The shortest route from London to York is 200 miles. A lorry is expected to take 4 hours to travel this route.
The lorry actually travels by a different route which increases the distance by 20%, but it still arrives in 4 hours.
By how many more mph than the expected speed does the lorry travel?

The lorry is traveling 10 mph over the expected speed.

Step-by-step explanation:

If 200 miles takes 4 hours, the speed is 200mi/4hr which  is 50 mph.

If the distance is increased by 20%, the distance is 240 miles.

240mi/4hr = 60mph

The difference is 10mph

answer: c is correct, a regular pentagon

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