MathYouLike MathYouLike
  • Toggle menubar
  • Toggle fullscreen
  • Toggle Search
  •    Sign up
  • Newest
  • Featured
  • Votes
  • Unanswered
  • First «
  • 378
  • 379
  • 380
  • 381
  • 382
  • » Last
  • QUESTIONS
  • TAGS
  • USERS
  • BADGES
  • UNANSWERD
  • ASK A QUESTION
  • BLOG

All questions

  • Newest
  • Featured
  • Votes
  • Unanswered

...
phanhuytien
16/08/2017 at 15:00
Answers
2
Follow

compare:

            8^20 and 2^80

  • ...
    Help you solve math 16/08/2017 at 15:02

    We have:

    8^20=(2^3)^20=2^80

    =>8^20=2^80Hiha

    phanhuytien selected this answer.
  • ...
    phanhuytien 18/08/2017 at 08:34

    2^80=(2^3)^20=8^20

    =>2^80=8^20


...
Lê Quốc Trần Anh Coordinator
30/08/2017 at 16:55
Answers
2
Follow

Express the power:

\(\dfrac{81^4.3^{10}.27^5:3^{12}}{3^{18}:9^3.243^2}\)

Power

  • ...
    Dao Trong Luan 30/08/2017 at 17:33

    \(\dfrac{81^4\cdot3^{10}\cdot27^5:3^{12}}{3^{18}:9^3\cdot243^2}=\dfrac{\left(3^4\right)^4\cdot3^{10}\cdot\left(3^3\right)^5:3^{12}}{3^{18}:\left(3^2\right)^3\cdot\left(3^5\right)^2}\)

    \(=\dfrac{3^{16}\cdot3^{10}\cdot3^{15}:3^{12}}{3^{18}:3^6\cdot3^{10}}=\dfrac{3^{16+10+15-12}}{3^{18-6+10}}=\dfrac{3^{29}}{3^{22}}=3^7=2187\)

    Lê Quốc Trần Anh selected this answer.
  • ...
    FA KAKALOTS 08/02/2018 at 22:00

    814⋅310⋅275:312318:93⋅2432=(34)4⋅310⋅(33)5:312318:(32)3⋅(35)2

    =316⋅310⋅315:312318:36⋅310=316+10+15−12318−6+10=329322=37=2187


...
Summer Clouds moderators
15/09/2017 at 08:49
Answers
4
Follow

Hazel wrote the integers 1 through 321 on the board. How many total digits did she write? 

  • ...
    Phan Thanh Tinh Coordinator 15/09/2017 at 09:33

    The number of 1-digit numbers is : (9 - 1) + 1 = 9 

    The number of 2-digit numbers is : (99 - 10) + 1 = 90

    The number of 3-digit numbers is : (321 - 100) + 1 = 222

    The number of digits she wrote is : 

    9 x 1 + 90 x 2 + 222 x 3 = 855

    Selected by MathYouLike
  • ...
    Vũ Trung Dũng 18/09/2017 at 05:53

    The number of 1-digit numbers is : (9 - 1) + 1 = 9 

    The number of 2-digit numbers is : (99 - 10) + 1 = 90

    The number of 3-digit numbers is : (321 - 100) + 1 = 222

    The number of digits she wrote is : 

    9 x 1 + 90 x 2 + 222 x 3 = 855

    Answer : 855

  • ...
    →இے๖ۣۜBoy™†hïếuGîa 16/09/2017 at 13:39

    he number of 1-digit numbers is : (9 - 1) + 1 = 9 

    The number of 2-digit numbers is : (99 - 10) + 1 = 90

    The number of 3-digit numbers is : (321 - 100) + 1 = 222

    The number of digits she wrote is : 

    9 x 1 + 90 x 2 + 222 x 3 = 855


...
Summer Clouds moderators
16/10/2017 at 08:35
Answers
0
Follow

A regular hexagon is drawn such that every side of the hexagon is tangent to a circle. Another regular hexagon is drawn such that each side of the new hexagon is tangent to 1 and only 1 vertex of the old hexagon. What is the ratio of the area of the new hexagon to the circle. Express your answer in simplified form.


...
Alone
01/01/2018 at 11:46
Answers
2
Follow

Find a,b,c are positive numbers and a+b+c=\(\dfrac{2a}{b+c}+\dfrac{2b}{a+c}+\dfrac{2c}{a+b}\).Find the value of A=\(a^{2012}+b^{2012}+c^{2012}\)

  • ...
    Lightning Farron 01/01/2018 at 21:28

    By Cauchy-Schwarz's ineq:

    \(VP=\dfrac{4a^2}{2ab+2ac}+\dfrac{4b^2}{2ab+2bc}+\dfrac{4c^2}{2ac+2bc}\)

    \(\ge\dfrac{\left(2a+2b+2c\right)^2}{4\left(a+b+c\right)}=\dfrac{4\left(a+b+c\right)^2}{4\left(a+b+c\right)}=a+b+c=VT\)

    When \(a=b=c=1 \Rightarrow A=3\)

    Alone selected this answer.
  • ...
    FA Liên Quân Garena 08/01/2018 at 21:58

    By Cauchy-Schwarz's ineq:

    VP=4a22ab+2ac+4b22ab+2bc+4c22ac+2bc

    ≥(2a+2b+2c)24(a+b+c)=4(a+b+c)24(a+b+c)=a+b+c=VT

    When a=b=c=1⇒A=3


...
Lê Quốc Trần Anh Coordinator
08/04/2018 at 06:04
Answers
0
Follow

 In how many ways can we divide the numbers 1, 2, 3, … , 12 into four groups,
each containing three numbers whose sum is divisible by 3?


...
Lê Quốc Trần Anh Coordinator
13/06/2018 at 02:04
Answers
1
Follow

Prove that there are no \(a,b,c>0\) satisfys: \(a+\dfrac{1}{b}< 2;b+\dfrac{1}{c}< 2;c+\dfrac{1}{a}< 2\)

  • ...
    Alone 13/06/2018 at 10:11

    We have:\(a+\dfrac{1}{b}+b+\dfrac{1}{c}+c+\dfrac{1}{a}< 6\)

    But \(a+\dfrac{1}{a}+b+\dfrac{1}{b}+c+\dfrac{1}{c}\ge2\sqrt{a.\dfrac{1}{a}}+2\sqrt{b.\dfrac{1}{b}}+2\sqrt{c.\dfrac{1}{c}}=2+2+2=6\)

    So there are no a,b,c>0 satisfys

    Lê Quốc Trần Anh selected this answer.

...
Bookname
04/08/2018 at 01:25
Answers
1
Follow

In the same year he lived in a house
Parenting in the harmony
The old man was three
An old man was two years old.
What is the trick?

  • ...
    Cristiano Ronaldo 04/08/2018 at 01:26

    In the same year he lived in a house
    Parenting in the harmony
    The old man was three
    An old man was two years old.
    What is the trick?

    Answer: It's five finger

    Bookname selected this answer.

...
Quoc Tran Anh Le Coordinator
09/09/2018 at 09:54
Answers
0
Follow

Determine the smallest positive integer y for which there is a positive integer x satisfying the equation \(2^{13}+2^{10}+2^x=y^2\)

AIMO


...
Summer Clouds moderators
28/06/2017 at 17:17
Answers
3
Follow

What is the value of \(2+4+6+....+998+1000\) ?

  • ...
    Phan Thanh Tinh Coordinator 28/06/2017 at 19:53

    \(2+4+6+....+996+998+1000\)

    \(=2\times\left(1+2+3+...+498+499+500\right)\)

    \(=2\times\dfrac{500\times501}{2}=250500\)

  • ...
    NGUYỄN SANH KIÊN 04/07/2017 at 07:07

    SUPER SAIYAN GOKU copy is not good

  • ...
    Super Saiyan Goku 30/06/2017 at 11:40

    Summer Clouds

    \(2+4+6+...+996+998+1000\)

    \(=2\times\left(1+2+3+...+498+499+500\right)\)

    \(=2\times\dfrac{500\times501}{2}=250500\)

    Ai mk,mk lại!


4801

questions

Weekly ranking

  • ...

    Trần Nhật Quỳnh

    This week's point: . Total: 0
  • ...

    haiplt

    This week's point: . Total: 6
  • ...

    at the speed of light

    This week's point: . Total: 0
  • ...

    Cô Nàng Lạnh Lùng

    This week's point: . Total: 0
  • ...

    Use Ka Ti

    This week's point: . Total: 0
  • ...

    lamber love liya

    This week's point: . Total: 0
  • ...

    Nguyễn Thị Huyền Mai

    This week's point: . Total: 0
  • ...

    Ngu Ngu Ngu

    This week's point: . Total: 24
  • ...

    phan gia huy

    This week's point: . Total: 1
  • ...

    Nguyễn Phương Ly Fan Triệu Lệ Dĩnh

    This week's point: . Total: 0

Tags

games 18  double counting 8  generating functions 2  probabilistic method 1  Polynomial 9  inequality 13  area 17  Equation 9  Primitive Roots Modulo Primes 1  Primitive in Arithmetic Progression 6  Base n Representatioons 4  Pell Equation 1  mixed number 1  Fraction 29  Circle 3  Imaginary numbers 1  Decimal number 2  Volume 2  percentages 6  simple equation 19  absolute value 19  rational numbers 20  Operation of Indices 21  Simulataneous Equation A System of Equations 25  Multiplication of Polynomial 17  divisibility 24  Maximum 5  Minimum 8  Fraction 4  Prime Numbers and Composite Numbers 13  Square Number 26  Even and Odd Numbers 13  GDC and LCM 11  GCD and LCM 12  Permutation and combination 9  combinations 5  interger 7  number 10  Diophantine equations 2  equations 1  Grade 6 19  Power 3  equality 2  maxima-minima 2  square root 1  Polygon 2  IGCSE 1  factorial 1  integers 2 
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:

© HCEM 10.1.29.225
Crafted with by HCEM