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數學問題...thx (40分)
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1) Suppose y = 4x^2. If x is decreased by 20%,what is the percentage change of y?2)If the height of a parallelogram is increased by 15% while its base is decreased by 15%, what is the percentage chandy of its area?3)Miss Mok deposits $55000 into a bank at an interest rate of 3% p.a. for two years. If... 顯示更多 1) Suppose y = 4x^2. If x is decreased by 20%,what is the percentage change of y? 2)If the height of a parallelogram is increased by 15% while its base is decreased by 15%, what is the percentage chandy of its area? 3)Miss Mok deposits $55000 into a bank at an interest rate of 3% p.a. for two years. If the interest is compound half-yearly, find the compound interest that she can get. 4)Ben uses a ruler with 1mm scale interval to measure the length of some identical ropes. The length of each rope is measured to be 6.2com Five ropes are joined together end to end.Find the total length of the rope and the accumulated error of your calculation. 5)Mary uses a ruler with 0.5cm scale interval to measure the dimensions of a rectangle. The results are as follows: length=7.5cm and width = 5.5cm. a) Find the perimeter and the area of the rectangle. b)Find the accumulated percentage errors in calculating the perimeter and the area. 更新: 6)A sphere with radius 9 cm is melted and recast into two identical smaller spheres. a)Find the radius of each of the smaller spheres. b)Find the percentage change in the total surface area. 7)Find the percentage increase in the volume of a sphere of its radius is increase by 15%.
1) y = 4x^2 If x is decreased by 40% x' = (1 - 20%) x = 0.8x 4x'^2 = 4(0.8x)^2 = 4(0.64)x^2 = 0.64y y is decreased by (1 - 0.64) = 36% 2) Let h be the height of the parallelogram b be the base Area = hb if h increased by 15% and b is decreased by 15% [(1 + 15%) h][(1 - 15%) b] = (1.15)(0.85) hb = 0.9775 hb Area of the parallelogram would be decreased by (1 - 0.9775) = 2.25% 3) since interest is compound half-yearly half year interest would be 3% / 2 = 1.5% 55000 x (1 + 1.5%)^4 - 55000 = 3375 4) Total length of the ropes = 6.2 x 5 = 31 cm Error = 1 mm / 2 = 0.5 mm accumulated error = 2.5 mm 5)(a) Perimeter = (7.5 + 5.5) x 2 = 26 cm Area = 7.5 x 5.5 = 41.25 cm^2 5)(b) Error = 0.5 cm / 2 = 0.25 cm accumulated percentage error for the perimeter = (0.25 x 4) / 26 = 0.0385 = 3.85% accumulated percentage error for area = [41.25 - (7.25 x 5.25)] / 41.25 = 0.0773 = 7.73%
其他解答:
1)15.5 2)6.9 3)9331 4)412.8 5)4521
數學問題...thx (40分)
發問:
1) Suppose y = 4x^2. If x is decreased by 20%,what is the percentage change of y?2)If the height of a parallelogram is increased by 15% while its base is decreased by 15%, what is the percentage chandy of its area?3)Miss Mok deposits $55000 into a bank at an interest rate of 3% p.a. for two years. If... 顯示更多 1) Suppose y = 4x^2. If x is decreased by 20%,what is the percentage change of y? 2)If the height of a parallelogram is increased by 15% while its base is decreased by 15%, what is the percentage chandy of its area? 3)Miss Mok deposits $55000 into a bank at an interest rate of 3% p.a. for two years. If the interest is compound half-yearly, find the compound interest that she can get. 4)Ben uses a ruler with 1mm scale interval to measure the length of some identical ropes. The length of each rope is measured to be 6.2com Five ropes are joined together end to end.Find the total length of the rope and the accumulated error of your calculation. 5)Mary uses a ruler with 0.5cm scale interval to measure the dimensions of a rectangle. The results are as follows: length=7.5cm and width = 5.5cm. a) Find the perimeter and the area of the rectangle. b)Find the accumulated percentage errors in calculating the perimeter and the area. 更新: 6)A sphere with radius 9 cm is melted and recast into two identical smaller spheres. a)Find the radius of each of the smaller spheres. b)Find the percentage change in the total surface area. 7)Find the percentage increase in the volume of a sphere of its radius is increase by 15%.
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最佳解答:1) y = 4x^2 If x is decreased by 40% x' = (1 - 20%) x = 0.8x 4x'^2 = 4(0.8x)^2 = 4(0.64)x^2 = 0.64y y is decreased by (1 - 0.64) = 36% 2) Let h be the height of the parallelogram b be the base Area = hb if h increased by 15% and b is decreased by 15% [(1 + 15%) h][(1 - 15%) b] = (1.15)(0.85) hb = 0.9775 hb Area of the parallelogram would be decreased by (1 - 0.9775) = 2.25% 3) since interest is compound half-yearly half year interest would be 3% / 2 = 1.5% 55000 x (1 + 1.5%)^4 - 55000 = 3375 4) Total length of the ropes = 6.2 x 5 = 31 cm Error = 1 mm / 2 = 0.5 mm accumulated error = 2.5 mm 5)(a) Perimeter = (7.5 + 5.5) x 2 = 26 cm Area = 7.5 x 5.5 = 41.25 cm^2 5)(b) Error = 0.5 cm / 2 = 0.25 cm accumulated percentage error for the perimeter = (0.25 x 4) / 26 = 0.0385 = 3.85% accumulated percentage error for area = [41.25 - (7.25 x 5.25)] / 41.25 = 0.0773 = 7.73%
其他解答:
1)15.5 2)6.9 3)9331 4)412.8 5)4521
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