#$&* course mth 151 8-8 6 029. Variation
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Given Solution: To say that y is proportional to x is to say that there exists some constant number k such that y = k x. Using the given values of y and x we can determine the value of k: Since y = 9 when x = 12, y = k x becomes 9 = k * 12. Dividing both sides by 12 we obtain 9 / 12 = k. Reducing and reversing sides we therefore obtain k =.75. Now our proportionality reads y = .75 x. Thus when x = 32 we have y = .75 * 32 = 24. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique rating #$&*:3 ********************************************* 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? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 8= k12^2 8/144 = k 1/18 = k y = 1/18*9^2 y = 4.5 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: To say that y is proportional to x is to say that there exists some constant number k such that y = k x^2. Using the given values of y and x we can determine the value of k: Since y = 8 when x = 12, y = k x^2 becomes 8 = k * 12^2, or 8 = 144 k. Dividing both sides by 144 we obtain k = 8 / 144 = 1 / 18. Now our proportionality reads y = 1/18 x^2. Thus when x = 9 we have y = 1/18 * 9^2 = 81 / 18 = 4.5. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique rating #$&*:3 ********************************************* 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? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 120 = k / 200 120*200=k 24000=k y=24000/500 y = 480 confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: To say that y is inversely proportional to x is to say that there exists some constant number k such that y = k / x. Using the given values of y and x we can determine the value of k: Since y = 120 when x = 200, y = k / x becomes 120 = k / 200. Multiplying both sides by 200 we obtain k = 120 * 200 = 24,000. Now our proportionality reads y = 24,000 / x. Thus when x = 500 we have y = 24,000 / 500 = 480. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique rating #$&*:3 ********************************************* 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? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 8 = k/12^2 1152 = k y = 1152 / 16^2 y= 4.5 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: To say that y is inversely proportional to the square of x is to say that there exists some constant number k such that y = k / x^2. Using the given values of y and x we can determine the value of k: Since y = 8 when x = 12, y = k / x^2 becomes 8 = k / 12^2, or 8 = k / 144. Multiplying both sides by 144 we obtain k = 8 * 144 = 1152. Now our proportionality reads y = 1152 / x^2. Thus when x = 16 we have y = 1152 / (16)^2 = 4.5. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique rating #$&*:3 ********************************************* 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? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 40 = k*10^2 / 4 40*4/10^2 = k 1.6= k y= 1.6 * 20^2 / 12 y= 640/12 y= 53.33333333 confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: To say that y is proportional to the square of x and inversely proportional to z is to say that the there exists a constant k such that y = k x^2 / z. Substituting the given values of x, y and z we can evaluate k: y = k x^2 / z becomes 40 = k * 10^2 / 4. Multiplying both sides by 4 / 10^2 we obtain 40 * 4 / 10^2 = k, or k = 1.6. Our proportionality is now y = 1.6 x^2 / z, so that when x = 20 and z = 12 we have y = 1.6 * 20^2 / 12 = 1.6 * 400 / 12 = 53 1/3. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK ------------------------------------------------ Self-critique rating #$&*:3 "