W is partly constant and partly varies invesly as the square of t, when w=24,t=4and when w=18,t=2
To solve this problem, we can start by setting up a mathematical relationship between w and t. Let's assume that the constant part of w is represented by "k".
Given that w is partly constant and partly varies inversely as the square of t, we can write the relationship as:
w = k * (1/t^2)
Now, we need to use the given data points to find the value of k.
Given: w = 24 when t = 4
Substituting these values into the equation, we get:
24 = k * (1/4^2)
24 = k * (1/16)
Multiplying both sides by 16, we find:
384 = k
So, the constant part of w is 384.
Now, let's use the second data point to find the value of k (the constant part) when w = 18 and t = 2.
18 = k * (1/2^2)
18 = k * (1/4)
Multiplying both sides by 4, we find:
72 = k
We have found two values for k using the two data points. This indicates that the constant part of w can have different values for different values of t.
Therefore, the equation that represents the relationship between w and t is:
w = k * (1/t^2)
where k can take different values based on the given data points.