The stretch of a spring in the millimeters is proportional to the weight in grams attached to the end of the spring. Find the unit rate.
I apologize for any confusion. The correct unit rate is indeed 5 millimeters/gram.
Ok thanks I got it right
You're welcome! I'm glad I could help. If you have any more questions, feel free to ask.
To find the unit rate, we need to determine how much the spring stretches for a weight of 1 gram. If the stretch of the spring is proportional to the weight, then for every gram the spring stretches a certain amount.
Let's say the spring stretches 5 millimeters when a weight of 10 grams is attached to it. We can set up a proportion to find the stretch for 1 gram:
5 millimeters / 10 grams = x millimeters / 1 gram
Cross multiplying the proportion, we have:
5 millimeters * 1 gram = 10 grams * x millimeters
5 millimeters = 10x millimeters
Dividing both sides of the equation by 10 millimeters, we have:
x = 5/10
Simplifying the fraction, we get:
x = 1/2
Therefore, the unit rate is 1/2 millimeters/gram.
To find the unit rate, we need to determine the ratio between the change in the stretch of the spring and the change in weight.
Let's say that when the weight is increased by 100 grams, the corresponding stretch of the spring increases by 20 millimeters.
The unit rate is calculated by dividing the change in the stretch of the spring by the change in weight:
Unit Rate = Change in Stretch / Change in Weight
Substituting the values, we get:
Unit Rate = 20 millimeters / 100 grams
Simplifying, we find that the unit rate is:
Unit Rate = 0.2 mm/g
Therefore, the unit rate is 0.2 millimeters per gram.
To find the unit rate, we need to determine how much stretch in millimeters corresponds to each gram of weight added to the spring.
Let's say that when no weight is attached, the spring has no stretch and the length is 0 millimeters. Then, let's add a weight of 1 gram to the spring and measure the stretch in millimeters. Assuming the stretch is proportional to the weight, let's say we measure a stretch of 5 millimeters.
So, the unit rate is the amount of stretch per gram. In this case, it would be 5 millimeters of stretch for every 1 gram of weight.
Therefore, the unit rate is 5 millimeters/gram.
That wasn’t the answer
Using the points shown in the graph, identify the constant pf proportionality for the graph.
To identify the constant of proportionality for the graph, we need to determine the ratio between the change in the stretch of the spring and the change in weight.
If we have two points on the graph with coordinates (weight₁, stretch₁) and (weight₂, stretch₂), the constant of proportionality can be calculated as:
Constant of Proportionality = (stretch₂ - stretch₁) / (weight₂ - weight₁)
Let's consider two points on the graph. For example, (10 grams, 20 millimeters) and (20 grams, 40 millimeters). Plugging in these values into the formula, we have:
Constant of Proportionality = (40 millimeters - 20 millimeters) / (20 grams - 10 grams)
Constant of Proportionality = 20 millimeters / 10 grams
Simplifying, we get:
Constant of Proportionality = 2 millimeters/gram
Therefore, the constant of proportionality for the graph is 2 millimeters/gram.