Answer:
x=nπ3, n∈I
Step-by-step explanation:
sin x + sin 5x = sin 2x + sin 4x
⇒⇒ 2 sin 3x cos 2x = 2 sin 3x cos x
⇒⇒ 2 sin 3x(cos 2x - cos x) = 0
⇒ sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3⇒ sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3 , n∈I, n∈I
or cos 2x−cos x=0 ⇒ cos 2x=cos xcos 2x-cos x=0 ⇒ cos 2x=cos x
⇒ 2x=2nπ±x ⇒ x=2nπ, 2nπ3⇒ 2x=2nπ±x ⇒ x=2nπ, 2nπ3 , n∈I, n∈I
But solutions obtained by x=2nπx=2nπ , n∈I, n∈I or x=2nπ3x=2nπ3 , n∈I, n∈I are all involved in x=nπ3x=nπ3 , n∈I
Each person should pay if the total bill should split is $60.30.
Given that,
- The two-person paid the waiter $100.50.
- Also, there is a 20% tip.
Based on the above information,
The total amount paid including the tip is
= $100.50 + 20% of $100.50
= $120.60
Now the above amount should be split into 2 persons so it should be $60.30.
Therefore we can conclude that each person should pay if the total bill should split is $60.30.
Learn more: brainly.com/question/19877146
Answer:
He earned $114 in interest.
The final amount in the account is $874
Step-by-step explanation:
Initial balance (b): $760
Interest rate (i): 0.05
Period (n): 3 months
Simple interest applications yield the same amount in interest every period. Therefore, the total simple interest earned can be defined by:
The final amount (A) in the account is the initial balance plus the interest earned in 3 months.
He earned $114 in interest and the final amount in the account is $874
Answer:
On the first hour she gathered 8 mushroons, on the second 15 mushroons and on the third she gathered 14 mushroons.
Step-by-step explanation:
Helen gathred a total of 37 mushroons in three hours. On the first hour she gathered "x" mushroons, on the second hour she gathered "x + 7" mushroons and on the third hour she gathered "x + 6". Therefore the sum of mushrrons she gathered on each hour should be equal to the total she gathered as shown below:
37 = x + (x+ 7) + (x + 6)
37 = 3*x + 13
3*x + 13 = 37
3*x = 37 - 13
3*x = 24
x = 24 / 3
x = 8
On the first hour she gathered 8 mushroons, on the second 15 mushroons and on the third she gathered 14 mushroons.
Good evening ,
Answer:
There are exactly 3 complex roots and that is due to the fundamental theorem of Algebra.
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