Maths Question (S.1) HELP!!!

[匿名]

2011-08-23 6:40 am

I need your help,please! >_<

1) Can you find the value of the expression (+1)+(-2)+(+3)+(-4)+......+(+99)+(-100) without using a calculator? Biefly explain how you can do it.

2) The sum of 2 consecutive odd numbers is 36. Find the product of these 2 numbers.

3)Consider the equation x-2x+3x-4x+5x-6x+....+99x-100x =200. Solve the equation and briefly how you can do it.

4) Suppose 2,9,16....form a sequence with a regular pattern. Find the sum of the first 4 numbers in the sequence.

5) Suppose the cost $y of making x booklets is given by the function
y= ax + 400. The following table shows some values of x and the corresponding values of y:

x 1000 2000 3000 4000
-----------------------------------------------------------------------------------
y= ax +400 2400 4400 6400 8400

Find the cost for making 5500 booklets.

6) How many terms are these when we expand the expression
99 98 97 2 <-------they are the 指數.
(x-1)(x99 + x98 + x97 +.... + x2 + x +1) ?
Briefly explain your answer.

I really really hope that you can help me.....thank you very much.

回答 (1)

Godfrey

2011-08-23 10:06 am

✔ 最佳答案

1) -50 (answer)

[(+1)+(-2)] + [(+3)+(-4)] …. + [(+99)+(-100)]
(-1) + (-1) + …. + (-1)
There are 50 terms of (-1), the sum of 50 terms is (-1)50 = -50

2) 323 (answer)
Let x be one number, the other number is (x + 2)
x + (x+2) = 36
2x + 2 = 36
2x = 36 – 2 = 34
x = 34/2 =17
These two number are 17 and 19.
The product of 17 and 19 = 17 is multiplied by 19 = 323

3)
x-2x+3x-4x+5x-6x+....+99x-100x =200
(x-2x) + (3x-4x) + (5x-6x) +....+ (99x-100x) =200
(-x) + (-x) + (-x) + ….. + (-x) = 200
There are 50 x,
-50x = 200
x = -200/40 = -4
x = -4

4)
The difference between each term and its previous term is 7,
2, (2 +7), (2 +7 +7), (2 +7 +7 + 7),….
2, 9, 16, 23…. The sum of first 4 numbers = 2 + 9 + 16 + 23 = 50

Alternatively, use arithmetic series formula
Sn = n/2[2a + (n-1)d],
where a (first term) = 2, n (total number of terms) = 4, d (common difference) = 7
S4 == 4/2[2(2) + (4-1)7]
S4 == 2[4 + 21]
S4 = 50

5)
When x = 1000, y = 2400,
2400 = 1000a + 400
1000 a = 2400 – 400
a = 2
When x = 4000, y = 8400, 8400 = 4000a + 400, a = 2
The equation y = 2x + 400
When x = 5500, y = 2(5500) + 400 = 11400
The cost for making 5500 booklets = $11400

6)
(x-1)(x99 + x98 + x97 +.... + x2 + x +1)
2 terms in (x – 1)
100 terms in ((x99 + x98 + x97 +.... + x2 + x +1)
When we expand the expression , there should be 200 terms

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