Find the length of the missing side. if necessary, round to the nearest tenth. 21.3 30 15 7.7 (it is a triangle and it has a right angle and you are looking for b and the numbers on the triangle are 16 [this is the longest side and slanted] and 14 [this is straight with no slant sorry couldnt upload a photo! ]

Based upon your info, the length of the hypotenuse is 16 and that of one of the legs is 14.  According to the Pythagorean Theorem, 14^2 + x^2 = 16^2.  Thus, 196 + x^2 = 256, and x^2 = 60.  

Take the square root of both sides, and remember that length is positive:

sqrt(x^2) = +sqrt(60)

              = +2sqrt(15)

              =  7.746

               = 7.7 (rounded to the nearest tenth)

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