---F.2 math?

[匿名]

2015-08-30 2:46 pm

1a. Factorize a^2 - 2a - 15

1b. Hence, factorize (b^2-4b)^2 - 2(b^2 - 4b) - 15

2a. Solve the simultaneous equations
{3x - 2y = 36
{-2x + 5y = -46

2b. Using the result of (a), solve the simultaneous equations
{3m - 6n = 36
{-2m +15n = -46

3. Sam is employed as a worker in a building site. He said to the employer, 'I would be very happy if I can have 1 cent for the first working day, then 2 cents for the second day, 4 cents for the third day, 8 cents for the fourth day... and so on.'

According to Sam's request, how many dollars will he earn on the 31st day? Give your answer in scientific notation, correct to 3 significant figures.

回答 (1)

andrew

2015-08-30 3:23 pm

✔ 最佳答案

1.
(a)
a² - 2a - 15
= (a + 3)(a - 5)

(b)
Let a = b² - 4b

(b² - 4b)² - 2(b² - 4b) - 15
= a² - 2a - 15
= (a + 3)(a - 5)
= (b² - 4b + 3)(b² - 4b - 5)
= (b - 1)(b - 3)(b + 1)(b - 5)

====
2.
(a)
3x - 2y = 36 ...... [1]
-2x + 5y = -46 ...... [2]

[1] × 2 :
6x - 4y = 72 ...... [3]

[3] × 3 :
-6x + 15y = -138 ...... [4]

[3] + [4] :
11y = -66
y = -6

Put y = -6 into [1] :
3x - 2(-6) = 36
3x = 24
x = 8

Hence, x = 8, y = -6

(b)
3m - 6n = 36 ...... [1]
-2m + 15n = -46 ...... [2]

Put m = x and n = 3n :
[1] : 3x - 2y = 36 ...... [1]
[2] : -2x + 5y = -46 ...... [2]

x = 8 and y = -6
m = 8 and 3n = -6
m = 8 and n = -2

====
3.
It is a geometric sequence :
first term, a = 1 (cent) and common ratio, r = 2

Amount that he will earn on the 31st day
= T(31)
= a r³¹⁻¹
= 1 × 2³⁰ cents
= 1073741824 cents
≈ $1.07 × 10⁷ (to 3 sig. fig.)

👍 3 👎 0