W is partly constant and partly varies inversely as the square of t. when w=24, t=4 and when w=18, t=2. i. determine the law connecting w and t ii. find t when w = 46
w = a+bt^2
using the given values,
a+4b = 24
a+2b = 18
solve for a and b, and then solve a+bt = 46
To determine the law connecting W and T, we can use the given information:
When W = 24, T = 4
When W = 18, T = 2
Let's solve for the constant part of W first.
Step 1: Write down the relationship
W = K * (1/T^2)
Step 2: Substitute the values of W and T from the first set of data
24 = K * (1/4^2)
24 = K * (1/16)
Step 3: Solve for K
K = 24 * 16
K = 384
So, the equation connecting W and T is W = 384 * (1/T^2).
Now let's proceed to find T when W = 46.
Step 1: Substitute the given value of W into the equation
46 = 384 * (1/T^2)
Step 2: Solve for T
1/T^2 = 46/384
T^2 = 384/46
T^2 = 8.3478
Taking the square root of both sides:
T = sqrt(8.3478)
T ≈ 2.893
Therefore, when W = 46, T ≈ 2.893.
To determine the law connecting W and T, we know that W is partly constant and partly varies inversely as the square of T. This means that we can express the relationship as:
W = k * (1/T^2)
Where k is the constant of variation.
To find the value of k, we can use the given values of W and T.
When W is 24 and T is 4:
24 = k * (1/4^2)
24 = k * (1/16)
k = 24 * 16 = 384
Now we have the value of k as 384.
To find T when W is 46, we can use the same formula:
W = k * (1/T^2)
Substituting the given values:
46 = 384 * (1/T^2)
To solve for T, we can rearrange the equation:
1/T^2 = 46/384
T^2 = 384/46
T^2 = 8.3478
Taking the square root of both sides:
T = √8.3478
T ≈ 2.887
Therefore, when W is 46, T is approximately 2.887.