#$&* course Mth 151 029. `query 29
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Given Solution: `a**If we multiply both sides by 6 * 18 we get 6 * 18 * (1/3 ) / 6 = 6 * 18 * (1 / 18) or 18 * 1/3 = 6. Note that the effect here is the same as that of 'cross-multiplying', but it's a good idea to remember that 'cross-multiplying' is really a shortcut way to think of multiplying both sides by the common denominator. Since 18 * 1/3 = 18 / 3 = 6, the equation 18 * 1/3 = 6 is true, which verifies the original equality. **
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Given Solution: `a**Multiply both sides by 8 * 56 to get 8 * 56 * z / 8 = 8 * 56 * 49 / 56. Simplify to get 56 * z = 8 * 49. Divide both sides by 56 to get z = 8 * 49 / 56. Simplify to get z = 7. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I got it right, and I think I did it the same way that you did….. ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q7.3.42 8 oz .45; 16 oz. .49; 50 oz. 1.59`sb Which is the best value per unit for green beans and how did you obtain your result? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: I believe what you would do is take each ounces and divided by the cost and it will give us what is cost per ounce and therefore telling us the best value per unit. .45/8 = .056 per unit .49/16 = .030 per unit 1.59/50 = .031 per unit The best value is the 16 oz for .49…. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): I got it right!!!! ------------------------------------------------ Self-critique Rating: ********************************************* 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: Even looking at the book I am not sure what to do. I understand that the 4/3 is to 4; 2 is to 6 and x is to 3. But from there I am not sure. confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** the 4/3 corresponds to 4, 2 corresponds to 6, and x corresponds to 3. The ratios of corresponding sides are all equal. So 4/3 / 4 = 2 / 6 = x / 3. Just using x / 3 = 2 / 6 we solve to get x = 1. We would have obtained the same thing if we had used x / 3 = 4/3 / 4. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Darn it I had it right. But I didn’t do the x/3 - 4/3/4; If I would done that one and got the 1 again, I would have said that. I hate that I do this so often. I do understand what we are supposed to do and why…. ------------------------------------------------ Self-critique Rating: ********************************************* Question: `qIf z = 9 when x = 2/3 and z varies inversely as x, find z when x = 5/4. Show how you set up and used an equation of variation to solve this problem. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: I just don’t know what to do!!!! When looking what the a part of the solution and not looking further I got that the z = 4.8 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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): I got this right; of course I cheated a little by seeing the first sentence in your given solution…. ------------------------------------------------ Self-critique Rating: ********************************************* 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: Once again, I just not sure what I need to do with this problem. confidence rating #$&*:: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a**Set up the variation equation I = k / r^2, where I stands for illumination and r for distance (you might have used different letters). This represents the inverse proportionality of illumination with the square of distance. Use I = 75 when r = 4 to get 75 = k / 4^2, which gives you k = 75 * 4^2 = 75 * 16 = 1200. Now rewrite the proportionality with this value of k: I = 1200 / r^2. To get the illumination at distance 9 substitute 9 for r to get I = 1200 / 9^2 = 1200 / 81 = 14.8 approx.. The illumination at distance 9 is about 14.8. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): I got it why you did what you did, but this will be another chapter that is going to get me!!! Ugh!! ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q7.3.66 length inv prop width; L=27 if w=10; w = 18. L = ? Explain how you set up and used a variation equation to obtain the length as a function of width, giving your value of k. Then explain how you used your equation to find the length for width 18 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: L = 15; I got this by doing the following: 27 = k/10; times each side by 10; 270 = k; 18 = 270/L; times each side by L; 18L = 270; divide each side by 18 Giving me L = 15 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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; I got this by doing the following: 27 = k/10; times each side by 10; 270 = k; 18 = 270/L; times each side by L; 18L = 270; divide each side by 18 Giving me L = 15 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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: #*&!