Solutions to Homework

7/24/2019 Solutions to Homework

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I. Assignment No. 2

Question 1: In a certain family, the sum of the parents ages istwice the sum of their childrens ages. Five years ago, the sumof the parents ages was four times the sum of the childrens

ages during that time. In fifteen years, the sum of the parentsages will be equal to the sum of their childrens ages. ow manychildren are there in the family!

a. "b. 5

c. #d. $

%olution:

Question &: 'f the #( students in class, &) are studying *erman,1) French and 1+ %panish. + are studying *erman and French - arestudying French and %panish & are studying *erman and %panish

and none is studying all + languages at the same time. ow manystudents are studying only one subect at a time!

a. /&b. 35

c. 1#d. +/

%olution:

Question +: %olve for 0: 23 4 +&( 20 4 /- 03 4#( 203 4 1/(.

a. )

b. -

c. 2

d. +%olution:


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Question -: If 5a 6 b7&4 +) and 5a 8 b7&4 /), then a&6 b&4 !

a. +)b. 50

c. "(d. (

%olution:

Question ): 9he constant term in the epansion of 5 6 8+;&71)is:a. "++/)

b. /-+)

c. 50

d. +)

%olution:

Question /: %implify 5a875b875c87...5y875


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Question #: In a two8digit number, the units digit is + greaterthan the tens digit. Find the number if it is - times as largeas the sum of its digits.

a. &)

b. -"

c. )#d. 36

%olution:

Question $: >t what time after 1&:(( noon will the hour hand andthe minute hand of a cloc? first form an angle of 1&(A!

a. 1&:&1.1#1b. 1&:1&.1#1

c. 12:21.818d. &1.1#1

%olution:

Question 1(: > and B can do a piece of wor? in -& days, B and =

in +1 days, and, > and = in &( days. 0or?ing together, how manydays can all of them finish the wor?!

a. 1$.-b. 1".#

c. &(.$d. 18.9

%olution:


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Question 11: Cary was four times as old as Dea ten years ago. Ifshe is now twice as old as Dea, how old is Cary!

a. &)b. -(

c. 30d. 1)

%olution:

Question 1&: > ship propelled to move at &) mi; hr in stillwater, travels -.& miles upstream in the same time that it can

travel ).# miles downstream. Find the speed of the stream.

a. #b. 4

c. 1(d. /

%olution:

Question 1+: Eoses rate of doing wor? three times as fast asBong. 'n given day Eose and Bong wor? together for - hours thenBong was called away and Eose finishes the rest of the ob in &hours. ow long would it ta?e Bong to do the complete ob alone!

a. 1#b. +1

c. 22d. 1/

%olution:


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Question 1-: 9he ratio of three numbers is &:):". If " issubtracted from the second number, the resulting numbers form anarithmetic progression. etermine the smallest of the threenumbers.

a. &1b. 28 c. "(d. 1)%olution:

Question 1): Gu?ia has nic?els, dimes, and quarters amounting toH1.#). If he has twice as many dimes as quarters, and the numberof nic?els is two less than twice the number of dimes, how manyquarters does he have!

a. /b. 3

c. #d. 1(

%olution:

Question 1/: 9hree men >, B, and = can do a piece of wor? in t

hours wor?ing together. 0or?ing alone, > can do the wor? in /hours more, B in 1 hour more, and = in twice the time if allwor?ing together. ow long would it ta?e to finish the wor? ifall wor?ed together!

a. +( minsb. )( mins

c. 40 minsd. &( mins

%olution:


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Question 1": >n = class of -( students too? eaminations inlectronics and =ommunications. If +( passed in lectronics, +/passed in =ommunication and & failed in both subects, how manystudents passed in both subects!

a. +&b. &/ c. +(d. 28%olution:

Question 1#: Find the )(thterm of a geometric progression if the&(thterm is 1&(( and the +(thterm is also 1&((.

a. -1((b. 1-((

c. &-((d. 1200

%olution:

Question 1$: 9he term involving $in the epansion of 5&6

&;71&

is:

a. )&+--J$b. &)-+-J$

c. 25344x^9d. &+)--J$

%olution:


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Question &(: 9hree eternally tangent circle have center tocenter distance of 11cm, 1+cm K 1-cm, respectively. 0hat is theradius of the largest circle!

a. 1b. 8

c. /

d. )%olution:


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II. Assignment No. 3

Question 1: 9he real part of the comple number < 4581 6 +i75+ 8)i7 is LAns. 12M

%olution:

Question &: 9he imaginary part of 5"eJ58(.i775"eJ5&.()i77 isLAns. 48.03M

%olution:

Question +: 9he imaginary part of the comple number < 45$ 6 "i75" 6$i7 is LAns. 130M

%olution:

Question -: Find the imaginary component of the comple number


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Question ): =alculate the magnitude of the conugate of nswer should be up to & decimal placesonly. LAns. 0.89M

%olution:

Question /: 0hat is the argument of the comple number5sin5pi;1)7 8 cos5pi;1)77 ; 5sin5pi;1$7 6 cos5pi;1$77!LAns. -2.77M

%olution:

Question ": If 4 sqrt58)7, then what is iJ! LAns. 0.03M

%olution:

Question #: 0hat is the real part of the comple number


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Question $: 0hat is eJ5sin5pi;& 6 81i77! LAns. 4.68M

%olution:

Question 1(: 0hat is the logarithm of


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p. Question 1+: 0hat is the Daplace transform of 5sin+t75cos&t7!

q.a. (.)5 );5sJ&6&)7 8 1;

5sJ&617 7

b. (.)5 1;5sJ&617 8 );5sJ&6&)7 7

c. 0.5% 5$%s^2'25& ' 1$%s^2'1& &

d. (.)5 );5sJ&6)7 6 1;5sJ&617 7e.f. %olution:g.h.i..?.l.m.n.o.p.q.r. Question 1-: 0hat is 8&i multiplied by logarithm of negative

1! LAns. 2.73Ms.t. %olution:u.v.w..

y.


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az.

ba.

bb.III. Assignment No. 4

bc.bd. Question 1: Euans age on his birthday in 1$#$ is equal

to the sum of the digits of the year 1$2 in which he wasborn. If and 2 satisfy the equation O 2 O / 4 (, findthe age of Euan in 1$$(. LAns. 19M

be.bf. %olution:bg.bh.bi.b.b?.bl.bm.bn.bo.bp.bq. Question &: ow many minutes after 1 'Ncloc? will the

hands of the cloc? forms an angle of # degrees for thefirst time! LAns. 57.82M

br.bs. %olution:bt.bu.bv.

bw.b.by.bnna is

+). 0hen Caria was &;+ her present age and >nna was +;- herpresent age, the sum of their ages was &). ow old is Caria&1 years from now! LAns. 36M

ce.cf. %olution:cg.ch.ci.c.c?.cl.cm.cn.co.

cp.cq. Question -: 0hat is &/& eceeds $ times the number &&!LAns. 460M

cr.cs. %olution:ct.cu.cv.


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cw.c.cy. Question ): >n iron bar - meters long has a 1/( pound

weight hang on the other end and a +1& pound weight hung atthe opposite end. ow far from the +1& pound weight should

the fulcrum be located to balance the bar! LAns. 1.36

Mc mon?ey ascends a greased pole +- meters

high. In the first minute he ascends # meters and in thenet minute he descends 1 meters. If he continues thisprocess, in how many minutes will he reach the top! LAns.9.71M

d.d?. %olution:dl.dm.dn.do.dp.dq.

dr.ds.dt.du. Question ": In how many ways can 1) boo?s be divided

among three students so that each student will receive )boo?s, + boo?s and " boo?s, respectively! LAns. 360360M

dv.dw. %olution:d.dy.d 1-"& ?g of steel containing 11 percent of

nic?el is to be made by miing steel containing 1$ percentnic?el with another steel containing - percent nic?el. owmuch of the steel containing 1$ percent nic?el is needed!LAns. 686.93M

ef.eg. %olution:

eh.ei.e.e?.el.em.en.eo.


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ep.eq.er.es. Question $: 0hat is the 1+thterm of the sequence &,

8/, 1#, ...! LAns. 1062882M

et.eu. %olution:ev.ew.e.ey.e piece of wire is shaped to enclose a

square whose area is -$) sq. cm. It is then reshaped toenclose a rectangle whose length is 1# cm. 9he area of therectangle is: LAns. 476.949M

fd.fe. %olution:ff.fg.fh.fi.f.f?.fl.fm.

fn.fo.fp. Question 11: > semiconductor company will hire " men

and # women. In how many ways can the company choose from 1+men and 1# women who qualified for the position! LAns.75088728M

fq.fr. %olution:fs.ft.fu.

fv.fw.f.fy.f man left Canila for Baguio =ity at past

$>C. Between - to ) hours, he arrived at Baguio and noticedthe minute and hour hands of his wrist watch interchanged inposition. In how many minutes after 1 oNcloc? did the manarrive at Baguio! LAns. 45.73M

ga.gb. %olution:

gc.gd.ge.gf.gg.gh.gi.g.


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g?.gl.gm.gn.go. Question 1+: Euan after wor?ing on a ob for - hours

was helped by Eose and it too? - hours more for them wor?ingtogether to finish the ob. ad they wor?ed together fromthe start, it would only require 1( hours to finish the ob.ow long would it ta?e Euan to finish the ob alone! LAns.6.67M

gp.gq. %olution:gr.gs.gt.gu.gv.gw.g.gy.g


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ig.

ih.

ii.ij.

ik.

il. IV. Assignment No. 5im.in. Question 1: If tan 4 1;&, tan y 4 1;+. 0hat is the

value of tan 5 6 y7!io.a. +b. 1

c. &d. -

e.f. %olution:g.h.i..?.l.m.n.o.p.q. Question &: > PD9 tower and a monument stand on a level

plane. 9he angles of depression of the top and bottom of themonument viewed from the top of the PD9 tower are 1+ degand +) deg respectively. 9he height of the tower is )( m.

Find the height of the monument.r.". 33.51 mb. +(.)" m

c. -".+ md. ".-# m

e.f. %olution:g.h.i..?.

l.m.n.o.p.q. Question +: >n observer wishes to determine the height of

the tower. e ta?es sight at the top of the tower from > andB, which are )( ft apart at the same elevation on a directline with the tower. 9he vertical angle at point > is +( degand at point B is -( deg. 0hat is the height of the tower!

r.

". 92.54 ftb. 1-+.$" ft c. #(./) ftd. 11(.&$ fte.f. %olution:g.h.i..


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?.l.m.n.o.

p. Question -: > man finds the angle of elevation of the top ofa tower to be +( degrees. e wal?s #) m nearer the tower andfinds its angle of elevation to be /( degrees. 0hat is theheight of the tower!

q.a. "/.+1 mb. "+.1/ m

c. "/.1+ md. 73.61 m

e.f. %olution:g.h.i..?.l.m.n.o.p.q.r. Question ): > ladder ) m long leans against the wall of an

apartment house forming an angle of )( degrees, +& minuteswith ground. ow high up the wall does it reach!

s.a. /.+# mb. +./# m

c. 3.86 md. #.+/ m

e.f. %olution:g.h.i..?.l.

m.n.o.p.q.r. Question /: %olve angle > of an oblique triangle with

vertices >B=, if a 4 &), b 4 1/ and = 4 $- degrees and /minutes.

s.". 54 de! "nd 30 minb. )( deg and -( min

c. )) deg and +& mind. -) deg and +) min

e.f. %olution:g.h.i..?.l.


18/24

m.n.o.p.q.

r.s. Question ": 0hich is identically equal to 5sec > 6 tan >7!t.a. csc > 6 1b. &;51 O tan >7

c. 1;5sec > 8 tan >7d. 1$%sec A ' t"n A&

e.f. %olution:g.h.i..?.l.m.n.o.p.q. Question #: If sin > 4 &.)11, cos > 4 +.(/ and sin &> 4

+.$+$, find the value of .r.a. (.&/)b. 0.256

c. (./&)d. (.)/&

e.

f. %olution:g.h.i..?.l.m.n.o.p.

q. Question $: %olve for in the equation: arctan 5 6 17 6arctan 5 O 17 4 arctan 51&7.r.a. 1.&(b. 1.&)

c. 1.34d. 1.)(

e.f. %olution:g.h.i..

?.l.m.n.o.p.q.r.


19/24

s.t.u.v.w.

. Question 1(: 9he angle of inclination of ascend of a roadhaving #.&)@ grade is .y.". 4.72b. -.&"

c. ".-&d. &."-

e.f. %olution:g.h.i..?.l.m.n.o. Question 11: =alculate the area of a spherical triangle

whose radius is ) m and whose angles are -(A, /)A, and 11(A.p.". 15.27 s(.m.b. 1&.+- sq.m.

c. 1/.-) sq.m.d. 1-.#$ sq.m.

e.f. %olution:g.

h.i..?.l.m.n.o.p.q.r.

s.t.u.v. Question 1&: > right spherical triangle has an angle = 4

$(A, a 4 )(A, and c 4 #(A. Find the side b.w.a. "+.-+Ab. ").#$A

c. "#./"Ad. 74.33)

e.f. %olution:g.

h.i..?.l.m.n.o.


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p.q.r.s.t. Question 1+: If the time is #:(( a.m. *C9, what is the time

in the Philippines, which is located at 1&(A ast longitude!u.". 4 *mb. - am

c. ) amd. ) pm

e.f. %olution:g.h.i..?.l.m. Question 1-: >n airplane flew from Canila 51-A +/R, 1&1A

()7 at a course of % +(A maintaining a certain altitudeand following a great circle path. If its groundspeed is +)(?nots, after how many hours will it cross the equator!

n.". 2.87 +rsb. +.$" hrs

c. +.1" hrsd. &.&" hrs

e.f. %olution:g.h.

i..?.l.m.n.o.p.q.r.s.

t.u.v.w..y.


21/24

am.an.ao.ap. Question 1): Find the distance in nautical miles

between Canila and %an Francisco. Canila is located at 1-A

+/R latitude and 1&1A () longitude. %an Francisco issituated at +"A -# R latitude and 1&&A &- 0 longitude.aq.". 6046.2 n",tic" miesb. )#$/.& nautical miles

c. "#)/.& nautical milesd. /+&/.& nautical miles


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e.f. %olution:g.

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j.k.

l.

m.n.

o.

p.q.

r.

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u.v.

w.x.

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z.aa.

ab.

ac.ad.

ae.

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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.


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bj.

bk.

bl.bm.

bn.

bo.bp.

bq.

br.bs.

bt.

bu.

bv.bw.

bx.

by.

bz.ca.

cb.cc.

cd.

ce.cf.

cg.

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ck.

cl.cm.

cn.

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cq.

cr.

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cv.cw.

cx.

cy.cz.

da.

db.

dc.dd.

de.

df.dg.

dh.

di.dj.

dk.

dl.dm.

dn.


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do.

dp.

dq.dr.

ds.

dt.du.

dv.

dw.dx.

dy.

dz.

ea.eb.

ec.

ed.

ee.ef.

eg. VI. Assignment o. !eh.

ei. VII. Assignment o. "ej.

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Solutions to Homework