 000 000 000 =109=29.59

    \(\Rightarrow\)1000000000 / (28x57)=2*52=50

    The answer ís 50


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Quoc Tran Anh Le Coordinator
28/02/2019 at 15:14
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How many lines of symmetry does an isosceles right triangle have?

 

Mathcounts

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    Kaka Lot 02/03/2019 at 13:33

    This is two


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