SET 10 (p. 157)

Question 1

1: If A=3x^2-x , find dA for x=3 and dx=0.01.

Answer 1

0.17 (p.161)

Question 2

Set 10 Problem 3: In how many ways can 5 different figurines and 3 different vases be exhibited in a row with the vases in consecutive positions?

Answer 2

4,320 (p.161)

Question 3

Set 10 Problem 8: A student can answer a certain test in 5 hours. A second student, who takes 3 minutes longer to answer each question, can answer the test in 6 1/2 hours. How many questions are there in the test?

Answer 3

28 (p.161)

Question 4

Set 10 Problem 9:. Solve the differential equation: y’=cscx+ycotx; if y=1 when x=π/2.

Answer 4

y=cosx-sinx (p.163)

Question 5

Set 10 Problem 10: Find the equation of a hyperbola with center at the origin, focus at (0,3), and y-2=0 as the directrix.

Answer 5

y^2-2x^2=6 (p.163)

Question 6

Set 10 Problem 11: There are 6 geometric means between 3 and 384. Find the common ratio.

Answer 6

2 (p.163)

Question 7

Set 10 Problem 14: Find the angle between the tangents of the curves x²+y²=20 and y²=8x at their intersection.

Answer 7

71.57° (p.164)

Question 8

Set 10 Problem 17: The fourth term of a geometric progression is 189 and the eight terms is 15,309. Find the 6th term.

Answer 8

1,701 (p.165)

Question 9

Set 10 Problem 19: Evaluate the integral of cos³xdx from x=0 to x=π/4.

Answer 9

-(3√2)/8 (p.165)

Question 10

Set 10 Problem 20: If y=x^5, what is the value of y^(4) when x=1.5?

Answer 10

180 (p.165)

Question 11

Set 10 Problem 24: Factor x^4 -24x^2+44 completely.

Answer 11

(x^2-24x-4) (x^2-2x-4) (p.166)

Question 12

Set 10 Problem 26: Two circles have radii 3 inches and 8 inches. The distance between their centers is 18 inches. How long is the common internal tangent segment between their points of tangency?

Answer 12

14.25 in (p.166)

Question 13

Set 10 Problem 29: The apothem of a regular polygon is 6 and its perimeter is 144. The area of the polygon is

Answer 13

432 (p.167)

Question 14

Set 10 Problem 30: Find the distance between P1(3,120°) and P2(4,30°).

Answer 14

5 (p.167)

Question 15

Set 10 Problem 31: A paraboloid of revolution is generated by revolving about the x-axis the parabola z^2=4x which lie on the x-z plane. Find its equation.

Answer 15

y^2+z^2=4x (p.167)

Question 16

Set 10 Problem 33: If y=xe^x, find the value of d²y/dx² when x=2.

Answer 16

29.56 (p.167)

Question 17

Set 10 Problem 36: A particle traveling a straight line has a velocity given by the law v(t)=6-2t+3t^2 and the distance (s) is equal to zero. How far has it travel after 5 seconds?

Answer 17

130 (p.168)

Question 18

A 100 kg block is moving horizontally to the right on a plane surface at a constant velocity of 3 m/s. The coefficient of friction between the block and the surface is 0.30. At a certain instant, a horizontal force of 400 N pushes the body to the right.
Set 10 Problem 40: What is the velocity of the block 5 seconds after the force is applied?

Answer 18

8.285 m/s (p.169)

Question 19

41. A 100 kg block is moving horizontally to the right on a plane surface at a constant velocity of 3 m/s. The coefficient of friction between the block and the surface is 0.30. At a certain instant, a horizontal force of 400 N pushes the body to the right.
    How many seconds after the force is applied will the block travel a distance of 50 m?

Answer 19

6.46 sec

Question 20

Set 10 Problem 43: A projectile is shot at an angle of 60° above the horizontal and strikes a vertical wall 24.40 m away from a point 14.6 m above the point of projection. Find the initial velocity.

Answer 20

20.55 m/s (p.169)

Question 21

44: A machine was purchased 5 years ago at a cost of P50,000 and estimated to have a salvage value of P5,000 at the end of its useful life of 10 years. Today, the owner decides to sell it for P30,000. Determine the sunk cost if money is worth 12%.

Answer 21

P3,709.47

Question 22

Set 10 Problem 50: Find the differential equation of the family of parabolas with vertex at the origin and axis coinciding the x-axis.

Answer 22

2xdy-ydx=0 (p.170)

Question 23

A shirt factory has a production capacity of 8,000 units per month. Material and labor cost is P180 per shirt and fixed monthly operating cost is P675,000. Each shirt can be sold for P450.
Set 10 Problem 53: What is the profit per month if at present it has able to produce and sell 75% of its full capacity?

Answer 23

P945,000 (p.171)

Question 24

56. Two parallel tangents 6 m apart are to be connected by a reversed curve with central angle of 8°. The radius of the first curve is 280 m and the P.C. is at station 12 + 120.40.
    Find the radius of the second curve.

Answer 24

337 m (p.171)

Question 25

When A and Z Company charges P 6,000 for a seminar on construction management techniques, it attracts 100 people. For each P 200 decrease in the fee, an additional 10 people will attend the seminar. The managers are wondering how much to charge for the seminar to maximize their revenue.
Set 10 Problem 61: How many people should attend to maximize revenue?

Answer 25

200 (p.172)

Question 26

When A and Z Company charges P 6,000 for a seminar on construction management techniques, it attracts 100 people. For each P 200 decrease in the fee, an additional 10 people will attend the seminar. The managers are wondering how much to charge for the seminar to maximize their revenue.
Set 10 Problem 62: How much is the charge for the seminar to maximize revenue?

Answer 26

P4,000 (p.172)

Question 27

66. A car traveling at 40 mph when the driver sees an obstruction at a certain distance ahead. The driver applies the brakes immediately (perception time is 3 seconds), and begins slowing the car at 6 m/sec². If the distance from the stopping point to the obstruction is 5 m, how far was the car from the obstruction upon perception?

Answer 27

114

Question 28

69. Evaluate (p. 12).

Answer 28

0 (p. 174) https://youtu.be/NmLljBAg82o?si=26PZJAaSBq7gAD6f, https://youtu.be/thEnl_gCjXA?si=taYok76XMFnhr84Z

Question 29

70. The load of a horizontal beam supported at the ends varies jointly as the breadth and the square of the depth of the beam, and inversely as the length between supports. A beam 75 mm wide, 200 mm deep, and 5 m long can safely support a 6,700 N load.
    What is the coefficient of proportionality?

Answer 29

67/6,000