When simplified, the value of the expression (15 - 11)^2 + square root 64 ÷ 4 is equal to . 24
10
18
4

28

Step-by-step explanation:

Simplify:  (15 - 11)^2 + square root 64 ÷ 4

"Order of operations rules"  apply here.  Any work inside parentheses must be done first:

(15 - 11)^2 = (4)^2 = 16 (since exponentiation is the next operation in priority)

Then we have:

16 + square root 64 ÷ 4 and remember that we must do division and multiplication before addition or subtraction:

16 + sqrt(16)  +  4

Note that sqrt(16) is a POWER function which must be carried out before other operations, yielding:

16 + sqrt(64) + 4, or

16 + 8 + 4, or

(evaluating this from left to right):  24 + 4 =28

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

-232

step-by-step explanation: