Variation-Check Problems

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Can you please check my answers? Thanxs!

Write an equation that expresses the relationship. Use k as the constant of variation.

20. f varies jointly as b and the square of c.
-I got: f=kbc^2

22. r varies jointly as the square of s and the square of t.
-I got: r=ks^2t^2

Find the variation equation for the variation statement.
31. z varies jointly as y and the cube of x; z=96 when x=2 and y=6 (I don't understand this one. My answer choices are: a.y=2x^3y,b.y=2xy^3, c.y=-2x^3y, or d. y=-2xy^3)

Determine the constant of variation for the stated condition.
40. z varies jointly as x and y, and z=84 when x=28 and y=12.
I got: z=xy, 84=k*22*12, 84=336k, I divided both sides by 336 and I got k=84/336, but it can be reduced, so k=1/4

Solve the problem.

46. h varies jointly as f and g. Find h when f=27, g=12, and k=3.
I got: h=kfg, h=3*27*12, h=972

Write an equation that expresses the relationship. Use k for the constant of proportinality.

50. p varies directly as r and inversely as s.
-I got: p=kr/s

53. r varies directly as s and inversely as the square of t.
-I got: r=ks/t^2

Determine the constant of variation for the stated condition.

58. z varies directly as x and inversely as y, and z=2 when x=30 and y=60.
I got: z=kx/y, 2=k*30/60, I multiplied each side by 60, and got 120=30k, I divided each side by 30, and got k=120/30, it reduces to k=4

60. z varies directly as x and inversely as y, and z=4 when x=77 and y=28.
-I got:z=kx/y, 4=k*77/25, I multiplied each side by 25 and got 112=77k, I divided both sides by 77, and got k=16/11.

Solve the problem.

66. y varies jointly as a and b inversely as the square root of c, y=24 when a=6,b=4, and c=49. Find y when a=2, b=5, and c=16.
-I got: y=kab/ sqrt of c, y=2*5/ sqrt of 16, y=10/4, which reduces to y=2.5

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