8. Anneke is swimming the 500-meter freestyle, which consists of swimming the length of a pool 20 times. If Anneke averages 26.4 seconds per length of pool, write an equation that could be used to determine the number of meters (m) Anneke has left in the event after swimming for s seconds.

Anneke will swim 20 lengths in the 500-meter event,

which means each length of the pool is = 500/20

= 25m

also since Anneke can swim one length in 26.4 seconds on average

hence her average speed is = 25/26.4 m/s

hence after a seconds,

the distance traveled = 25s/26.4 meter

thus, the remaining distance Anneke need to travel is:

m = 500 - (25s/26.4)

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

answer: 1 and 3

step-by-step explanation: