Rewrite as a simplified fraction3.83 =
2 answers:
Answer:
3 83/100
Step-by-step explanation:
Hello Applebannana11!
Let's take a slower more simple approach first.
Since the places for decimals are ten() and hundred(
), we can see that it is going to be
.
Since, 3 is our whole digit, it will be the first thing.
3 .
Now, we check if can be simplified.
We see the GCF of and
is 1.
Therefore, cannot be simplified.
Since we don't need to simplify 3, our final answer is .
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Important formula we will use.
First formula
2 cos α sin β = sin (α + β) - sin (α - β)
Second formula
∫ sin x dx = - cos x + c
We should change the trigonometry expression from multiplication into addition. Use the first formula above
∫ 8 sin (2x) cos (3x) dx
= ∫ 4 ( 2 sin (2x) cos (3x) dx)
= 4 ∫ 2 cos (3x) sin (2x) dx
= 4 ∫ sin (3x + 2x) - sin (3x - 2x) dx
= 4 ∫ sin 5x - sin x dx
After changing into addition, solve the integration. Use the second formula.
= 4 ∫ sin 5x - sin x dx
This is the answer.
First formula
2 cos α sin β = sin (α + β) - sin (α - β)
Second formula
∫ sin x dx = - cos x + c
We should change the trigonometry expression from multiplication into addition. Use the first formula above
∫ 8 sin (2x) cos (3x) dx
= ∫ 4 ( 2 sin (2x) cos (3x) dx)
= 4 ∫ 2 cos (3x) sin (2x) dx
= 4 ∫ sin (3x + 2x) - sin (3x - 2x) dx
= 4 ∫ sin 5x - sin x dx
After changing into addition, solve the integration. Use the second formula.
= 4 ∫ sin 5x - sin x dx
This is the answer.