What is the range of possible
lengths of the third side of a
triangle with side lengths of
3 and 7?

4<C <10

Step-by-step explanation:

Theorem: Given a triangle with sides A, B and C the sum of the lengths of any two sides of a triangle must be greater than the third side:

1.  A+B>C

2.  B +C >A

3.  A+C>B

Thus given two sides of A=3 and B=7 C can be:

7 −3<C < 7+3

C range  

4<C <10

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

what statement? is there an image?