Need help. please. 8

Step-by-step explanation:

sin²(x) + cos²(x) = 1

cos²(x) = 1 - sin²(x)

cos(x/2) = ±sqrt((1 + cos(x))/2)

in our case

sin(x) = 1/4, tan(x) > 0, so cos(x) is positive too.

sin²(x) = 1/4² = 1/16

cos²(x) = 1 - 1/16 = 15/16

cos(x) = sqrt(15)/4

cos(x/2) = sqrt((1 + sqrt(15)/4)/2) = sqrt(1/2 + sqrt(15)/8) =

= sqrt(8/16 + 2×sqrt(15)/16) =

= 1/4 × sqrt(8 + 2×sqrt(15))

so, D is correct

69

step-by-step explanation:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet