91Ó°ÊÓ

Find, if possible, \(A B\) and \(B A\). $$A=\left[\begin{array}{rrr} 3 & 0 & -1 \\ 0 & 4 & 2 \\ 5 & -3 & 1 \end{array}\right], \quad B=\left[\begin{array}{rrr} 1 & -5 & 0 \\ 4 & 1 & -2 \\ 0 & -1 & 3 \end{array}\right]$$

Find, if possible, \(A B\) and \(B A\). $$A=\left[\begin{array}{rrr} 4 & -3 & 1 \\ -5 & 2 & 2 \end{array}\right], \quad B=\left[\begin{array}{rr} 2 & 1 \\ 0 & 1 \\ -4 & 7 \end{array}\right]$$

Sketch the graph of the system of Inequalities. $$\left\\{\begin{aligned}3 x+y & \leq 6 \\\y-2 x & \geq 1 \\\x & \geq-2 \\\y & \leq 4\end{aligned}\right.$$

A crayon 8 centimeters in length and 1 centimeter in diameter will be made from \(5 \mathrm{cm}^{3}\) of colored wax. The crayon is to have the shape of a cylinder surmounted by a small conical tip (see the figure). Find the length \(x\) of the cylinder and the height \(y\) of the cone. (PICTURE CANNOT COPY)

A large table for a conference room is to be constructed in the shape of a rectangle with two semicircles at the ends (see the figure). The table is to have a perimeter of 40 feet, and the area of the rectangular portion is to be twice the sum of the areas of the two ends. Find the length \(I\) and the width \(w\) of the rectangular portion. (PICTURE CANNOT COPY)