The work of a student to solve a set of equations is shown:

equation 1: m = 8 + 2n
equation 2: 6m = 4 + 4n

step 1: −6(m) = −6(8 + 2n) [equation 1 is multiplied by −6.]
6m = 4 + 4n [equation 2]
step 2: −6m = −48 − 12n [equation 1 in step 1 is simplified.]
6m = 4 + 4n [equation 2]
step 3: −6m + 6m = −48 − 12n + 4n [equations in step 2 are added.]
step 4: 0 = −48 − 8n
step 5: n = −6

in which step did the student first make an error?
step 3
step 5
step 4
step 2

If you would like to know in which step did the student first make an error, you can find this using the following steps:

m = 8 + 2n
6m = 4 + 4n

-6(m) = -6(8+2n)
6m = 4 + 4n

-6m = -48 - 12n
6m = 4 + 4n

-6m + 6m = -48 - 12n + 4 + 4n ... Step 3

0 = -44 - 8n

8n = -44

n = -44/8 = -11/2

The correct result would be: Student made an error in Step 3.

step-by-step explanation:

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