Video Discussion: MSTE-00 Problem Set 6

Set 6 Part 1

1. A commuter drives from Mandaue to Bogo 120 km away at an average speed of 60 kph and returned to Mandaue at an average speed of 40 kph. What was the average speed of the commuter for the whole journey?
2. A group of dancers consists of x boys and x girls. If two of the boys are replaced by two girls, then 48% of the group members will be boys. Find the original value of the boys.
3. A and B can finish the job in 8 days and the working speed of A is twice that of B. How many days would it take A to finish the job alone?
4. If an arc length is 12 m subtends a central angle $\phi$ in a circle of radius 3, find the measure of $\phi$ in terms of radians.
5. When the population growth of a certain city was first studied, the population was 22,000. It was found that the population P grows with respect to time t in years by the exponential formula $P = 22,000(10^{0.0163t})$. How long will it take for the city to double its population?

Set 6 Part 2

1. Find the area of a sector of a circle of radius 6 cm and a central angle of 60°.
2. Convert $5\pi / 6$ into degree measure.
3. A sector of a circle with radius 10 cm has a central angle of 120°. Find the arc length of the sector.
4. In the figure, AB = BC. The value of $\theta$ is:
5. In how many ways can 4 couples be seated at a round table with the men and women alternating?

Set 6 Part 3

1. A circle of radius 1 unit is shown. AD is the diameter of the circle and O is the center. Find the length of arc BC.
2. Mary was 4 times as old as Ann 4 years ago and if Mary will be twice as old as Ann 4 years hence, how old is Ann?
3. At what time between 7 and 8 o’clock will the hands of the clock be directly opposite each other?
4. Stations A and B are placed 1000 m apart on a straight road running East and West. From A, the bearing of the tower C is 32° West of North and from B the bearing of C is 26° North of East. Find the shortest distance of the tower from the road.
5. Situation. A triangular lot ABC have side AB of length 94 m and bearing N 45° E and side AC of length 88 m, in clockwise direction. A dividing line DE with D alongside AB and E alongside AC is to be made and with D 43 meters from A. The area of triangle EAD is 1/7 of the total area of the lot. The lot has a total area of 4,100 square meters.
   
   1. What is the bearing of side BC?
   2. How far is point E from corner A?
   3. What is the length of the dividing line DE in meters?