Teresa graphs the following 3 equations: y=2^x, y=x^2+2, and y=2x^2. she says that the graph of y=2^x will eventually surpass both of the other graphs. is teresa correct? why or why not? a. teresa is correct. the graph of  y=2xy=2x  grows at an increasingly increasing rate, but the graphs of  y=x2+2y=x2+2  and  y=2x2y=2x2  both grow at a constantly increasing rate. therefore, the graph of  y=2xy=2x  will eventually surpass both of the other graphs. b. teresa is not correct. the graph of  y=2xy=2x  grows at an increasing rate and will eventually surpass the graph of  y=x2+2y=x2+2.however, it will never surpass the graph of  y=2x2y=2x2  because the  yy-value is always twice the value of  x2x2.c. teresa is not correct. the graph of  y=2x2y=2x2  already intersected and surpassed the graph of  y=2xy=2x  at  x=1x=1.once a graph has surpassed another graph, the other graph will never be higher.

The graph of will eventually surpass both of the other graphs.

Step-by-step explanation:

Given three equations

Now, Teresa says that the graph of will eventually surpass both of the other graphs. we have to find is she correct whether the graph surpass which means there exist any value of x such that  grows at an increasingly increasing rate, but the graphs of   both grow at a constantly increasing rate.

Therefore, the graph of will eventually surpass both of the other graphs.

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 answer is b