Answer:
Step-by-step explanation:
Since it is an equilaterla triangle, we can see the side opposite to that of side length 4 is 60 degrees. Since the other angle is a right angle (90 degrees), we can find that the other side is 30 degrees (the degrees add up to 180). We can also see that this is a 30-60-90. We can see that the side x, through the identity (you can find 30-60-90 identity online), we see that the side x is . However, it is also asking us to simplify this, so we multiply the top and bottom by and get
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:
B just b
Step-by-step explanation:
Answer:
b and c
Step-by-step explanation:
Answer:
I think it's s
Step-by-step explanation:
I think it's set equation.