Ms o'malley cousin live 1,650 miles away. ms o'malley won a gift card for 100 gallons of gas. if her car can travel 35 miles on each gallon, can she drive roundtrip to see her cousin on the free gas? explain how you know

 Yes, she can drive round-trip to see her cousin on the free gas.

Step-by-step explanation:

Given : Ms o'Malley cousin live 1,650 miles away.

Ms o'Malley won a gift card for 100 gallons of gas.

I her car can travel 35 miles on each gallon.

Then, the total distance she can cover in 100 gallons of gas =

Since 3500 miles > 1,650 miles

It means she can drive round-trip to see her cousin on the free gas.

hence, the correct answer is "Yes".

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