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中四math數6 條 (20點)
1. If cosθ= -2/3, then sinθ+tanθ/2sinθ-tanθ=2. Then perimeter of a rectangular playground is 324 m. The length is increased by 6 m and the width by 3 m. The area is then increased by 1/9 of its former value. Find the original dimensions of the playground.3. The figure shows a... 顯示更多 1. If cosθ= -2/3, then sinθ+tanθ/2sinθ-tanθ= 2. Then perimeter of a rectangular playground is 324 m. The length is increased by 6 m and the width by 3 m. The area is then increased by 1/9 of its former value. Find the original dimensions of the playground. 3. The figure shows a hillside in which the plane ABFE inclines 25° to the horizontal. Find the slope of the path BE on the hill that makes an angle of 45° with a line of the greatest slope BF. http://i6.photobucket.com/albums/y222/wing_hing/23.jpg 4. In the figure, UVW is a straight line and ST=SU. Prove that SV bisects ∠TVW. http://i6.photobucket.com/albums/y222/wing_hing/19.jpg 5. In the figure, AFE and BCD are straight lines. Prove that AB is parallel to ED. http://i6.photobucket.com/albums/y222/wing_hing/10.jpg 6. Sketch the graph of y=tan(x+30°) for 0°<=x<=360°, and hence sketch the graph of y-1=tan(x+30°) for 0°<=<=360°
最佳解答:
1. (sinx + tanx)/(2sinx - tanx) = tanx(sinx/tanx + 1)/tanx (2sinx/tanx - 1) = (cosx + 1)/(2cosx - 1) = [(-2/3) + 1]/[2(-2/3) - 1] = (1/3)/(-4/3 - 1) = (1/3)/(-7/3) = -1/7. 2.Let width of playground = w, therefore, length of playground = 324/2 - w = 162-w. New length of playground = 162 - w + 6 = (168 - w). New width of playground = w + 3. Therefore, new area = (168 - w)(w +3). Original area = w(162 - w). Therefore, (168 - w)(w + 3) = w(162 -w) ( 1 + 1/9) 9(168 - w)(w + 3) = 10w(162 - w) 4536 - 9w^2 + 1485w = 1620w - 10w^2 w^2 - 135w + 4536 = 0 (w -72)(w -63) = 0 So width, w = 72 or 63. When w = 72 , length = 162 - 72 = 90. When w = 63, length = 99. 6. Graph of y = tan(x + 30) is exactly the same as y = tanx but shifted to the left by 30 degree. Graph of y - 1 = tan(x + 30) is exactly the same as y = tan(x + 30) but shifted upwards by 1.
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中四math數6 條 (20點)
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發問:1. If cosθ= -2/3, then sinθ+tanθ/2sinθ-tanθ=2. Then perimeter of a rectangular playground is 324 m. The length is increased by 6 m and the width by 3 m. The area is then increased by 1/9 of its former value. Find the original dimensions of the playground.3. The figure shows a... 顯示更多 1. If cosθ= -2/3, then sinθ+tanθ/2sinθ-tanθ= 2. Then perimeter of a rectangular playground is 324 m. The length is increased by 6 m and the width by 3 m. The area is then increased by 1/9 of its former value. Find the original dimensions of the playground. 3. The figure shows a hillside in which the plane ABFE inclines 25° to the horizontal. Find the slope of the path BE on the hill that makes an angle of 45° with a line of the greatest slope BF. http://i6.photobucket.com/albums/y222/wing_hing/23.jpg 4. In the figure, UVW is a straight line and ST=SU. Prove that SV bisects ∠TVW. http://i6.photobucket.com/albums/y222/wing_hing/19.jpg 5. In the figure, AFE and BCD are straight lines. Prove that AB is parallel to ED. http://i6.photobucket.com/albums/y222/wing_hing/10.jpg 6. Sketch the graph of y=tan(x+30°) for 0°<=x<=360°, and hence sketch the graph of y-1=tan(x+30°) for 0°<=<=360°
最佳解答:
1. (sinx + tanx)/(2sinx - tanx) = tanx(sinx/tanx + 1)/tanx (2sinx/tanx - 1) = (cosx + 1)/(2cosx - 1) = [(-2/3) + 1]/[2(-2/3) - 1] = (1/3)/(-4/3 - 1) = (1/3)/(-7/3) = -1/7. 2.Let width of playground = w, therefore, length of playground = 324/2 - w = 162-w. New length of playground = 162 - w + 6 = (168 - w). New width of playground = w + 3. Therefore, new area = (168 - w)(w +3). Original area = w(162 - w). Therefore, (168 - w)(w + 3) = w(162 -w) ( 1 + 1/9) 9(168 - w)(w + 3) = 10w(162 - w) 4536 - 9w^2 + 1485w = 1620w - 10w^2 w^2 - 135w + 4536 = 0 (w -72)(w -63) = 0 So width, w = 72 or 63. When w = 72 , length = 162 - 72 = 90. When w = 63, length = 99. 6. Graph of y = tan(x + 30) is exactly the same as y = tanx but shifted to the left by 30 degree. Graph of y - 1 = tan(x + 30) is exactly the same as y = tan(x + 30) but shifted upwards by 1.
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