SET 5 (p. 73)

Question 1

1. Find the gradient of F(x, y, z) = 4x² + x²y - 2xy² - z³ at the point ( 3, -2, 1 ).

Answer 1

4i + 33j - 3k (p. 77)

Question 2

3. Find the length of one arc of the curve whose equation is represented in parametric form: x =8( θ - sin⁡θ ), y = 8( 1 - cos⁡θ ).

Answer 2

64 (p. 77)

Question 3

7. The bearing of 2 lines AB and BC are N 30° W and N 20° E respectively. A 5-degree simple curve is to connect these 2 lines as tangents. Use arc basis.
   Compute the length of the curve.

Answer 3

200 m

Question 4

10. What is the longest 1.8 m-wide shuffle board court that will fit in a 6 m x 9 m rectangular room?

Answer 4

9.017 m (p.78)

Question 5

13. Find the third proportional to 4 and 10.

Answer 5

25 (p. 79)

Question 6

15. A car’s stopping distance varies directly with the speed it travels and inversely with the friction value of the road surface. If a car takes 60 ft to stop at 32 mph on a road whose friction value is 4, what would be the stopping distance of a car traveling at 60 mph on a road with a friction value of 2?

Answer 6

ft

Question 7

16: Evaluate (Wp. 13).

Answer 7

0

Question 8

18: Two square lots of unequal sizes lie adjacent to each other. Together the 2 lots contain contain an area of 6568 m^2. To enclose them in a single enclosure, it would require 356 m of fence. Find the distance of the smaller lot.

Answer 8

22 m x 22 m

Question 9

On the first 7 tests in his Surveying subject, James’ score were 82, 78, 86, 82, 94, 95, and 92.
22: Determine the mode of his scores.

Answer 9

82

Question 10

24. Determine the standard deviation of the set of the numbers { 5, 8, 6, 4, 10, 3, 8, 12, 15, 8 }.

Answer 10

3.506

Question 11

27. The color of messages when painted on pavements.

Answer 11

White

Question 12

29. The sum of two numbers is 18. Find the smaller of the 2 numbers if the product of one by the square of the other is a maximum.

Answer 12

6 (p. 82)

Question 13

The ages of the faculty members of the Civil Engineering Department of ZIT-University are as follows: 27, 24, 40, 27, 30, 25, 27, 31, 37, and 35.
32: Determine the first quartile.

Answer 13

27 (p. 83)

Question 14

37. A paint mixture contains yellow, blue, and red in a ratio 3:2:1. If the mixture contains 12 pints of yellow paint, how many pints are there altogether?

Answer 14

24

Question 15

38: A 30-m tape is of standard length at a temperature of 20° C. The coefficient of thermal expansion of the tape is 11.7 x 10^-6/° C. At a temperature of 38° C, this tape is used to lay out a 350-m line. What must be
the distance to be laid out?

Answer 15

349.927 m

Question 16

42. It is the process of moving soil or rock from one location to another and processing it so that it meets construction requirements of location, elevation, density, moisture content and so on.

Answer 16

Earth-moving

Question 17

43: Find the 6th term in the expansion of (p. 12)

Answer 17

(Wp. 12)

Question 18

44. Evaluate: (1-i)⁷.

Answer 18

8+8i (p. 84)

Question 19

47: A dart target consists of 3 concentric circles with different radii, 2 inches, 4 inches, and 6 inches. A dart thrower always hit the area of a 6-inch radius but hit the area randomly. What is the probability that the dart hits the area between the 2-inch radius and the 4-inch radius of the circle in the next throw?

Answer 19

1/3 (p. 84)

Question 20

51. A box contains 10 brass washers, 18 copper washers, and 22 steel washers. One washer is taken at random, retained, and a second washer is similarly drawn. Determine the probability that one is copper and one is steel.

Answer 20

0.323

Question 21

53. Simplify: ((y²-1)/(y²+3y-4))/(y+1)

Answer 21

1/(y+4)

Question 22

56. Evaluate the first derivative, y’ when x = 1 of y = 3e^4x - 5/(2e^3x) + 8ln5x.

Answer 22

585

Question 23

58: Find the area of a regular octagon inscribed in a circle of radius 5 cm.

Answer 23

70.71 cm^2

Question 24

60. What is the value of x in the equation| x + 2 |= 11 - 2x?

Answer 24

{ 3 } (p. 86)

Question 25

61. An isosceles trapezoid will have 2 diagonals AC and BD. Given that AC=5x+13 and BD=11x-5, the length of the diagonal is nearest to

Answer 25

28

Question 26

66: A busy manager leaves his office at one afternoon. At that time, the hands of a clock in the course of normal operation describe a time somewhere between 4:00 and 5:00 on a standard clock face. Within one hour or less, he returns and noticed the hands have exactly exchanged positions. What time did the manager leave his office?

Answer 26

4:26.853 PM

Question 27

68. Find the particular solution of the differential: dy/dx - 3y/x = (x cubed); y(1) = 4

Answer 27

y = (x to the 4th power)

Question 28

70. An oil well which could produce a net income of P1.5 million per year for 20 years is being considered to be purchased by a group of businessmen. If the return on investment is targeted to be 15% and a sinking fund at 10% interest is to be established to recover the investment, how much must be paid to the oil well?

Answer 28

P8,957,383