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  1. Replies
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    You don't tell us what answer you got from the...

    You don't tell us what answer you got from the quadratic formula or how you got it. So it is impossible to tell where your train flew off the tracks.

    3x^2 - 2x + 7 = 0 \implies x = \dfrac{-\ (-\...
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    Lovely

    Lovely
  3. I do not believe "numeral" means "digit." The...

    I do not believe "numeral" means "digit." The Arabic numeral for "twenty" is 20, and the Roman numeral for "twenty" is XX. "Numeral" means a symbol representing a unique number.

    "Digit" is a word...
  4. Because our students NEVER post in the wrong...

    Because our students NEVER post in the wrong forum!
  5. \text {Area of rectangle in first quadrant} =...

    \text {Area of rectangle in first quadrant} = a_1.

    \text {Area of rectangle in first and second quadrant} = a_2.

    a_1 = (x - 0) * (12 - x^2) = 12x - x^3 \implies

    \dfrac{da_1}{dx} = 12 - 3x^2...
  6. I think what is being asked is whether, to...

    I think what is being asked is whether, to compute the maximum area of a rectangle bounded by the x-axis, y-axis, and the given parabola, you can halve the maximum area of a rectangle bounded by the...
  7. Whether mmm's answer is algebra in disguise...

    Whether mmm's answer is algebra in disguise depends on how we define algebra. I don't think his answer depends on elementary algebra in its traditional sense. It is more a combination of trial and...
  8. \text {Let } u = k + 1 \implies \{3(k + 1) -...

    \text {Let } u = k + 1 \implies \{3(k + 1) - 1\}^2 = (3u - 1)^2 = (3u - 1)(3u - 1) =

    3u(3u - 1) - 1(3u - 1) = 9u^2 - 3u - 3u + 1 = 9u^ 2 - 6u + 1 \implies

    \{3(k + 1) - 1\}^2 = 9(k + 1)^2 - 6(k...
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    I am going to try again. When you want to...

    I am going to try again.

    When you want to eliminate fractions from an equation, you multiply both sides by the least common multiple of the denominators. You multiplied both sides by 2, WHICH IS...
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    NO WONDER YOU ARE CONFUSED. I made an error. My...

    NO WONDER YOU ARE CONFUSED. I made an error. My original post made NO SENSE. My abject apologies. I do not have the time to correct myself right now. I shall be back in a little over an hour and try...
  11. Formulating questions carefully is frequently far...

    Formulating questions carefully is frequently far more than half the battle when answering them.
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    GREAT question, but I disagree slightly with...

    GREAT question, but I disagree slightly with tkhunny's answer on this one.

    Let's start with a point of logic. "P or Q" is exactly equivalent to "Q or P." Agree?

    What does x = \dfrac{-\ b \pm...
  13. I cannot read the second picture, too small. ...

    I cannot read the second picture, too small.

    You have a circle with the origin at O and perpendicular diameters AOB and COD. The midpoint of AO is at E. You construct the right triangle EOD. The...
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    I now see a much simpler solution based on these...

    I now see a much simpler solution based on these two lemmas.

    (a + b)^2 - (a - b)^2 = a^2 + 2ab + b^2 - (a^2 - 2ab + b^2) = 4ab.

    (c + c^{-1})^2 = c^2 + 2c^{(1-1)} + c^{-2} = c^2 + 2 +...
  15. Very likely outcome.

    Very likely outcome.
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    14 - 6 + 21 - 6 = 8 + 15 = 23. 14 - 6 + 21 - 6...

    14 - 6 + 21 - 6 = 8 + 15 = 23.

    14 - 6 + 21 - 6 \ne 14 + 21 = 35.

    Do you see your major error now? You were to subtract BC twice, which is the same as subtracting twice BC. Instead you cancelled...
  17. I have no idea what you are saying. What does...

    I have no idea what you are saying. What does median i even mean? Similarly with median j. What is the relevance of n? Is S a sequence or a sum?

    If I want the differences between the elements in...
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    Answering your last question first, there is a...

    Answering your last question first, there is a fussy formatting language available here, but I recommend that students ignore it and concentrate on math. Just write things out in line using grouping...
  19. Look. We really want to help you. And some of us...

    Look. We really want to help you. And some of us at various times in our career have done things with computers. But to answer a math question, we need to translate the practical problem into...
  20. OK, but did you not say in post # 8 that the...

    OK, but did you not say in post # 8 that the factory could only run for 20,000 hours per period and that it took 2 hours to produce one unit of x and only 1 hour to produce one unit of y. In that...
  21. I'd like to thank both Dr. Peterson and ksdhart...

    I'd like to thank both Dr. Peterson and ksdhart for their pertinent and extended answers.
  22. Bob Ahh I see. Not a problem. I really did...

    Bob

    Ahh I see. Not a problem. I really did think there might have been something subtle going on.

    Thanks for following up.
  23. As I said, I am not a mathematician. I merely...

    As I said, I am not a mathematician. I merely tutor in the basics that I learned decades ago and used often enough since then to remember well. So I cannot advise on books. I suspect that the...
  24. As I read what you have written, I must assume...

    As I read what you have written, I must assume that the objective function is:

    c(x, y) = -\ 0.1x^2 + 395x + 100y.

    But I see only one relevant constraint, namely 2x + y \le 20,000.

    How did...
  25. That is MUCH better. The objective function is...

    That is MUCH better.

    The objective function is the contribution margin:

    c(x, y) = -\ 0.1x^2 + 395x + 100y.

    I shall assume that this is correct. Obviously, it is to be maximized. But it is...
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