The Binomial Expansion of 2x3 5 is a mathematical formula that allows us to expand a binomial expression in the form (ax + b)n into a summation of terms. It is often used to simplify long algebraic equations or to calculate the probability of certain events. The formula is given as: Answer: (ax + b)n = Σk=0n (n\k)an-kbk
Related Video:
Questions and Answers:
1. what is the expansion of x^2+2xy+y^2
like that, insyaAllahx² + 2xy + y² is the expansion from :
= (x + y)(x + y)
= (x + y)²
proof can be seen from the picture above
2. what is the binomial name of pine tree
Penjelasan:
Pinus
A pine is any conifer in the genus Pinus (/ˈpiːnuːs/) of the family Pinaceae. Pinus is the sole genus in the subfamily Pinoideae.
Pine.
Pine treeOrder:Pinales
Family:Pinaceae
Subfamily:Pinoideae
Genus:Pinus L.
3. 1. What is Expansion of Heat??
Jawaban:
expansion of shape due to heat (pemuaian)
Penjelasan:
maaf kalo salah
4. one of the factors driving the ground of the pharmaceutical industry is the expansion of membership coverage from JKN or BPJS . according to your opinion what are the advantages and disadvantages become JKN or BPJS member ?
the advantages of being the member bpjs is we can get the easier in payment for the hospital
disadvantages we dont get a satisfying service from the hospital
5. Find the expansion of( 2x -1/x)^5 Hence find the coefficient of x in the expansion of (1+3x^2) (2x-1/x)^5
Find the expansion of
[tex](2x-\frac{1}{x} )^5[/tex]
the coefficient of [tex]x^5[/tex] is [tex]C(5,5)\times2^5\times(-1)^0=1\times32\times1=32[/tex]
the coefficient of [tex]x^3[/tex] is [tex]C(5,4)\times2^4\times(-1)^1=5\times16\times(-1)=-80[/tex]
the coefficient of [tex]x[/tex] is [tex]C(5,3)\times2^3\times(-1)^2=10\times8\times1=80[/tex]
the coefficient of [tex]\frac{1}{x}[/tex] is [tex]C(5,2)\times2^2\times(-1)^3=10\times4\times(-1)=-40[/tex]
the coefficient of [tex]\frac{1}{x^3}[/tex] is [tex]C(5,1)\times2^1\times(-1)^4=5\times2\times1=10[/tex]
the coefficient of [tex]\frac{1}{x^5}[/tex] is [tex]C(5,0)\times2^0\times(-1)^5=1\times1\times(-1)=-1[/tex]
so, [tex](2x-\frac{1}{x} )^5=32x^5-80x^3+80x-\frac{40}{x} +\frac{10}{x^3} -\frac{1}{x^5}[/tex]
will look for the coefficient of [tex]x[/tex] in the expansion of
[tex](1+3x^2)(2x-\frac{1}{x} )^5[/tex]
since [tex]x=x^2\times\frac{1}{x}[/tex], the coefficient is
[tex]k=1\times80+3\times(-40)=-40[/tex]
6. A steel bar has length of 3 × 10² m, heated from 20°C to 120°C. If the length coefficient expansion is 1,2 × 10^-5 / °C and the length of steel to be affected by the first length, temperature changing and length linear coefficient expansion. Calculate the length of the end of the steel!
Materi: Pemuaian <<<<<<<<<Lo = 3 x 10² m
Δt = 120°C - 20°C = 100°C
α = 1,2 x 10⁻⁵/°C
Lt = ... ?
Problem solving:
Lt = Lo (1 + α x Δt)
Lt = 3 x 10² (1 + 1,2 x 10⁻⁵ x 100)
Lt = 3 x 10² (1 + 1,2 x 10⁻³)
Lt = 3 x 10² (1 + 0,0012)
Lt = (3 x 10²)(1,0012)
Lt = 300,36 m
7. The coefficient of x² in the expansion of (4 + ax)(1 + x/2)⁶ is 3. Find the value of the constant a.
[tex]a = - 4[/tex]
STEP :[tex]( {x + y})^{6} = {x}^{6} + 6 {x}^{5} y + 15 {x}^{4} {y}^{2} + 20 {x}^{3} {y}^{3} + 15 {x}^{2} {y}^{4} + 6 x {y}^{5} + {y}^{6} [/tex]
[tex](4 + ax)( {1 + \frac{x}{2} })^{6} = [/tex]
[tex](4 + ax) ({1}^{6} + 6( {1})^{5}( \frac{x}{2}) + 15( {1})^{4} ( {\frac{x}{2}})^{2} + 20( {1})^{3} ( {\frac{x}{2}})^{3} + 15( {1})^{2} ( {\frac{x}{2}})^{4} +6( {1}) ( {\frac{x}{2}})^{5} + ( {\frac{x}{2}}^{6} ) )[/tex]
[tex] = (4 + ax)(1 + 3x + \frac{15 {x}^{2} }{4} + \frac{ 20{x}^{3} }{8} + \frac{ 15{x}^{4} }{16} + \frac{ 6{x}^{5} }{32} + \frac{ {x}^{6} }{64} )[/tex]
unit that contains x² is :
[tex] = 4( \frac{15 {x}^{2} }{4} ) + ax(3x)[/tex]
[tex]= 15 {x}^{2} + 3a {x}^{2} [/tex]
[tex] = (15 + 3a) {x}^{2} [/tex]
The coefficient of x² is 3, so :
[tex]15 + 3a = 3[/tex]
[tex]3a = 3 - 15[/tex]
[tex]3a = - 12[/tex]
[tex]a = - 4[/tex]
8. Using the general binomial expansion expand thefollowing expressionsa. (x-3)⁴
Jawaban:
x⁴ + 36x² + 81
Penjelasan dengan langkah-langkah:
(x - 3) ( x-3) = x² - 6x + 9
(x² - 6x + 9) (x² - 6x + 9)
= x⁴ + 36x² + 81
9. Write 5 terms in the expansion (2x − 3y)⁴
Jawab:
Penjelasan dengan langkah-langkah:
The expansion of (2x - 3y)⁴ is a polynomial with the sum of multiple terms, each of them with different degrees and coefficients. The term of a polynomial refers to each element of the polynomial, it can be a constant, a variable with a coefficient, or a combination of variables with coefficients.
To find the terms of the expansion of (2x - 3y)⁴, we can use the binomial theorem:
(2x - 3y)⁴ = (2x - 3y)(2x - 3y)(2x - 3y)(2x - 3y)
= (2x)⁴ - 4(2x)³(3y) + 6(2x)²(3y)² - 4(2x)(3y)³ + (3y)⁴
So the terms in the expansion of (2x - 3y)⁴ are:
(2x)⁴ = 16x⁴
-4(2x)³(3y) = -48x³y
6(2x)²(3y)² = 216x²y²
-4(2x)(3y)³ = -144xy³
(3y)⁴ = 81y⁴
So the expansion of (2x - 3y)⁴ is :
(2x - 3y)⁴ = 16x⁴ - 48x³y + 216x²y² - 144xy³ + 81y⁴
10. What was the role of geography in Rome’s expansion and growth? Explain
Jawaban:
of Geography
Penjelasan:
Rome's location on the Italian peninsula, and the Tiber River, provided access to trade routes on the Mediterranean Sea. ... As the empire continued to expand, it became difficult for farmers in Rome to produce enough food to meet the demand of the growing population.
11. What is a correct way of naming an organism using the binomial system?
Jawaban:
Scientific Names
Scientists use a two-name system called a Binomial Naming System. Scientists name animals and plants using the system that describes the genus and species of the organism. The first word is the genus and the second is the species. The first word is capitalized and the second is not.
12. if the area expansion coefficient of iron is 0.000024/c, the volume expansion coeffcient of iron is
Jawaban:
The volume expansion coefficient of iron is 0.000072/°C.
Bantu dan apresiasi penjawab dengan mengunjungi dan mengeksplorasi situs web sodiqi .com
13. An ideal gas 1mol is kept at 0C during expansion from 2L to 8L . Find the amount of work done on the gas during expansion
Jawaban:
Gas ideal 1 mol dijaga pada 0C selama ekspansi dari 2L ke 8L. Hitunglah usaha yang dilakukan gas selama pemuaian.
14. If the coofficien linier expansion of copper is 0.00007 dc calculate the amount of space Carea) expansion of copperpake , given , ask ama solving oke
Penjelasan dengan langkah-langkah:
given:
[tex] \alpha = 7 \times {10}^{ - 5} \\ [/tex]
asked:
[tex]dx = ...[/tex]
solving:
[tex]dx = 2\alpha \times dt \times x \\ = 14 \times {10}^{ - 5 } \times dt \times x[/tex]
where dx is the amount of expansion, dt is the difference in temperatures, 2alpha is the area coefficient, and x is the starting length
15. A metal bar is 100cm long. Change length 0,11cm if temperature change 90°C. What is the coefficient of linear expansion metal
Jawaban:
The coefficient of linear expansion of metal is 0.11 cm/°C.
Bantu dan apresiasi penjawab dengan mengunjungi dan mengeksplorasi situs web sodiqi .com
16. At 30℃ the volume of an aluminum sphere is 30 cm3. The coefficient of volume expansion is 72 x 10 -6℃. If the final volume is 30.5 cm3, what is the final temperature of the aluminum sphere? A.231,48 ℃ B.201,48 ℃ C.261,48 ℃ D.216,48 ℃
Jawaban:
C. 261,48 C
Penjelasan:
maaf kalo salah
Jawaban:
nomer 12 ap
C. 261.48°C
17. The volume of a glass at a temperature of 20 C is 500ML if the length expansion coefficient of the glass is 0.00009/C, then the volume of the glass at a temperature of 75C is
Jawaban:
Vo = 500 ml = 500 cm³
To = 20°C
koef muai panjang gelas = 9 × 10^-5/°C
T = 75°C
V?
V = Vo ( 1 + 3. koef. gelas × ∆T)
= 500 (1 + 3 × 0.00009 × (75-20))
= 500 (1 + 0.00027 × 55)
= 507.425 cm³= 507.425 ml
18. a copper bar at 10c is 100m long, then it heated up to 150c. determine the length expansion of that copper bar during the heated progress if its expansion coefficient is 0.000017
Jawaban:
The length expansion of the copper bar during the heated process would be 0.17 m.
Bantu dan apresiasi penjawab dengan mengunjungi dan mengeksplorasi situs web sodiqi .com
19. . A metal is 20 cm in length, if the linear expansion coefficient of the metal is 0,000017/°C. What temperature change is needed in order to make the copper expand 0,08 cm?bantu jawab kak
Penjelasan:
Perubahan suhu sebesar 235⁰C
Lo = 20 cm
@ = 0,000017/⁰C
∆L = 0,08 cm
dit. perubahan suhu ∆T?
jawab :
∆L = Lo x @ x ∆T
0,08 = 20 x 0,000017 x ∆T
0,08 = 0,00034 ∆T
∆T = 0,08/0,00034
∆T = 235 (dengan pembulatan)
20. A train track which is made of steel has length of 500 m on 00C. How long is its expansion if it is heated until 400C? The coefficient of length expansion of steel is 1.3 x 10-5/0C.
Penjelasan dengan langkah-langkah:
cmiiw yaaa hope it helps