Answer:
176 books
Step-by-step explanation:
Let's call the number of fiction books 'F', and the number of non-fiction books 'N'. Then, we can write the following system of equations:
eq1:
eq2:
Using the 'F' value from the first equation, we have:
The total number of books is:
<span>6n+12=2n+36
We move all terms to the left:
6n+12-(2n+36)=0
We get rid of parentheses
6n-2n-36+12=0
We add all the numbers together, and all the variables
4n-24=0
We move all terms containing n to the left, all other terms to the right
4n=24
n=24/4
n=6</span>
I think we can use the identity sin x/2 = sqrt [(1 - cos x) /2]
cos x - sqrt3 sqrt ( 1 - cos x) /sqrt2 = 1
cos x - sqrt(3/2) sqrt(1 - cos x) = 1
sqrt(3/2)(sqrt(1 - cos x) = cos x - 1 Squaring both sides:-
1.5 ( 1 - cos x) = cos^2 x - 2 cos x + 1
cos^2 x - 0.5 cos x - 0.5 = 0
cos x = 1 , -0.5
giving x = 0 , 2pi, 2pi/3, 4pi/3 ( for 0 =< x <= 2pi)
because of thw square roots some of these solutions may be extraneous so we should plug these into the original equations to see if they fit.
The last 2 results dont fit so the answer is x = 0 , 2pi Answer
