Example Question - constant of proportionality
Here are examples of questions we've helped users solve.
Proportional Relationship Between Variables
To solve the question in the image, we need more information about the relationship between y and x. If the relationship is linear and directly proportional, then we can use a simple ratio to find the value of y when x = 2. Assuming the relationship is y = kx, where k is the constant of proportionality, we can first find k using the information we have: y = 96 when x = 4. So: 96 = k * 4 Solving for k: k = 96 / 4 k = 24 Now that we have the value of k, we can find y when x = 2: y = k * x y = 24 * 2 y = 48 Therefore, if the relationship between y and x is directly proportional, then y = 48 when x = 2. However, without additional information about the specific relationship between y and x (such as the equation of a curve, if it's not linear), we cannot definitively solve for y.
Determining the Equation of a Proportional Relationship
To find the equation of the form y = kx that represents the proportional relationship between x and y, we must first determine the constant of proportionality k by dividing the value of y by the value of x for any given point in the table. The constant of proportionality should be the same for any pair of x and y values listed, as long as the relationship is truly proportional. For example, take the first row where x is 18 and y is 153. k = y / x = 153 / 18 = 8.5 Now we should check this value of k to see if it applies to the other rows. If the relationship is proportional, then all rows should have the same value of k. For the second row, with x as 24 and y as 204: k = y / x = 204 / 24 = 8.5 For the third row, with x as 30 and y as 255: k = y / x = 255 / 30 = 8.5 Since all rows give us the same k value, we can confirm that the relationship is proportional and the constant of proportionality k is 8.5. Therefore, the equation that represents the relationship is y = 8.5x.
Proportional Relationship Calculation
This question seems to involve a direct variation between the two variables \( w \) and \( u \), where \( w = k \cdot u \) for some constant of proportionality, \( k \). Given that \( w = -2 \) when \( u = 6 \), you can find the constant of proportionality \( k \) by dividing \( w \) by \( u \): \[ k = \frac{w}{u} = \frac{-2}{6} = -\frac{1}{3} \] Now that you have \( k \), you can find \( w \) when \( u = -15 \) using the same relationship: \[ w = k \cdot u = -\frac{1}{3} \cdot -15 = \frac{1}{3} \cdot 15 \] \[ w = 5 \] Therefore, when \( u = -15 \), \( w \) would be \( 5 \).
Calculating Miles Driven Over Time
To solve this question, let's do it step by step. a) To find the unit rate, we determine the number of miles Meng can drive in one hour. The unit rate is found by dividing the total distance by the total time. The equation would be: Unit rate = Total miles / Total hours Plug in the numbers: Unit rate = 150.75 miles / 4.5 hours = 33.5 miles/hour So Meng drives at a rate of 33.5 miles per hour. b) The constant of proportionality, \( k \), in this context is the same as the unit rate since it represents the constant value that relates the number of hours driven to the number of miles covered. Therefore, \( k = 33.5 \) miles per hour. c) To complete the table, multiply the constant of proportionality, \( k \), by each number of hours. For 1 hour: Miles = k * Hours = 33.5 miles/hour * 1 hour = 33.5 miles For 2 hours: Miles = k * Hours = 33.5 miles/hour * 2 hours = 67 miles For 3 hours: Miles = k * Hours = 33.5 miles/hour * 3 hours = 100.5 miles For 4 hours: Miles = k * Hours = 33.5 miles/hour * 4 hours = 134 miles For 5 hours: Miles = k * Hours = 33.5 miles/hour * 5 hours = 167.5 miles Therefore, the completed table is: | Hours | 1 | 2 | 3 | 4 | 5 | |-------|-------|------|--------|-------|--------| | Miles | 33.5 | 67 | 100.5 | 134 | 167.5 |
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