Video Discussion: MSTE-00 Problem Set 3

The videos are grouped into 5 so that it is easier in my end to manage the recordings. The sequence of problems discussed in each video is according to the numbering listed below the video. Just look for the problem you need most and play the video on top of it. Drag the progress bar to the problem that you need. I hope you find this arrangement better than our previous arrangement.
 

Set 3 - Part 1

1. In how many ways can you line up 5 persons if two persons refuse to follow each other?
2. Two triangles have equal bases. The altitude of one triangle is 3 units more than its base while the altitude of the other is 3 units less than its base. If the areas of the triangles differ by 21 square units, find the altitude of the smaller triangle.
3. Find the maximum and minimum values of $3^{\sin x}$ for $0 \le x \le 360^\circ$.
4. At what value of x will the function $f(x) = \dfrac{x - 4}{x + 2}$ is discontinuous?
5. Situation: Given the digits 0, 1, 2, 3, 4, and 5. How many 3-digit numbers can be made from the given digits if…
   
   1. repetition of digit is not allowed.
   2. the numbers are even and repetition of digit is not allowed.
   3. the numbers are odd and repetition of digit is not allowed.

Set 3 - Part 2

1. Find the capacity of a conical vessel that is made from a semi-circular tin of radius 2.5 m.
2. Determine the volume of a regular tetrahedron of edge 2 ft.
3. A man invested P100,000 at an interest rate of 10% compounded annually. What will be the final amount of his investment, in terms of today’s peso, after 5 years, if inflation remains the same at the rate of 8% per year?
4. Through a given cone of altitude h and base A, two planes are passed parallel to the base, cutting the altitude h/3 and 2h/3 units from the base. Find the ratio of the volumes of the two frustums thus formed.
5. Find the area of the spherical lune of radius 2.5 m and a central angle of 15°

Set 3 - Part 3

1. What is the number that is one half of one quarter of one tenth of 400?
2. Two men starting at the same point walk in opposite direction for 4 meters turn left and walk another 3 meters. What is the distance between them?
3. Find the radius of the circumscribing circle of the regular octagon having an area of 320 cm².
4. P3000 quarterly for ten years accumulates to P181,205.95, find the nominal rate of interest compounded quarterly.
5. Find the area reflected by the triangle ABC on the xy-plane with A(1, 10, 10), B(6, 2, 4) and C(12, 6, 1).