The quantity is partly constant and partly varies inversely as the square of x. When w=1,x=11 and when w=2,x=5. Find the formula connecting w and x find w when x=4.
To find the formula connecting the values of w and x, we need to determine the relationship between them based on the given information.
Let's break down the problem into two parts:
Part 1: The quantity is partly constant:
When w=1, x=11
When w=2, x=5
Here, we notice that as w increases from 1 to 2, x decreases from 11 to 5. This means that there is no direct relationship between w and x when the quantity is constant.
Part 2: The quantity varies inversely as the square of x:
Let's assume the formula connecting w and x is:
w = k / (x^2)
where k is a constant.
Using the given data:
When w=1, x=11:
1 = k / (11^2)
1 = k / 121
Solving for k:
k = 121
Therefore, the formula connecting w and x is:
w = 121 / (x^2)
To find w when x=4, substitute the value of x into the equation:
w = 121 / (4^2)
w = 121 / 16
w ≈ 7.5625
So, when x=4, the value of w is approximately 7.5625.
To find the formula connecting w and x, we need to determine the relationship between the two quantities based on the given information.
We are told that the quantity (let's call it Q) is partly constant and partly varies inversely as the square of x. This means we can write the equation as:
Q = k/x^2
where k is the constant of proportionality.
Now, we need to use the specific values given to find the value of k.
When w = 1 and x = 11, we have:
Q = k/(11^2) = k/121
When w = 2 and x = 5, we have:
Q = k/(5^2) = k/25
Since Q is partly constant, we can equate the two expressions for Q and solve for k:
k/121 = k/25
Cross-multiplying, we get:
25k = 121k
Subtracting 121k from both sides:
-96k = 0
Dividing by -96:
k = 0
Now that we have the value of k, we can write the formula connecting w and x as:
Q = 0/x^2
Simplifying, we have:
Q = 0
So, the formula linking w and x is Q = 0.
To find w when x = 4, we substitute x = 4 into the formula:
Q = 0/(4^2)
Q = 0/16
Q = 0
Therefore, when x = 4, the value of w is 0.