I’m not sure but I never went over this
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:
There will be 
billion messages sent or received in November.
Step-by-step explanation:
Given.
Number of text messages sent or received 
billion.
Increment on the very next month 
Lets find what is 
⇒
⇒
So we will add this value to our previous months data.
Now
Number of text messages sent in the month of November 
billion.
Rounding to the nearest tenth the answer will be billion.
So billion text messages were sent or received in November.
Answer: the amount of interest that she would earn is $192.
Step-by-step explanation:
We would apply the formula for determining simple interest which is expressed as
I = PRT/100
Where
I represents interest paid on the amount of money deposited.
P represents the principal or amount of money deposited.
R represents interest rate on the deposit.
T represents the duration of the deposit in years.
From the information given,
P = $800
R = 4%
T = 6 years
Therefore,
I = (800 × 4 × 6)/100
I = $192
