73 qa 1

#$&*

course Mth151

1158 am 12/9/12

If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

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=y/32

9*32=12*y

288=12y

24=y

confidence rating #$&*:

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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):

I think I did that a different way, I cross multiplied……….

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Self-critique Rating:

@&
I don't acknowledge cross multiplication or cancellation in my solutions, though if done correctly both are valid.

My reason is simply that I want to keep the number of rules to a minimum. As you can see from the given solution, you don't need anything but the principle that you can add or subtract the same quantity on both sides, multiply or divide both sides by the same number (as long as you don't divide by zero), or reverse sides.

Cross multiplication is equivalent to multiplying both sides by the common denominator and simplifying.
*@

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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:

Y:x^2

8:12

y:9

I am not sure.

confidence rating #$&*:

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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):

…ok

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Self-critique Rating:

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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:

120/200

y/500

y=300

confidence rating #$&*:

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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):

Ok, I understand.

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Self-critique Rating:

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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:

Y=k/x^2

8=k/12^2

8=k/144

1152=k

y = 1152 / x^2

y=1152/(16)^2

y=1152/256

y=4.5

confidence rating #$&*:

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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):

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Self-critique Rating:

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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:

y = k x^2 / z

40=k(10)^2/4

40=k25

1.6k

y=1.6(20^2)/12

Y=1.6*400/12

y=53.33333

confidence rating #$&*:

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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):

Ok…

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Self-critique Rating:2

Self-critique (if necessary):

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Self-critique rating:

73 qa 1

@& Very good. You caught on very well to the idea of setting up the proportionality and solving for the proportionality constant. *@

@&
Very good. You caught on very well to the idea of setting up the proportionality and solving for the proportionality constant.
*@