MATH SOLVE

6 months ago

Q:
# Simonne has been following the stock ratings of Carter's Pork Bellies. She has noticed that the pattern can be modeled by a cosine function. During her observations, she has found the stock to have a maximum of x = 6, minimum of x = −2, and period of π. Which of the following cosine functions could model Simonne's stock rating?a. f(x) = 4 cos 2x − 4b. f(x) = 6 cos pi over 2 x + 2c. f(x) = 6 cos pi over 2 x − 4d. f(x) = 4 cos 2x + 2

Accepted Solution

A:

y=a cos (bx+c) + d

Maximun: M=6

Minimum: m=-2

Period: P=π

d=(M+m)/2

d=(6+(-2))/2

d=(6-2)/2

d=4/2

d=2

P=2π/b

π=2π/b

Sollving for b. Cross multiplication:

πb=2π

Dividing both sides by π:

πb/π=2π/π

b=2

Amplitude=a=(M-m)/2

a=(6-(-2))/2

a=(6+2)/2

a=8/2

a=4

y=4 cos (2x+0) + 2

y=4 cos 2x +2

Answer: Option d. f(x) = 4 cos 2x + 2

Maximun: M=6

Minimum: m=-2

Period: P=π

d=(M+m)/2

d=(6+(-2))/2

d=(6-2)/2

d=4/2

d=2

P=2π/b

π=2π/b

Sollving for b. Cross multiplication:

πb=2π

Dividing both sides by π:

πb/π=2π/π

b=2

Amplitude=a=(M-m)/2

a=(6-(-2))/2

a=(6+2)/2

a=8/2

a=4

y=4 cos (2x+0) + 2

y=4 cos 2x +2

Answer: Option d. f(x) = 4 cos 2x + 2