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Marizza181 [45]
3 years ago
8

Find the 4th term (x-y)^12

Mathematics
1 answer:
maria [59]3 years ago
3 0

Answer:

The fourth term of the expansion is -220 * x^9 * y^3

Step-by-step explanation:

Question:

Find the fourth term in (x-y)^12

Solution:

Notation: "n choose k", or combination of k objects from n objects,

C(n,k) = n! / ( k! (n-k)! )

For example, C(12,4) = 12! / (4! 8!) = 495

Using the binomial expansion formula

(a+b)^n

= C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + C(n,3)a^(n-3)b^3 + C(n,4)a^(n-4)b^4 +....+C(n,n)b^n

For (x-y)^12, n=12, k=3, a=x, b=-y, and the fourth term is

C(n,3)a^(n-3)b^3

=C(12,3) * x^(12-3) * (-y)^(3)

= 220*x^9*(-y)^3

= -220 * x^9 * y^3

You might be interested in
Write the equation for a line perpendicular to y=-3x+18 that goes through the point (-12,6)
Hatshy [7]

Answer:

y=\frac{1}{3} x -14

Step-by-step explanation:

The equation of the line you will find should be in the form y =mx+c , where m is the gradient and c is the y intercept.

The gradient of a line that is perpendicular to a line [of a known gradient] is the negative reciprocal of the gradient of the first. i.e. if a is the known gradient and the perpendicular gradient is b, ab = -1. Therefore the -3b=-1 and b= 1/3

you can now write y = mx +c as y = 1/3x +c

As you have been given a coordinate, you can input these values into y= 1/3x + c

-12 = 1/3(6) +c

-12 - 2 = c

c = -14

hence the equation of the line is y= 1/3x -14

5 0
2 years ago
URGENT!! Need help can someone explain please!!!
forsale [732]

Answer:

The answer to your question is 1 = 69°

Step-by-step explanation:

To solve this problem remember that the sum of the internal angles in a triangle equals 180°.

Let the third angle of the triangle be x.

             39° + 30° + x = 180

Solve for x

             x = 180 - 39 - 30

             x = 111°

Angle x and angle 1 are supplementary so their sum equals 180°.

            111° + 1 = 180

                      1 = 180 - 111

                       1 = 69°      

5 0
2 years ago
Read 2 more answers
Kevin buys
algol [13]

Answer:

1:350 i think

Step-by-step explanation:

i could be wrong

7 0
2 years ago
Read 2 more answers
What are the coordinates of R' for the dilation D(0.5. p)(PQRS)?
11111nata11111 [884]

Answer:

R' = (-1,-0.5)

Step-by-step explanation:

See attachment for complete question.

From the attachment:

P = (-3,-3)

R = (1,2)

Dilation:

D_{(0.5,P)}

Required

Determine R'

First, subtract the coordinates of P from R. This means that R is measured from P.

R = (1-(-3),2-(-3))

R = (1+3,2+3)

R = (4,5)

Next, apply dilation factor 0.5

R' = R * 0.5

R' = (4,5) * 0.5

R' = (4* 0.5,5* 0.5)

R' = (2,2.5)

Lastly, measure R' from the origin by adding the coordinates of P to R'

R' = (2+(-3),2.5+(-3))

R' = (2-3,2.5-3)

R' = (-1,-0.5)

6 0
2 years ago
Answer please it’s due tomorrow I just need the four in the middle I’m really bad at math...
m_a_m_a [10]

Answer:

Number 2: 126

Number 3: 128

Number 4: 75

Number 5: 204

Step-by-step explanation:

7 0
3 years ago
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