SET 7 (p. 107)

Question 1

3: A conical vessel with horizontal bottom base is filled with water to three-fourths of its height. Compute the ratio of the volume of water to the volume of the vessel.

Answer 1

63/64 (p. 111)

Question 2

Set 7 Problem 5: A car weighing 1,200 kg rounds an unbanked curve at 60 kph. The curve has a radius of 100 m. Find the force of friction on the tires to prevent the car from sliding.

Answer 2

3,335 N (p.111)

Question 3

9. A lighthouse located on a small island 3 km away from the nearest point P on a straight shoreline and its line makes 2 revolutions per minute. How fast is the beam of the light moving along the shoreline when it is 1.2 km from P?

Answer 3

43.73 km/min (p. 112)

Question 4

11. A cell phone company estimates that the cost in dollars (in dollars) in producing x units is given by C(x) = 2,600 + 2x + 0.001x^2.
    What is the average cost in producing 1000 times?

Answer 4

$ 5.60

Question 5

15. Which of the following is an eigenvalue of the given matrix?
    (p. 12)

Answer 5

1

Question 6

16. Which of the following is the second derivative of x² - 2y² = 6?

Answer 6

-4/y²

Question 7

20: A motor boat takes 1 1/2 times as long to go 160 miles upstream as it goes to return. If the boat cruises at 40 mph in still water, what is the speed of the current?

Answer 7

8 mph (p.114)

Question 8

22. A chemistry experiment calls for a 30% solution of copper sulfate. Karla has 40 ml of 25% solution. How many ml of 50% solution should she add to obtain the required 30% solution?

Answer 8

10 ml

Question 9

24: Under normal conditions, a siren can be heard from only 125 feet. A car and an emergency vehicle are heading toward each other. The car is traveling at a speed of 44 fps while the emergency vehicle is traveling at 74 fps. If the vehicles are 1000 feet apart and under normal conditions, in how many seconds will the driver of the car first hear the siren?

Answer 9

7.42 sec (p. 115)

Question 10

26. In 1990, the average annual cost of tuition and fees at 4-year colleges in the U.S. was approximately $ 1,980. In 2000, the average annual cost of tuition and fees was $ 3510. Let y be the average annual cost and x is the number x is the number of years after 1990. Write a linear equation that models the cost of tuition and fees for any given year after 1990.

Answer 10

y = 153x + 1980

Question 11

28. Zach and Kurt are going to an amusement park. They cannot decide in which order to ride the 10 roller coasters in the park. If they have only time to ride 7 of the roller coasters, how many ways can they do this?

Answer 11

604,800 (p. 115)

Question 12

32. The perimeter of a rectangular lot is 136 m and its diagonal is 52 m. Compute its area.

Answer 12

960 m^2

Question 13

35: A parabola has an equation x^2 = 4y. Find the equation if the diameter which bisects a system of chords parallel to the line x - 2y = 10.

Answer 13

1 (p. 116)

Question 14

38. Find an angle whose supplement exceeds 5 times its complement by 20°.

Answer 14

52°

Question 15

40. Find the center of mass from the x-axis of a semicircle bounded by x² + y² = 16 and the x-axis.

Answer 15

1.70 (p. 117)

Question 16

46. The denominator of a fraction is 5 more than the numerator. If half the numerator plus one is added to both terms of the fraction, the resulting fraction will be 5/6. What is the original fraction?

Answer 16

12/17

Question 17

48. Solve the inequality: 5/3 (x+1) greater than or equal to ( 2 - x ).

Answer 17

[ 1/8, +∞ ) (p. 118)

Question 18

52. Given the equation of the ellipse: 25x² + 9y² - 250x - 54y + 481 = 0. Compute the second eccentricity.

Answer 18

1.67

Question 19

56. Two chords of a circle AB and CD intersect at point E. If it is known that EB = 12 cm, EA = 8 cm, and EC = 6 cm, compute the length of chord CD.

Answer 19

22 cm (p. 120)

Question 20

57: An equipment has a first cost of P28,000 and has a salvage value of P3,000 at the end of its 5-year operational life. What is the book value of the equipment after 3 years if depreciation is computed using the double declining balanced method?

Answer 20

P6,048

Question 21

59. A marksman fires a bullet to a target. Three seconds later, he heard the bullet hits the target. If the speed of the bullet is 800 m/s and the speed of sound is 300 m/s, how far is the target?

Answer 21

654.55 m (p. 120)

Question 22

60. Compute the volume of the solid bounded by a circular base of radius 5 cm if every section perpendicular to a fixed diameter of the base is an isosceles right triangle with the hypotenuse on the base.

Answer 22

166.67 cm^3 (p. 120)

Question 23

61: Given a regular pentagon of sides 15 cm. Compute the difference in areas between the circumscribed circle and the inscribed circle of the pentagon.

Answer 23

176.92 cm² (p. 121)

Question 24

66: Find the curvature of the curve x²=8y at the point (4, 2).

Answer 24

0.0884

Question 25

67. The bases of a right prism are pentagons with sides 8 cm each. Find the distance between the bases if the volume is 1,182.64 cm³.

Answer 25

8.68 cm

Question 26

69. Find the volume of a solid bounded by the coordinate planes and the plane 3x + 4y + 6z = 24.

Answer 26

32 (p. 122)

Question 27

70. Two tangents are drawn to a circle from an external point P and intersect the circle at points Q and R. The angle between the tangents is 42°. Point S is a point on the circle and is nearer to P than Q and R. Find the angle QSR.

Answer 27

103°

Question 28

71. The process in which granular material is often used to produce a well-graded mixture without excessive fines, which is suitable for compaction.

Answer 28

Soil blending

Question 29

72. Is the placing of additional load on the soil surface used to densify cohesive soil.

Answer 29

Surcharging

Question 30

31: In a precision manufacturing process, ball bearings must be made with radius of 0.60 mm with a maximum error in the radius ± 0.15 mm. Estimate the maximum error in the volume of the ball bearing.

Answer 30

± 0.70 mm³ (p. 116)