# Video Discussion: MSTE-00 Problem Set 4

## Set 4 Part 1

*Situation:*A line on the*xy*-plane has an equation 5*x*+ 12*y*= 60. A*uv*-plane of the same origin has its*u*-axis rotated at an angle of +arctan (4/3) from the*x*-axis.

- Find the
*uv*-coordinates of the*y*-intercept of the given line. - Find the
*uv*-coordinates of the*x*-intercept of the given line. - Find the equation of the given line in the
*uv*-plane.

- Find the
*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…

- Determine the volume of earthwork by end area.
- Determine the volume of earthwork by prismoidal formula.
- Determine the volume of earthwork by prismoidal correction.

## Set 4 Part 2

*Situation:*For vectors**A**= 8**i**+ 4**j**- 2**k**and**B**= 2**j**+ 6**k**.

- Find the magnitude of the sum
**A**+**B** - Find the dot-product
**A**·**B** - Find the magnitude of the cross-product
**A**×**B**

- Find the magnitude of the sum
- Three adjacent faces of a rectangular parallelepiped measures 8 square inches, 10 square inches, and 20 square inches, respectively. Find its volume.
- 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

- 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?
- 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?
- Determine the coordinates of the center of the circle defined by the equation $x^2 + y^2 + 4x - 6y - 12 = 0$.
- 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.
- For a spherical triangle:
*A*= 63° 19.6',*b*= 124° 17.8',*c*= 83° 16.6'. Find*a*.