Answer:
Step-by-step explanation:
Let number of songs are played in a commercial be a
number of songs are played in a movie be b
Adrian earned a total of $1010 -> a*40 + b*130 = 1010 (1)
14 commercials and movies -> a+b = 14 (2)
(1) - (2)*40 = a*40 + b*130 - a*40 -b*40 = 1010 -14*40
-> b*90 = 450
-> b = 5
-> a = 14-5 = 9
cot(<em>θ</em>) = cos(<em>θ</em>)/sin(<em>θ</em>)
So if both cot(<em>θ</em>) and cos(<em>θ</em>) are negative, that means sin(<em>θ</em>) must be positive.
Recall that
cot²(<em>θ</em>) + 1 = csc²(<em>θ</em>) = 1/sin²(<em>θ</em>)
so that
sin²(<em>θ</em>) = 1/(cot²(<em>θ</em>) + 1)
sin(<em>θ</em>) = 1 / √(cot²(<em>θ</em>) + 1)
Plug in cot(<em>θ</em>) = -2 and solve for sin(<em>θ</em>) :
sin(<em>θ</em>) = 1 / √((-2)² + 1)
sin(<em>θ</em>) = 1/√(5)
Answer:
The total length of fabric sue buys is 8.5 yards and total cost of the fabric is $42.5 .
Step-by-step explanation:
As given
Sue buys 5 pieces of fabric.

i.e



In the decimal form
Total length of fabric sue buys = 8.5 yards
As given
One yard of the fabric costs $5

= $ 42.5
Therefore the total length of fabric sue buys is 8.5 yards and total cost of the fabric is $42.5 .