Given that the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linear equations, do the following. (Use x, y, and z as your variables, each representing the columns in turn.) 0 1 0 1 4
0 0 1 −4 5
0 0 0 0 0
0 0 0 0 0

Required:
a. Determine whether the system has a solution.
b. Find the solution or solutions to the system, if they exist.

The diameter of a ball is 8 in. what is the volume of the ball? use 3.14 for pi. enter your answer as a decimal in the box. round only your final answer to the nearest hundredth.

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)

Line u passes through points (-52, -18) and (-29, 53). line v passes through points (90, 33) and (19, 56). are line u and line v parallel or perpendicular?