Length: 2/6/8/9/10
Breaking Weight 24/16/13/11/9
Explain how your equation shows that breaking weight decreases as length increases. Is this pattern reasonable for this situation? Explain.
I used inverse variation equation and found that the equation would be y=96/x with the given data. How do I explain that and is the pattern resonable?
It is reasonable, however, itis not an exact fit.
If according to you y=96/x, then xy=96
Now look at your table. I will take the products of lenght*breaking weight
48,96,104,99,90
So it is not an exact fit.
To explain why the breaking weight decreases as the length increases using the given inverse variation equation, let's analyze the equation y = 96/x.
The inverse variation equation states that when two variables are inversely proportional, their product remains constant. In this case, the breaking weight (y) and the length (x) are inversely proportional, as indicated by the equation.
The constant value in this equation is 96, which was obtained from the given data. This means that, for each value of the length (x), when multiplied by the corresponding breaking weight (y), the product is always 96.
Now, let's consider the situation. As the length increases, the breaking weight decreases. This pattern can be explained as follows:
When the length is small, the force required to break the object (represented by the breaking weight) is greater. As the length of the object increases, the force needed to break it decreases. This is because longer objects usually have a larger cross-sectional area, resulting in distributed forces and reduced stress on the material. Consequently, the breaking weight decreases.
Therefore, the pattern of breaking weight decreasing as the length increases is reasonable for this situation because it aligns with the concept of increased cross-sectional area reducing stress and decreasing the force required to break the object.
To explain how the equation shows that breaking weight decreases as length increases, you can use the concept of inverse variation. Inverse variation, also known as inverse proportionality, is a relationship in which one variable increases while the other decreases, and their product remains constant.
In this case, the length and breaking weight are inversely related. As length increases, breaking weight decreases. This is because, in general, longer objects have a greater tendency to break under the same amount of force compared to shorter objects. This is due to factors such as structural integrity, distribution of forces, and leverage.
By using the given data, we can formulate an inverse variation equation using the equation y = k/x, where y represents the breaking weight and x represents the length. The constant k is the product of y and x for any given data point.
To find the equation, we can use one set of data points. For example, let's use the length 2 and corresponding breaking weight 24. Plugging these values into the equation, we get 24 = k/2. Solving for k, we get k = 48.
Now we have the equation y = 48/x. By substituting the different lengths into x, you can find the corresponding breaking weights. For instance, when x = 6, y = 48/6 = 8. Similarly, when x = 8, y = 48/8 = 6, and so on.
This pattern of decreasing breaking weight as length increases is reasonable for this situation. It aligns with our understanding that longer objects are more prone to breaking due to various structural factors. Therefore, the inverse variation equation you found, y = 96/x, is a reasonable representation of the relationship between length and breaking weight in this scenario.