Video Discussion: MSTE-00 Problem Set 5

Set 5 Part 1

1. Find the volume of a circular cone having a base radius of 20 cm and axis 30 cm, if the axis makes an angle of 60° from the base.
2. A sphere is circumscribing a cubical box having a volume of 8000 cm3. Compute the volume of the space between the cubical box and the sphere.
3. A pole cast a shadow 15 m long when the angle of elevation of the sun is 61°. If the pole has lean 15° from the vertical directly towards the sun, what is the length of the pole?
4. An airplane flew from Davao whose latitude is 14° N and longitude of 121° 30' E on a course of S 30° W and maintaining uniform altitude. At what longitude will the plane cross the equator?
5. Determine the distance from point (2, 1) to the line $4x - 3y + 5 = 0$.

Set 5 Part 2

1. What is the length of the line with slope 4/3 from point (6, 4) to the y-axis?
2. Find the equation of the radical axis of the two circles having equations of $x^2 + y^2 + 4x + 6y - 3 = 0$ and $x^2 + y^2 + 12x + 14y + 60 = 0$.
3. Given $f(x) = (x - 4)(x + 3) + 4$. When $f(x)$ is divided by $x - k$, the remainder is $k$, find the value of $k$.
4. The geometric mean and arithmetic mean of two numbers are respectively 8 and 17. Find the harmonic mean.
5. In the CE Board examinations, the probability that an examinee will pass in each subject is 0.80. What is the probability that the examinee will pass at least two subjects.

Set 5 Part 3

1. The scale on the map is 1:n. A square field has an area of 1600 sq. m. is represented by 1 cm², the value of n is:
2. If five masons can earn P675 in 6 days, how much can 12 carpenters receiving the same rate earn in 10 days?
3. Situation. Two flat belt pulleys have a center to center distance of 137 cm, and diameters of 72 cm and 36 cm, respectively. Neglecting the sagging of belt,
   
   1. Compute the length of belt if both pulleys will rotate in the same direction.
   2. Compute the length of belt if the belt will be cross-connected to make the pulleys rotate in opposite directions.
   3. Determine the distance of the point from the center of the bigger pulley where the belt will cross when cross-connected.