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
The second side of a triangular deck is 4 feet longer than the shortest side
(s+4) = the 2nd side
and a third side that is 4 feet shorter than twice the length of the shortest side.
(2s-4) = the 3rd side
If the perimeter of the deck is 48 feet, what are the lengths of the three sides?
s + (s+4) + (2s-4) = 48
Combine like terms
s + s + 2s + 4 - 4 = 48
4s = 48
s = 48/4
s = 12 ft is the shortest side
I'll let you find the 2nd and 3rd sides, ensure they add up to 48
Hope this helps!
The height of the model is 6.1 inches.
If 1 inch represents 50 feet, to find the answer, divide 305/50.
the answer is 6.1 inches.
Hope this helps, and have a fantastic day.
You can use proportions in all of these as I explained in another one of your questions. I'll post the answers if you still want them.
