Solutions To Homework

I.

Assignment No. 2

Question 1: In a certain family, the sum of the parents’ ages is twice the sum of their children’s ages. Five years ago, the sum of the parents’ ages was four times the sum of the children’s ages during that time. In fifteen years, the sum of the parents’ ages will be equal to the sum of their children’s ages. How many children are there in the family? a. b.

7 5

c. d.

8 9

Solution:

Question 2: Of the 80 students in class, 25 are studying German, 15 French and 13 Spanish. 3 are studying German and French; 4 are studying French and Spanish; 2 are studying German and Spanish; and none is studying all 3 languages at the same time. How many students are studying only one subject at a time? a. b.

62 35

c. d.

18 36

Solution:

Question 3: Solve for W: 80; YWZ = 160. a. b.

5 4

Solution:

XYZ = 320; c. d.

XYW = 64; 2 3

XWZ =

Question 4: If (a + b)2 = 35 and (a - b)2 = 65, then a2 + b2 = ? a. b.

35 50

c. d.

70 280

Solution:

Question 5: The constant term in the expansion of (x + x-3/2)15 is: a. b.

73365 6435

c. d.

50 35

Solution:

Question 6: Simplify (a-x)(b-x)(c-x)...(y-x)(z-x) / abcd..xyz . a. b.

1 Infinite

c. d.

Cannot be determined Zero

Solution:

Question 7: A 100-kilogram salt solution originally 4% by weight. Salt in water is boiled to reduce water content until the concentration is 5% by weight salt. How much water is evaporated? a. b.

10 15

Solution:

c. d.

20 25

Question 8: In a two-digit number, the unit’s digit is 3 greater than the ten’s digit. Find the number if it is 4 times as large as the sum of its digits. a. b.

25 47

c. d.

58 36

Solution:

Question 9: At what time after 12:00 noon will the hour hand and the minute hand of a clock first form an angle of 120°? a. b.

12:21.181 12:12.181

c. d.

12:21.818 21.181

Solution:

Question 10: A and B can do a piece of work in 42 days, B and C in 31 days, and, A and C in 20 days. Working together, how many days can all of them finish the work? a. b.

19.4 17.8

Solution:

c. d.

20.9 18.9

Question 11: Mary was four times as old as Lea ten years ago. If she is now twice as old as Lea, how old is Mary? a. b.

25 40

c. d.

30 15

Solution:

Question 12: A ship propelled to move at 25 mi/ hr in still water, travels 4.2 miles upstream in the same time that it can travel 5.8 miles downstream. Find the speed of the stream. a. b.

8 4

c. d.

10 6

Solution:

Question 13: Jose’s rate of doing work three times as fast as Bong. On given day Jose and Bong work together for 4 hours then Bong was called away and Jose finishes the rest of the job in 2 hours. How long would it take Bong to do the complete job alone? a. b.

18 31

Solution:

c. d.

22 16

Question 14: The ratio of three numbers is 2:5:7. If 7 is subtracted from the second number, the resulting numbers form an arithmetic progression. Determine the smallest of the three numbers. a. b.

21 28

c. d.

70 15

Solution:

Question 15: Rukia has nickels, dimes, and quarters amounting to $1.85. If he has twice as many dimes as quarters, and the number of nickels is two less than twice the number of dimes, how many quarters does he have? a. b.

6 3

c. d.

8 10

Solution:

Question 16: Three men A, B, and C can do a piece of work in t hours working together. Working alone, A can do the work in 6 hours more, B in 1 hour more, and C in twice the time if all working together. How long would it take to finish the work if all worked together? a. b.

30 mins 50 mins

Solution:

c. d.

40 mins 20 mins

Question 17: An ECE class of 40 students took examinations in Electronics and Communications. If 30 passed in Electronics, 36 passed in Communication and 2 failed in both subjects, how many students passed in both subjects? a. b.

32 26

c. d.

30 28

Solution:

Question 18: Find the 50th term of a geometric progression if the 20th term is 1200 and the 30th term is also 1200. a. b.

4100 1400

c. d.

2400 1200

Solution:

Question 19: The term involving x9 in the expansion of (x2 + 2/x)12 is: a. b.

52344x^9 25434x^9

Solution:

c. d.

25344x^9 23544x^9

Question 20: Three externally tangent circle have center to center distance of 11cm, 13cm & 14cm, respectively. What is the radius of the largest circle? a. b.

1 8

Solution:

c. d.

6 5

II.

Assignment No. 3

Question 1: The real part of the complex number z =(-1 + 3i)(3 5i) is [Ans. 12] Solution:

Question 2: The imaginary part of (7e^(-0.28i))(7e^(2.05i)) is [Ans. 48.03] Solution:

Question 3: The imaginary part of the complex number z =(9 + 7i) (7 +9i) is [Ans. 130] Solution:

Question 4: Find the imaginary component of the complex number z, if z = 5(cos(pi/8) - j sin(pi/8)) / (cos(pi/3) - j sin(pi/3)). [Ans. 3.04] Solution:

Question 5: Calculate the magnitude of the conjugate of z, if z = (2 + 4i) / (3 + -4i). Answer should be up to 2 decimal places only. [Ans. 0.89] Solution:

Question 6: What is the argument of the complex number (sin(pi/15) - j cos(pi/15)) / (sin(pi/19) + j cos(pi/19))? [Ans. -2.77] Solution:

Question 7: If x = sqrt(-5), then what is i^x?

[Ans. 0.03]

Solution:

Question 8: What is the real part of the complex number z, if z = ln(6 + 3i)? [Ans. 1.9] Solution:

Question 9: What is e^(sin(pi/2 + -1i))?

[Ans. 4.68]

Solution:

Question 10: What is the logarithm of zero? (Write your answer in words.) [Ans. – infinity or negative infinity] Solution:

Question 11: What is the Laplace Transform of e^4t? a. b. e. f. g. h. i. j. k. l. m. n. o. p. q. r. a. b. e. f. g. h. i. j. k. l. m. n. o.

-1/(s-4) 4/(s-1)

c. 1/(s+4) d. 1/(s-4)

Solution:

Question 12: What is the Laplace transform of sin(2t - pi)? s/(s^2+4) -2(s^2-4) Solution:

c. -2/(s^2+4) d. -1/(s^2+4)

p. Question 13: What is the Laplace transform of (sin3t) (cos2t)? q. a. 0.5( 5/(s^2+25) - 1/ c. 0.5( 5/(s^2+25) + 1/ (s^2+1) ) (s^2+1) ) b. 0.5( 1/(s^2+1) - 5/ d. 0.5( 5/(s^2+5) + 1/ (s^2+25) ) (s^2+1) ) e. f. Solution: g. h. i. j. k. l. m. n. o. p. q. r. Question 14: What is -2i multiplied by logarithm of negative 1? [Ans. 2.73] s. t. Solution: u. v. w. x. y. z. aa. ab. ac. ad. ae. af. ag. ah. Question 15: What is the value of y at t = -1.39pi, given the differential equation y'' - y = 4cost, when t= 0, y = 0 and y' = 1. [Ans. 40.09] ai. aj. Solution: ak. al. am. an. ao. ap. aq. ar. as. at. au. av. aw. ax. ay.

az. ba. bb. III. Assignment No. 4 bc. bd. Question 1: Juan’s age on his birthday in 1989 is equal to the sum of the digits of the year 19XY in which he was born. If X and Y satisfy the equation X – Y – 6 = 0, find the age of Juan in 1990. [Ans. 19] be. bf. Solution: bg. bh. bi. bj. bk. bl. bm. bn. bo. bp. bq. Question 2: How many minutes after 1 O'clock will the hands of the clock forms an angle of 288 degrees for the first time? [Ans. 57.82] br. bs. Solution: bt. bu. bv. bw. bx. by. bz. ca. cb. cc. cd. Question 3: The sum of the ages of Maria and Anna is 35. When Maria was 2/3 her present age and Anna was 3/4 her present age, the sum of their ages was 25. How old is Maria 21 years from now? [Ans. 36] ce. cf. Solution: cg. ch. ci. cj. ck. cl. cm. cn. co. cp. cq. Question 4: What is 262 exceeds 9 times the number 22? [Ans. 460] cr. cs. Solution: ct. cu. cv.

cw. cx. cy. Question 5: An iron bar 4 meters long has a 160 pound weight hang on the other end and a 312 pound weight hung at the opposite end. How far from the 312 pound weight should the fulcrum be located to balance the bar? [Ans. 1.36] cz. da. Solution: db. dc. dd. de. df. dg. dh. di. Question 6: A monkey ascends a greased pole 34 meters high. In the first minute he ascends 8 meters and in the next minute he descends 1 meters. If he continues this process, in how many minutes will he reach the top? [Ans. 9.71] dj. dk. Solution: dl. dm. dn. do. dp. dq. dr. ds. dt. du. Question 7: In how many ways can 15 books be divided among three students so that each student will receive 5 books, 3 books and 7 books, respectively? [Ans. 360360] dv. dw. Solution: dx. dy. dz. ea. eb. ec. ed. ee. Question 8: A 1472 kg of steel containing 11 percent of nickel is to be made by mixing steel containing 19 percent nickel with another steel containing 4 percent nickel. How much of the steel containing 19 percent nickel is needed? [Ans. 686.93] ef. eg. Solution: eh. ei. ej. ek. el. em. en. eo.

ep. eq. er. es. Question 9: What is the 13th term of the sequence 2, -6, 18, ...? [Ans. 1062882] et. eu. Solution: ev. ew. ex. ey. ez. fa. fb. fc. Question 10: A piece of wire is shaped to enclose a square whose area is 495 sq. cm. It is then reshaped to enclose a rectangle whose length is 18 cm. The area of the rectangle is: [Ans. 476.949] fd. fe. Solution: ff. fg. fh. fi. fj. fk. fl. fm. fn. fo. fp. Question 11: A semiconductor company will hire 7 men and 8 women. In how many ways can the company choose from 13 men and 18 women who qualified for the position? [Ans. 75088728] fq. fr. Solution: fs. ft. fu. fv. fw. fx. fy. fz. Question 12: A man left Manila for Baguio City at past 9AM. Between 4 to 5 hours, he arrived at Baguio and noticed the minute and hour hands of his wrist watch interchanged in position. In how many minutes after 1 o'clock did the man arrive at Baguio? [Ans. 45.73] ga. gb. Solution: gc. gd. ge. gf. gg. gh. gi. gj.

gk. gl. gm. gn. go. Question 13: Juan after working on a job for 4 hours was helped by Jose and it took 4 hours more for them working together to finish the job. Had they worked together from the start, it would only require 10 hours to finish the job. How long would it take Juan to finish the job alone? [Ans. 6.67] gp. gq. Solution: gr. gs. gt. gu. gv. gw. gx. gy. gz. ha. hb. Question 14: The arithmetic mean of two positive numbers exceeds their geometric mean by 2. Find the smaller number if it is 40 less than the larger number. [Ans. 81] hc. hd. Solution: he. hf. hg. hh. hi. hj. hk. hl. hm. hn. ho. Question 15: If three sticks are drawn from 5 sticks whose lengths are 1, 3, 5, 7 and 9, what is the probability that they will form a triangle? [Ans. 0.3] hp. hq. Solution: hr. hs. ht. hu. hv. hw. hx. hy. hz. ia. ib. ic. id. ie. if.

ig. ih. ii. ij. ik. il. IV. Assignment No. 5 im. in. Question 1: If tan x = 1/2, tan y = 1/3. What is the value of tan (x + y)? io. a. 3 c. 2 b. 1 d. 4 e. f. Solution: g. h. i. j. k. l. m. n. o. p. q. Question 2: A PLDT tower and a monument stand on a level plane. The angles of depression of the top and bottom of the monument viewed from the top of the PLDT tower are 13 deg and 35 deg respectively. The height of the tower is 50 m. Find the height of the monument. r. a. 33.51 m c. 47.3 m b. 30.57 m d. 7.48 m e. f. Solution: g. h. i. j. k. l. m. n. o. p. q. Question 3: An observer wishes to determine the height of the tower. He takes sight at the top of the tower from A and B, which are 50 ft apart at the same elevation on a direct line with the tower. The vertical angle at point A is 30 deg and at point B is 40 deg. What is the height of the tower? r. a. 92.54 ft c. 80.65 ft b. 143.97 ft d. 110.29 ft e. f. Solution: g. h. i. j.

k. l. m. n. o. p. Question 4: A man finds the angle of elevation of the top of a tower to be 30 degrees. He walks 85 m nearer the tower and finds its angle of elevation to be 60 degrees. What is the height of the tower? q. a. 76.31 m c. 76.13 m b. 73.16 m d. 73.61 m e. f. Solution: g. h. i. j. k. l. m. n. o. p. q. r. Question 5: A ladder 5 m long leans against the wall of an apartment house forming an angle of 50 degrees, 32 minutes with ground. How high up the wall does it reach? s. a. 6.38 m c. 3.86 m b. 3.68 m d. 8.36 m e. f. Solution: g. h. i. j. k. l. m. n. o. p. q. r. Question 6: Solve angle A of an oblique triangle with vertices ABC, if a = 25, b = 16 and C = 94 degrees and 6 minutes. s. a. 54 deg and 30 min c. 55 deg and 32 min b. 50 deg and 40 min d. 45 deg and 35 min e. f. Solution: g. h. i. j. k. l.

m. n. o. p. q. r. s. t. a. b. e. f. g. h. i. j. k. l. m. n. o. p. q. r. a. b. e. f. g. h. i. j. k. l. m. n. o. p. q.

Question 7: Which is identically equal to (sec A + tan A)? csc A + 1 2/(1 – tan A)

c. 1/(sec A - tan A) d. 1/(sec A + tan A)

Solution:

Question 8: If sin A = 2.511x, cos A = 3.06x and sin 2A = 3.939x, find the value of x. 0.265 0.256

c. 0.625 d. 0.562

Solution:

Question 9: Solve for x in the equation: arctan (x + 1) + arctan (x – 1) = arctan (12).

r. a. 1.20 b. 1.25 e. f. Solution: g. h. i. j. k. l. m. n. o. p. q. r.

c. 1.34 d. 1.50

s. t. u. v. w. x. Question 10: The angle of inclination of ascend of a road having 8.25% grade is ______. y. a. 4.72 c. 7.42 b. 4.27 d. 2.74 e. f. Solution: g. h. i. j. k. l. m. n. o. Question 11: Calculate the area of a spherical triangle whose radius is 5 m and whose angles are 40°, 65°, and 110°. p. a. 15.27 sq.m. c. 16.45 sq.m. b. 12.34 sq.m. d. 14.89 sq.m. e. f. Solution: g. h. i. j. k. l. m. n. o. p. q. r. s. t. u. v. Question 12: A right spherical triangle has an angle C = 90°, a = 50°, and c = 80°. Find the side b. w. a. 73.43° c. 78.67° b. 75.89° d. 74.33° e. f. Solution: g. h. i. j. k. l. m. n. o.

p. q. r. s. t. Question 13: If the time is 8:00 a.m. GMT, what is the time in the Philippines, which is located at 120° East longitude? u. a. 4 pm c. 5 am b. 4 am d. 5 pm e. f. Solution: g. h. i. j. k. l. m. Question 14: An airplane flew from Manila (14° 36’N, 121° 05’E) at a course of S 30° E maintaining a certain altitude and following a great circle path. If its groundspeed is 350 knots, after how many hours will it cross the equator? n. a. 2.87 hrs c. 3.17 hrs b. 3.97 hrs d. 2.27 hrs e. f. Solution: g. h. i. j. k. l. m. n. o. p. q. r. s. t. u. v. w. x. y. z. aa. ab. ac. ad. ae. af. ag. ah. ai. aj. ak. al.

am. an. ao. ap. Question 15: Find the distance in nautical miles between Manila and San Francisco. Manila is located at 14° 36’N latitude and 121° 05’ E longitude. San Francisco is situated at 37° 48’ N latitude and 122° 24’ W longitude. aq. a. 6046.2 nautical miles c. 7856.2 nautical miles b. 5896.2 nautical miles d. 6326.2 nautical miles

e. f. Solution: g. h. i. j. k. l. m. n. o. p. q. r. s. t. u. v. w. x. y. z. aa. ab. ac. ad. ae. af. ag. ah. ai. aj. ak. al. am. an. ao. ap. aq. ar. as. at. au. av. aw. ax. ay. az. ba. bb. bc. V. Assignment No. 6 bd. be. bf. bg. bh. bi.

bj. bk. bl. bm. bn. bo. bp. bq. br. bs. bt. bu. bv. bw. bx. by. bz. ca. cb. cc. cd. ce. cf. cg. ch. ci. cj. ck. cl. cm. cn. co. cp. cq. cr. cs. ct. cu. cv. cw. cx. cy. cz. da. db. dc. dd. de. df. dg. dh. di. dj. dk. dl. dm. dn.

do. dp. dq. dr. ds. dt. du. dv. dw. dx. dy. dz. ea. eb. ec. ed. ee. ef. eg. VI. eh. ei. VII. ej.

Assignment No. 7 Assignment No. 8