Video Discussion: MSTE-00 Problem Set 4

Set 4 Part 1

1. Situation: A line on the xy-plane has an equation 5x + 12y = 60. A uv-plane of the same origin has its u-axis rotated at an angle of +arctan (4/3) from the x-axis.
   
   1. Find the uv-coordinates of the y-intercept of the given line.
   2. Find the uv-coordinates of the x-intercept of the given line.
   3. Find the equation of the given line in the uv-plane.
2. Situation: The following is a set of notes of the earthwork of a road embankment. Sta 5 + 040: 12/-3, -5, 24/-9; Sta 5 + 140: 15/-4.5, -7, 30/-12. If the width of roadway is 12 m and the side slope is 2:1…
   
   1. Determine the volume of earthwork by end area.
   2. Determine the volume of earthwork by prismoidal formula.
   3. Determine the volume of earthwork by prismoidal correction.

Set 4 Part 2

1. Situation: For vectors A = 8i + 4j - 2k and B = 2j + 6k.
   
   1. Find the magnitude of the sum A + B
   2. Find the dot-product A · B
   3. Find the magnitude of the cross-product A × B
2. Three adjacent faces of a rectangular parallelepiped measures 8 square inches, 10 square inches, and 20 square inches, respectively. Find its volume.
3. A Ferris wheel, 9 m in radius, is rotating such that the riders will experience zero gravity at the topmost part of the wheel. How many revolutions it made in every minute?

Set 4 Part 3

1. How many three-digit even numbers can be made out from the digits 1, 2, 3, 4, 5, 6, and 7 if repetition of digit is not allowed?
2. An altar for ancient rituals is in the form of a cube of edge 1.5 m. If you double the size of the cube, what will be the dimension of its edges?
3. Determine the coordinates of the center of the circle defined by the equation $x^2 + y^2 + 4x - 6y - 12 = 0$.
4. Compute the cost of lumber necessary to resurface a foot-bridge 16 feet wide and 150 feet long with 2-inches planks, if lumber is P48.00 per board foot.
5. For a spherical triangle: A = 63° 19.6', b = 124° 17.8', c = 83° 16.6'. Find a.