S1 English Maths (20點 ) !!

2012-08-11 8:37 pm

1.
Goods , Coke , Toliet paper , Peanuts , Chocolate
Rounded unit price , $6 , $3 , $8 , $6

Now, the estimation of the total price is $(8×6+10×3+6×8+5×6) = $156 , which is less than $160. Therefore, we can conclude that Macy has enough money to buy the goods.

If the estimation were less than $160 after applying rounding off or rounding down atrategy, we are unable to make any conalusion. Briefly explain why no conclusion can be made.

2 In the expression (ax + b)(cx^2 + dx + e), find two sets of values of a, b, c, d and e so that the coefficients of x^3 and terms after expansion are 4 and 10 respectively.

回答 (1)

子路

2012-08-12 2:04 am

✔ 最佳答案

1.
The original price of these things can be $R-0.5 ≦ $N < $R+0.5.
(R = Rounded unit price, N = original price)

Therefore, when we count each one in,
there will be a -$0.5 to nearly +$0.5 error.

If she buy 8+10+6+5=29 of these things,
there can be nearly a +$0.5×29 = +$14.5 error

Hence, only if the rounded unit price is lower than the money she have by
$0.5 × (the number of goods),
we can make a conclusion that she has enough money to buy the goods.

2.
(ax + b) (cx² + dx + e)
= acx³ + adx² + aex + bcx² + bdx + be
= acx³ + (ad+bc)x² + (ae+bd)x + be
If the coefficients of x³ and terms after expansion are 4 and 10,
ac=4, (a+b)(c+d+e)=10
Let a=2, c=2.
(a+b)(c+d+e) = (2+b)(2+d+e) = 10
Let 2+b=2.5, 2+d+e=4
b=0.5
d can be 1.5 or 1.25
e can be 0.5 or 0.75
Thus, (a,b,c,d,e) can be (2, 0.5, 2, 1.5, 0.5) or (2, 0.5, 2, 1.25, 0.75).

We can find lots of values to replace a, b, c, d, and e. You can try if you like.

參考: me

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