Equation 3 - Equation 2
I am doing this to eliminate C from these equations
9a + 3b + c = 24 –eqn3
- 4a + 2b + c = 12 –eqn2
5a + b = 12 –eqn4
Equation 2 – Equation 1
I am doing this to eliminate C and form a fifth equation that I will subtract with equation 4.
4a + 2b + c = 12 –eqn2
- a + b + c = 4 –eqn1
3a + b = 8 –eqn5
Equation 4 – Equation 5
I am doing this to eliminate B and finally work out what A is worth.
5a + b = 12 –eqn4
- 3a + b = 8 –eqn5
2a = 4
A = 4/2
A = 2
Substitute A =2 into equation 5
I am doing this to find what B is worth.
3a + b = 8
3 x 2 + b = 8
6 + b = 8
B = - 6
B = 2
Substitute A =2 and B = 2 into equation 1.
I am doing this to find what C is worth.
A + B + C = 4
2 + 2 + C = 4
4 + C = 4
C = 0
F (n) = an² + bn + c
F (n) = 2n² + 2n
Try n = 1
F (1) = 2 x 1² + 2 x 1
= 2 + 2
= 4
Try n = 2
F (2) = 2 x 2² + 2 x 2
= 8 + 4
= 12
Try n = 100
F (100) = 2 x 100² + 2 x 100
= 10000 + 200
= 20200
Length of longest side:
F (n) = an² + bn +c
F= (1) = a x 1² + b x 1 + c
= a + b + c = 5 – eqn1
F= (2) = a x 2² + b x 2 + c
= 4a + 2b + c = 13 – eqn2
F= (3) = a x 3² + b x 3 + c
= 9a + 3b + c = 25 – eqn3
Equation 3 - Equation 2
I am doing this to eliminate C from these equations
9a + 3b + c = 25 –eqn3
- 4a + 2b + c = 13 –eqn2
5a + b = 12 –eqn4
Equation 2 – Equation 1
I am doing this to eliminate C and form a fifth equation that I will subtract with equation 4.
4a + 2b + c = 13 –eqn2
- a + b + c = 5 –eqn1
3a + b = 8 –eqn5
Equation 4 – Equation 5
I am doing this to eliminate B and finally work out what A is worth.
5a + b = 12 –eqn4
- 3a + b = 8 –eqn5
2a = 4
A = 4/2
A = 2
Substitute A =2 into equation 5
I am doing this to find what B is worth.
5a + b = 12
5 x 2 + b = 12
10 + b = 12
B = 12 – 10
B = 2
Substitute A =2 and B = 2 into equation 1.
I am doing this to find what C is worth.
A + B + C = 5
2 + 2 + C = 5
4 + C = 5
C = 1
F (n) = an² + bn + c
F (n) = 2n² + 2n + 1
Try n = 1
F (1) = 2 x 1² + 2 x 1 +1
= 2 + 2 + 1
= 5
Try n = 2
F (2) = 2 x 2² + 2 x 2 + 1
= 8 + 4 + 1
= 13
Try n = 100
F (100) = 2 x 100² + 2 x 100 + 1
= 10000 + 200
= 20201
Perimeter of the triangle:
12 , 50 , 156 , 190 , 132
18 , 26 , 34 , 42
8 8 8
F (n) = an² + bn +c
F= (1) = a x 1² + b x 1 + c
= a + b + c = 12 – eqn1
F= (2) = a x 2² + b x 2 + c
= 4a + 2b + c = 30 – eqn2
F= (3) = a x 3² + b x 3 + c
= 9a + 3b + c = 56 – eqn3
Equation 3 - Equation 2
I am doing this to eliminate C from these equations
9a + 3b + c = 56 –eqn3
- 4a + 2b + c = 30 –eqn2
5a + b = 26 –eqn4
Equation 2 – Equation 1
I am doing this to eliminate C and form a fifth equation that I will subtract with equation 4.
4a + 2b + c = 30 –eqn2
- a + b + c = 12 –eqn1
3a + b = 18 –eqn5
Equation 4 – Equation 5
I am doing this to eliminate B and finally work out what A is worth.
5a + b = 26 –eqn4
- 3a + b = 18 –eqn5
2a = 8
A = 8/2
A = 4
Substitute A = 4 into equation 5
I am doing this to find what B is worth.
3a + b = 18
3 x 4 + b = 18
12 + b = 18
B = 18 - 12
B = 6
Substitute A = 4 and B = 6 into equation 1.
I am doing this to find what C is worth.
A + B + C = 12
4 + 6 + C = 12
10 + C = 12
C = 12 - 10
C = 2
F (n) = an² + bn + c
F (n) = 4n² + 6n + 2
Try n = 1
F (1) = 4 x 1² + 6 x 1 +2
= 4 + 6 + 2
= 12
Try n = 2
F (2) = 4 x 2² + 6 x 2 + 2
= 16 + 12 + 2
= 30
Try n = 100
F (100) = 4 x 100² + 6 x 100 + 2
= 10000 + 200
= 400000602
Area of the triangle:
6 , 30 , 84 , 180 , 330
24 , 54 , 96 , 150
30 42 54
12 12
F (n) = an³ + bn² +cn + d
F= (1) = a x 1³ + b x 1² + c x 1
= a + b + c + d = 6 – eqn1
F= (2) = a x 2³ + b x 2² + c x 2 + d
= 8a + 4b + 2c + d = 30 – eqn2
F= (3) = a x 3³ + b x 3² + c x 3 + d
= 27a + 9b + 2c + d = 84 – eqn3
F= (4) = a x 4³ + b x 4² + c x 4 + d
= 64a + 16b + 4c + d = 180 – eqn4
Equation 4 - Equation 3
I am doing this to eliminate D from these equations
64a + 16b + 4c + d = 180 –eqn4
- 27a + 9b + 2c + d = 84 – eqn3
37a + 7b + c = 96 –eqn5
Equation 3 – Equation 2
I am doing this to eliminate D and form a sixth equation that I will subtract with equation 5.
27a + 9b + 3c + d = 84–eqn3
- 8a + 4b + 2c + d = 30 –eqn2
19a + 5b + c = 54 –eqn6
Equation 2 – Equation 1
I am doing this to eliminate D and form a seventh equation that I will subtract with equation 5 and 6.
8a + 4b 2c + d = 30 –eqn2
- a + b + c + d = 6 –eqn1
7a + 3b + c = 24- eqn7
Equation 6 – Equation 7
I am doing this to eliminate C.
19a + 5b + c = 54 –eqn6
- 7a + 3b + c = 24- eqn7
12a + 2b = 30- eqn8
Equation 5 – Equation 6
I am doing this to eliminate C.
37a + 7b + c = 96 –eqn5
- 19a + 5b + c = 54 –eqn6
18a + 2b = 42- eqn9
Equation 9 – Equation 8
I am doing this to eliminate B and to find the value of A is worth.
18a + 2b = 42- eqn9
- 12a + 2b = 30- eqn8
6a = 12
A = 12/6
A = 2
Substitute A = 2 into equation 9.
I am doing this to find what B is worth.
12a + 26 = 30
12 x 2 + 2b = 30
24 + 2b = 30
2b = 30 – 24
2b = 6
b = 6/2
B=3
Substitute A = 2 and B = 3 into equation 6.
I am doing this to find what C is worth.
19a + 5b + c = 54
19 x 2 + 5 x 3 + c = 54
38 + 15 + c = 54
53 + 15 + c = 54
c = 54 – 53
C = 1
Substitute A = 2 and B = 3 and C = 1 into equation 1.
I am doing this to find what D is worth.
A + B + C + D = 6
2 + 3 + 1 + D = 6
6 + D = 6
D = 6 – 6
D = 0
F (n) = a³ + bn² + cn + d
F (n) = 2n³ + 3n² + n
Try n = 1
F (1) = 2 x 1³ + 3 x 1² + 1 x 1
= 2 + 3 + 1
= 6
Try n = 2
F (2) = 2 x 2³ + 3 x 2² + 1 x 2
= 16 + 12 + 2
= 30
By:
Kamran Ali 10.1
