1. **Problem:** Diego measured diameters and circumferences of circular objects. One measurement is inaccurate. Identify which and explain. 2. **Formula:** Circumference $C = \pi d$, where $d$ is diameter. 3. **Step 1:** Calculate expected circumference for each object using $\pi \approx 3.14$. - Half dollar coin: $C = 3.14 \times 3 = 9.42$ cm (measured 10 cm) - Flying disc: $C = 3.14 \times 23 = 72.22$ cm (measured 28 cm) - Jar lid: $C = 3.14 \times 8 = 25.12$ cm (measured 25 cm) - Flower pot: $C = 3.14 \times 15 = 47.1$ cm (measured 48 cm) 4. **Step 2:** Compare measured vs expected. - Half dollar coin: close (10 vs 9.42) - Flying disc: very different (28 vs 72.22) - Jar lid: close (25 vs 25.12) - Flower pot: close (48 vs 47.1) 5. **Conclusion:** Flying disc's circumference measurement (28 cm) is inaccurate. --- 1. **Problem:** Complete the table using $\pi \approx 3.14$. 2. **Formula:** $C = \pi d$ and $d = \frac{C}{\pi}$. 3. **Step 1:** Calculate missing values. - Hula hoop circumference: $C = 3.14 \times 35 = 109.9$ in - Circular pond diameter: $d = \frac{556}{3.14} \approx 177.07$ ft - Magnifying glass circumference: $C = 3.14 \times 5.2 = 16.33$ cm - Car tire diameter: $d = \frac{71.6}{3.14} \approx 22.83$ in 4. **Completed table:** | object | diameter | circumference | |-----------------|----------|---------------| | hula hoop | 35 in | 109.9 in | | circular pond | 177.07 ft| 556 ft | | magnifying glass| 5.2 cm | 16.33 cm | | car tire | 22.83 in | 71.6 in | --- 1. **Problem:** Given circle with center A and segment CD = 15 cm. 2. **a. Radius:** Segment AB is a radius. - Radius length equals half diameter. - Since CD is diameter, radius $= \frac{15}{2} = 7.5$ cm. 3. **b. Diameter:** Segment CB is a diameter. - Diameter length is 15 cm. --- 1. **Problem:** For $y = 1.5x + 2$, find four $(x,y)$ pairs and plot. 2. **Step 1:** Choose $x = 0, 2, 4, 6$. 3. **Step 2:** Calculate $y$ values: - $x=0$: $y=1.5(0)+2=2$ - $x=2$: $y=1.5(2)+2=5$ - $x=4$: $y=1.5(4)+2=8$ - $x=6$: $y=1.5(6)+2=11$ 4. **Points:** $(0,2), (2,5), (4,8), (6,11)$ 5. **Step 3:** Plot these points on the coordinate plane. 6. **Step 4:** Is this a proportional relationship? - No, because proportional relationships have $y = kx$ and pass through origin. - Here, $y$-intercept is 2, so not proportional. **Final answers:** - Inaccurate measurement: Flying disc circumference. - Completed table values as above. - Radius AB = 7.5 cm, diameter CB = 15 cm. - Four points for $y=1.5x+2$: $(0,2), (2,5), (4,8), (6,11)$. - Relationship is not proportional.