I don’t understand this one

Step-by-step explanation:

Considering the given triangle, to determine b, we would apply the sine rule. It is expressed as

SinA/a = SinB/b = SinC/c

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Likening it to the given triangle, the expression becomes

Sin 55/8 = SinB/b

The sum of the angles in a triangle is 180°. Therefore,

Angle B = 180 - (82 + 55) = 43°

Therefore,

Sin 55/8 = Sin43/b

Cross multiplying, it becomes

bSin55 = 8Sin43

0.819b = 8 × 0.682 = 5.456

b = 5.456/0.819

b = 6.7 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

1,8,15,22,29,36,43,50

step-by-step explanation: