Question

1. complete the table. explain or show your reasoning.

object	radius	circumference
windmill	210 ft
button		31.4 mm
flying disc		34.5 in

1. a car dealership pays $9,425 for a car. they mark up the price by 16.7% to get the retail price. what is the retail price of the car at this dealership?

1. the graph shows the relationship between the radius and the circumference of a circle with the point (1,2π) shown. find 3 more points that are on the line.

(graph: x-axis labeled radius, y-axis labeled circumference. point (1, 2π) is on the line, which passes through the origin. grid lines are present with x from 0 to 5 and y from 0 to 40.)

Explanation:

Problem 6 (Table Completion)

Use the circle circumference formula $C = 2\pi r$ (or $r = \frac{C}{2\pi}$), use $\pi \approx 3.14$ for calculations.

Step1: Calculate clock circumference

$C = 2 \times \pi \times 7.5 = 15\pi \approx 47.1$ cm

Step2: Calculate windmill circumference

$C = 2 \times \pi \times 210 = 420\pi \approx 1318.8$ ft

Step3: Calculate button radius

$r = \frac{31.4}{2 \times 3.14} = 5$ mm

Step4: Calculate flying disc radius

$r = \frac{34.5}{2\pi} \approx \frac{34.5}{6.28} \approx 5.49$ in

Step1: Convert markup to decimal

$16.7\% = 0.167$

Step2: Calculate retail price factor

$1 + 0.167 = 1.167$

Step3: Compute retail price

$\text{Retail Price} = 9425 \times 1.167 \approx 11000$

The line follows $C=2\pi r$, so pick integer radii and compute $C$.

Step1: Radius = 2, find circumference

$C=2\pi \times 2 = 4\pi$

Step2: Radius = 3, find circumference

$C=2\pi \times 3 = 6\pi$

Step3: Radius = 4, find circumference

$C=2\pi \times 4 = 8\pi$

Answer:

object	radius	circumference
windmill	210 ft	$420\pi$ (≈1318.8 ft)
button	5 mm	31.4 mm
flying disc	≈5.49 in	34.5 in

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Problem 1 (Car Retail Price)