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By the Pythagorean theorem, the magnitude of the resultant force is [(-10) 2 + (-8) 2] 1/2 ≈ 12.8 N, which is also the magnitude of the equilibrant force. The angle of the equilibrant force can be found by trigonometry to be approximately 51 degrees north of east. Because the angle of the equilibrant force is opposite of the resultant force ...
[1] [2] as a ratio of one part rise to so many parts run. For example, a slope that has a rise of 5 feet for every 1000 feet of run would have a slope ratio of 1 in 200. (The word "in" is normally used rather than the mathematical ratio notation of "1:200".) This is generally the method used to describe railway grades in Australia and the UK.
The arc length of one branch between x = x 1 and x = x 2 is a ln y 1 / y 2 . The area between the tractrix and its asymptote is π a 2 / 2 , which can be found using integration or Mamikon's theorem. The envelope of the normals of the tractrix (that is, the evolute of the tractrix) is the catenary (or chain curve) given by y = a ...
Let p be an interior point of the disk, and let n be a multiple of 4 that is greater than or equal to 8. Form n sectors of the disk with equal angles by choosing an arbitrary line through p, rotating the line n / 2 − 1 times by an angle of 2 π / n radians, and slicing the disk on each of the resulting n / 2 lines.
The thread angle is the included angle, measured at a section parallel to the axis, between the two bearing faces of the thread. The angle between the axial load force and the normal to the bearing surface is approximately equal to half the thread angle, so the thread angle has a great effect on the friction and efficiency of a screw, as well ...
Langley's Adventitious Angles Solution to Langley's 80-80-20 triangle problem. Langley's Adventitious Angles is a puzzle in which one must infer an angle in a geometric diagram from other given angles. It was posed by Edward Mann Langley in The Mathematical Gazette in 1922. [1] [2]