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
they are all right! Good job
If y is directly proportional to x3 and y = 17 when x = 7, find y if x = 5. (Round off your answer to the nearest hundredth.)
Your answers are mostly correct. Here are the corrections:
For question 31, the correct answer is: d) y = -2xy^3. You made a sign error.
For question 58, the correct answer is: k = 2. You made a calculation error when solving for k.
For question 60, the correct answer is: k = 16/77. You made a calculation error when solving for k.
For question 66, the correct equation is: y = kab/√c. With the given values, y = (6 * 4) / √49 = 24 / 7. So when a = 2, b = 5, and c = 16, y = (2 * 5) / √16 = 10 / 4 = 2.5.
So overall, you did a good job. Just pay attention to signs and double-check your calculations to avoid errors.
20. Your answer is correct: f = kbc^2.
22. Your answer is correct: r = ks^2t^2.
31. To find the variation equation for this statement, we need to express z in terms of y and x. Since z varies jointly as y and the cube of x, the variation equation would be z = kyx^3. From the given information, z = 96 when x = 2 and y = 6. Plugging these values into the variation equation, we get 96 = k * 6 * 2^3 = 96 = 48k. To solve for k, divide both sides by 48: k = 96 / 48 = 2. So the variation equation is z = 2yx^3. Comparing this with the answer choices, none of the given choices match the correct variation equation. Therefore, the answer is not provided.
40. Your steps are correct. The variation equation is z = xy, and when x = 28 and y = 12, we have 84 = k * 28 * 12. Solving for k, we get k = 1/4.
46. You're almost correct. Since h varies jointly as f and g, the variation equation is h = kfg. Plugging in f = 27, g = 12, and k = 3, we get h = 3 * 27 * 12 = 972.
50. Your answer is correct: p = kr/s.
53. Your answer is correct: r = ks/t^2.
58. Your steps are correct. The variation equation is z = kx/y, and when z = 2, x = 30, and y = 60, we have 2 = k * 30 / 60. Solving for k, we get k = 4.
60. Your steps are correct. The variation equation is z = kx/y, and when z = 4, x = 77, and y = 28, we have 4 = k * 77 / 28. Solving for k, we get k = 16/11.
66. Your steps are correct. The variation equation is y = kab / sqrt(c), and when y = 24, a = 6, b = 4, and c = 49, we have 24 = k * 6 * 4 / sqrt(49). Solving for k, we get k = 24 / (6 * 4 / 7) = 7. Now, plugging in a = 2, b = 5, c = 16, and k = 7 into the variation equation, we get y = 7 * 2 * 5 / sqrt(16) = 70 / 4 = 17.5. So, y = 17.5.