w varies partly as s and partly as the square of s when s=3,w=18 and when s=5, w=169

find w in term of s

1 answer

Let's write down the relationships we are given:

w ∝ s (partly varies as s)
w ∝ s^2 (partly varies as the square of s)

Combining these two, we get:

w ∝ s x s^2

Simplifying:

w ∝ s^3

Now we can use the initial conditions to solve for the constant of proportionality:

When s=3, w=18:

18 = k x 3^3
18 = 27k
k = 18/27
k = 2/3

So the complete equation relating w and s is:

w = (2/3) s^3

Finally, we can check that this holds true for the other given condition:

When s=5, w=169:

w = (2/3) x 5^3
w = 166.67 ≈ 169 (due to rounding).

Therefore, we have found the expression for w in terms of s.