Math Quiz: Math for - Nested Constructions

  1. An engineering team is designing a support beam. The beam requires three identical segments, each $3.25$ meters long. After joining the segments, they need to trim $0.15$ meters from the total length for a precise fit. What is the final length of the support beam?

  2. Evaluate the following expression: $50 - (3 \times (4.5 + (10 \div 2)))$.

  3. Calculate the value of: $(24.8 \div 4) + (3 \times \frac{1}{2} - 0.5)$.

  4. A robotic arm is programmed to move a certain distance. It first moves forward $12.75$ cm. It then retracts by an amount calculated as $(2 \times (1.5 + 0.75))$ cm. Finally, it moves forward again by half of its initial forward movement ($12.75 \text{ cm}$). What is the net displacement of the robotic arm from its starting position? (Consider forward movement as positive and retraction as negative).

  5. Consider the expression used to calculate a specific engineering tolerance: $T = \frac{100}{L - W}$. If $L$ represents the total allowed length and $W$ represents the measured length of a part, what value of $W$ would make the tolerance $T$ undefined if $L = 15$ units? Explain your reasoning.