Query 29

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course Mth 151

029.  `query 29 

 

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Question:  `q7.3.18  (1/3) / 6 = 1/18.  Is this ratio equation valid or not and how did you determine your answer?

 

 

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Your solution: 

 Valid

 

 

confidence rating #$&*: 3

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Given Solution: 

`a**If we multiply both sides by 6 * 18 we get

 

6 * 18 * (1/3 ) / 6 = 6 * 18 * (1 / 18) or

 

18 * 1/3 = 6.  Note that the effect here is the same as that of 'cross-multiplying', but it's a good idea to remember that 'cross-multiplying' is really a shortcut way to think of multiplying both sides by the common denominator.

 

Since 18 * 1/3 = 18 / 3 = 6, the equation 18 * 1/3 = 6 is true, which verifies the original equality. **

 

 

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Self-critique (if necessary): ok

 

 

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Self-critique Rating: 3

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Question:  `q7.3.20  z/8 = 49/56.  Solve this proportionality for z.

 

 

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Your solution: 

 Z = 7

 

 

confidence rating #$&*: 3

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Given Solution: 

`a**Multiply both sides by 8 * 56 to get

 

8 * 56 * z / 8 = 8 * 56 * 49 / 56.  Simplify to get

 

56 * z = 8 * 49.  Divide both sides by 56 to get

 

z = 8 * 49 / 56.  Simplify to get

 

z = 7.  **

 

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Self-critique (if necessary): ok

 

 

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Self-critique Rating: 3

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Question:  `q7.3.42  8 oz .45; 16 oz. .49; 50 oz. 1.59`sb   Which is the best value per unit for green beans and how did you obtain your result?

 

 

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Your solution: 

 Best value is 16 oz for .49

 

 

confidence rating #$&*: 3

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Given Solution: 

`a** 45 cents / 8 oz = 5.63 cents / oz.

49 cents / 16 oz = 3.06 cents / oz.

159 cents / 50 oz = 3.18 cents / oz.

 

16 oz for .49 is the best value at 3.06 cents / oz. **

 

 

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Self-critique (if necessary): ok

 

 

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Self-critique Rating: 3

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Question:  `q7.3.45  triangles 4/3, 2, x; 4, 6, 3.  What is the value of x and how did you use an equation to find it?

 

 

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Your solution: 

 X = 1

 

 

confidence rating #$&*: 3

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Given Solution: 

`a** the 4/3 corresponds to 4, 2 corresponds to 6, and x corresponds to 3.

 

The ratios of corresponding sides are all equal.

 

So 4/3 / 4 = 2 / 6 = x / 3.

 

Just using x / 3 = 2 / 6 we solve to get x = 1. 

 

We would have obtained the same thing if we had used x / 3 = 4/3 / 4.  **

 

 

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Self-critique (if necessary): ok

 

 

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Self-critique Rating: 3

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Question:  `qIf z = 9  when x = 2/3 and z varies inversely as x, find z when x = 5/4.  Show how you set up and used an equation of variation to solve this problem.

 

 

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Your solution: 

 If z varies inversely as x then z = k / x.

 z = 6 / (5 /4 ) = 24 / 5 = 4.8

 

 

confidence rating #$&*: 3

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Given Solution: 

`a** If z varies inversely as x then z = k / x. 

 

Then we have

 

9 = k / ( 2/3).  Multiplying both sides by 2/3 we get

 

2/3 * 9 = k so

 

k = 6. 

 

Thus z = 6 / x.  So when x = 5/4 we have

 

z = 6 / (5 /4 ) = 24 / 5 = 4.8. Note that the translations of other types of proportionality encountered in this chapter include:

 

z = k x^2:  z varies as square of x.

 

z = k / x^2:  z varies inversely as square of x.

 

z = k x:  z is proportional to x. **

 

 

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Self-critique (if necessary): ok

 

 

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Self-critique Rating: 3

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Question:  `q7.3.72. Illumination is inversely proportional to the square of the distance from the source.  Illumination at 4 ft is 75 foot-candles.  What is illumination at 9 feet? 

 

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Your solution: 

 k = 1200

At distance, 9 the illumination is about 14.8

 

 

confidence rating #$&*: 3

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Given Solution: 

`a**Set up the variation equation I = k / r^2, where I stands for illumination and r for distance (you might have used different letters).   This represents the inverse proportionality of illumination with the square of distance.

 

Use I = 75 when r = 4 to get

 

75 = k / 4^2, which gives you

 

k = 75 * 4^2 = 75 * 16 = 1200. 

 

Now rewrite the proportionality with this value of k:  I = 1200 / r^2. 

 

To get the illumination at distance 9 substitute 9 for r to get

 

I = 1200 / 9^2 = 1200 / 81 = 14.8 approx.. 

 

The illumination at distance 9 is about 14.8.

 

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Self-critique (if necessary): ok

 

 

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Self-critique Rating: 3

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Question:  `q7.3.66 length inv prop width; L=27 if w=10; w = 18.  L = ?

 

Explain how you set up and used a variation equation to obtain the length as a function of width, giving your value of k.  Then explain how you used your equation to find the length for width 18

 

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Your solution:  L = 15

 

 

confidence rating #$&*: 3

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Given Solution: 

`a**Set up the variation equation L = k / w, which is the inverse proportion.

 

Use L = 27 when w = 10 to get

 

27 = k / 10, which gives you

 

k = 27 * 10 = 270. 

 

Now we know that L = 270 / w. 

 

So if w = 18 you get

 

L = 270 / 18 = 15. **

 

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Self-critique (if necessary):

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Self-critique rating:

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Question:  `q7.3.66 length inv prop width; L=27 if w=10; w = 18.  L = ?

 

Explain how you set up and used a variation equation to obtain the length as a function of width, giving your value of k.  Then explain how you used your equation to find the length for width 18

 

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Your solution:  L = 15

 

 

confidence rating #$&*: 3

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Given Solution: 

`a**Set up the variation equation L = k / w, which is the inverse proportion.

 

Use L = 27 when w = 10 to get

 

27 = k / 10, which gives you

 

k = 27 * 10 = 270. 

 

Now we know that L = 270 / w. 

 

So if w = 18 you get

 

L = 270 / 18 = 15. **

 

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Self-critique (if necessary):

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Self-critique rating:

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