Solve.
-The distance D that a spring is stretched by a hanging object varies directly as the weight W of the object. If a 16-kg object stretches a spring 76 cm, find the distance when the weight is 19-kg. Round to the nearest Hundredths when necessary.
A)4.75 cm
B)111 cm
C)90.25 cm
D)4 cm

Question

Quizplus · Accepted Answer

The relationship between the distance $D$ that a spring is stretched and the weight $W$ of the object is directly proportional, which can be represented as $D = k \cdot W$, where $k$ is the constant of proportionality. Given that a 16-kg object stretches the spring 76 cm, we can find $k$ by rearranging the formula: $k = \frac{D}{W} = \frac{76}{16}$. To find the distance when the weight is 19-kg, we substitute $W = 19$ and the calculated $k$ into the original formula: $D = k \cdot 19$, which gives $D = \frac{76}{16} \cdot 19$, resulting in approximately 90.25 cm.

Solve. -The Distance D That a Spring Is Stretched by a a Hanging