MathYouLike MathYouLike Practice Q & A
  • Toggle menubar
  • Toggle fullscreen
  • Toggle Search
  • Practice
  • Q & A
  •    Sign up
  • Newest
  • Featured
  • Votes
  • Unanswered
  • First «
  • 1
  • 2
  • 3
  • 4
  • 5
  • » Last

Featured Questions

  • Unanswered
  • Votes
  • Featured
  • Newest
...
Uchiha Sasuke
21/04/2017 at 08:40
Votes Answers Follow

If f (x) = px7 + qx3 + rx - 4 and f (-7) = 3 then the value of  f (7) is...

Help me please!gianroi

 

  • ...
    Phan Thanh Tinh Coodinator 21/04/2017 at 08:48

    f(7) = p.77 + q.73 + r.7 - 4 = -p.(-7)7 - q.(-7)3 - r.(-7) - 4

    = -[p.(-7)7 + q.(-7)3 + r.(-7)] - 4 = -[f(-7) + 4] - 4

    = -(3 + 4) - 4 = -7 - 4 = -11

    Selected by MathYouLike
  • ...
    Khánh Lê Minh 23/04/2017 at 09:06

    f(7) = p.77 + q.73 + r.7 - 4 = -p.(-7)7 - q.(-7)3 - r.(-7) - 4

    = -[p.(-7)7 + q.(-7)3 + r.(-7)] - 4 = -[f(-7) + 4] - 4

    = -(3 + 4) - 4 = -7 - 4 = -11banhqua

  • ...
    ichigodangyeu123 22/04/2017 at 20:58

    What grade are you in?Uchiha Sasuke 


...
Carter
18/04/2017 at 15:09
Votes Answers Follow

 Simplify the expression (where a, b, and c are different real numbers) :

\(\dfrac{\left(x-a\right)\left(x-b\right)}{\left(c-a\right)\left(c-b\right)}+\dfrac{\left(x-b\right)\left(x-c\right)}{\left(a-b\right)\left(a-c\right)}+\dfrac{\left(x-c\right)\left(x-a\right)}{\left(b-c\right)\left(b-a\right)}\)

  • ...
    An Duong 21/04/2017 at 07:27

    Let \(f\left(x\right)=\dfrac{\left(x-a\right)\left(x-b\right)}{\left(c-a\right)\left(c-b\right)}+\dfrac{\left(x-b\right)\left(x-c\right)}{\left(a-b\right)\left(a-c\right)}+\dfrac{\left(x-c\right)\left(x-a\right)}{\left(b-c\right)\left(b-a\right)}-1\)

    We have:

      \(f\left(a\right)=0+1+0-1=0\)

    Similarity \(f\left(b\right)=0,f\left(c\right)=0\)

    f(x) is a degree of 2 and have 3 different solotutions (a, b, c) .

    => f(x) = 0

    => \(\dfrac{\left(x-a\right)\left(x-b\right)}{\left(c-a\right)\left(c-b\right)}+\dfrac{\left(x-b\right)\left(x-c\right)}{\left(a-b\right)\left(a-c\right)}+\dfrac{\left(x-c\right)\left(x-a\right)}{\left(b-c\right)\left(b-a\right)}=1\)

    Selected by MathYouLike
  • ...
    Ban quản trị 16/09/2018 at 09:47

    Let \(f\left(x\right)=\dfrac{\left(x-a\right)\left(x-b\right)}{\left(c-a\right)\left(c-b\right)}+\dfrac{\left(x-b\right)\left(x-c\right)}{\left(a-b\right)\left(a-c\right)}+\dfrac{\left(x-c\right)\left(x-a\right)}{\left(b-c\right)\left(b-a\right)}-1\)

    We have:

    \(f\left(a\right)=0+1+0-1=0\)

    Similarity \(f\left(b\right)=0,f\left(c\right)=0\)

    \(f\left(x\right)\) is a degree of 2 and have 3 different solotutions \(\left(a,b,c\right)\)

    \(\Rightarrow f\left(x\right)=0\)

    \(\Rightarrow\dfrac{\left(x-a\right)\left(x-b\right)}{\left(c-a\right)\left(c-b\right)}+\dfrac{\left(x-b\right)\left(x-c\right)}{\left(a-b\right)\left(a-c\right)}+\dfrac{\left(x-c\right)\left(x-a\right)}{\left(b-c\right)\left(b-a\right)}=1\)


...
Mr Puppy
05/07/2018 at 09:06
Votes Answers Follow

Five pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all extremely intelligent, treatrous and selfish (especially the captain). The captain always proposes a distribution of the loot. All pirates vote on the proposal and if at least half of the crew (which includes himself) approve, the loot will be divided as proposal, as no pirates would be willing to take on the captain without superior force on their side. Otherwise he will face a mutiny: all pirates will turn against him and make him walk the plank. The pirates will start over again with the next senior pirate as captain. What's the maximum number of coins the captain can keep without risking his life?

  • ...
    Thái Ninh Nguyễn Phạm 18/07/2018 at 08:44

    hihi mình nha!

    Năm tên cướp biển đã thu được 100 đồng tiền vàng và phải phân chia chiến lợi phẩm. Các hải tặc đều cực kỳ thông minh, treatrous và ích kỷ (đặc biệt là đội trưởng). Đội trưởng luôn đề nghị một bản phân phối của loot. Tất cả các hải tặc biểu quyết về đề nghị này và nếu có ít nhất một nửa số thuyền viên (trong đó bao gồm bản thân) phê duyệt, các chiến lợi phẩm sẽ được phân chia như đề nghị, như là không có hải tặc sẽ sẵn sàng để đưa vào các đội trưởng mà không cần lực lượng vượt trội về phía họ. Nếu không anh sẽ phải đối mặt với một cuộc nổi loạn: tất cả các tên cướp biển sẽ quay lưng lại với anh và làm cho anh ta bước đi trên tấm ván. Các hải tặc sẽ bắt đầu lại một lần nữa với cướp biển cao cấp tiếp theo là đội trưởng. số lượng tối đa của đồng tiền các đội trưởng có thể giữ mà không mạo hiểm cuộc sống của mình là gì?

    Mr Puppy selected this answer.
  • ...
    Việt Anh Nguyễn Đình 10/10/2018 at 13:41

    I don no

  • ...
    Mr Puppy 20/07/2018 at 04:15

    vậy mấy bạn có biết ông thuyền trưởng có thể lấy nhiều nhất bao nhiêu đồng ko nhonhung 


...
Huỳnh Anh Phương
09/07/2018 at 11:13
Votes Answers Follow

Find x; y , know that x and y is postive ỉterger to be satisfied 2 calculations:

1) xy = yx

2) \(x\times y=8\)

 
 
Find x
  • ...
    Lê Quốc Trần Anh Coodinator 13/07/2018 at 04:10

    Because x,y are positive integers and \(x\times y=8\)

    => \(\left\{{}\begin{matrix}x=1;y=8\\x=2;y=4\\x=4;y=2\\x=8;y=1\end{matrix}\right.\)

    Because \(x^y=y^x\)

    => \(\left\{{}\begin{matrix}x=2;y=4\\x=4;y=2\end{matrix}\right.\)

    Huỳnh Anh Phương selected this answer.
  • ...
    Kalila Thao Van 30/01/2019 at 06:05

    i think the first x and y are 2 . the second i don't do it


...
Lê Quốc Trần Anh Coodinator
24/06/2018 at 04:07
Votes Answers Follow

Suppose a regular hexagon has a perimeter equal to the circumference of a circle. What is the ratio of a side of the hexagon to the radius of the circle? Express your answer as a common fraction in terms of π

  • ...
    Nguyễn Mạnh Hùng 24/06/2018 at 08:36

    Call the hexagon's side is x

    the circle's radius is y

    => The hexagon's perimeter is 6x

    The circle's perimeter is 6,28y

    If 6x = 6,28y

    => \(\dfrac{x}{y}=\dfrac{6,28}{6}=\dfrac{3,14}{3}=\dfrac{\Pi}{3}\)

    Selected by MathYouLike

...
Lê Quốc Trần Anh Coodinator
25/06/2018 at 03:07
Votes Answers Follow

Let T be a positive integer whose only digits are 0s and 1s. If X = T ÷ 12, and X is an integer, what is the smallest possible value of X?

  • ...
    Nguyễn Mạnh Hùng 25/06/2018 at 08:07

    We have:

    12 = 3 x 4 

    So T \(⋮12\) <=> T \(⋮3and4\)

    T \(⋮3\Leftrightarrow\)The sum of all the number of T \(⋮3\)

    \(\Leftrightarrow\left(1+1+1+...+1+0+...+0\right)⋮3\)

    But T's sum must be different than 0 

    => The smallest sum must be 3 = 1 + 1 + 1 + 0 + 0 + ... + 0

    T divided by 4 <=> Two-last digit must be divided by 4

    => Two last digits must be 00

    => T = 11100

    It's too big :) 

    Lê Quốc Trần Anh selected this answer.

...
Lê Quốc Trần Anh Coodinator
25/06/2018 at 03:10
Votes Answers Follow

Equilateral triangle ABC has a side length of 6 units. Point D lies on segment BC such that DC = 2(BD). What is the length of the altitude of triangle ADC from point C? Express your answer as a common fraction in simplest radical form.

Mathcounts
  • ...
    Alone 25/06/2018 at 06:54

    A B C D H 6 K

    Draw AK is the altitude of triangle ABC(\(K\in BC\)),the altitude of triangle ADC from point C cut AD at I

    So \(BK=CK=\dfrac{1}{2}BC\)

    Applying Pitago's theorem we have:

     \(AK^2+CK^2=AC^2\Rightarrow AK^2=AC^2-CK^2=AC^2-\left(\dfrac{1}{2}BC\right)^2=6^2-3^2=27\)

    \(\Rightarrow AK=3\sqrt{3}\)\(\Rightarrow S_{ADC}=\dfrac{AK.CD}{2}=\dfrac{3\sqrt{3}.4}{2}=6\sqrt{3}\)

    Because BD+DK=BK \(\Rightarrow DK=BK-BD=3-2=1\)

    Applying Pitago's theorem in triangle ADK we have:

     \(AD^2=AK^2+DK^2=27+1^2=28\)\(\Rightarrow AD=2\sqrt{7}\)

    But \(S_{ADC}=6\sqrt{3}\)\(\Rightarrow\dfrac{AD.CH}{2}=6\sqrt{3}\Rightarrow AD.CH=12\sqrt{3}\Rightarrow CH=\dfrac{12\sqrt{3}}{2\sqrt{7}}=\dfrac{6\sqrt{21}}{7}\)

    Selected by MathYouLike

...
Lê Quốc Trần Anh Coodinator
25/06/2018 at 03:11
Votes Answers Follow

  In trapezoid ABCD, bases AB and CD are 13 and 39 units, respectively. Legs BC and DA are 24 and 10 units, respectively, and sides BC and DA lie on lines that are perpendicular to each other. What is the area of ABCD? 

Mathcounts
  • ...
    Nguyễn Mạnh Hùng 25/06/2018 at 07:40

    13 units 39 units 24 units 10 units E A B D C a b

    Call \(AD\perp BC=\left\{E\right\}\)

    We have: \(a^2+b^2=13^2=169\)(Pythagorean theorem in triangle EAB)

    We also have: 

    \(\left(a+10\right)^2+\left(b+24\right)^2=39^2=1521\)

    \(\Rightarrow a^2+20a+100+b^2+48b+576=1521\)

    \(\Rightarrow a^2+20a+b^2+48b=1521-576-100=845\)

    Because \(a^2+b^2=169\)

    \(\Rightarrow20a+48b=845-169=676\)

    \(\Rightarrow5a+12b=169\)

    \(a^2+b^2=169\)

    => \(\left\{{}\begin{matrix}a^2=5a\\b^2=12b\end{matrix}\right.\)

    \(\Rightarrow a=5;b=12\)

    => DE = 15

    BE = 12 

    => \(S_{DBE}=\dfrac{15.12}{2}=90\left(units^2\right)\)
    \(S_{ABE}=\dfrac{5.12}{2}=30\left(units^2\right)\)

    \(\Rightarrow S_{ABCD}=90-30=60\left(units^2\right)\)

    Lê Quốc Trần Anh selected this answer.

...
Uchiha Sasuke
14/06/2018 at 11:29
Votes Answers Follow

There are 2017 points on the plane. The area of any triangle with verticles does not exceed 1. Assume that in any case, all these points can be placed in a triangle whose area is a positive integer K. Find the least value of K.

Triangle

...
Mr. Bee moderators
25/06/2018 at 02:53
Votes Answers Follow

A polygon is a closed figure whose sides are straight lines. The above figure shows a six-sided polygon (a hexagon). Show that the sum of the angles of a hexagon, \(S^o\), is \(S^o= 540^o\).

Then, show that the generalized formula for the sum of the angles of an n-sided polygon is \(S^o= 180^o(n-2)\).

PolygonIGCSE
  • ...
    Alone 25/06/2018 at 07:10

    A B C D E F

    \(S^o=\)\(\angle\)BAF + \(\angle\)ABC + \(\angle\)BCD + \(\angle\)CDE + \(\angle\)DEF + \(\angle\)EFA

      =\(\angle\)AFB + \(\angle\)BAF + \(\angle\)ABF + \(\angle\)CBF + \(\angle\)BCF + \(\angle\)DCF + \(\angle\)CDF + \(\angle\)EDF + \(\angle\)DEF + \(\angle\)EFD + \(\angle\)CFD + \(\angle\)BFC

     =\(180^o+180^o+180^o+180^o=720^o\)

    Selected by MathYouLike
  • ...
    Mr. Bee moderators 25/06/2018 at 07:31

    Sory, I mistyped. It should've been \(720^o\) not \(540^o.\)


...
Lê Quốc Trần Anh Coodinator
22/06/2018 at 07:36
Votes Answers Follow

A bird collection has exactly four types of birds (eagles, doves, crows and sparrows). The eagles and doves make up 60% of the collection, and the doves and crows make up 20% of the collection. If the 18 crows in the collection represent 5% of the total number of birds, how many of the birds are sparrows? 


...
Lê Quốc Trần Anh Coodinator
22/06/2018 at 07:36
Votes Answers Follow

A 20-foot-high rectangular room has a floor that measures 18’ by 15’. Its doorway measures 3’ by 12’, and its only window measures 7’ by 10’. How many square feet of wall space does the room have?  


...
Lê Quốc Trần Anh Coodinator
22/06/2018 at 07:36
Votes Answers Follow

A square and a circle overlap such that a vertex of the square is at the center of the circle. The 4-inch radius of the circle is one-half the length of a side of the square. What is the area of the portion of the square region that is outside the circular region? Express your answer in terms of π.

  • ...
    A.R.M.Y 09/08/2018 at 15:55

    I don't know I'm sorry but i'm grade 4 =)


...
Lê Quốc Trần Anh Coodinator
11/06/2018 at 02:11
Votes Answers Follow

Prove that the product of three consecutive integers is not a square number.


...
Lê Quốc Trần Anh Coodinator
13/06/2018 at 02:05
Votes Answers Follow

Given \(a^3+b^3=2\) Prove that \(a+b\le2\)

  • ...
    Nguyễn Mạnh Hùng 13/06/2018 at 09:35

    We have:

    \(a^3+b^3=\left(a+b\right)\left(a^2+ab+b^2\right)=2\) (*)

    Other way:

    \(a^2+ab+b^2=a^2+2.\dfrac{1}{2}b+\left(\dfrac{1}{2}b\right)^2+\dfrac{3}{4}b^2\)

    \(=\left(a+\dfrac{1}{2}b\right)^2+\dfrac{3}{4}b^2\)

    Because \(\left(a+\dfrac{1}{2}b\right)^2\ge0\) with \(\forall a,b\)

    \(\dfrac{3}{4}b^2\ge0\) with \(\forall b\)

    So \(\left(a+\dfrac{1}{2}b\right)^2+\dfrac{3}{4}b^2\ge0\) with \(\forall a,b\)

    or \(a^2+ab+b^2\ge0\) with \(\forall a,b\) (**)

    From (*) and (**) we have  \(a+b\le2\)

    Your ex is so hard to do :) 

    Lê Quốc Trần Anh selected this answer.
  • ...
    Lê Thành 23/06/2018 at 05:27

    We have:

    a3+b3=(a+b)(a2+ab+b2)=2a3+b3=(a+b)(a2+ab+b2)=2 (*)

    Other way:

    a2+ab+b2=a2+2.12b+(12b)2+34b2a2+ab+b2=a2+2.12b+(12b)2+34b2

    =(a+12b)2+34b2=(a+12b)2+34b2

    Because (a+12b)2≥0(a+12b)2≥0 with ∀a,b∀a,b

    34b2≥034b2≥0 with ∀b∀b

    So (a+12b)2+34b2≥0(a+12b)2+34b2≥0 with ∀a,b∀a,b

    or a2+ab+b2≥0a2+ab+b2≥0 with ∀a,b∀a,b (**)

    From (*) and (**) we have  a+b≤2a+b≤2

    Your ex is so hard to do :) 


...
Lê Quốc Trần Anh Coodinator
13/06/2018 at 02:07
Votes Answers Follow

Prove that with a,b,c > 0: \(\dfrac{a^2}{b^2}+\dfrac{b^2}{a^2}\ge\dfrac{a}{b}+\dfrac{b}{a}\)


...
Lê Quốc Trần Anh Coodinator
09/06/2018 at 03:41
Votes Answers Follow

In June, Casey counted the months until he would turn 16, the minimum age at which he could obtain his driver’s license. If the number of months Casey counted until his birthday was 45, in what month would Casey turn 16? 


...
Lê Quốc Trần Anh Coodinator
09/06/2018 at 04:36
Votes Answers Follow

Given \(P\left(x\right)+3P\left(2\right)=5x^2\left(\forall x\right)\). Calculate P(3)

  • ...
    Alone 13/06/2018 at 10:16

    With x=2 then \(4P\left(2\right)=5.2^2=20\Rightarrow P\left(2\right)=5\)

    With x=3 then \(P\left(3\right)+3P\left(2\right)=5.3^2=45\Rightarrow P\left(3\right)=45-5.3=30\)

    Lê Quốc Trần Anh selected this answer.

...
Lê Quốc Trần Anh Coodinator
10/06/2018 at 06:31
Votes Answers Follow

Find x,y,z satisfys: \(\dfrac{x}{8}=\dfrac{y}{3}=\dfrac{z}{10}\) and xy + yz + zx = 1206

  • ...
    Alone 14/06/2018 at 01:07

    \(\dfrac{x}{8}=\dfrac{y}{3}=\dfrac{z}{10}\Rightarrow\dfrac{x^2}{64}=\dfrac{xy}{24}=\dfrac{yz}{30}=\dfrac{zx}{80}=\dfrac{xy+yz+zx}{24+30+80}=\dfrac{1206}{134}=9\)

    \(\Rightarrow x^2=64.9=8^2.3^2\Rightarrow x=\pm24\)

    With x=24 then y=24:8.3=9;z=30

    With x=-24 then y=-9;z=-30

    Lê Quốc Trần Anh selected this answer.
  • ...
    Nguyễn Mạnh Hùng 15/06/2018 at 01:35

    We have:

    \(\dfrac{x}{8}=\dfrac{y}{3}=\dfrac{z}{10}\)

    \(\Rightarrow\dfrac{x^2}{64}=\dfrac{xy}{24}=\dfrac{yz}{30}=\dfrac{xz}{80}\)

    Apply the same sequence properties, we have:

    \(\dfrac{x^2}{64}=\dfrac{xy}{24}=\dfrac{yz}{30}=\dfrac{xz}{80}=\dfrac{xy+yz+xz}{24+30+80}=\dfrac{1206}{134}=9\)

    So \(x^2=9.64=576\)\(\Rightarrow x=24\)

    \(\dfrac{xy}{24}=9\Rightarrow xy=24.9=216\Rightarrow y=9\)

    \(\dfrac{yz}{30}=9\Rightarrow yz=270\Rightarrow z=30\)

    So \(\left(x;y;z\right)=\left(24;9;30\right)\)


...
Lê Quốc Trần Anh Coodinator
10/06/2018 at 06:32
Votes Answers Follow

Compare: \(8\sqrt{3}\) with \(5\sqrt{7}\)

  • ...
    Nguyễn Mạnh Hùng 14/06/2018 at 02:22

    We have:

    \(8\sqrt{3}=\sqrt{8^2.3}=\sqrt{64.3}=\sqrt{192}\)

    \(5\sqrt{7}=\sqrt{5^2.7}=\sqrt{25.7}=\sqrt{175}\)

    Because 192>175 so \(\sqrt{192}>\sqrt{175}\)

    or \(8\sqrt{3}>5\sqrt{7}\) 

    Lê Quốc Trần Anh selected this answer.

4694

questions

Weekly ranking

  • ...

    Nguyễn Mạnh Hùng

    This week's point: 1. Total: 139
  • ...

    falcon handsome

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

    Hà Đức Thọ

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

    Account Test

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

    Admin

    This week's point: . Total: 14
  • ...

    demo acc

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

    Nguyen The Thao

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

    acctest

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

    nguyễn ngọc bảo hân

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

    Chibi

    This week's point: . Total: 7

Tags

games 18  double counting 8  generating functions 2  probabilistic method 1  Polynomial 8  inequality 11  area 16  Equation 8  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 6  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 1 
© 2016 MATHYOULIKE
Crafted with by OLM.VN