Video Discussion: MSTE-00 Problem Set 8

Set 8 Part 1

1. A closed right circular cylinder 2 meter in diameter and 2-meter tall is partially filled with water. When lying in a horizontal position, the depth of water is 2/3 the diameter. When the cylinder is in the vertical position, what is the depth of water?
2. A circle having a radius of 18 cm is cut by a chord 5 cm from the center. What is the area of the of the smaller segment?
3. A polygon has 104 diagonals. How many sides have this polygon?
4. A hemispherical dome is 16 meters in diameter. If the bottom 1-meter strip of the dome’s surface painted, what is the total painted area?
5. A certain lotto game consists of 30 different balls numbered 1 to 30. If five balls are drawn at random without replacement, how many possible winning combinations can be made?

Set 8 Part 2

1. The sides of a triangle measure 10 cm, 14 cm, and 8 cm, respectively. What is the smallest interior angle of this triangle?
2. The total surface area of a regular tetrahedron is 339.482 cm². Find the measure of the edge of this tetrahedron.
3. A sphere of radius 18 inches is cut by two parallel planes that are 16 inches apart. Find the volume on the sphere included between these cutting planes if the radius of one of the circles cut is 15 inches.
4. In a bowling game, how many ways can the 10 pins fall in the first throw?
5. A closed conical tank has a base diameter of 2 m and is 5 m tall. When standing in upright position, the water in the tank is 3 m deep. How deep will the water stand in the tank when in inverted position?

Set 8 Part 3

1. Find the first derivative of y with respect to x of the following function, when x = 2.
   $$ y = \dfrac{\ln x^2}{\sin 2x} $$
2. A disease is known to affect 1 in 10,000 people. It can be fatal, but it is treatable if it is detected early. A screening test for the disease shows a positive result for 99% of the people with the disease. The test also shows positive for 2% of people who do not have the disease. Find the probability that somebody is healthy given that they have positive test result?
3. Situation. Five hundred pesos is deposited monthly to an account earning 7% compounded monthly.
   
   1. What is the amount of the deposit after five years?
   2. If the monthly deposit after two years is increased to P1,000, what is the amount of the deposit after five years?
   3. Repeat Part 2 of this question if the interest rate is 18% compounded monthly.