Anna walked to a friends house m miles away at an average rate of 4mph. the m mile walk home was only at 3 mph however. express the time anna spent walking as a single fraction. !

First of, Anna walked to a friend's house which is 'm' miles away and she walked at an average speed of 4 miles per hour.

So, to find the time we will use formula given below:

So the time taken by Anna to get to her friend's house is:

We have the time taken by Anna to walk to her friend's house.

Now we will find the time taken by Anna to walk back home. While walking back home Anna walked at a speed of 3 miles per hour.

So the time taken by Anna to walk back home is:

Now that we have the both the times, we can find out the total time that Anna spent walking.

Total time that Anna spent walking is:

Anna spent hours while walking.

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