Solve for y -72=8(y-3)

Step-by-step explanation:

y - 72 = 8(y - 3)

Distribute the 8 into (y - 3).

y - 72 = 8y - 24

Subtract 8y from both sides.

-7y - 72 = -24

Add 72 to both sides.

-7y = 48

Divide both sides by -7.

y = -48/7 or approxametly -6.9.

Proof:

y - 72 = 8(y - 3)

Substitute variable.

-48/7 - 72 = 8(-48/7 - 3)

Subtract.

-552/7 = 8(-69/7)

Multiply 8 by the inside term -69/7.

-552/7 = -552/7.

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