The quadratic function f ( x ) = a x 2 + b x + c is graphed in the x y -plane above, where y = f ( x ) . The equation a x 2 + b x + c = d x , where d is a nonzero constant, has how many solutions?

What is the value of the expression below? (81^2)^1/8

Multiply and simplify. 2x2y3z2 · 4xy4x2 how to do?

Find a parametrization for the curve「and determine the work done on a particle moving along γ in r3 through the force field f: r^3--r^3'where f(x,y,z) = (1,-x,z) and (a) im (γ) is the line segment from (0,0,0) to (1,2,1) (b) im (γ) is the polygonal curve with successive vertices (1,0,0), (0,1,1), and (2,2,2) (c) im (γ) is the unit circle in the plane z = 1 with center (0,0,1) beginning and ending at (1,0,1), and starting towards (0,1,1)