1. Problem: Convert Luca's walking speed from $5 \frac{14}{1}$ km/hr to m/s. Since $5 \frac{14}{1}$ is ambiguous, interpret as $5 \frac{14}{1} = 5+14=19$ km/hr. We convert km/hr to m/s by multiplying by $\frac{1000}{3600} = \frac{5}{18}$. Speed in m/s = $19 \times \frac{5}{18} = \frac{95}{18} \approx 5.28$ m/s. 2. Problem: Find radius of a circle with area $4355$ cm$^2$. Recall area formula $A = \pi r^2$. Solve for $r$: $$r = \sqrt{\frac{A}{\pi}} = \sqrt{\frac{4355}{\pi}}.$$ Using $\pi \approx 3.1416$: $$r = \sqrt{\frac{4355}{3.1416}} = \sqrt{1386.6} \approx 37.24 \text{ cm}.$$ 3. Problem: Calculate circumference of a circle with diameter $6$ m. Formula $C = \pi d$. Calculate: $$C = 3.1416 \times 6 = 18.85 \text{ m}.$$ 4. Problem: Find an expression for the perimeter of the cuboid in terms of $x$ and $y$. Given the diagram is a rectangle divided into 5 vertical sections with width $x$ and height $y$ and a side marked $(2-1)$ with total 20. For the cuboid, perimeter $P = 4(l + w + h)$ where $l, w, h$ are lengths. From context, interpret length = $x$, width = $y$, height = $(2 - 1) = 1$. Thus, $$P = 4(x + y + 1).$$ 5. Problem: Find $a$, $b$, and $c$ in a sequence where the same number is added to get the next term. Given first five terms: $a, b, c, \ldots$ with $a, b, c \in \mathbb{R}$. The sequence is arithmetic, so: $$b = a + d, \quad c = b + d = a + 2d,$$ where $d$ is the common difference. We need more data to find numeric values, so answer is: $a = a$, $b = a + d$, $c = a + 2d$, with $d$ unknown. Final answers: 1. Speed in m/s: $\frac{95}{18} \approx 5.28$ m/s 2. Radius: $\approx 37.24$ cm 3. Circumference: $\approx 18.85$ m 4. Perimeter expression: $4(x + y + 1)$ 5. Sequence terms: $a = a$, $b = a + d$, $c = a + 2d$ (with unknown $a, d$).