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2 years ago

helppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp

Mathematics

1 answer:

Alex787 [66]2 years ago

6 0

B then C
i have a 20 character limit so i’m just typin here

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2 years ago

Expand (2x+2)^6<br> How would you find the answer using the binomial theorem?

Yanka [14]

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Step-by-step explanation:

$\displaystyle\\\sum\limits _{k=0}^n\frac{n!}{k!*(n-k)!}a^{n-k}b^k .\\\\k=0\\\frac{n!}{0!*(n-0)!}a^{n-0}b^0=C_n^0a^n*1=C_n^0a^n.\\\\ k=1\\\frac{n!}{1!*(n-1)!} a^{n-1}b^1=C_n^1a^{n-1}b^1.\\\\k=2\\\frac{n!}{2!*(n-2)!} a^{n-2}b^2=C_n^2a^{n-2}b^2.\\\\k=n\\\frac{n!}{n!*(n-n)!} a^{n-n}b^n=C_n^na^0b^n=C_n^nb^n.\\\\C_n^0a^n+C_n^1a^{n-1}b^1+C_n^2a^{n-2}b^2+...+C_n^nb^n=(a+b)^n.$

$\displaystyle\\(2x+2)^6=\frac{6!}{(6-0)!*0!} (2x)^62^0+\frac{6!}{(6-1)!*1!} (2x)^{6-1}2^1+\frac{6!}{(6-2)!*2!}(2x)^{6-2}2^2+\\\\ +\frac{6!}{(6-3)!*3!} (2a)^{6-3}2^3+\frac{6!}{(6-4)*4!} (2x)^{6-4}b^4+\frac{6!}{(6-5)!*5!}(2x)^{6-5} b^5+\frac{6!}{(6-6)!*6!}(2x)^{6-6}b^6. \\\\$

$(2x+2)^6=\frac{6!}{6!*1} 2^6*x^6*1+\frac{5!*6}{5!*1}2^5*x^5*2+\\\\+\frac{4!*5*6}{4!*1*2}2^4*x^4*2^2+ \frac{3!*4*5*6}{3!*1*2*3} 2^3*x^3*2^3+\frac{4!*5*6}{2!*4!}2^2*x^2*2^4+\\\\+\frac{5!*6}{1!*5!} 2^1*x^1*2^5+\frac{6!}{0!*6!} x^02^6\\\\(2x+2)^6=64x^6+384x^5+960x^4+1280x^3+960x^2+384x+64.$

8 0

1 year ago

How do I solve this question I’ve been stuck on this since last night

meriva

Observation one

From the markings on the diagram <1 = 60o The left triangle is at least isosceles. Therefore equal sides produce equal angles opposite them.

Now we have accounted for 2 angles that are equal (each is 60 degrees) and add up to 120 degrees. The third angle (angle 2) is found from this equation.

<1 + 60 + <2 = 180 degrees. All triangles have 180 degrees.

60 + 60 + <2 = 180

Observation 2

<2 = 60 degrees.

120 + <2 = 180

m<2 = 180 - 120

m<2 = 60 degrees.

Observation 3

m<3 = 120

<2 and <3 are supplementary.

Any 2 angles on the same straight line are supplementary

60 + <3 = 180

<3 = 180 - 60

<3 = 120

Observation 4

m<4 = 40 degrees.

All triangles have 180 degrees. No exceptions.

m<4 + 20 +m<3 = 180

m<4 + 20 + 120 = 180

m<4 + 140 = 180

m<4 = 180 - 140

m<4 = 40

8 0

2 years ago