請詳細步驟教我計以下二條 :
(不要網址回答)
1. tan x=(2+cos x)/3sin x . (where 0度<= x <360度)
2. Mr Wong is a poultry stall owner. He bought a number of chickens for $1000 and sold each of them at a price of $18 more than its cost. A day before the start of the rest day for the poultry outlets. Mr Wong slaughtered all the 5 unsold live chickens and sold each of them at a price of $10 less than its cost. If Mr Wong made a total profit of $220. how many chickens did he buy ?
急!F5 more equations 1exq8
2012-08-22 7:19 am
回答 (2)
2012-08-24 8:39 pm
✔ 最佳答案
1. tan x = (2 + cos x) / (3 sin x) 3 sin x tan x = 2 + cos x
3 sin² x / cosx = 2 + cos x
3 (1 - cos² x) = 2cos x + cos² x
4cos² x + 2cos x - 3 = 0
cos x = [ - 2 ± √ (2² - 4(4)(- 3)) ] / [2(4)]
cos x = ( - 2 + √52 ) / 8 or ( - 2 - √52 ) / 8 (rejected)
x = 49.35° or x = 310.65° (3 sig fig)
2. Let he bought u chickens = 1000/u.The price of chickens = (u-5)(1000/u + 18)
The price of 5 unsold live chickens = (5)(1000/u - 10)
(u - 5)(1000/u + 18) + (5)(1000/u - 10)= 220+1000
(1000+18u-5000/u-90)+(5000/u-50)=1220
18u=360
u= 20He bought 20 chickens.
2012-08-22 8:02 am
1) tan x = (2 + cos x) / (3 sin x)
3 sin x tan x = 2 + cos x
3 sin² x / cosx = 2 + cos x
3 (1 - cos² x) = 2cos x + cos² x
4cos² x + 2cos x - 3 = 0
cos x = [ - 2 ± √ (2² - 4(4)(- 3)) ] / [2(4)]
cos x = ( - 2 + √52 ) / 8 or ( - 2 - √52 ) / 8 (rejected since cos x ≥ - 1)
x = 49.35368° or x = 310.64632°
2)Let he bought x chickens , then the cost of each = 1000/x.The price of x - 5 chickens = 1000/x + 18
The price of 5 unsold live chickens = 1000/x - 10
(x - 5)(1000/x + 18) + (5)(1000/x - 10) - 1000 = 220
(x - 5 + 5)(1000/x) + (x - 5)18 - 50 = 1220
1000 + (x - 5)18 - 50 = 1220
(x - 5)18 = 270
x = 20He bought 20 chickens.
3 sin x tan x = 2 + cos x
3 sin² x / cosx = 2 + cos x
3 (1 - cos² x) = 2cos x + cos² x
4cos² x + 2cos x - 3 = 0
cos x = [ - 2 ± √ (2² - 4(4)(- 3)) ] / [2(4)]
cos x = ( - 2 + √52 ) / 8 or ( - 2 - √52 ) / 8 (rejected since cos x ≥ - 1)
x = 49.35368° or x = 310.64632°
2)Let he bought x chickens , then the cost of each = 1000/x.The price of x - 5 chickens = 1000/x + 18
The price of 5 unsold live chickens = 1000/x - 10
(x - 5)(1000/x + 18) + (5)(1000/x - 10) - 1000 = 220
(x - 5 + 5)(1000/x) + (x - 5)18 - 50 = 1220
1000 + (x - 5)18 - 50 = 1220
(x - 5)18 = 270
x = 20He bought 20 chickens.
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