Graph y = x 3 and y = 16/x on the same set of coordinate axes. use the graphs to find the exact solutions to the equation x 3 = 16/x . verify by substitution that they satisfy the equation.

Refer the attached figure.    

Step-by-step explanation:

Given : Equations   and  

To find : Graph both the equations and Use the graphs to find the exact solutions to the equation

Solution :

Let, ........[1]

 .......[2]

Now, we plot these two equations.

The graph of    is shown with green line.

The graph of  is shown with violet line.

Now, using the graph,

The solution to this system will be their intersection point.  

The intersection points are (2,8) and (-2,-8).

If we substitute y from [1] equation into [2]

We get,

Refer the attached figure below.

the answer is c

step-by-step explanation:

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