In 1 h the minute hand on a clock moves through a complete circle, and the hour hand moves through 1/12 of a circle. Through how many radians do the minute hand and the hour hand move between 1:00 p. m. and 6:45 p. m. (on the same day)?

9514 1404 393

  12 11/24 radians (combined angular motion)

Step-by-step explanation:

In one hour, the combined angular motion is ...

  (2π)(1 +1/12) = 13π/6 radians

Then in the 5 3/4 hours between 1 pm and 6:45 pm, the angular motion of the two hands will total ...

  (23/4)(13π/6) radians = 299π/24 radians = 12 11/24 radians

Additional comment

Maybe you're asking for the separate motions.

  minute hand: 2π×5.75 = 11.5π radians

  hour hand: (π/6)×5.75 = 23π/24 radians

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

the f

last graph i believe

step-by-step explanation:

worked it out i believe