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Min Hoang moderators
16/03/2017 at 10:24
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A circle was inscribed within the triangle ABC. The circle is tangent to AB at point M with AM = 10 and MB = 6. The area of triangle ABC is \(120\sqrt{3}\) .

a) Find the perimeter of triangle ABC.

b) Find the measure of angle A.

Circle

  • ...
    mathlove 16/03/2017 at 19:06

    We have  \(AB=AM+BM=10+6=16;BC=BN+CN=6+x;CA=CP+AP=x+10\).

    The triangle ABC has his edges   \(a=10+6=16;b=6+x;c=x+10\) . Call  \(p\)  is the halp perimeter of \(ABC\) then  \(p-a=10,p-b=6,p-c=x\) and the area of ABC is

                                          \(\sqrt{p\left(p-a\right)\left(p-b\right)\left(p-c\right)}=\sqrt{60x\left(16+x\right)}\) .

    By the assumptions we have    \(60x\left(x+16\right)=\left(120\sqrt{3}\right)^2\Leftrightarrow x^2+16x-720=0\Leftrightarrow x\in\left\{20;-36\right\}\).

    So, \(x=20;p=36\), the perimeter of  ABC is  72.

    Suppose CH is the height of CAB, then \(CH=\dfrac{2.120\sqrt{3}}{16}=15.\)  The triangle CHA has

                                      \(CHA=90^0;CH=15;CA=30\Rightarrow A=60^0\). 

    The measure of angle A is    \(60^0\) .

    Selected by MathYouLike
  • ...
    FA KAKALOTS 03/02/2018 at 12:37

    We have  AB=AM+BM=10+6=16;BC=BN+CN=6+x;CA=CP+AP=x+10

    .

    The triangle ABC has his edges   a=10+6=16;b=6+x;c=x+10

     . Call  p  is the halp perimeter of ABC then  p−a=10,p−b=6,p−c=x

     and the area of ABC is

                                          √p(p−a)(p−b)(p−c)=√60x(16+x)

     .

    By the assumptions we have    60x(x+16)=(120√3)2⇔x2+16x−720=0⇔x∈{20;−36}

    .

    So, x=20;p=36

    , the perimeter of  ABC is  72.

    Suppose CH is the height of CAB, then CH=2.120√316=15.

      The triangle CHA has

                                      CHA=900;CH=15;CA=30⇒A=600

    . 

    The measure of angle A is    600

     .


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HỦY DIỆT THE WORLD
09/02/2018 at 21:26
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solution of the equation : \(\dfrac{x+2}{89}+\dfrac{x+5}{86}>\dfrac{x+8}{83}+\dfrac{x+11}{80}\)

Operation of Indices

  • ...
    FA KAKALOTS 09/02/2018 at 21:34

    We have :

    \(=\dfrac{x+2}{89}+1+\dfrac{x+5}{86}+1>\dfrac{x+8}{83}+1+\dfrac{x+11}{80}+1\)

    \(=\dfrac{x+91}{89}+\dfrac{x+91}{86}>\dfrac{x+91}{83}+\dfrac{x+91}{80}\)

    \(=\dfrac{x+91}{89}+\dfrac{x+91}{86}-\dfrac{x+91}{83}-\dfrac{x+91}{80}>0\)

    \(=\left(x+91\right)\left(\dfrac{1}{89}+\dfrac{1}{86}-\dfrac{1}{83}-\dfrac{1}{80}\right)>0\)

    To \(\dfrac{1}{89}+\dfrac{1}{86}-\dfrac{1}{83}-\dfrac{1}{80}\) different 0


    \(=x+91>0\)

    \(=x< -91\)

    HỦY DIỆT THE WORLD selected this answer.
  • ...
    Fc Alan Walker 10/02/2018 at 14:16

    e have :

    =x+289+1+x+586+1>x+883+1+x+1180+1

    =x+9189+x+9186>x+9183+x+9180

    =x+9189+x+9186−x+9183−x+9180>0

    =(x+91)(189+186−183−180)>0

    To 189+186−183−180

    different 0


    =x+91>0

    =x<−91


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Min Hoang moderators
16/03/2017 at 11:12
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Mrs Taylor decided to buy bags for her two daughters. She bought her older daughter a black bag for 18.03 dollars , and she bought her younger daughter a green bag for 19.94 dollars. How much did she spend in all?

Decimal number

  • ...
    Nguyễn Thị Thu Thủy 17/05/2017 at 12:17

    The amount of money she spends in all is:

    18.03 + 19.94 = 37.97 (dollars)

  • ...
    Nguyễn Phương Linh 24/03/2017 at 21:52

    The amount of money she spends in all is:

    18.03 + 19.94 = 37.97 (dollars)

                            

  • ...
    Kudo Shinichi 22/03/2017 at 22:10

    She spent in all : 18,03 + 19,94 = 37.97 ( dollars )

    ......

    mình nha


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Carter
13/04/2017 at 08:43
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Two armies are advancing towards each other, each one at 1 mph. A messenger leaves the first army when the two armies are 10 miles apart and runs towards the second at 9 mph. Upon reaching the second army, he immediately turns around and runs towards the first army at 9 mph. How many miles apart are the two armies when the messenger gets back to the first army?

  • ...
    An Duong 17/04/2017 at 08:26

    The messenger reaches the second army after : 10/(9 +1) = 1 hour.

    At the time of the messenger leaving the second army, the distance between him and the first army is:  10 - 2.1 = 8 miles.

    The messenger meets the first army after 8/(9 + 1) = 0.8 hours more.

    When the messenger gets back to the first army, two armies take 1 + 0.8 = 1.8 hours.

    And the distance between two armies is : 10 - (1 + 1) 1.8 = 6.4 miles.


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Đỗ Duy Mạnh
13/04/2017 at 18:24
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Bài 1 : Find x

x : 3 : 2 = 9

 

number

  • ...
    Ngu Ngu Ngu 13/04/2017 at 22:23

    \(x\div3\div2=9\)

    \(\Rightarrow x=9.3.2\)

    \(\Rightarrow x=54\)

    Vậy \(x=54\) thì thỏa mãn

  • ...
    Trần Quỳnh Anh 28/12/2017 at 13:10

    x:3:2=9

    \(\Leftrightarrow x=9.2.3\)

    \(\Leftrightarrow x=54\)

    So the answer is 54

  • ...
    Nguyễn Huy Quân 16/04/2017 at 16:17

    X : 3 : 2 = 9

    X : 3 = 9 x 2

    X : 3 = 18

    X = 18 x 3

    X = 54


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Help you solve math
01/01/2018 at 10:37
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Cho mk nói tiếng việt

Dạo này bạn FA Liên Quân Garena đã đánh dấu rất nhiều mong CLOUD giải quyết hộ em để không có lỗi gian lận trong học tập để lấy giải thưởng và cũng mong FA Liên Quân Garena bỏ tính tự đánh dấu đi

Ai có ý kiến gì bình luận ở dưới

Em chân thành cảm ơn

 

  • ...
    Help you solve math 01/01/2018 at 10:52

    FA Liên Quân Garena còn mắc 1 lỗi đó là copy bài của người khác như 1 người ngu

    Bạn làm như vậy rồi sẽ bị cloud khóa nick thôi

    Tuy cách đây 2 tháng mk có tự nhưng giờ mk bỏ rồi không làm như vậy nữa

  • ...
    Phan Thanh Tịnh 02/01/2018 at 19:26

    thấy chưa vừa chửi đó luôn 

  • ...
    FA Liên Quân Garena 01/01/2018 at 10:47

    thằng cho Help you solve math .


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Kaya Renger Coordinator
16/08/2017 at 15:01
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Prove that with n is a positive number : \(\sqrt[3]{\left(n+1\right)^2}-\sqrt[3]{n^2}< \dfrac{2}{3\sqrt[3]{n}}< \sqrt[3]{n^2}-\sqrt[3]{\left(n-1\right)^2}\)


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Tran Nhat Quynh
19/04/2017 at 11:35
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2
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There are 2562 fifth graders taking the National Violympic Competition. Of which the number of students who won the silver medal was twice that of the gold medal, the number of students who won the bronze medal was twice the number of the silver medalists, the number of students who were twice the number of students recommended. Won the bronze medal and the number of unsatisfactory students was 1602. Know that 12.5% of the students won the gold medal with an absolute score of 300 points. Ask how many students have 300 points?

  • ...
    Trần Nhật Quỳnh 19/04/2017 at 11:38

    Number of prize winners: 2562 - 1602 = 960 (you)
    Call a number of Gold Medal students
    Because: The number of Silver medal students is twice the number of Gold medal students, the number of Bronze medal students twice the number of Silver medal students, Won the bronze medal. Inference: The number of Gold Medal students is:
    A + 2a + 4a + 8a = 960
    15a = 960
    A = 960: 15
    A = 64
    Because: There are 12.5% of the students winning the gold medal has an absolute score of 300 points. Find out: The number of Gold medalists scoring an absolute 300 points is: 64 x 12.5: 100 = 8 (you)

    Tran Nhat Quynh selected this answer.
  • ...
    Trần Nhật Quỳnh 19/04/2017 at 11:38

    Number of prize winners: 2562 - 1602 = 960 (you)
    Call a number of Gold Medal students
    Because: The number of Silver medal students is twice the number of Gold medal students, the number of Bronze medal students twice the number of Silver medal students, Won the bronze medal. Inference: The number of Gold Medal students is:
    A + 2a + 4a + 8a = 960
    15a = 960
    A = 960: 15
    A = 64
    Because: There are 12.5% of the students winning the gold medal has an absolute score of 300 points. Find out: The number of Gold medalists scoring an absolute 300 points is: 64 x 12.5: 100 = 8 (you)


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Vũ Mạnh Hùng
05/12/2017 at 19:48
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abcd*2 =dcba

dcba can disivible 2,5,11 or 3

 


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Megumi Kato
26/03/2017 at 12:07
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The distance between John’s home and the park is 3000m. John walked from his home to the park at a speed of 100m per minute and then walked back home at a speed of 150m per minute. What is the John’s average speed in meter per minute? 

  • ...
    Megumi Kato 26/03/2017 at 12:08

    The distance between the houses is: 3000: 100 = 30 (minute)
    Homeownership is: 3000: 150 = 20 (minutes)
    Average by John in a minute: 3000: (20 + 30) = 60 (minute)
    Answers:60 minute

  • ...
    Megumi Kato 26/03/2017 at 12:07

    The distance between the houses is: 3000: 100 = 30 (minute)
    Homeownership is: 3000: 150 = 20 (minutes)
    Average by John in a minute: 3000: (20 + 30) = 60 (minute)
                                                  Answers:60 minute

  • ...
    Kathryn Bernardo 29/03/2017 at 07:46

    The distance between the houses is: 3000: 100 = 30 (minute)
    Homeownership is: 3000: 150 = 20 (minutes)
    Average by John in a minute: 3000: (20 + 30) = 60 (minute)
                                                  Answers:60 minute


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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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