Solve the equation by first using a sum-to-product formula. (enter your answers as a comma-separated list. let k be any integer. round terms to three decimal places where appropriate.) sin(5θ) − sin(3θ) = cos(4θ)

Solutions of the equation are 22.5°, 30°.

Step-by-step explanation:

The given equation is sin(5θ) - sin(3θ) = cos(4θ)

We take left side of the equation

sin(5θ) - sin(3θ) =

= [From sum-product identity]

Now we can write the equation as

2cos(4θ)sin(θ) = cos(4θ)

2cos(4θ)sinθ - cos(4θ) = 0

cos(4θ)[2sinθ - 1] = 0

cos(4θ) = 0

4θ = 90°

θ =

θ = 22.5°

and (2sinθ - 1) = 0

sinθ =

θ = 30°

Therefore, solutions of the equation are 22.5°, 30°

answer: 1) twenty-seven times y

              2) twenty-seven multiplied by y

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .