The distance d when a spring is stretched by a hanging object varies directly as the weight w of the object. If the distance is 58cm when the weight is 3kg, what is the distance when the weight is 8kg
The distance d when a spring is stretched by a hanging object varies directly as the weight w of the object. If the distance is 58cm when the weight is 3kg, what is the distance when the weight is 8kg
To find the distance when the weight is 8kg, we can use the concept of direct variation. In a direct variation, two variables are related in such a way that when one variable increases, the other variable increases proportionally.
In this case, the distance d and the weight w of the object are directly proportional. We can express this relationship as:
d = kw
where k is the constant of variation.
To find the value of k, we can use the given information that the distance is 58cm when the weight is 3kg. Plugging these values into the equation, we get:
58 = k * 3
To solve for k, divide both sides of the equation by 3:
k = 58 / 3
Now that we have the value of k, we can use it to find the distance when the weight is 8kg. Plug in the weight w = 8 into the equation:
d = (58 / 3) * 8
Simplify the expression:
d = (58 * 8) / 3
Evaluate the expression to find the distance:
d ≈ 154.67 cm
Therefore, when the weight is 8kg, the distance is approximately 154.67 cm.