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April 1st, 2019, 03:55 PM   #11
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H is Hamilton, but that's quite irrelevant. I think the plane crashed at (-71,25) rounded; is this correct?

Last edited by skipjack; April 1st, 2019 at 04:24 PM.
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April 1st, 2019, 04:10 PM   #12
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Quote:
Originally Posted by helpmeddddd View Post
I think the plane crashed at (-71,25) rounded; is this correct?
I don't know ... need more information

Quote:
Originally Posted by helpmeddddd View Post
its approx position is at a place equidistant from Miami and San Juan and on altitude from Miami,
a point equidistant from Miami and San Juan is on the perpendicular bisector of line segment MS.

What about the altitude from Miami to ... where?

Last edited by skipjack; April 1st, 2019 at 04:27 PM.
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April 1st, 2019, 04:18 PM   #13
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The altitude part confuses me also. I believe it says on altitude to Miami, so I don't think we have to solve altitude. Perpendicular bisectors are correct; that's how I solved. I found the perpendicular bisector of HS and MH.

Last edited by skipjack; April 1st, 2019 at 04:29 PM.
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April 1st, 2019, 04:24 PM   #14
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The attitude part confuses me also. I believe it says on altitude to Miami, so I don't think we have to solve altitude. Perpendicular bisectors are correct; that's how I solved. I found the perpendicular bisector of HS and MH.
I thought you said point H was irrelevant?

Last edited by skipjack; April 1st, 2019 at 04:29 PM.
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April 1st, 2019, 04:27 PM   #15
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I see how you could get that; I meant what H stands for is irrelevant. Sorry for this confusion.

Basically, I found the midpoints of HS and MH, found their slopes/gradients, then did the equations of the gradients. After solving for x, I put x into one of my equations to solve for y.

Last edited by skipjack; April 1st, 2019 at 04:57 PM.
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April 1st, 2019, 04:55 PM   #16
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1 knot = 1.852 km/hr.
More accurately, 1 knot = 1.853184 km/hr.
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April 1st, 2019, 05:06 PM   #17
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You have three non-collinear points, M(-80,26) H(-65,32) and S(-66,18 ), that form a triangle.

The perpendicular bisector of segment MS passes through its midpoint, (-73,22). The slope of MS is -4/7, therefore, the slope of the perpendicular bisector slope 7/4.
The equation of the perpendicular bisector of MS is $y = \dfrac{7}{4}(x + 66) + 18$


The altitude from M to HS passes through M(-80,26) and is perpendicular to HS ...
The slope of HS is 14, so the altitude to HS has slope -1/14.
The equation of the altitude from M to HS is $y = -\dfrac{1}{14}(x + 80) + 26$

The intersection of the altitude from M to HS and the perpendicular bisector of MS can be found by setting the two lines equal.

You calculated (-71,25) rounded.
Your y-value is good ... your x-coordinate is off according to my calculation.
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April 1st, 2019, 05:21 PM   #18
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Quote:
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More accurately, 1 knot = 1.853184 km/hr.
Source for that value?

Last edited by skipjack; April 1st, 2019 at 05:31 PM.
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April 1st, 2019, 05:54 PM   #19
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Quote:
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The perpendicular bisector of segment MS passes through its midpoint, (-73,22). The slope of MS is -4/7, therefore, the slope of the perpendicular bisector slope 7/4.
The equation of the perpendicular bisector of MS is $y = \dfrac{7}{4}(x + 66) + 18$ ... your x-coordinate is off according to my calculation.
You gave the equation of the perpendicular bisector of MS incorrectly, as you used the coordinates of S instead of the coordinates of the midpoint of MS.

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Source for that value?
I had used an outdated value of 6080 feet for the nautical mile. The currently used value is exactly 1.852 km, so you were correct.

According to wikipedia, this value was first defined in 1929 (at an international conference held in Monaco). However, the United States adopted this value in 1954 and Britain adopted it in 1970.
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April 1st, 2019, 06:25 PM   #20
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You gave the equation of the perpendicular bisector of MS incorrectly, as you used the coordinates of S instead of the coordinates of the midpoint of MS.
I certainly did ... good catch.

perpendicular bisector of MS should be

$y = \dfrac{7}{4}(x+73)+22$

making the intersection coordinates approx (-71,25)

so the OP is correct
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