The price of fresh, organic blueberries varies over the course of the year. In early July, when blueberries are abundant, a quart of organic blueberries may cost only $4. However, in January, a quart of organic blueberries may cost as much as $9. Model the price of blueberries using a sine or a cosine function. Let x represent the number of months since the beginning of the year(so x=0 means the beginning of January, and x= 6 means the beginning of July). Clearly indicate following: a. the maximum and minimum
b. the midline
c. the period and rate constant
d. write a formula for the function
e. Clearly label all parts
f. Sketch the graph

May check work by graphing your function on a graphing calculator etc.

Step-by-step explanation:

Use the formula y = A cos (Bx - C) + D    where

Given: Max = 9, Min = 4, (1/2)Period = 6 → Period = 12

Amplitude (A) = (Max - Min)/2

                      = (9 - 4)/2

                      = 5/2

Midline (D) = (Max + Min)/2  

                  = (9 + 4)/2

                  = 13/2                

Period = 2π/B    

→ B = 2π/Period

      = 2π/12

      = π/6

Notice that the Maximum touches the y-axis so there is no phase shift and no reflection → C-value = 0 & A-value is positive

Now, let's put it all together:

A = 5/2, B = π/6, C = 0, D = 13/2

Note that your graph will NOT fit the graph given because the max occurs in January (x = 0) and the min occurs in July (x = 6). The graph provided has the min at x = 0 and the max at x = 6. 

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

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