course Mth 151 ېyyd률assignment #029
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13:28:00 7.3.18 (1/3) / 6 = 1/18. Is this ratio equation valid or not and how did you determine your answer?
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RESPONSE --> (1/3) / 6 = 1/18 1/3(18) = 6(1) 6 = 6 valid
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13:28:19 **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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RESPONSE --> ok
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13:30:35 7.3.20 z/8 = 49/56. Solve this proportionality for z.
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RESPONSE --> z/8 = 49/56 49(8) = 56z 392 = 56z z = 7
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13:30:39 **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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RESPONSE --> ok
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13:31:58 7.3.42 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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RESPONSE --> .45/8 = .056 .49/16 = .0306 1.59/50 = .0318 The 16 oz is the cheapest.
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13:33:17 ** 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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RESPONSE --> ok
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13:35:20 7.3.45 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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RESPONSE --> I compared the two triangles in the following way: (4/3)/4 x/3 2/6 I reduced the 2/6 to 1/3 and then thought that x/3 is the same as 1/3, so x = 1. I don't think this way is quite right, but the triangle part confused me just a little.
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13:35:53 ** 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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RESPONSE --> Oh. I guess I was right.
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13:39:08 If 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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RESPONSE --> y = k/x^2 9 = k/(2/3)^2 9 = k/(4/9) multiply both sides by 4/9 k = 4 y = 4/(5/4)^2 y = 4/(25/16) multiply both sides by 25/16 y = 2.56 or 64/25
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13:41:33 ** 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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RESPONSE --> Don't you square the first x (2/3)?
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13:48:36 7.3.72. 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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RESPONSE --> I couldn't seem to figure out the problem using the inverse variations (y = k/x or y = k/x^2) so I tried working the problem using a proportion equation. 4/75 = 9/x 4x = 9(75) 4x = 675 x = 168.75
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13:53:39 **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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RESPONSE --> When I started to use the appropriate formulas (instead of cross multiplying) I mixed up where the numbers should go. My beginning equation was 4 = k/75^2. In general, I get confused on what x and y could stand for. Now that I reread the problem in the book, I see why 75 was y and 4 is x^2.
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13:58:41 7.3.66 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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RESPONSE --> My question 66 isn't about the length inv prop width; L=27 if w=10; w = 18. L = ?. I see now, number 64. x - width y - length k - area xy = k 10(27) = k k = 270 y = k/x y = 270/18 y = 15
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13:58:50 **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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RESPONSE --> ok
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