#$&* course Mth 151 029. `query 29
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Given Solution: `a**If we multiply both sides by 6 * 18 we get 6 * 18 * (1/3 ) / 6 = 6 * 18 * (1 / 18) or 18 * 1/3 = 6. Note that the effect here is the same as that of 'cross-multiplying', but it's a good idea to remember that 'cross-multiplying' is really a shortcut way to think of multiplying both sides by the common denominator. Since 18 * 1/3 = 18 / 3 = 6, the equation 18 * 1/3 = 6 is true, which verifies the original equality. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `q7.3.20 z/8 = 49/56. Solve this proportionality for z. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Z = 7 confidence rating #$&*: 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: 3 ********************************************* 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? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: Best value is 16 oz for .49 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** 45 cents / 8 oz = 5.63 cents / oz. 49 cents / 16 oz = 3.06 cents / oz. 159 cents / 50 oz = 3.18 cents / oz. 16 oz for .49 is the best value at 3.06 cents / oz. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `q7.3.45 triangles 4/3, 2, x; 4, 6, 3. What is the value of x and how did you use an equation to find it? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: X = 1 confidence rating #$&*: 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. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: 3 ********************************************* 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. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: If z varies inversely as x then z = k / x. z = 6 / (5 /4 ) = 24 / 5 = 4.8 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** If z varies inversely as x then z = k / x. Then we have 9 = k / ( 2/3). Multiplying both sides by 2/3 we get 2/3 * 9 = k so k = 6. Thus z = 6 / x. So when x = 5/4 we have z = 6 / (5 /4 ) = 24 / 5 = 4.8. Note that the translations of other types of proportionality encountered in this chapter include: z = k x^2: z varies as square of x. z = k / x^2: z varies inversely as square of x. z = k x: z is proportional to x. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: 3 ********************************************* Question: `q7.3.72. Illumination is inversely proportional to the square of the distance from the source. Illumination at 4 ft is 75 foot-candles. What is illumination at 9 feet? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: k = 1200 At distance, 9 the illumination is about 14.8 confidence rating #$&*: 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. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ok ------------------------------------------------ Self-critique Rating: 3 ********************************************* 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 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: L = 15 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a**Set up the variation equation L = k / w, which is the inverse proportion. Use L = 27 when w = 10 to get 27 = k / 10, which gives you k = 27 * 10 = 270. Now we know that L = 270 / w. So if w = 18 you get L = 270 / 18 = 15. ** " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: `q7.3.66 length inv prop width; L=27 if w=10; w = 18. L = ? Explain how you set up and used a variation equation to obtain the length as a function of width, giving your value of k. Then explain how you used your equation to find the length for width 18 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: L = 15 confidence rating #$&*: 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. ** " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!