Jason started a hat-making business. he spent $750 to purchase supplies to get started and he uses about $3.50 worth of supplies per hat made. jason charges $15 for each hat. let h represent the number of hats. what is the minimum number of hats jason will need to sell to make a profit? which inequality models this problem? a.) 15h> 750+3.5h b.) 3.5h> 750+15h c.) 15h< 750+3.5h d.) 3.5h≥750+15h

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

x=6 and x=3

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