Answer:
c
Step-by-step explanation:
Use the double angle identity:
sin(2<em>x</em>) = 2 sin(<em>x</em>) cos(<em>x</em>)
Now rewrite
sin(2<em>x</em>) sin(<em>x</em>) + cos(<em>x</em>) = 0
as
2 sin²(<em>x</em>) cos(<em>x</em>) + cos(<em>x</em>) = 0
Factor out cos(<em>x</em>) :
cos(<em>x</em>) (2 sin²(<em>x</em>) + 1) = 0
Consider the two cases,
cos(<em>x</em>) = 0 OR 2 sin²(<em>x</em>) + 1 = 0
Solve for cos(<em>x</em>) and sin²(<em>x</em>) :
cos(<em>x</em>) = 0 OR sin²(<em>x</em>) = -1/2
Squaring a real number always gives a non-negative number, so the second case doesn't offer any real solutions. We're left with
cos(<em>x</em>) = 0
Cosine is zero for odd multiples of <em>π</em>/2, so we have
<em>x</em> = (2<em>n</em> + 1) <em>π</em>/2
where <em>n</em> is any integer.
Answer:
There is no mode
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
I'm going to solve this question by expanding the logarithm (note that you can also solve this equation by solving for a, b, and c)
We know the following
Which means we can split the numerator into
We also know that
Which means that we can rewrite the following as
We can evaulate this and get
-1+12= 11
for the numerator
Now we need to take care of the denominator
we know the following
which means that we have
11-2log(a)
solve and get
11-2
9