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
Selection C is appropriate.
_____
A. The population is constant at 8.
B. The population is constant at 24.
C. Matches the problem description.
D. The initial population is 24 and after 1 hour is 72.
Answer:
Step 1) y=16-x2. Swap the sides so that all terms of the variables are on the left side. Step 2) 16-x_{2}=y. Subtract 16 from both sides. Step 3) -x_{2}=y-16 Divide the two sides by -1. Step 4). \frac{-x_{2}}{-1}=\frac{y-16}{-1} Dividing by -1 undoes the multiplication by -1. Step 5). x_{2}=\frac{y-16}{-1} Step 6) dived y-16 by -1 And the final answer = x_{2}=16-y
Step-by-step explanation:
