Final Assignment QA

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19:50:34 `q001. Note that there are five questions in this set. If y is proportional to x, and if y = 9 when x = 12, then what is the value of y when x = 32?

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RESPONSE --> Since y=kx when y varies directly as x, then 9=k12. divide by 12, k= 9/12 = 4/3. Enter in values: y = (4/3) * 32 y = 42.666

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19:52:05 To say that y is proportional to x is to say that there exists some constant number k such that y = k x. Using the given values of y and x we can determine the value of k: Since y = 9 when x = 12, y = k x becomes 9 = k * 12. Dividing both sides by 12 we obtain 9 / 12 = k. Reducing and reversing sides we therefore obtain k =.75. Now our proportionality reads y = .75 x. Thus when x = 32 we have y = .75 * 32 = 24.

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RESPONSE --> I put in 12/9 rather than 9/12. I see my mistake.

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19:54:23 `q002. If y is proportional to the square of x, and y = 8 when x = 12, then what is the value of y when x = 9?

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RESPONSE --> y = kx^2 8 = k 12^2 8 = k*144 div. by 144 k = 1/18 y = (1/18) * 9^2 y = 4.5

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19:54:44 To say that y is proportional to x is to say that there exists some constant number k such that y = k x^2. Using the given values of y and x we can determine the value of k: Since y = 8 when x = 12, y = k x^2 becomes 8 = k * 12^2, or 8 = 144 k. Dividing both sides by 144 we obtain k = 8 / 144 = 1 / 18. Now our proportionality reads y = 1/18 x^2. Thus when x = 9 we have y = 1/18 * 9^2 = 81 / 18 = 4.5.

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RESPONSE --> ok

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19:56:24 `q003. If y is inversely proportional to x and if y = 120 when x = 200, when what is the value of y when x = 500?

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RESPONSE --> y = k/x 120 =k / 200 k = 24000 y = 24000/500 y = 48

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19:57:00 To say that y is inversely proportional to x is to say that there exists some constant number k such that y = k / x. Using the given values of y and x we can determine the value of k: Since y = 120 when x = 200, y = k / x becomes 120 = k / 200. Multiplying both sides by 200 we obtain k = 120 * 200 = 24,000. Now our proportionality reads y = 24,000 / x. Thus when x = 500 we have y = 24,000 / 500 = 480.

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RESPONSE --> ok

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19:58:50 `q004. If y is inversely proportional to the square of x and if y = 8 when x = 12, then what is the value of y when x = 16?

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RESPONSE --> y = k/x^2 8 = k/12^2 k = 1152 y = 1152/16^2 y = 4.5

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19:58:59 To say that y is inversely proportional to the square of x is to say that there exists some constant number k such that y = k / x^2. Using the given values of y and x we can determine the value of k: Since y = 8 when x = 12, y = k / x^2 becomes 8 = k / 12^2, or 8 = k / 144. Multiplying both sides by 144 we obtain k = 8 * 144 = 1152. Now our proportionality reads y = 1152 / x^2. Thus when x = 16 we have y = 1152 / (16)^2 = 4.5.

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RESPONSE --> right

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20:04:00 `q005. If y is proportional to the square of x and inversely proportional to z, then if y = 40 when x = 10 and z = 4, what is the value of y when x = 20 and z = 12?

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RESPONSE --> y = kx^2 / z 40 = (k*10^2)/4 40 = k100 /4 160 = k100 k = 1.6 y = (1.6 *20^2)/12 y = 640/12 y = 53.33

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20:04:29 To say that y is proportional to the square of x and inversely proportional to z is to say that the there exists a constant k such that y = k x^2 / z. Substituting the given values of x, y and z we can evaluate k: y = k x^2 / z becomes 40 = k * 10^2 / 4. Multiplying both sides by 4 / 10^2 we obtain 40 * 4 / 10^2 = k, or k = 1.6. Our proportionality is now y = 1.6 x^2 / z, so that when x = 20 and z = 12 we have y = 1.6 * 20^2 / 12 = 1.6 * 400 / 12 = 53 1/3.

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RESPONSE --> right

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You appear to be in great shape here. Good luck on the Chapter 7 test.