Answer:
x = {nπ -π/4, (4nπ -π)/16}
Step-by-step explanation:
It can be helpful to make use of the identities for angle sums and differences to rewrite the sum:
cos(3x) +sin(5x) = cos(4x -x) +sin(4x +x)
= cos(4x)cos(x) +sin(4x)sin(x) +sin(4x)cos(x) +cos(4x)sin(x)
= sin(x)(sin(4x) +cos(4x)) +cos(x)(sin(4x) +cos(4x))
= (sin(x) +cos(x))·(sin(4x) +cos(4x))
Each of the sums in this product is of the same form, so each can be simplified using the identity ...
sin(x) +cos(x) = √2·sin(x +π/4)
Then the given equation can be rewritten as ...
cos(3x) +sin(5x) = 0
2·sin(x +π/4)·sin(4x +π/4) = 0
Of course sin(x) = 0 for x = n·π, so these factors are zero when ...
sin(x +π/4) = 0 ⇒ x = nπ -π/4
sin(4x +π/4) = 0 ⇒ x = (nπ -π/4)/4 = (4nπ -π)/16
The solutions are ...
x ∈ {(n-1)π/4, (4n-1)π/16} . . . . . for any integer n
Answer:
The mixtures are not proportional.
3 fluid ounces of vinegar has to be added in the second mixture to make it proportional to the first mixture.
its =3
Step-by-step explanation:
The one mixture contains 6 fluid ounces and 10 fluid ounces of water and vinegar respectively.
Therefore, the ratio of water to vinegar in the first mixture is 6 : 10 = 3 : 5
Now, a second mixture contains 9 fluid ounces of water and 12 fluid ounces of vinegar.
Hence, the ratio of water to vinegar in the second mixture is 9 : 12 = 3 : 4
Therefore, the mixtures are not proportional.
Therefore, we have to add x fluid ounces of vinegar to the second mixture to make it in the ratio of 3 : 5.
So,
⇒ 12 + x = 15
⇒ x = 3 fluid ounces.
Therefore, 3 fluid ounces of vinegar has to be added in the second mixture to make it proportional to the first mixture. (Answer
Answer:
4km
Step-by-step explanation:
x
For this case we have the following product:
We must use the distributive property correctly to solve the problem.
We have then:
Then, we must add similar terms.
We have then:
Answer:
The final product is given by:
option 2
Answer:
C AND D
Step-by-step explanation:
it is a rational and real number
