Assignment 29 QA

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course Mth 151

12/19 11

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 = k * 12

9 / 12 = k k =.75.

y = .75

x = 32

y = .75 * 32 = 24

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):

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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:

8 = k * 12^2

8 = 144 k

k = 8 / 144 = 1 / 18.

y = 1/18 x^2 x = 9

y = 1/18 * 9^2 = 81 / 18 = 4.5

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):

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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 = k / 200

k = 120 * 200 = 24,000

y = 24,000 / x x = 500

y = 24,000 / 500 = 480

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):

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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 / 12^2

8 = k / 144

k = 8 * 144 = 1152.

y = 1152 / x^2 x = 16

y = 1152 / (16)^2 = 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:

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):

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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:

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:

confidence rating #$&*:

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Self-critique Rating: