QA 28

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course Mth 151

4/10

If your solution to stated problem does not match the given solution, you should self-critique per instructions athttp://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

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Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

029. Variation

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Question: `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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Your solution: 9/12 32-12=20

Y=29

confidence rating #$&*: 2

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Given Solution:

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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Self-critique (if necessary):Oh, that makes more sense than what I tried to do!

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Self-critique Rating:0

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Right. You really want to think in terms of ratios here--that is, multiplication and division, not addition and subtraction.

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Question: `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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Your solution: 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 = 8 when x=12 ^2, y=kx becomes

8=k*144

.06=k

Now our proportionality reads y=.75x. Thus when x = 12 we have .06 * 81 = 4.86, or 5.

confidence rating #$&*: 2

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Given Solution:

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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Self-critique (if necessary): Well, I was closish.

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Self-critique Rating: 1

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If k = .06, then the proportionality is

y = .06 x

rather than y = .75 x.

You would in any case end up with the product .06 * 81, so you basically did this right. Better than closish (which, incidentally, is sort of an interesting-looking word; I've used it but never acually looked at it in print).

The only difference between your result and the given answer is roundoff error. Had you rounded 1/18 to, say, .055, your result would have been pretty much the same as the given result.

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Question: `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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Your solution: 120 = k * 200

.6 = k

500*.6= 300

confidence rating #$&*: 3

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Given Solution:

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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Self-critique (if necessary): Aw, shucks! Just when I had gotten the other way figured out! : )

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Self-critique Rating:0

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If the proportionality had been direct this would have been right on.

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Question: `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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Your solution: 8 = k/12^2

8*144 = k

1152=k

1152/16= 72

confidence rating #$&*: uhhh,.. I don’t think I did it right.

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Given Solution:

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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Self-critique (if necessary): Aha! I forgot to square the 16.

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Self-critique Rating:0

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Very good. You've got the process. Just watch out for the details.

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Question: `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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Your solution: 4 and 16?

confidence rating #$&*: 1

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Given Solution:

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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Self-critique (if necessary):

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Self-critique Rating:0

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Self-critique (if necessary):

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Self-critique rating:

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Self-critique (if necessary):

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Self-critique rating:

#*&!

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Good. I predict that you'll be in good shape with the text problems.

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Check my notes.

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