Math Assignment: Problem-Solving, Equations, and Calculations

This assignment provides solutions to a range of mathematical problems. The solutions cover various topics, including basic arithmetic operations such as addition, subtraction, multiplication, and division. It includes problems involving fractions, percentages, and ratios. The assignment also touches upon algebra with solutions for equations, and calculations of financial and physics problems. The solutions demonstrate step-by-step processes to arrive at the answers, along with explanations where necessary. The assignment offers a comprehensive overview of foundational mathematical concepts and their practical applications.

Q1 (BODMAS)
a. ,
X=−26
4 – - 18
= - 6.5 - 18
= - 24.5
b. ,
Dividing first
X= 5 x 8 + 4 x 7 - 5
Multiplication
= ( 5 x 8) + (4 x 7) - 5
= 40 + 28 – 5
Addition
= 68 -5
Subtraction
= 63
Q2
a.
X = 5 x 6
7 x 8
= 30
56
= 0.5357

b. ,
X= 6.76
0.008
= 845.00
Q3
a. ,
25% of $ 950
→ 25
100 x $ 950
= $ 237.50
b. ,
Total for 192 m3 before increase
= $235 x 192
= $ 45,120
Total for 192 m3 after increase
= ( 235 x 103.3 % ) x 192
= $ 46, 608.96
How much more paid?
= $ 46, 608.96 - $ 45,120
= $ 1,488.96
c. ,
Profit = $ 920, 000 – $ 755,000
= $ 165, 000

The number of years = 2015 – 2011
= 4 years
The profit per year = $ 165, 000/ 4 years
= $ 41,250 / year
Annual percentage = increment per year
original price
= ( $ 41,250
year )
755 ,000
x 100
= 5.46 %
Q4
a. ,
→48 : 12
¿ (48/12): (12/12)
¿ 4: 1
b. ,
→64:8:16
¿ (64/8): (8/8) : (16/8)
=8:1:2
Q 5
Total ratio = 3+4+2
= 9

Sand = 3
9 x 2700 kg
= 900 kg
Gravel = 4
9 x 2700 kg
= 1200 kg
Cement = 2
9 x 2700 kg
= 600 kg
Q6
7896 into 2 s.f becomes 7800
Q7
a. ,
x = 4.89 x 108 x 9.34 x 10−4
1.06 x 10−9
= 4.56728 x 105
1.06 x 10−9
= 4.31 x 1014
b. ,
x = √¿ ¿ ¿
= 29600
Q8
a. ,

x = √ ( ( −7 ) 2+62 )
= 49 + 36
= 87
b. ,
x= (-7 x 6) + (6 x-3) + (-7 x -3)
= -42 – 18 + 21
= -39
c. ,
x= ( −7 ) 2− ( −3 ) 2
−7−−3
= 10
Q10
a. ,
Y= 20x – 20 – 26 x + 48
= 28- 6x
b. ,
z=6 x2−12 xy−40 x2−10 xy
= −34 x2−22 xy
Q 12
a. ,

T = 2 π √ 1.2
9.8
= 2.1 s
b. ,
764 cm = 7.64m
Therefore
T = 2 π √ 7.64
9.8
= 5.547 s
c. ,
0.55 = 2 π √ l
9.8
0.08753 = √ l
9.8
0.0751 m = l
Q 13
EK =1
2 M V 2
a . ,
= 0.5 x 125
1000 x 1272
= 1,008.0625 J
b . ,
= 0.5 x 24.5 x 1025 x 210002

= 5.40 x 1034 J
Q15
2 x2 −3 x +1=0
a = 2 , b= -3 and c= 1
x=−b ± √ b2−4 ac
2 a
= ( −−3 ) ± √ ( −3 ) 2−4 ( 2 ) ( 1 )
2 x 2
= 3−1
4 or 3+1
4
= 0.5 or 1