Suppose that b is proportional to c, and inversely
proportional to the square of d. If b = 45 when
c = 40 and d = 2, find b when c =20 and d = 3.
we have b = kc/d^2
So, bd^2/c = k is constant
That mean you want b such that
9b/20 = 45*2^2/40
...
I'm not that good at math Steve. Would you describe for me in a simpler way?
Thank you,
Kim
To solve this problem, we need to use the concept of direct and inverse proportionality. The relationship between b, c, and d can be expressed as:
b ∝ c
b ∝ 1/d^2
Let's find the constant of proportionality first. When b = 45, c = 40, and d = 2:
45 ∝ 40 (Equation 1)
45 ∝ 1/2^2 = 1/4 (Equation 2)
Now, we can equate the two proportionality equations to find the constant of proportionality:
40 = k/4
k = 160
We have determined that k, the constant of proportionality, is equal to 160.
Now, we can find b when c = 20 and d = 3 using the constant of proportionality:
b ∝ c implies b = k * c
b = 160 * 20
b = 3200
b ∝ 1/d^2 implies b = k/(d^2)
b = 160 / (3^2)
b = 160 / 9
So, when c = 20 and d = 3, b is equal to 3200 and 160/9, respectively.