Find Y

A: 14.3
B: -6.3
C: 7.0
D: 11.6

D

Step-by-step explanation:

Using the sine ratio in the right triangle

sin51° = = ( multiply both sides by y )

y × sin51° = 9 ( divide both sides by sin51° )

y = ≈ 11.6 ( to 1 dec. place ) → D

chad should not have included the values (1, 2) and (3, 6) because that would mean he only had half a healing card.

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