A boat tour guide expects his tour to travel at a rate of x mph on the first leg of the trip. On the return route, the boat travels against the current, decreasing the boat's rate by 10 mph. The group needs to travel an average of at least 24 mph. The inequality represents the possible rates.

1/x + 1/ (x-10) >= 2/24

Solve the inequality. Which intervals are included in the solution? Check all that apply.

(-infinity, 0)

(0, 4]

[4, 10)

(10, 30]

[30, infinity)

(0,4) and (10,30)

"if it is my birthday, then it is snowing"

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