QA 73

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course mth 151

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:

y=kx

9=x*12

9/12=x*12/12

.75=x

y=.75*32

y=24

confidence rating #$&*:3

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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):

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Self-critique Rating:

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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=kx^2

8/144=k*12^2/144

1/18=k

y=1/18*9^2

1/18*81/1=4.5

y=4.5

confidence rating #$&*:3

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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):

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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:

y=k/x

20*120=k/200*200

24,000=k

y=24000/500

k=480

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):

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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:

8=k/x^2

8=k/12^2

144*8=k/144*144

k=1152

y=1152/16^2

1152/256

y=4.5

confidence rating #$&*:3

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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=kx^2

4*40=k*10^2/4*4

160/100=k*10^2 100k/100

k=1.6

y=1.6*20^2/12

1.6*400/12

640/12

y=53.3333

y=53 1/3

confidence rating #$&*:3

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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:

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Question: `q006. If y is proportional to x^2, with y = 9 when x = 2, what is the value of y when x = 17?

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Your solution:

9=k*2^2

9/4=k*4/4

k=2.25

y=2.25*17^2

y=650.25

confidence rating #$&*:

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Question: `q007. If y is inversely proportional to x^3, with y = 9 when x = 7, then what is the value of y when x = 2?

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Your solution:

9=k/7^3

9=k/343

k=3087

y=3087/8

y=385.875

confidence rating #$&*:

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Self-critique Rating:

&#Your work looks very good. Let me know if you have any questions. &#