a rare coin is currently worth $450 The value of the coin increases 4% each year Detemine the value of the coin after 7 years.

576

Step-by-step explanation:

450 x 0.04 (0.04 meaning 4%) is 18, then 18 x 7 by the number of years listed, thats 126, then 450 + 126 = 576, by 7 years it would be worth 576, went up by 28%.

10

step-by-step explanation:

7+3=10

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