Question

Combine variation

if R varies directly as S and inversely as the square of U. And R=2 when S=18 And U=2 find
R when u=3 and s=27
S when u-2 and y=4
U when r=1 and s=36​

Answer 1

If R varies directly as S and inversely as the square of U, we can use the equation R = k(S/U^2), where k is the constant of proportionality. By substituting the given values, we can solve for k. Then, we can use the value of k to find R, S, and U in different scenarios.

Step-by-step explanation:

Given that R varies directly as S and inversely as the square of U, we can write the equation as R = k(S/U^2), where k is the constant of proportionality.

We are given that R=2 when S=18 and U=2. Using this information, we can solve for k. Substitute the given values into the equation: 2 = k(18/2^2), 2 = k(18/4), 2 = k(4.5). Divide both sides by 4.5 to isolate k: k = 2/4.5 = 4/9.

Now we can use the value of k to find R in other scenarios.

To find R when U=3 and S=27, substitute the values into the equation: R = (4/9)(27/3^2)

= (4/9)(27/9)

= (4/9)(3)

= 12/9

= 4/3.

To find S when U=2 and R=1, rearrange the equation and solve for S: R = (4/9)(S/2^2), 1

= (4/9)(S/4), 1

= (1/9)(S), 9

= S.

To find U when R=1 and S=36, rearrange the equation and solve for U: R = (4/9)(36/U^2),

1 = (4/9)(36/U^2),

1 = (4/9)(36/U^2). Multiply both sides by U^2 and divide by 4/9: U^2 = (36)(9/4),

U^2 = 81,

U = ±9.