Two trains leave stations 168 miles apart at the same time and travel toward each other. One train travels at 75 miles per hour while the other travels at 65 miles per hour. How long will it take for the two trains to meet?

they would meet after 1.2 hours

Step-by-step explanation:

Let t represent how long will it take for the two trains to meet.

If the two trains leave stations 168 miles apart at the same time and travel toward each other, it means that after t hours, they would have covered 168 miles.

Distance = speed × time

One train travels at 75 miles per hour. It means that the distance travelled by this train in t hours is 75t miles.

The other train travels at 65 miles per hour. It means that the distance travelled by this train in t hours is 65t miles.

Since the total distance covered is 168 miles, it means that

75t + 65t = 168

140t = 168

t = 168/140

t = 1.2

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

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it