中二數學問題求幫忙(15點)

銀

2012-08-29 8:18 pm

Linear Equation in Two Unknowns
1.Prudy spend $89 on buying some hamburgers and sundaes in a fast food shop.The numbers of hamburger and a sundae are $11 and $6 respectively,find the values of x and y.

Rational and Irrational Numbers
evaluate(can be expressed in surd form.Questions2-5)
2.(3√27)*(2√12)*(√5)

3.(4/√6)-(√6/3)

4.[(3√5)-(√3)][(2√3)+(4√5)]

5.[(√5)-(√2)][(√5)+(√2)]

6.If √2=1.414,without using a calculator,find the value of √32/8.(corr to 3 sig. fig.)

7.If a=√2 and b=√7,express the following in terms of a and b:

a.√14

b.(√28)-(√18)

8.If √3=a and √5=b,find (√45)-(√3/√25).(express in terms of a and b.)

回答 (1)

用戶2053

2012-08-30 2:43 am

✔ 最佳答案

1)Let there be x hamburgers and y sundaes :11x + 6y = 89
11x + 6y = 77 + 12
6y - 12 = 77 - 11x
6(y - 2) = 11(7 - x)
y - 2 = 11 (7 - x)/6Let 7 - x = 6n , then x = 7 - 6n ,
so y - 2 = 11n, then y = 11n + 2.For x = 7 - 6n > 0 , n = 1 only.
So x = 7 - 6(1) = 1 and y = 11(1) + 2 = 13.
2) 3√27 * 2√12 * √5
= (3√3 √9) (2√3 √4) √5
= 9√3 * 4√3 * √5
= 9 * 4 * 3 * √5
= 108√5
3)4/√6 - √6/3
= 4√6 / 6 - √6 / 3
= 2√6 / 3 - √6 / 3
= √6 / 3
4) (3√5 - √3) (2√3 + 4√5)
= 3√5 (2√3 + 4√5) - √3 (2√3 + 4√5)
= 6√15 + 12 * 5 - (2 * 3 + 4√15)
= 6√15 + 60 - 6 - 4√15
= 54 + 2√15
5)(√5 - √2) (√5 + √2)
= √5² - √2²
= 5 - 2
= 3
6) √32 / 8
= √16 * √2 / 8
= 4 *√2 / 8
= √2 / 2
= 1.414 / 2
= 0.707
7a)√14
= √2 * √7
= a bb)√28 - √18
= √4 * √7 - √9 * √2
= 2√7 - 3√2
= 2b - 3a
8) √45 - √3 / √25
= √9 * √5 - √3 / 5
= 3√5 - √3 / 5
= 3b - a/5

2012-08-29 19:06:00 補充：
I miss a solution at Q1 sorry!

The last 2 lines :

For x = 7 - 6n > 0 , n = 1 or n = 0 ,
So x = 7 - 6(1) = 1 and y = 11(1) + 2 = 13.
or x = 7 - 6(0) = 7 and y = 11(0) + 2 = 2.

Sorry for my mistakes.

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