June 2016
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at June 22, 2016 0
VERIFIED MATH OBJ:
1-10: ADADDDCEBE
11-20: CCDCAACECA
21-30: DCDAECAEED
31-40: EAADBEEADC
41-50: BBDCCBCECD
51-60: CADBAECDEC
(1a)
Tabulate: Draw both vertical and horizontal
lines across the digits. I drew only verticals cos
it's txt messaging.
x|1|2|3|4
1|1|2|3|4
2|2|4|0|2
3|3|0|3|0
4|4|2|0|4
(1b)
S.I=PRT
P=N15,000, R=10%, T=3yrs
S.I=#15,000, R=10%, T=3yrss
S.I=15,000* 10/100 *3
S.I=N4,500
A=P+S.I
A=N15,000+N4,500
A=#19,500
============================
3)
Let x represent Donald's age
and let y represent his son's age
x=5y—(1)
(x-4(y-4)=448—(11)
substitute for x in (11)
5y^2-20y-4y+16=448
5y^2-24y+16-448=0
5y^2-24y-432=0
y=-b+_sqroot(b^2-4ac)/2a
a=5, b=-24 c=-432
y=24+_sqroot[(-24^2)-4*5*-432]/2*5
y=24+_sqroot(576+8640)/10
y=24+_sqroot(9216)/10
y=24+_96/10
y=24+96/10 or 24-96/10
y=120/10 or -72/10
y=12 or -7.2
since age cannot be negative
y=12years
but x=5y
x=5*12
x=60years
================================
(4a)
Convert 30000 litres to metres
= 30000/1000 metres
= 30metres
Depth of fuel = h * 7.5*4.2 = 30m^3
= 31.5hm^3 = 30m^3
= h = 30m^3/31.5m
= h = 0.9m
(4b)
Depth of the tank = l*b*h
where l= 7.5, b = 4.2, h = 1.2
=(7.5 * 4.2 * 1.2)m^3
=37.8m^3
Convert metres to litres = 37.8*
1000litres
= 37800litres
Litres of fuel needed to fill the
tank=37800litres/30800litres
=7800litres
================================
(5a)
sector for building project
=48000/144000*360=120degree
sector for education =
32,000/144000*360=80degree
sector for saving = 19200/144000*360=48degree
sector for maintenance =
12000/144000*360=30degree
sector for miscellaneous =
7200/144000*360=18degree
sector for food items = 360-(120+80+48+30+18)
=360-296
=64degree
THEN DRAW A PIE CHART WITH THE ANSWERS
YOU GOT ABOVE.
(5b)
Food = 48000 + 32000 + 19200 +
1200 +7200 + x = 144000
Food => 118400 + x = 144000
Food => x = 144000 — 118400
Food = x = #25,600
=================================
(6)
3sqroot[(41.02*sqroot0.7124)/
(42.87*0.207*0.0404)]
Tabulate
No|log
41.02|16130
*sqroot0.7124|(1^-.8527)/2
|(2^-+1.8527)/2
|1^-9264
41.02*sqroot0.7124|1.6130
|+1^-.9264
|=1.5394
42.87|1.6322
*0.207|+1^-.3160
|0.9482
*0.0404|+2^-.6064
|=1^-.5546
|1.5394
|1^-.5546
|=(1.9848)/3
antilog4.588|0.6616
Answer=4.588
===============================
(7a)
3^2n+1 – 4(3^n+1)+9=0
3^2-3 – 4(3^n -3)+9=0
(3^n)^2-3 – 4(3^n -3)+9=0
let 3^n = p
p^2 -3 – 4(p-3)+9=0
3p^2/3 – 12p/3 + 9/3 = 0
p^2 – 4p + 3 = 0
p^2 – 3p – p + 3 = 0
p^2p(p-3) – 1(p-3) = 0
(p-1)(p-3) = 0
p-1 = 0 or p-3 = 0
p = 1 or 3
Recall 3^n = p
when p=1
3^n = 3^0
n = 0
when p = 3
3^n = 3^1
n = 1
(7b)
log(x^2+4) = 2+logx – log^20
log(x^2+4) = log^100 = log^x – log^20
(x^2+4) = log(xx)
x^2+4 = 5x
x^2-5x+4 = 0
x^2-4x – x +4 = 0
x(x-4) – 1(x-4) = 0
(x-1)(x-4) = 0
x-1 = 0 or x-4 = 0
x = 1 or 4
=============
(8ai)
In <> ABC
Cos B=(a^2+c^2-b^2)/2ac
Cos B=(13^3+13^2-10^2)/(2*13*13)
Cos B=(338-100)/338
Cos B=238/338
Cos B=0.7041
B=cos^-0.7041
B=45.2degrees
therefore =90.4degrees
In <>AOC
By sine rule
r/sine44.8=10/sine90.4
r=10sin44.8/sin90.4
r=7.05cm
(8aii)
Circumference =2*pie*R
=2*22/7*7.05
=44.31
=44.3cm(1d.p)
(8b)
p(-1,2) , (2,6)
(y-y1)/(y2-y1)=(x-x1)/(x2-x1)
(y-2)/(6-2)=(x+1)/(2+1)
(y-2)/4=(x+1)/3
3(y-2)=4(x+1)
3y-6=4x+4
3y-4x=10
==========================
(9a)
Let the lens digit x and unit digit be y,
therefore x-y=5 —(1)
3xy-(10x+y)=14 —-(2)
3xy-10x-y=14 —–(3)
frm eq(1); x=5+y — (4)
therefore, 5(5+y)(y)-10(5+y)-y=14
(15+3y)y-50-10y-y=14
3y^2+4y-50-14=0
3y^2+4y-64=0
3y^2 -12y + 16y-64=0
3y(y-4)+16(y-4)=0
(3y+16)(y-4)=0
y=-16/3 or 4
therefore from eqn(1);
x+4=5
x=5+4=9
the number is 94
(9b)
(3-2x)/ 4 + (2x-3)/3
(3(3-2x)+4(2x-3))/12
(9-6x+8x-12)/12
=(2x-3)/12
============================
(10a)
y=(2x^2 + 3)^5
let U=2x^2 + 3
Y=u^5
du/dx = 4x
dy/du = 5u^4
dy/du = (2x^2 + 3)^4
dy/dx = du/dx dy/du
dy/dx = 4x.5(2x^2 + 3)^4
dy/dx = 20x(2x^2 + 3)^4
(10b)
y=3x^2 + 2x +5
dy/dx =6x + 2
dy/dx =6(3) +2
dy/dx =18+2
dy/dx =20
(10c)
R-W=Wv^2/gx
Wv^2=gx(R-W)
Wv^2=gRx-Wgx
Wv^2+Wgx=gRx
W(v^2 + gx) =gRx
W=gRx/V^2 + gx
R=2, g=10, x=3/2, V=3
W= 10*2*3/2/3^2 + 10*3/5
W=30/9+15
W=30/24
W=5/4
(12a)
TABULATE
class interval:50-54,55-59,60-64,65-69,70-74
F:5,5,15,12,3=40
x:52,57,62,67,72
x:260,285,930,804,216=2495
x-x^-:-10.4,-5.4,-0.4,4.6,9.6
(x-x^-)^2:108.16,29.16,0.16,23.16,92.16
F(x-x^-)^2:540.8,145.8,2.4,253.92,276.48=1219.4
(12bi)
Mean(x^-)=Efx/Ef=2495/40
=62.4
(12bii)
Variance=Ef(x-x^-)^2/Ef=1219.4/40
=30.485
(12biii)
Standard deviation=sqroot[Ef(x-x^-)^2/Ef
=Sqroot1219.4/40
=sqroot30.485
=5.52
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at June 16, 2016 0
1. HONESTY IS THE BEST LEGACY
Do you think that "Honesty is the best
legacy"?
This is an old and often repeated proverb, but
it is true? It has a
suspiciously worldly flavor, for it meansthat
from a worldly point of view it pays
to have honesty. Now a man of complete
honesty will not ask whether honesty
pays or not. He feels he must be honest,even if
honesty brings him loss or
suffering,simply because it is right to be honest
and wrong to be dishonest.
This proverb is therefore of little use to people
of sincere honesty: it is really
meant only for those unprincipled men who
will be honest only if honesty pays,
and will be dishonest if they think honesty will
pay them worse.
Probably honesty does pay in the long run. In
business, for example,
a man who deals straight forwardly with the
pubic, who sells at fair prices,
who gives good quality, and can be relied upon
not to cheat,will generally
establish a reputation that will be a fine
business asset.
People will be glad to deal with him; and
though he may not make a
fortune he will have a sound and satisfactory
business. On the other hand,
there is no doubt that success is often due to
trickery, and great fortunes
have been built up upon dishonesty.
Too many successful rogues have proved by
experience that for them
dishonesty had been the best policy.
Of course some of these people come to a bad
end, and lose all they
have gained by their lies; but many maintain
their worldly success is
more due to ability, lucky opportunities, and
business cunning,
than to honesty.
And many examples could be given of men
who, from a worldly point of view,
have failed because they have scrupulous
honesty.
A martyr who prefers to be burned at the stake
rather than say what he believes to be false,
may be a hero; but in the eyes of a worldly
man, who
thinks only of worldly success, he is a sad
failure.
But if we look at such cases from the spiritual
point of view – if we consider
that truth and righteousness are far more
important than wealth and rank
and prosperity – then, in the highest sense,
honesty is the best policy in the
end. "For what it shall profit a man if he gain
the whole world and lose his own
soul?"
5a )
Because they had opposed Africa as a site
5b )
they claimed that the writer wants the fight to
be
moved to
new York
5c )
Because the writer don't t want the work of
honest
boxing
promoters ruined for new York
5d )
the open massage is that the president should
not
let
George and dick out of the city
5e )
i ) Adverbial clause
ii) Modifying the verb rumour
5f )
they felt unhappy
5g )
they had a joyful mood
5h )
i ) circulated – – spread
ii) ruined – – destroyed
iii) routine – – regular
iv ) jammed – – stuck
v ) appeal – – plead
vi ) atmosphere – – feeling
6a )
Because, many deadly diseases which are
highly
contagious are as a result of unhygienic habits
6aii )
in oder to help people develop good health
habits
and maintain a healthy environment
6bi)
vaccines are administered because many
disease
which can easily become fetal can be
prevented through
vaccination
6bii )
Because vaccines helps the person's body to
quickly provide immunity against the germ by
producing
appropriate germ fighting anti bodies which
will
later prevent any further of future infection of
the
person
6ci )
they poison the body system causing great
pain, malfunctioning and eventually debility
and
death
6cii )
they have caused diseases and epidemic which
has wiped out towns and villages
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