急! F5 About equations 1exq04

38.
(a)
3sin²x + 4sinxcosx - 4cos²x = 0
(3sin²x + 4sinxcosx - 4cos²x) / cos²x = 0
3tan²x + 4tanx - 4 = 0

(b)
3sin²x + 4sinxcosx - 4cos²x = 03tan²x+ 4tanx - 4 = 0
(3tanx - 2)(tanx + 2) = 0
tanx = 2/3 or tanx = -2
x = 33.69°, (180+33.69)° or x = (180-63.43)°, (360-63.43)°
x = 33.69°,116.57°,213.69°,296.57°


39.
(a)
xy = 35
(10x + y) - (10y + x) = 18

(b)
xy = 35 ...... [1]
(10x + y) - (10y + x) = 18 ...... [2]

From [2] :
10x + y - 10y - x = 18
9x - 9y = 18
x - y = 2
x = y + 2 ...... [3]

Put [3] into [1] :
(y + 2)y = 35y² + 2y - 35 = 0
(y - 5)(y + 7) = 0
y = 5 or y = -7(rejected)

Put y = 5 into [3] :
x = 5 + 2
x = 7

The original two-digit number = 75


40.
(a)
x²+ y² = 500
2x + 2(x + y) = 100

(b)
x² + y² = 500 ...... [1]
2x + 2(x + y) = 100 ...... [2]

From [2] :
4x + 2y = 100
2x + y = 50
y = 50 - 2x ...... [3]

Put [3] into [1] :
x² + (50 - 2x)² = 500
x² + 2500 - 200x + 4x² = 500
5x² - 200x + 2000 = 0
x² - 40x + 400 = 0
(x - 20)² = 0
x = 20 (double roots)

Put x = 20 into [3] :
y = 50 - 2*20
y = 10

The longest side of the foundation
= (20 + 10) cm
= 30cm