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Math Help - [SOLVED] Calling Mr Fantastic,help and tie-breaker needed

  1. #1
    Newbie haflore's Avatar
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    [SOLVED] Calling Mr Fantastic,help and tie-breaker needed

    Mr Fantastic, I really appreciated your clear explanation with my other questions, and hope that you will help me with these too!

    I need to check my answers to these two questions:

    simplify by dividing:

    x^3+2x^2+3x-6/x-1{my answer was: x^2+3x+(6/x-1)}

    n^3-27/n-3{my answer was n^2+3n-9}
    __________________________________________________ _
    I'm having a bit trouble with this question:

    the sum of a number and its reciprocal is 10/3. what is the number?
    __________________________________________________ _
    I also need to make sure that my method is correct and the answer is sound, for this question.

    One eighth of the square root of seven less than a number is two. What is the number?
    My answer is 263. I came to this answer by working it backward, if 2*8=16, then 16*16=256 and 256+7=263. So if the equation version of the word problem was: (1/8)sqrtN-7=2 then the answer is: (2*8)^2+7=263

    Finally, a little while back I posted the following question:

    Quote Originally Posted by haflore View Post
    I have a very strange proportion that I need to solve.

    the question is as follows:

    Complete. If x/y=3/5, then x/3=_______

    I have deduced that the answer must be either,3/3 or y/5, am I correct?


    Thanks in advance for the help!
    To which I got these two replies:

    Quote Originally Posted by galactus View Post
    It would appear that x=3. Then, x/3=1
    Quote Originally Posted by icemanfan View Post
    The correct answer is y/5. In order to arrive at that conclusion, multiply both sides of the original equation by y/3.
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  2. #2
    GAMMA Mathematics
    colby2152's Avatar
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    I may not be Mr. Fantastic, but I will help you with at least one of these questions...

    the sum of a number and its reciprocal is 10/3. what is the number?
    The reciprocal of a number is one over that number, (x -> 1/x), so:

    x+ \frac{1}{x} = \frac{10}{3}

    Multiply the entire equation by 3x, the LCD

    3x^2 + 3 = 10x

    3x^2-10x+3=0

    Use the quadratic equation:

    x = \frac{10 \pm \sqrt{100 - 4(3)(3)}}{6} \Rightarrow \frac{10 \pm \sqrt{64}}{6} = \frac{10 \pm 8}{6} \Rightarrow \frac{5 \pm 4}{3} = \frac{1}{3}, 3
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  3. #3
    Moo
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    A Cute Angle Moo's Avatar
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    Hello,

    I'm nor Mr, nor Fantastic, nor Mr Fantastic... But I'll try to help ya, k ?

    Quote Originally Posted by haflore View Post
    Mr Fantastic, I really appreciated your clear explanation with my other questions, and hope that you will help me with these too!

    I need to check my answers to these two questions:

    simplify by dividing:

    x^3+2x^2+3x-6/x-1{my answer was: x^2+3x+(6/x-1)}
    Ok

    n^3-27/n-3{my answer was n^2+3n-9}
    A little typo or mistake, it's not -9 but +9

    __________________________________________________ _
    I'm having a bit trouble with this question:

    the sum of a number and its reciprocal is 10/3. what is the number?
    Let x be this number and \frac 1x its reciprocal.

    We have x+\frac 1x=\frac{10}{3}

    Multiplying by x, and assuming it's \neq 0:
    \implies x^2+1=\frac{10}{3} \cdot x \implies x^2-\frac{10}{3} x+1=0

    Can you go through it ?

    __________________________________________________ _
    I also need to make sure that my method is correct and the answer is sound, for this question.

    One eighth of the square root of seven less than a number is two. What is the number?
    My answer is 263. I came to this answer by working it backward, if 2*8=16, then 16*16=256 and 256+7=263. So if the equation version of the word problem was: (1/8)sqrtN-7=2 then the answer is: (2*8)^2+7=263
    I don't like much doing it backward, but I don't know how you've learnt it. Your result is correct, but I'd do this way :

    Taking the problem from the end ~
    "seven less than a number" : this means N-7
    "square root of ..." : this means sqrt(N-7)
    "one eighth of the ..." : this means (1/8)sqrt(N-7)
    And this is equal to 2, which yields your equation


    Finally, a little while back I posted the following question:



    To which I got these two replies:
    I agree with icemanfan...

    Complete. If x/y=3/5, then x/3=_______
    Multiplying by y :
    x=3y/5

    Making appear x/3, by dividing each side by 3 :
    x/3=(3y)/(5*3)=y/5
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  4. #4
    Newbie haflore's Avatar
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    Wow! Those were some fast replies! Thanks very much Moo and colby2152,
    you have been very helpful!
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  5. #5
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    Quote Originally Posted by haflore View Post

    I need to check my answers to these two questions:

    simplify by dividing:

    x^3+2x^2+3x-6/x-1{my answer was: x^2+3x+(6/x-1)}
    not sure I agree.

    Synthetic Division

    Following the math, I get no remainder:

    x^2 + 3x + 6

    if your constant term was positive 6, I'd get a remainder of 12/(x-1)

    Solving the cubic the long way here, I get 1 as the real root, which means there should be no remainder when you divide by x minus root:

    Soving Cubic Equations
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  6. #6
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    Quote Originally Posted by mathceleb View Post
    not sure I agree.

    Synthetic Division

    Following the math, I get no remainder:

    x^2 + 3x + 6

    [snip]
    Agreed.

    And thanks to all who filled my somewhat small shoes ....... Only problem is that those shoes have been stretched and are now too big for me .....
    Last edited by mr fantastic; May 20th 2008 at 04:03 PM.
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  7. #7
    Newbie haflore's Avatar
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    Quote Originally Posted by colby2152 View Post
    I may not be Mr. Fantastic, but I will help you with at least one of these questions...



    The reciprocal of a number is one over that number, (x -> 1/x), so:

    x+ \frac{1}{x} = \frac{10}{3}

    Multiply the entire equation by 3x, the LCD

    3x^2 + 3 = 10x

    3x^2-10x+3=0

    Use the quadratic equation:

    x = \frac{10 \pm \sqrt{100 - 4(3)(3)}}{6} \Rightarrow \frac{10 \pm \sqrt{64}}{6} = \frac{10 \pm 8}{6} \Rightarrow \frac{5 \pm 4}{3} = \frac{1}{3}, 3

    Thank you for your invaluable help, I understand everything except; why 3x is the LCD, I can understand either 3 or x being the LCD but 3x seems to suggest that 10/3 was multiplied by 1/x ???.
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  8. #8
    GAMMA Mathematics
    colby2152's Avatar
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    Quote Originally Posted by haflore View Post
    Thank you for your invaluable help, I understand everything except; why 3x is the LCD, I can understand either 3 or x being the LCD but 3x seems to suggest that 10/3 was multiplied by 1/x ???.
    \frac{x}{1} + \frac{1}{x} = \frac{10}{3}

    The denominators are: 1, x, 3

    The LCD is the product of these three: 3*1*x = 3x

    This way, when you multiply out by the LCD, all fractions will disappear and the polynomial will simpler to solve via quadratic equation.
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