Question

read the following description of a relationship: an engineer is constructing a newtons pendulum using a frame that weighs 32 kilograms and steel balls that weigh 12 kilograms each. let b represent the number of steel balls used and w represent the total weight of the pendulum. complete the table using the relationship between b and w. b | w 3 | 6 | 8 | 10 |

Explanation:

Step1: Find the relationship formula

The total weight \( w \) is the weight of the frame plus the weight of the steel balls. The frame weighs 32 kg, and each steel ball weighs 12 kg. So the formula is \( w = 32 + 12b \).

Step2: Calculate for \( b = 3 \)

Substitute \( b = 3 \) into the formula: \( w = 32 + 12\times3 = 32 + 36 = 68 \).

Step3: Calculate for \( b = 6 \)

Substitute \( b = 6 \) into the formula: \( w = 32 + 12\times6 = 32 + 72 = 104 \).

Step4: Calculate for \( b = 8 \)

Substitute \( b = 8 \) into the formula: \( w = 32 + 12\times8 = 32 + 96 = 128 \).

Step5: Calculate for \( b = 10 \)

Substitute \( b = 10 \) into the formula: \( w = 32 + 12\times10 = 32 + 120 = 152 \).

Answer:

For \( b = 3 \), \( w = 68 \); for \( b = 6 \), \( w = 104 \); for \( b = 8 \), \( w = 128 \); for \( b = 10 \), \( w = 152 \). So the completed table is:

\( b \)	\( w \)
6	104
8	128
10	152