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Thread: Real world Radical Formula???

  1. #1

    Real world Radical Formula???

    I have not been in math for a while and am a little lost. the problem is : C=4(23245)^-1/3 (13.50) I am not sure how to multiply 23245 by the negitive 1/3 exponent. This is the example from class: C = 4d-1/3b
    C = 4(8500)-1/3(8.17)C = 4(.049)(8.17)
    C = .196(8.17)
    C = 1.60

    Not sure how she got the .049. Please help.

  2. #2
    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by Cadensmom0608 View Post

    I have not been in math for a while and am a little lost.

    the problem is : C = 4 (23245)^(-1/3) (13.50)
    Note the grouping symbols around exponent; very important, to show that the exponent is -1/3 and not just -1.




    I am not sure how to multiply 23245 by [-1/3 exponent].
    Oh, we do not ever "multiply by exponent" when evaluating a power.



    The number -1/3 is a Rational number.

    When exponents are Rational numbers, they indicate taking roots (not multiplying)

    x^(1/2) means the square root of x

    texted as x^(1/2) = sqrt(x)

    x^(1/3) means the cube root of x

    texted as x^(1/3) = cuberoot(x)



    Negative exponents indicate reciprocals.

    x^(-1/2) means 1/sqrt(x)

    x^(-1/3) means 1/cuberoot(x)



    I think that you need to review the meaning of exponentiation and also roots of numbers. There are a few elementary properties for you to memorize.



    This is the example from class: C = 4d-1/3b

    C = 4(8500)-1/3(8.17)

    C = 4(.049)(8.17)

    C = .196(8.17)

    C = 1.60

    Not sure how she got the .049. Please help.
    She used a scientific calculator to evaluate the power 8500^(-1/3)

    That is, she found the value of 1/cuberoot(8500)

    Do you have a scientific calculator? If not, there are several free web-based scientific calculators to be found on the Internet.
    Last edited by mmm4444bot; 11-04-2012 at 03:17 PM.
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  3. #3
    Elite Member mmm4444bot's Avatar
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    Here is what the reciprocal of the cube root of 8500 looks like, using radical-sign notation:

    [tex]8500^{-1/3} = \dfrac{1}{\sqrt[3]{8500}}[/tex]
    Last edited by mmm4444bot; 11-04-2012 at 03:21 PM. Reason: Major typo!
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  4. #4
    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by Cadensmom0608 View Post

    not sure how to multiply 23245 by the negative 1/3 exponent
    Oh, another point: where did you get the number 23245?

    I see 4(23245) and I see 4(8500) -- which is it supposed to be?

    I am concerned that you may not be following the Order of Operations.

    Memorizing and understanding how to use the Order of Operations should come before studying radicals.
    Last edited by mmm4444bot; 11-04-2012 at 03:16 PM. Reason: Grammar, again
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  5. #5

    23245

    I got the 23245 from a word problem I am solving. The problem is: Sailboat stability. To be considered safe for ocean sailing, the capsize screening value C should be less than 2. For a boat with a beam (or width) b in feet and displacement d in pounds, C is determined by the function





    a) Find the capsize screening value for the Tartan 4100, which has a displacement of 23,245 pounds and a beam of 13.5 feet.
    b) Solve this formula for d.
    c) The accompanying graph shows C in terms of d for the Tartan 4100 (b = 13.5). For what displacement is the Tartan 4100 safe for ocean sailing?

    The 8500 was from an example the teacher gave.
    Last edited by mmm4444bot; 11-04-2012 at 03:39 PM. Reason: Removed link to facade web site

  6. #6
    Elite Member mmm4444bot's Avatar
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    I think that I understand, now. You posted both an exercise and an example mixed together.

    We evaluate the reciprocal of the cube root of 23245 in the same way as shown above (where 8500 was the power's base, instead).

    23245^(-1/3) = 1/cuberoot(23245)
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  7. #7

    ok think I got it.

    Ok so I got 4(.035)(13.5)=1.89
    Yay no capsizing.
    Now to figure out how to use the same equation but solve for D. I am slow when it comes to math but am getting there. Thanks for your help

  8. #8
    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by Cadensmom0608 View Post

    I got C = 4(.035)(13.5) = 1.89
    Yes, C = 1.89 when d = 23245 and b = 13.5

    Are you taking an on-line math course? Those courses generally skip lots of stuff.
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  9. #9

    Ashford University Math

    Yes I go to Ashford University and I am lost and praying on passing this is my last math course I believe and it doesnt help that the last math I took was in high school and I am 29 now.

    I have another question if you dont mind part b of this question then says solve for d. in her example she has D=1.1g^(-1/4)h
    I am confused as to where this comes from. I thought d was 23245. How do I find what I need to solve for d for my equation. I am not sure where she got these numbers/formula from

  10. #10
    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by Cadensmom0608 View Post

    Yes I go to Ashford University and I am lost and praying on passing this is my last math course I believe and it doesnt help that the last math I took was in high school and I am 29 now.

    I have another question if you dont mind part b of this question then says solve for d. in her example she has D=1.1g^(-1/4)h

    I am confused as to where this comes from. I thought d was 23245. How do I find what I need to solve for d for my equation. I am not sure where she got these numbers/formula from
    Are you mixing up another example with the exercise?

    D = 1.1*g^(-1/4)*h

    This equation with D, g and h is of the same form as the formula in your exercise using C, d, and b.

    C = 4*d^(-1/3)*b


    I am guessing that her example shows the steps for solving for g?


    You would follow the same steps to solve your equation for d.


    My steps would be:

    (1) Divide both sides by 4b (to isolate the power of d on the righthand side)

    (2) Raise both sides to the power of -4 (this changes the exponent on d from -1/4 to 1)

    (3) Simplify expression for d -- that is, rewrite with positive exponent (if your machine teacher requires specific form for on-line entry)


    I am curious, if you don't mind answering, did Ashford U make you take a math-placement test, before enrolling in first required math course?
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

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