We have the equations:
<span>C(n,k) / C(n,k+1) = 1/2
</span>C(n,k+1) / C(n, k+2) = 2/3<span>
</span>[n! / (n-k)!k! ]/[ <span>n! / (n- (k+1))! (k+1)! ]= 1/2
You can cancel out similar terms. The definition of factorials is this
n! = n(n -1)(n -2)(n -3)...1
So,
</span> (n- (k+1))! (k+1)! / (n-k)!k! = 1/2
(n- k - 1)(n - k - 1 -1)! (k+1)(k + 1 - 1)! / (n-k)!k! = 1/2
(n- k - 1)(n - k - 2)! (k+1)(k)! / (n-k)!k! = 1/2
Cancel out terms.
(n- k - 1)(n - k - 2)! (k+1)/ (n-k)!= 1/2 [eqn 1]
[n! / (n-k+1)!(k+1)! ]/[ n! / (n- (k+2))! (k+2)! ]= 2/3
(n- (k+2))! (k+2)! / (n-(k+1))!(k+1)! = 2/3
(n- k-2)! (k+2)! / (n-k-1)!(k+1)! = 2/3
(n- k-2)(n - k -3)! (k+2)( k+1)k! / (n-k-1)(n-k-2)(n-k-3)!(k+1)k! = 2/3
Cancel out terms
(k+2)/ (n-k-1) = 2/3
You can solve for n in terms of k and substitute this to the fist equation which will allow you to solve for k.
Answer:
1-342.1
2-557.2
3-285.2
4-201.6
5-33.1
6-6
7-356.4
8-1000
Step-by-step explanation:
Answer:
PEMDAS
Step-by-step explanation:
(VERY SIMPLE)
Answer:
The longer leg is opposite the 60, so to get the shorter leg you have to divide by \sqrt{3}
18 / \sqrt{3} = 6 \sqrt{3}
The volume of any prism is given by
.. V = Bh . . . . B is the area of the base, h is the height
You have
.. 300 = B*3
.. 300/3 = B = 100
The area of the base is 100 square units.