1. **Problem Statement:** We need to find and draw the function $$z(t) = 10 \cdot x_1(t) \times 5 \cdot x_2(t) = 50 \cdot x_1(t) \cdot x_2(t)$$ where $$x_1(t)$$ is a rectangular pulse from $$t = -4$$ to $$t = 1$$ with height 2, and $$x_2(t)$$ is a rectangular pulse from $$t = -1$$ to $$t = 4$$ with depth -2. 2. **Understanding the pulses:** - $$x_1(t) = 2$$ for $$-4 \leq t \leq 1$$, and 0 otherwise. - $$x_2(t) = -2$$ for $$-1 \leq t \leq 4$$, and 0 otherwise. 3. **Multiplying the pulses:** The product $$x_1(t) \cdot x_2(t)$$ is nonzero only where both pulses overlap. 4. **Finding the overlap interval:** - $$x_1(t)$$ is nonzero on $$[-4,1]$$ - $$x_2(t)$$ is nonzero on $$[-1,4]$$ - Overlap is $$[-1,1]$$ 5. **Value of the product in the overlap:** - $$x_1(t) = 2$$ - $$x_2(t) = -2$$ - So, $$x_1(t) \cdot x_2(t) = 2 \times (-2) = -4$$ 6. **Calculate $$z(t)$$:** $$z(t) = 50 \times (-4) = -200$$ for $$t \in [-1,1]$$, and 0 otherwise. **Final answer:** $$z(t) = \begin{cases} -200, & -1 \leq t \leq 1 \\ 0, & \text{otherwise} \end{cases}$$ This is a rectangular pulse of height -200 from $$t = -1$$ to $$t = 1$$.