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
w = a + b/x^2
So, now you have
a + b/121 = 1
a + b/25 = 2
b = 3025/96
now find a, and w(4)
Alright thanks
To find the formula connecting \(w\) and \(x\) when \(w = 1\) and \(x = 11\), we can start by writing the relationship between the quantity and \(x\) as a combination of a constant and an inverse relationship.
Let's assume that the constant value is \(k\). We can write the relationship as:
Quantity = \(k \cdot \frac{1}{{x^2}}\)
Substituting the values \(w = 1\) and \(x = 11\) into the equation, we get:
1 = \(k \cdot \frac{1}{{11^2}}\)
1 = \(k \cdot \frac{1}{{121}}\)
Simplifying further, we get:
1 = \(\frac{k}{{121}}\)
Now, solve for the value of \(k\):
k = 121
So, the formula connecting \(w\) and \(x\) is:
Quantity = \(121 \cdot \frac{1}{{x^2}}\)
To find \(w\) when \(x = 4\), we will use the formula we found. Substitute the value \(x = 4\) into the equation:
Quantity = \(121 \cdot \frac{1}{{4^2}}\)
Simplifying:
Quantity = \(121 \cdot \frac{1}{16}\)
Quantity = \(7.5625\) (approximately)
Therefore, when \(x = 4\), \(w\) is approximately equal to \(7.5625\).