Let RRR be the region enclosed by the line y=-1y=−1y, equals, minus, 1, the line x=2x=2x, equals, 2, and the curve y=x^2-1y=x 2 −1y, equals, x, squared, minus, 1. Line y = negative 1 and parabola y = x squared minus 1 are graphed. The parabola moves downward with decreasing steepness to the negative y axis, then moves upward. Y = negative 1 is tangent to the parabola, meeting it at (0, negative 1). The area enclosed by the two plots to the left of x = 2 is shaded, representing region R. A solid is generated by rotating RRR about the line y=-1y=−1y, equals, minus, 1. Which one of the definite integrals gives the volume of the solid?

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

i think its a and d

step-by-step explanation:

should have been evaluated with one odd value and one even value. the expressions have equivalent values when . when , the first expression has a value of 3 and the second

step-by-step explanation: