Video Discussion: MSTE-00 Problem Set 10

Set 10 Part 1

1. Which of the following most nearly gives the value of x from $\sqrt[4]{8 \, \sqrt[3]{2 \, \sqrt{8x}}} = 2$?
2. The area of the triangle inscribe in a circle is 39.19 cm² and the radius of the circle is 7.14 cm. If the two sides of the triangle are 8 cm and 10 cm respectively, find the 3^rd side.
3. The arc of the parabola $y = x^2$ from (1, 1) to (2, 4) is rotated about the y-axis. Find the area of the resulting surface.
4. Car A drives East at 20 kph at half an hour earlier than car B that started at the same point at 50 kph. How long will car B overtakes car A, in minutes?
5. An angle of a triangle is four times as large as another and 45° more than the third angle. Find the angle.

Set 10 Part 2

1. A couple decides to entertain 24 friends by giving 4 dinners with 6 guests each. In how many ways can the 1st group be chosen?
2. Find the equation of the line through (4, 7) and passing at a distance of 1 unit from the origin.
3. An airline does a survey of the weights of adult passengers traveling on its flights. It finds that 5% weigh more than 84.3 kg and 2% weigh less than 57.2 kg. Assuming that the weights of adult passengers on its flight are normally distributed, find the mean of the weights.
4. Find the area of the region that lies inside the circle $r = 3 \sin \theta$ and outside the cardioid $r = 1 + \sin \theta$.
5. If P10,000 is deposited each year for 9 years, how much can a person get annually from the bank every year for 8 years starting 1 year after the 9th deposit is made. Cost of money is 14%.
6. A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into equilateral triangle. What is the perimeter of the square so that the total area enclosed is minimum?

Set 10 Part 3

1. Situation. A horn is generated by a circle which moves in the following manner: The plane of the circle is always parallel to the yz-plane with center always on the xy-plane, and its diameter is a line segment cut off by the curve $x = y^2$ and $x = 9y^2$ on the 1st quadrant of the xy-plane.
   
   1. What is the diameter of the circle at x = 3?
   2. What is the lateral area of the horn from x = 0 to x = 3?
   3. What is the volume generated from x = 0 to x = 3?
2. Situation. An unsymmetrical parabolic curve has a forward tangent of -8% and backward tangent of +5%. The length of curve on the left side is 40 m long while that of the right side is 60 m long. PC is at Sta 6 + 780 and at elevation 110 m.
   
   1. Determine the stationing of the highest point.
   2. Determine the elevation at Sta 6 + 820.
   3. Determine the elevation of the PT.