SET 3 (p. 37)

Question 1

2. Evaluate the limit of (p. 12) as x approaches infinity.

Answer 1

1/4 (p. 41)

Question 2

3. Mr. Manuel Do is planning his retirement. He has estimated that he will need P10,000 per year to live on, in addition to his Social Security System pension and a private pension plan. How much money should he have in the bank at the date of his retirement, if the bank pays 10% per year, compounded continuously, and if Mr. Manuel Do wants to make 15 annual withdrawals of P10,000 each?

Answer 2

P73,867

Question 3

4. Find the length of one arc of the curve represented by the parametric equation x = 4( θ - sin⁡θ ), y = 4( 1 - cos⁡θ ).

Answer 3

32 (p. 42)

Question 4

8. Find the value of y if ( 2 + i ) divided by ( 1 - i ) equals i times ( x + yi ).

Answer 4

-1/2

Question 5

9. Solve for y from the systems of equations: xy = 10, yz = 12, xz = 30

Answer 5

2

Question 6

Given the following equations in polar form. Convert each to rectangular form.
15: r = 2/(1 + sin⁡θ)

Answer 6

x^2 + 4y - 4 = 0 (p. 43)

Question 7

26. A layer of stone chippings coat laid over a hot to make the surface water-proof.

Answer 7

prime coat

Question 8

28. The tangent to y = x^3 - 6x^2 + 8 x at ( 3, -3 ) intersects the curve at another point. Find this point.

Answer 8

( 0, 0 ) (p. 46)

Question 9

29. Solve the triangle with the given parts: a = 8 cm, b = 10 cm, c = 18 cm. Which of the following is true?
    A. A = 90°
    B. B = 60°
    C. C = 194°
    D. impossible triangle

Answer 9

A

Question 10

31: Find the area of the surface generated by revolving about the y-axis the arc of y = x^2 from x = 0 to x = 6/5.

Answer 10

(1036/375)pi (p. 46)

Question 11

33. MCIA is designing an airport for small planes. This is use for airplanes that must reach a speed before takeoff of at least 100 kph and can accelerate at 2 m/s². Find the minimum length must the runway have.

Answer 11

192.20 m (p. 47)

Question 12

37. An isosceles trapezoid has constant bases of 6 and 12 inches, respectively. Using differentials, find the approximate change in its area when the equal sides changes from 5 to 5.2 inches.

Answer 12

2.25 (p.47)

Question 13

38. Find the equation of the locus of a point which moves so that the sum of its distances from (2,0) and (-2,0) is always 8.

Answer 13

3x^2+4y^2=48 (p. 48)

Question 14

39. It takes Alex 60 seconds to run around a 440-yard track. How long does it take Rubin to run around the track if he and Alex meet in 32 seconds after they start together in a race around the track in opposite direction?

Answer 14

72.57 sec

Question 15

40: At how many minutes after 3 P.M. will the minute hand of the clock overtakes the hour hand?

Answer 15

16.364 (p. 48)

Question 16

41: A motorboat that can travel 20 mph in still water, takes 3/5 as long to travel downstream on a river from A to B, as to return. Find the rate of current.

Answer 16

5 mph (p. 49)

Question 17

43: Compute the length of the latus rectum of the conic whose polar equation is rcos^2=2sinθ

Answer 17

2 (p. 49)

Question 18

44: Joseph is evaluating a more efficient stainless water tank that will cost P17,500 to install. The cost savings will be P3,200 each year. After 10 years, the water tank will be sold for P1,000. The interest rate is 12%. What is the present worth?

Answer 18

P903

Question 19

Set 3 Problem 48: A lot in the form of quadrilateral is situated on the corner of 2 streets intersecting at an angle of 78°. On one street, the side is 134.28 m and on the other street, the side is 106.74 m. The other two sides are perpendicular to each side of the street. Compute the area of the lot.

Answer 19

11,524.74 m^2 (p.50)

Question 20

Set 3 Problem 51:Find the slope of the curve r=3/(2 - cos⁡θ) at ⁡θ=π/2.

Answer 20

0.50 (p. 50)

Question 21

53. A spiral curve with a length of 80 m is to be laid to each side of a 6° central simple curve. Find the required super elevation in percent of the spiral per meter width for a design speed of 60 kph.

Answer 21

14.89% (p. 51)

Question 22

54. A trapezoidal piece of land has parallel sides 438 m and 576 m respectively. The non-parallel sides are 290 m and 354 m. This lot is to be divided into 2 parts in the ratio 2:3 by a line parallel to the parallel sides, the larger part to be adjacent to the smaller parallel side. Compute the length of the dividing line.

Answer 22

525.17 m

Question 23

57. The probability of Steve Carry hitting a 3-point shot is 0.80. How many attempts will he make in order to make sure of at least 90% having a 3-point?

Answer 23

4

Question 24

61. Determine the required length of spiral with a design speed of 80 kph if the central circular curve has a degree of 5.

Answer 24

80 m

Question 25

62: Given the equation of the circle x^2 + y^2 - 8x - 12y + 2 = 0. Find the area of the circle.

Answer 25

157.08 (p. 53)

Question 26

63: An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.50 kg is hung from it. What will its frequency be if only 0.42 kg hangs from it?

Answer 26

4.33 Hz (p. 53)

Question 27

64: Find the value x_0 as prescribed by the generalized law of the mean, given f(x) = 3x + 1 and g(x) = x^2- 1, 0 ≤ x ≤ 3.

Answer 27

3/2 (p. 53)

Question 28

67: Danny and Tony belong to the same basketball team. After so many 3-point attempts. Danny recorded 12 shots out of 20 attempts, while Tony had 10 shots out of 16 attempts. Judging on this present performance record, what is the probability that both will get a shot in their next attempts?

Answer 28

3/5 (p. 54)

Question 29

69. Charlie bought two cars, one for P600,000 and the other for P400,000. He sold the first at a gain of 12% and the second at a loss of 10%. What was his total percentage, gain or loss?

Answer 29

3.2% gain

Question 30

71: The number of days of final curing for concrete cement pavement is done for

Answer 30

14 days

Question 31

72. A distance was measured on an 8% slope and found to be 1,654.30 m. What is the horizontal distance measured in meters?

Answer 31

1,559.294 m

Question 32

73. What is the period of the graph y = tan 2x?

Answer 32

π/2 (p. 54)