y varies directly as the product of s and r
y = ksr
When a variable "y" varies directly as the product of two other variables, "s" and "r," we can write it as a direct variation equation. In this case, we can express it as:
y = k * s * r
Here, "k" is the constant of variation, which remains constant through different values of "y," "s," and "r." To find the value of "k," we need additional information or data.
If you have specific values for "y," "s," and "r," we can substitute them into the equation to solve for "k."
To understand the given relationship, let's break it down step by step:
"y varies directly" means that y is directly proportional to the product of s and r. In other words, as the product of s and r increases, y also increases, and as the product of s and r decreases, y also decreases.
To mathematically represent this relationship, we can write it as:
y = k * s * r
where k is the constant of variation. The constant of variation ensures that y remains directly proportional to the product of s and r.
If we know the value of k, we can directly calculate the value of y for a given value of s and r. However, the value of k is typically unknown.
To find the value of k, we need additional information or data. This can be obtained by conducting experiments or surveys. By collecting different values of y, s, and r, we can find the constant of variation (k) using the following steps:
1. Select a set of known values of y, s, and r from the data collected.
2. Substitute these values into the equation y = k * s * r.
3. Solve the equation for k by dividing both sides by (s * r).
4. Calculate the value of k.
5. Once the value of k is determined, it can be used to find the value of y for any other combination of s and r.
Remember that the relationship "y varies directly as the product of s and r" represents a proportional relationship between y, s, and r, governed by the constant of variation (k).