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:
see below
Step-by-step explanation:
— 7x — бу = — 15
To find the x intercept set y = 0 and solve for x
-7x - 0 = -15
-7x= -15
Divide by -7
-7x/-7 = -15/-7
x = 15/7
The x intercept is (15/7,0)
To find the y intercept set x = 0 and solve for y
o— бу = — 15
— бу= -15
Divide by -6
— бу/-6= -15/-6
у= 5/2
The y intercept is (0,5/2)
Answer:
7
Step-by-step explanation:
You can divide both 14 and 21 by seven and get a whole number.
Answer:0.4375
Step-by-step explanation:
To solve the problem, we start by labeling 1/2 of 7/8 like this:
N1/D1 of N2/D2
Then we use this fraction of a fraction formula to solve the problem:
(N1 x N2) / (D1 x D2)
When we enter 1/2 of 7/8 into the formula, we get:
(1 x 7) / (2 x 8) = 7/16
Therefore, the answer to 1/2 of 7/8 in its lowest form is:
1/2 of 7/8 = 7/16
