SET 4 (p. 55)

Question 1

7. A 3-degree simple curve has an external distance of 9.12 m. What is the central angle using chord basis?

Answer 1

24.80°

Question 2

8. An employee is earning P25,000 a month and he can afford to purchase a car which will require a down payment of P115,000 and a monthly amortization of 30% of his salary. What is the maximum value of a car that he can purchase if the balance is paid by end of the month payments in 4 years, the first payment is due at the end of the first month. Money is worth 18% compounded monthly?

Answer 2

P370,319 (p. 61)

Question 3

10. Find the area of a piece of land with an irregular boundary as follows:
    (p. 11)
    The stations are on a straight line boundary. Use Trapezoidal Rule.

Answer 3

170.65 m²

Question 4

12. Mc Naldo’s Deli offers a lunch special in which you can choose a sandwich, a side dish, and a beverage. If there are 10 different sandwiches, 12 different side dishes, and 7 different beverages from which to choose, how many lunch special can you order?

Answer 4

840

Question 5

17. Compute the total number of 8-letter arrangements of the letters of the word ENGINEER.

Answer 5

3,360 (p. 62)

Question 6

18. It is the term of the angle that the sides of a soil bank or pile naturally form with the horizontal when the excavated soil is dumped onto the pile.

Answer 6

Angle of repose

Question 7

21. A machine has a first cost of P 580,000 and estimated to have a book value of P 42,000 at the end of its 10-year operational life. Money is worth 12%. Compute the book value after 4 years using the Declining Balance Method.

Answer 7

P 202,936 (p. 62)

Question 8

24: Find the sum to infinity of the series 4, 4/3, 4/9,…..

Answer 8

6 (p. 63)

Question 9

27. A triangle has vertices at A(1,3), B(7,0), and C(4,6). Locate the coordinates the orthocenter.

Answer 9

(3,4) (p. 63)

Question 10

Find the capacity of the following tanks whose shape and dimensions are given:
30: A tank in the form of a cylinder with diameter 6 m and a height of 7.5 m.

Answer 10

212.06 m^3 (p. 64)

Question 11

32. Find the angle between the curves xy = 4 and x^2 = 2y.

Answer 11

71.57°

Question 12

35. How long will it take in years money to quadruple if it earns 14% compounded continuously?

Answer 12

10 (p. 65)

Question 13

37: What is the derivative of 4cos(2-x^3)?

Answer 13

12x^2sin(2-x^3) (p. 65)

Question 14

38: A closed traverse has the following data:
(p. 12)
Compute the distance CD in meters.

Answer 14

77.60 m

Question 15

41. Determine the capitalized cost of an equipment whose first cost is P284,600 with a salvage value of P 5,000 after its life of 5 years. Money is worth 10%.

Answer 15

P 724,578

Question 16

43. A projectile is thrown from the top of a building 30 m high above the ground with a velocity of 300 m/s directed at an angle of 20° from the horizontal. How long will the ball hit the ground?

Answer 16

32.2 sec

Question 17

44. Given the inequality 3 < x < 7 and 6 > x > 2. What are the possible values of x?

Answer 17

3 < x < 6

Question 18

45: How many integers do the solutions of the inequalities 3x - 5 > 7 and x < or equal to 18 - x share?

Answer 18

5

Question 19

46: Find the solution set: |3-2x|≥7

Answer 19

(-∞,-2)U(5,∞) (p. 66)

Question 20

48. The volume of a square prism is numerically equal to its lateral area. Calculate the length of the side of the base if its height is not equal to the length of its base.

Answer 20

4 (p. 67)

Question 21

53. A point within a equilateral triangle has distances of 3 m, 4 m, and 5 m respectively from the vertices.
    Compute the distance from the circumcenter of the circle to one of the sides.

Answer 21

1.95 m

Question 22

57. Given the following notes from BM_12 to BM_14:
    (p. 12)
    Compute the difference in elevation between BM_12 and BM_13.

Answer 22

4.51 m

Question 23

59:. A highway curve having a radius of 340 ft is banked so that there will be no lateral pressure on the car’s wheel at a speed of 45 kph. What is the angle of elevation of the embankment in degrees?

Answer 23

8.74°

Question 24

63. The slope of a line joining a moving point (1,-5) is always twice the slope of the line joining it to the origin. Find the equation of the locus of the moving point.

Answer 24

xy+5x+2y=0 (p. 69)

Question 25

67. Find the first derivative of y=x^lnx.

Answer 25

1-lnx^2x

Question 26

68: Find the equation of the normal to the curve y + (x+y)^(1/2) = x at (3, 1).

Answer 26

5x + 3y = 18 (p. 70)

Question 27

69. Find the area bounded by the parabolas x = y² - 4y and x = 2y - y².

Answer 27

9

Question 28

71. Given that cos A = 3s. Find the tangent of A.

Answer 28

((1-9s^2)^1/2)/3s (p. 71)

Question 29

72. There exists a value of x such that the tangent of the expression (2x+18) is equal to the cotangent of the expression (4x-12). The value of x could be

Answer 29

14°

Question 30

74: A tangent and a secant are drawn to a circle from the same external point. If the internal segment of the secant is 6 units and the tangent is 8 units long to the point of tangency, determine the length of the secant.

Answer 30

11.44 units (p. 72)