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Quoc Tran Anh Le Coordinator
09/09/2018 at 09:55
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0
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Consider a shortest path along the edges of a 7 × 7 square grid from its bottom-left vertex to its top-right vertex. How many such paths have no edge above the grid diagonal that joins these vertices?

AIMO


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Kayasari Ryuunosuke
22/03/2017 at 15:07
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8
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Shorter the expression :

A = |x + 0.8| - |x - 25| + 1.9 with a < -0.8 

  • ...
    Kurosaki Akatsu Coordinator 22/03/2017 at 15:11

    We have :

    x < -0.8 \(\Rightarrow\) x + 0,8 < 0 \(\Rightarrow\)|x + 0.8| = -(x + 0.8)

    x < -0.8 \(\Rightarrow\) x < 25 \(\Rightarrow\) |x - 25| = 25 - x

    \(\Rightarrow\) A = -(x + 0.8) - (25 - x) + 1.9

         A = -x - 0.8 - 25 + x + 1.9

         A = -23.9 

    Kayasari Ryuunosuke selected this answer.
  • ...
    →இے๖ۣۜQuỳnh 23/03/2017 at 05:50

    We have : x < -0.8 ⇒ x + 0,8 < 0 ⇒|x + 0.8| = -(x + 0.8)

                     x < -0.8 ⇒ x < 25 ⇒ |x - 25| = 25 - x

    Candle A = -(x + 0.8) - (25 - x) + 1.9

                    = -x + 0,8 - 25 + x + 1,9

                    = -x + x - 0,8 - 25 + 1,9

                    = -25,8 + 1,9

                A = -23,8

         A = -x - 0.8 - 25 + x + 1.9

         A = -23.9 

  • ...
    →இے๖ۣۜQuỳnh 22/03/2017 at 20:04

    We have : x < -0.8 ⇒ x + 0,8 < 0 ⇒|x + 0.8| = -(x + 0.8)

                     x < -0.8 ⇒ x < 25 ⇒ |x - 25| = 25 - x

    Candle A = -(x + 0.8) - (25 - x) + 1.9

                    = -x + 0,8 - 25 + x + 1,9

                    = -x + x - 0,8 - 25 + 1,9

                    = -25,8 + 1,9

                A = -23,8

         A = -x - 0.8 - 25 + x + 1.9

         A = -23.9 


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Maths
18/05/2017 at 22:18
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5
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Find the area of shaded triangle

36cm 1dm

  • ...
    Vũ Hà Vy Anh 18/05/2017 at 22:20

    1dm=10cm

    the area of shaded triangle :

    10x36:2=180(cm2)

    Maths selected this answer.
  • ...
    Fujitora Ishito 19/05/2017 at 09:45

    \(\text{1dm=10cm }\) 

    \(\text{ The area of shaded triangle : 10x36:2=180(cm2)}\) 

    \(Answer:180cm^2\) 

    Good Maths haha

  • ...
    Phan Minh Anh 21/05/2017 at 14:53

    180 cm2


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Kantai Collection
20/07/2017 at 18:40
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1
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Find x know :

(x - 1)4 = (x - 1)6

  • ...
    Kayasari Ryuunosuke Coordinator 20/07/2017 at 18:44

    We have :

    \(\left(x-1\right)^4=\left(x-1\right)^6\)

    \(\Rightarrow\left(x-1\right)^6-\left(x-1\right)^4=0\)

    \(\left(x-1\right)^4.\left[\left(x-1\right)^2-1\right]=0\)

    So \(\left(x-1\right)^4=0\)           or          \(\left(x-1\right)^2-1=0\)

    \(\Leftrightarrow x-1=0\)                or           \(\left(x-1\right)^2=1\)

    \(\Leftrightarrow x=1\)                       or            \(\left[{}\begin{matrix}x-1=1\\x-1=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=0\end{matrix}\right.\)

    So , x = {0,1,2}

    Selected by MathYouLike

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Summer Clouds moderators
08/08/2017 at 08:52
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1
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If (2x − 5)(2x + 5) = 5, what is the value of \(4x^2\) ?

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    Kayasari Ryuunosuke Coordinator 08/08/2017 at 08:54

    (2x - 5)(2x + 5) = 5

    \(\Leftrightarrow\left(2x\right)^2-5^2=5\)

    \(\Leftrightarrow4x^2=5+25=30\)

    Selected by MathYouLike

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Lê Quốc Trần Anh Coordinator
30/08/2017 at 16:56
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1
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Find x:

\(\left(3-4x\right)^3=-125\)

  • ...
    Dao Trong Luan 30/08/2017 at 17:28

    \(\left(3-4x\right)^3=-125\)

    \(\Leftrightarrow\left(3-4x\right)^3=\left(-5\right)^3\)

    => 3 - 4x = -5

    => 4x = 3 - \(\left(-5\right)\)

    => 4x = 8

    => x = 2

    Lê Quốc Trần Anh selected this answer.

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Summer Clouds moderators
15/09/2017 at 08:51
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In how many ways can one knife, one fork and one spoon be distributed, in any order, to three people, if each person is given 0, 1, 2 or 3 utensils?


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Summer Clouds moderators
16/10/2017 at 08:40
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1
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What is the remainder when the sum 1 + 7 + 13 + 19 + ..... + 253 + 259 is divided by 6?
 

  • ...
    Phan Thanh Tinh Coordinator 16/10/2017 at 10:12

    We notice that every term of the sum is divided by 6 with remainder 1 (since each term is 6 less than the next term and 1 is the first term)

    The sum has : (253 - 1) : 6 + 1 = 43 (terms)

    We have : \(1\times43\equiv43\equiv1\left(mod6\right)\) . So, the answer is 1


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Cloud moderators
01/12/2017 at 14:21
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At noon, Randy’s family left the Texas-Oklahoma border, traveling north on I-35. At noon, Marco’s family left their home in Minnesota, 1029 miles from the Texas-Oklahoma border, traveling south on I-35. If Randy’s family is traveling 45 mi/h and Marco’s family is traveling 53 mi/h, how many hours will it take for the two families to pass each other? Express your answer as a decimal to the nearest tenth.

  • ...
    Phan Thanh Tinh Coordinator 15/01/2018 at 21:14

    The answer is : \(1029:\left(45+53\right)=10.5\) (hours)


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Alone
01/01/2018 at 11:53
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2
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Prove that :If \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=3\) and a+b+c=abc so we have \(\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}=7\)

  • ...
    Dao Trong Luan Coordinator 01/01/2018 at 12:50

    \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=3\)

    \(\Rightarrow\left(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\right)^2=3^2\)

    \(\Rightarrow\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}+2\left(\dfrac{1}{ab}+\dfrac{1}{bc}+\dfrac{1}{ca}\right)=9\)

    \(\Rightarrow\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}+\dfrac{2\left(a+b+c\right)}{abc}=9\)

    \(\Rightarrow\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}+\dfrac{2abc}{abc}=9\)

    \(\Rightarrow\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}+2=9\)

    \(\Rightarrow\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}=7\)

    Alone selected this answer.
  • ...
    FA Liên Quân Garena 02/01/2018 at 12:33

    1a+1b+1c=3

    ⇒(1a+1b+1c)2=32

    ⇒1a2+1b2+1c2+2(1ab+1bc+1ca)=9

    ⇒1a2+1b2+1c2+2(a+b+c)abc=9

    ⇒1a2+1b2+1c2+2abcabc=9

    ⇒1a2+1b2+1c2+2=9

    ⇒1a2+1b2+1c2=7


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Trigonometric
sin cos tan cot sinh cosh tanh
Lim-log

Combined operations

 

α β γ δ θ σ ∂ ε ω φ ϕ π μ λ Ψ ξ η χ ζ ι κ ν ψ Ω ρ τ υ Γ Δ Λ Φ Π Σ Υ Ξ ϑ Θ ς ϰ
∞ ⊻ ⩞ ⋎ ⋏ ≀ ∪ ⊎ ⋓ ∩ ⋒ ⊔ ⊓ ⨿ ⊗ ⊙ ⊚ ⊛ ⊘ ⊝ ⊕ ⊖ ⊠ ◯ ⊥
⇔ ⇒ ⇐ → ← ↔ ↑ ↓
Operations
+ - ÷ × ≠ = ⊂ ⊃ ⊆ ⊇ ≈ ∈ ∉ ∃ ∄ ≤ ≥ ± ∓ ≠ ∅ ≃ ≅ ≡ ⋮ ⋮̸ ∀
(□) [□] {□} |□|

The type of system

m×n 1×2 1×3 1×4 1×5 1×6
2×1 2×2 2×3 2×4 2×5 2×6
3×1 3×2 3×3 3×4 3×5 3×6
4×1 4×2 4×3 4×4 4×5 4×6
5×1 5×2 5×3 5×4 5×5 5×6
6×1 6×2 6×3 6×4 6×5 6×6

Recipe:

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