| L | = | p.l |
| L | = | (80 – x)(30 – x) |
| 275 | = | 2400 – 110x + x2 |
| 0 | = | 2125 – 110x + x2 |
| 0 | = | (x – 25)(x – 85) |
no. 2
Garis y=2x+n menyinggung x2+y2-2x-4y=0
| * | P(1,2) dengan | |
| * | r | |
| | ||
| 5 | ||
| n | = ±5 |
| * | untuk n=5 → y=2x+5 | |
| x2+y2-2x-4y | =0 | |
| x2+(2x+5)2-2x-4(2x+5) | =0 | |
| x2+(4x2+20x+25)-2x-8x-20 | =0 | |
| 5x2+10x+5 | =0 | |
| x2+2x+1 | =0 | |
| (x+1)2 | =0 | |
| x=-1 |
| * | untuk n = – 5 → y=2x-5 | =0 |
| x2+y2-2x-4y | =0 | |
| x2+ (2x-5)2-2x-4(2x-5) | =0 | |
| x2+(4x2-20x+25)-2x-8x+20 | =0 | |
| 5x2-30x+45 | =0 | |
| x2-6x+9 | =0 | |
| (x-3)2 | =0 | |
| x=3 |
no. 3
| | | |
| | ||
| x2 (x – 4) | | x2(x–4) 2 |
| x2 (x – 4) – x2(x–4) 2 | | 0 |
| x2(x–4) (1 – (x – 4)) | | 0 |
| x2(x–4) (5–x) | | 0 |
Syarat:
| 1. | x – 4 ≥ 0 | → x ≥ 4 |
| 2. | x ≥ 0 |
4
no. 4
Angka pada kupon: 0, 1, 3, 5, 7
Angka pertama tidak 0:
Angka terakhir tidak 0:
Angka pertama dan terakhir tidak 0:
Sehingga banyak kupon yang bisa di buat adalah:
500 + 500 - 400 = 600
no. 5
Barisan Geometri : U1 , U2 ,....., U5
| * | U1+ U2 + U3 | = 9 |
| a + ar + ar2 | = 9 | |
| a(1 + r + r2) | = 9 | |
| * | U3+ U4 + U5 | = 36 |
| a 2 + ar 3 + ar4 | = 36 | |
| ar2 (1 + r + r2) | = 36 | |
| r2(9) | = 36 | |
| r2 | = 4 | |
| r | = ± 2 | |
| * | untuk r= –2 | |
| a(1 – 2 + 4) | =9 | |
| a(3) | =9 | |
| a | = 3 |