Micah invests $5,280 in an account that earns 4.2% interest, compounded monthly.

Hence By End of the year with monthly compounded interest it will have 5522.56 $

Step-by-step explanation:

Given:

Initial investment =5.280 $

Rate of interest =4.2%

To Find:

Amount after the 1 year

Solution:

As the investment follows the rule for compound interest as ,

A=P(1+R)^t

Here A=amount after t years

R= rate of interest , P= principal amount   t is time period

So given is monthly compounded interest

so t will divided into 12 parts as there 12 months in one year.

P=5280 $ , R=4.2/12 %  , t=12

^12

A=5522.56 $

$7384.18

Step-by-step explanation:

5,280 (1 + .042 / 12)^ 12(8)

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

i would need to see the dot plot : )