It looks like the given equation is
sin(2x) - sin(2x) cos(2x) = sin(4x)
Recall the double angle identity for sine:
sin(2x) = 2 sin(x) cos(x)
which lets us rewrite the equation as
sin(2x) - sin(2x) cos(2x) = 2 sin(2x) cos(2x)
Move everything over to one side and factorize:
sin(2x) - sin(2x) cos(2x) - 2 sin(2x) cos(2x) = 0
sin(2x) - 3 sin(2x) cos(2x) = 0
sin(2x) (1 - 3 cos(2x)) = 0
Then we have two families of solutions,
sin(2x) = 0 or 1 - 3 cos(2x) = 0
sin(2x) = 0 or cos(2x) = 1/3
[2x = arcsin(0) + 2nπ or 2x = π - arcsin(0) + 2nπ]
… … … or [2x = arccos(1/3) + 2nπ or 2x = -arccos(1/3) + 2nπ]
(where n is any integer)
[2x = 2nπ or 2x = π + 2nπ]
… … … or [2x = arccos(1/3) + 2nπ or 2x = -arccos(1/3) + 2nπ]
[x = nπ or x = π/2 + nπ]
… … … or [x = 1/2 arccos(1/3) + nπ or x = -1/2 arccos(1/3) + nπ]
I’ve done these questions before and i’ve gotten confused because I have trouble with nagative numbers but i’ve gotten better st it. It’s -5
Answer: 0.4512
Step-by-step explanation:
A bit string is sequence of bits (it only contains 0 and 1).
We assume that the 0 and 1 area equally likely to any place.
i.e. P(0)= P(1)= 
The length of bits : n = 10
Let X = Number of getting ones.
Then , 
Binomial distribution formula : 
, where p= probability of getting success in each event and q= probability of getting failure in each event.
Here , 
Then ,The probability that a bit string of length 10 contains exactly 4 or 5 ones.
Hence, the probability that a bit string of length 10 contains exactly 4 or 5 ones is 0.4512.
The value of y from the expression is y = 3/2(j-k)
<h3>Subject of formula</h3>
Given the expression below
2/3y + k = j.
Subtract k from both sides
2/3y = j - k
Divide both sides by 2/3
(2/3y)/2/3 = (j-k)/(2/3)
y = 3/2(j-k)
Hence the value of y from the expression is y = 3/2(j-k)
Learn more on subject of formula here; brainly.com/question/657646
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(1,000,000 centimeters) x (1 skewer/30centimeters) =
1,000,000 /30 skewers = 33,333 whole skewers,
plus one piece of one more skewer
cut into 3 equal pieces with the other
two pieces discarded.
Another way to look at it: <em>33,334 skewers</em>,
with 2/3 of one of them not included.
