A model rocket is launched from a platform 12 meters high at a speed of 35 meters per second. Its height h can be modeled by the equation h= -4.9t'2+35t+12 where t is the time in seconds. at what time will the rocket be altitude of 60 meters.

Step-by-step explanation:

so set the given equation equal to 60 and solve for t

60= -4.9 +35t +12

0= -4.9 +35t - 48

now use the quadratic equation to solve for t

-b +- sq rt ( - 4 a c )  /  2 a

t = -35 +- sq. rt [ 1225 -4(-4.9)(-48) ] / 2 (-4.9)

t = -35 +- sq. rt [ 284.2] / -9.8

t = -35 +- 16/858 / - 9.8

t = 3.571 +- 1.72

t  = 1.85 seconds ( on the way up ) or  t = 5.29 seconds ( on the way down)

at both of those times the rocket will be at 60 meters  :)

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

536

step-by-step explanation: