SET 9 (p. 141)

Question 1

1. The formula for the area of the circle with its diameter is A=(πD²)/4. Express the diameter D in terms of the area A in rationalized denominator form.

Answer 1

(2√(πA))/π (p.145)

Question 2

13: Maintenance costs for a small bridge with an expected 50-yr life are estimated to be P2,000 each year for the first 5 years, followed by P10,000 expenditure in the 15th year and a P20,000 expenditure in the 25th year. If i=12% per year, what is the equivalent uniform annual maintenance costs over the entire 50-yr period?

Answer 2

P1,320

Question 3

17. A stone is dropped from the top of a building 50 m high. After it has fallen 10 m below, a second stone is thrown vertically upward from the ground. What must be the initial velocity of the second stone so that both reach the ground at the same time?

Answer 3

8.63 m/s

Question 4

18. A new Civil Engineer 24 yrs old accepts a good job and desires to establish his own retirement fund. At the end of each year thereafter he plans to deposits P 2,000 on a fund at 15% annual interest. How old will he be when the fund has an accumulated value of P 1,000,000?

Answer 4

55

Question 5

19. The base of a solid is a circle of radius 5 ft. Find the volume if every section perpendicular to a fixed diameter of the base is a square with one side on the base.

Answer 5

666.67 (p.148)

Question 6

20. The number of bacteria in a certain culture grows at a rate which is exactly 3/4 the number present. If there are 10,000 bacteria initially, find the number at any time (t).

Answer 6

10^4 e^(3/4t) (p. 148, 149)

Question 7

21. Standard sign shape for directional signs, roadwork signs, signs for special purposes, and supplementary plates for warning signs.

Answer 7

Rectangle

Question 8

23. A certain printing machine costs P210,000 and has a life of 4 years with a salvage value of P10,000. The production output of this machine is as follows, 1st year 1,200 copies, 2nd year 2,500 copies, 3rd year 2,000 copies, and 4th year 1,500 copies. What is the depreciation change on the 3rd year based on its output?

Answer 8

P55,556 (p. 149)

Question 9

26: In Naga City, the police record revealed that the need for money to buy drugs is given as the reason for 70% of all thefts. What is the probability that in the next 5 theft cases reported in this city at least 3 resulted from the need of money to buy drugs?

Answer 9

0.837 (p.149)

Question 10

28. Which of the following is the orthogonal trajectories of the family of parabola y²=4ax?

Answer 10

2x+y²=C

Question 11

32: A line was measured with a 50-m tape. There are 2 tallies, 6 pins, and the distance from the last pin to the end of the line is 3.48 m. Find the length of the line, in meters.

Answer 11

1,303.48 m

Question 12

33: Using the chord basis, what is the radius of a 5° simple curve?

Answer 12

229.26 m

Question 13

36: The provision of safety sight distance depends on the characteristics of the driver such as:
I. Alertness of driver
II. Recognition of the hazard
III. Actions available to the driver - to stop or to change direction
IV. Decision of the driver

Answer 13

I, II, and III only

Question 14

38. The altitude to the hypotenuse of a right triangle divides the hypotenuse into 2 segments of lengths 6 cm and 8 cm. Find the area of the triangle.

Answer 14

48.51 m^2 (p.151)

Question 15

40. A set out to walk at the rate of 4 km an hour. After he had been walking 2 3/4 hours, B set out to overtake him and went 4 1/2 km the first hour, 4 3/4 the second hour, 5 km the third hour and so on gaining a quarter of a km every hour. In how many hours would B overtake A?

Answer 15

8 hours (p. 151)

Question 16

48: Other aspects that could contribute to loss of control on curves are:
I. Adverse superelevation;
II. Poor sight distance; and
III. Poor surface condition

Answer 16

All of the above

Question 17

49. Find the moment of inertia with respect to the y - axis of the area bounded by x² = 4y, y = 4 and x = 0.

Answer 17

34.13

Question 18

50. Two interior angles of a triangle are 64° and 32°. The perimeter of the triangle is 68 m. Compute the shortest side of the triangle.

Answer 18

22.18 m

Question 19

51: An ordinary annuity is paid quarterly for 4 years at a nominal rate of 16% compounded quarterly. Compute the value of the capital recovery factor.

Answer 19

0.0858

Question 20

55. Compute angle A of a spherical triangle whose parts are: a = 58°, b = 112°, c = 70°.

Answer 20

40°57’

Question 21

58. A regular tetrahedron has its edge equal to 10 cm. Compute the volume of the tetrahedron.

Answer 21

100.68 cm³

Question 22

60. A regular tetrahedron has its edge equal to 10 cm. Compute the radius of the sphere inscribed in the tetrahedron.

Answer 22

2.64 cm

Question 23

61. Evaluate the value of the determinant of X.
    (p. 12)

Answer 23

232 (p. 154)

Question 24

64: Find the equation of the plane through the points (4, -2, -3), (5, 4, 1), and (0, 6, 5).

Answer 24

2x - 3y + 4z - 2 = 0 (p. 155)

Question 25

67. A triangle has an area of 128.48 cm² with 2 interior angles 38° and 74°, respectively. Compute the perimeter of the triangle.

Answer 25

38.72 m

Question 26

70. What retarding force is required to stop a 0.45 caliber bullet of mass 20 grams and speed of 350 m/sec, as it penetrates a wooden block to a depth of 75 cm?

Answer 26

16,333.33 (p. 156)

Question 27

71: A wall 8 ft high is 12 ft from a house. Find the length of the shortest ladder that will reach the house, with one end resting on the ground outside the wall.

Answer 27

28 ft (p.156)

Question 28

Set 9 Problem 72: Differentiate y=lncos3x.

Answer 28

3cot3x 28 ft (p.156)

Question 29

74: There are 4 flights from Houston to Chicago, 3 flights from Chicago to Memphis, and 5 flights from Memphis to Atlanta. How many choices does a passenger have for flights that include Houston - Chicago - Memphis - Atlanta connection?

Answer 29

60 (p.156)