# Video Discussion: MSTE-00 Problem Set 10

## Set 10 Part 1

- Which of the following most nearly gives the value of
*x*from $\sqrt[4]{8 \, \sqrt[3]{2 \, \sqrt{8x}}} = 2$? - The area of the triangle inscribe in a circle is 39.19 cm
^{2}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. - 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. - 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? - 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

- 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?
- Find the equation of the line through (4, 7) and passing at a distance of 1 unit from the origin.
- 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.
- Find the area of the region that lies inside the circle $r = 3 \sin \theta$ and outside the cardioid $r = 1 + \sin \theta$.
- 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%.
- 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

*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.- What is the diameter of the circle at
*x*= 3? - What is the lateral area of the horn from
*x*= 0 to*x*= 3? - What is the volume generated from
*x*= 0 to*x*= 3?

- What is the diameter of the circle at
*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.- Determine the stationing of the highest point.
- Determine the elevation at Sta 6 + 820.
- Determine the elevation of the PT.