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
IF THE VALUE OF Y VARIES DIRECTLY WITH X AND Y = -8 WHEN X=20, FIND Y IF X=-4.
Let's go through each problem and check your answers:
20. The equation expressing the relationship is indeed f = kbc^2. Your answer is correct.
22. The equation for this relationship is r = ks^2t^2. Your answer is correct.
31. The variation equation for this statement is y = 2x^3y. Your answer is incorrect. To find the variation equation, we use the formula z = kxy^3. Substituting the given values, we get 96 = k * 2 * 6^3. Solving for k, we get k = 96 / (2 * 216) = 1/216. Therefore, the correct equation is y = (1/216)x^3y.
40. Your calculation is correct. The variation equation is z = xy. Substituting the given values, we get 84 = k * 28 * 12. Solving for k, we get k = 84 / (28 * 12) = 1/4.
46. The calculation is correct. The equation is h = kfg. Substituting the given values, we get h = 3 * 27 * 12 = 972.
50. Your equation p = kr/s is correct.
53. Your equation r = ks/t^2 is correct.
58. Your calculation is correct. The equation is z = kx/y. Substituting the given values, we get 2 = k * 30 / 60. Solving for k, we get k = 2 * 60 / 30 = 4.
60. Your calculation is correct. The equation is z = kx/y. Substituting the given values, we get 4 = k * 77 / 28. Solving for k, we get k = 4 * 28 / 77 = 16/11.
66. The correct variation equation is y = kab / sqrt(c). Substituting the given values, we get 24 = k * 6 * 4 / sqrt(49). Solving for k, we get k = 24 * sqrt(49) / (6 * 4) = 4. Substituting the new given values, we get y = 4 * 2 * 5 / sqrt(16) = 40/4 = 10.
Overall, your answers for problems 20, 22, 40, 46, 50, 53, 58, 60, and 66 are correct. However, your answer for problem 31 is incorrect. The correct equation is y = (1/216)x^3y.