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26 April, 22:44

An angle measuring (468n) ° is in standard position. For which value of n will the terminal side fall along the negative portion of the x-axis?

n = 4

n = 5

n = 6

n = 7

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Answers (2)
  1. 26 April, 23:01
    0
    The answer is n=5.

    I got the answer through solving all ns and graphing them.

    If n = 4 - > 468 (4) = 1848 degrees. It falls on the first quadrant, thus it does not fall along the negative portion of the x-axis.

    If n=5 - > 468 (5) = 2310 degrees. It falls on the second quadrant, thus it falls along the negative portion of the x-axis.

    If n=6 - > 468 (6) = 2808 degrees. It falls on the fourth quadrant, thus it does not fall along the negative portion of the x-axis.

    If n=7 - > 468 (7) = 3276 degrees. It falls on the first quadrant, thus it does not fall along the negative portion of the x-axis.
  2. 26 April, 23:06
    0
    The correct answer is:

    n = 5.

    Explanation:

    On a coordinate grid, an angle starts on the positive x-axis, at 0°. Multiples of 360° will have their terminal side here as well.

    If the terminal side of an angle is on the negative x-axis, this means it is a multiple of 180°.

    This gives us 468n° and 180°. We want the LCM of these two. To find this, we first find the prime factorization of each number:

    468 = 2*234

    234 = 2*117

    117 = 3*39

    39 = 3*13

    This gives us:

    468 = 2*2*3*3*13

    468 = 2² (3²) (13)

    We now find the prime factorization of 180:

    180 = 2*90

    90 = 2*45

    45 = 5*9

    9 = 3*3

    This gives us:

    180 = 2*2*3*3*5

    180 = 2² (3²) (5)

    For the LCM, we multiply the common factors by the uncommon. The common factors of 468 and 180 are:

    2² (3²)

    The uncommon factors are:

    5*13

    This gives us an LCM of:

    2² (3²) (5) (13) = 2340

    To find the value of n, we solve the equation:

    468n = 2340

    Divide both sides by 468:

    468n/468 = 2340/468

    n = 5
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