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Math Help - Regarding direct proportions

  1. #1
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    Regarding direct proportions

    If y is directly proportional to x^2 and y=1/8 when x=1/2, what is the positive value of x when y=9/2?

    a) 3/4
    b) 3/2
    c) 9/4
    d) 3
    e) 9

    what i did:
    y: 1/8
    x^2: 1/4

    1/8 * 36 = 9/2

    therefore

    1/4 * 36 = 9

    but the answer is 3, not 9...
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  2. #2
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    Hello juliak
    Quote Originally Posted by juliak View Post
    If y is directly proportional to x^2 and y=1/8 when x=1/2, what is the positive value of x when y=9/2?

    a) 3/4
    b) 3/2
    c) 9/4
    d) 3
    e) 9

    what i did:
    y: 1/8
    x^2: 1/4

    1/8 * 36 = 9/2

    therefore

    1/4 * 36 = 9

    but the answer is 3, not 9...
    Translate the phrase " y is directly proportional to x^2" in symbols as:
    y = kx^2, where k is a constant
    Then plug in the two values that you've been given:

    When y = \tfrac18, x= \tfrac12. So:
    \tfrac18=k(\tfrac12)^2
    =\tfrac14k
    \Rightarrow k = \tfrac12
    So the equation is:
    y = \tfrac12x^2
    When y = \tfrac92:
    \tfrac92=\tfrac12x^2

    \Rightarrow x^2 = 9

    \Rightarrow x = 3
    Grandad
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  3. #3
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    earboth's Avatar
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    Quote Originally Posted by juliak View Post
    If y is directly proportional to x^2 and y=1/8 when x=1/2, what is the positive value of x when y=9/2?

    a) 3/4
    b) 3/2
    c) 9/4
    d) 3
    e) 9

    what i did:
    y: 1/8
    x^2: 1/4

    1/8 * 36 = 9/2

    therefore

    1/4 * 36 = 9

    but the answer is 3, not 9...
    If y is directly proportional to x both values have to satisfy the equation:

    y = k \cdot x^2

    for a certain proportionality factor k.

    You know

    \frac18 = k \cdot \left( \frac12 \right)^2

    Solve for k.

    Then plug in y = \frac92 into the equation and solve for x.
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  4. #4
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    Quote Originally Posted by juliak View Post
    If y is directly proportional to x^2 and y=1/8 when x=1/2, what is the positive value of x when y=9/2?

    a) 3/4
    b) 3/2
    c) 9/4
    d) 3
    e) 9

    what i did:
    y: 1/8
    x^2: 1/4

    1/8 * 36 = 9/2

    therefore

    1/4 * 36 = 9

    but the answer is 3, not 9...
    Because, just as "1/4" was x^2= (1/2)^2 so is this 9= x^2. You need to take the square root to get x.
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