x
is inversely proportional to y. x=22 while y=5. Find y when x is 10.
Solution
x ⍺ k
y
x = k
y
22 = k
5
k =
22 x 5
k =
110
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
k =
110, y= ?, x = 10.
x = k
y
10 = 110
y
y x 10 = 110
x y (multiply by y on both sides)
y
10y = 110
10
10
Hence y = 11.
TRY THIS…………….
x
is inversely proportional to y. x=80 while y=4. Find y when x is 8.
The
1st term of an arithmetic progression is 33 and the common difference is 40. Find
the nth term
solution
A1=33,
d= 40, n=?
An
=A1 + (n-1) d
An=33
+ (n-1)40
An=33
+ 40n -40
An=40n
+ 33-40
An=40n
– 7 since 33-40= (-7)
Hence the nth term
is An=40n - 7
TRY THIS…………………..
The
1st term of arithmetic progression is 140 and the common difference is 74. Find
the nth term
Change 760 nautical miles into kilometers.
Solution
1
nautical mile= 1.852 km
760
nautical mile= ?
= 1.852 x 760
1
= 1407.52
= 1407.52 to 2 d.p
Hence
760 nautical miles= 1407.52km.
TRY THIS…………….
Change 80 nautical miles into kilometers
Prepare a profit and loss account for the year ended 31ST
May 2018 from the following balances:
Transport……………………..…………..sh.
59,000
Advertising …………..………………… sh.
70,000
General expenses…………..……….
sh 34,000
Sundry expenses…………..………..
sh 5,000
Interest received …………..……….sh.
30,000
Carriage …………..……………………..sh
42,000
Gross profit …………..………………
sh 124,000
Solution
|
Dr
PROFIT
AND LOSS ACCOUNT FOR THE YEAR ENDED ON 31TH, MAY-2018 Cr |
|||||
|
Particulars |
Folio |
Amount |
Particulars |
Folio |
Amount |
|
Transport |
|
59,000 |
Gross profit |
b/d |
124,000 |
|
Advertising |
70,000 |
Interest received |
30,000 |
||
|
General expenses |
34,000 |
Net Loss |
56,000 |
||
|
Sundry expenses |
5,000 |
|
|
||
|
Carriage |
42,000 |
|
|
||
|
|
|
210,000 |
|
|
210,000 |
TRY THIS………..
Prepare a profit and loss account for the year ended 31ST
November 2016 from the following balances:
Transport
----------------------sh. 77,000
Advertising --------------------sh.
57,000
General
expenses------------- sh 38,000
Sundry expenses
--------------sh 9,000
Interest
received------------- sh. 34,000
Carriage
-------------------------sh 24,000
Gross
profit----------------------sh 104,000
The sum of four consecutive
numbers is 606. Find the 3rd number.
Solution
Let the numbers be as shown
in the table below
|
1st number |
2nd number |
3rd number |
4th number |
TOTAL |
|
n |
n+1 |
n+2 |
n+3 |
606 |
Then, n + (n+1) + (n+2) +
(n+3) = 606
4n + 1+2+3= 606
4n + 6 = 606
4n = 606 – 6
4n = 600
4n = 600
4
4
n = 150
3rd number = n +2
= 150 + 2
= 152
Hence the 3rd number is 152
TRY THIS…………………..
The sum of five consecutive
numbers is 1035. Find the largest number.
Given that F(x) = 3x + 11.
Find F(-2) – 2F(5)
Solution
CASE 1: We find F(-2)
F(x) = 3x + 11
F(-2) = 3(-2) + 11
F(-2) = -6 + 11
F(-2) = 5
Hence F(-2) = 5
============================================================
CASE 2: We find F(5)
F(x) = 3x + 11
F(5) = 3(5) + 11
F(5) = 15 + 11
F(5) = 26
Hence F(5) = 26
2F(5) = 2(26) = 52
=====================
CASE 3: We find F(-2) – 2F(5)
= F(-2) – 2F(5)
= 5 – 52
= -47
TRY THIS………………..
Given
that F(x) = 12x + 78. Find F(-20) – 2F(10)
Change the following into Logarithmic form.
i) 42 = 16
ii) 53 = 125
iii) 30 = 1
Solution
42 = 16 ⇔ log4
16 = 2
53 = 125 ⇔ log5
125 = 3
30 = 1 ⇔ log3
1 = 0
TRY
THIS………………….
Change the following into Logarithmic form.
i) 72 = 49
ii) 34 = 81
iii) 80 = 1
Given that F(x) = 7x + 11.
Find F(-2)
Solution
F(x) = 7x + 11
F(-2) = 7(-2) + 11
F(-2) = -14 + 11
F(-2) = -3
Hence F(-2) = -3
TRY THIS………………..
Given
that F(x) = 16x + 23. Find F(-3)
Change 32.6
liters of water into centiliters
Solution
1L
= 100cl
32.6L = ?
___________________________
= 32.6
x 100
1
= 32.6 x
100
= 3260cl. Answer
TRY THIS...................................
Change 154.3 liters of milk into centiliters
