Question 374756: two trains leave the station at the same time, one heading east and the other west. the eastbound train travels at 75 miles per hour. the westbound train travels at 95miles per hour. how long will it take for the two trains to be 238 miles apart?

Let the number of hours = X

Multiply the speed of each train by the number of hours (x) and add them together to equal the total miles:

75x + 95x = 238

Simplify:

170x = 238

Divide both sides by 170:

x = 238/170

x = 1.4 hours.

Check:

75 x 1.4 = 105 miles

95 x 1.4 = 133 miles

105 + 133 = 238 miles

It will take 1.4 hours ( 1 hour and 24 minutes).

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

10 you would take 50/ .2

step-by-step explanation: