ac1 query

Good work. Be sure to see my note in answer to your question.

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Applied Calculus I Asst # 09-09-2005

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Applied Calculus I Asst # 1 09-09-2005

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18:31:18

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**** query AppCal1 Section 0.1 solve x/2-x/3>5

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18:44:21 To solve you must find a common Denominator which is 6. You multiply both sides by 6. 6(x/2-x/3)>6(5) 6x/2-6x/3>30 Then you take the equation and simplify 3x-2x>30 x>30

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18:44:23

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**** Did you multiply a common denominator (easier) or make it hard on yourself and put everything over a common denominator?

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18:44:47 Multiply a common denominator

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18:44:47

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**** What was your equation after this step?

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18:45:19 6x/2-6x/3>30

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18:45:20

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**** What is your solution?

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18:45:30 x>30

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18:45:30

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**** Describe the interval or intervals you shaded on your graph.

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18:47:06 You put an open interval at 30 and shade to the right to infinity

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18:47:06

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**** query AppCal1 Section 0.1 solve 2x^2+1<9x-3

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18:56:10 2x^2+1<9x-3 You subtract 9x-3 from both sides to get 2x^2-9x+4. You then use the quadratic formula to solve the equation. -(9)+or- the square root of [(9)^2-4(2)(4)]/2(2) = -9+or- the square root of [49]/4. Then you solve for the + and -. -9+7/4=-1/2 -9-7/4=-4

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18:56:10

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**** Did you express this equation in the form quad<0 or 0

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18:56:28 quad<0

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**** If not, what did you do? If so, what were the zeros of your quadratic?

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18:56:42 did it

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18:56:44

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**** Your zeros divide the x axis into three intervals. Over which interval(s) is the equation true?

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19:12:01 all intervals

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**** Query Add comments on any surprises or insights you experienced as a result of this assignment.

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19:14:14 I had trouble determining the intervals for the second problem. How do you determine if it will be < or > fro the x.

The given solution should have detailed this process, and you should have self-critiqued your solution in response to the given solution. Had you done so the solution would be shown here.

Briefly, though, the zeros you show for the function divide the real line into the intervals (-infinity, -4), (-4, -1/2) and (-1/2, infinity). The quadratic expression can change sign only by going through one of these zeros. So on each interval, the solution is always positive or always negative. To test, you just plug in the x coordinate of some point in the interval and see which it is.

The interval(s) on which the expression 2x^2-9x+4 is negative are the solutions to the equation 2x^2-9x+4 < 0.

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19:14:18 Your response has been entered.

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19:14:18 Your response has been entered.

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19:14:22 ok

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