close
標題:
有 Simplify、L.C.M.、恒等式、Percentage、Map、Polygon area 英文 20 分
發問:
( / = 份線 ) 所有問題要 show step 同答案，唔該晒 =]1. 3/2 - 2/y / 4x/y - 9y/4x =2. The L.C.M. of 2-b , 4-b^2 and 8-b^3 is3. If (2x+3)(x-a) ≡ 2x^2+b(x+1) , find a and b.4. John's daily working hours have increased from 8 hours to 10 hours but his hourly pay has decreased by 25%. Find the percentage change in... 顯示更多 ( / = 份線 ) 所有問題要 show step 同答案，唔該晒 =] 1. 3/2 - 2/y / 4x/y - 9y/4x = 2. The L.C.M. of 2-b , 4-b^2 and 8-b^3 is 3. If (2x+3)(x-a) ≡ 2x^2+b(x+1) , find a and b. 4. John's daily working hours have increased from 8 hours to 10 hours but his hourly pay has decreased by 25%. Find the percentage change in John's daily income. 5. The scale of a map is 1:4 000. If the actual area of a sports field is 8 000m^2, find its area on the map. 更新: 6. The length of a side of a regular 8-sided polygon is 6 cm. Find its area, correct to 3 significant figures.
最佳解答:
1) 3/2 - 2/y / 4x/y - 9y/4x =3/2 - 2/y (y/4x) - 9y/4x =3/2 - 1/2x-9y/4x = 3/2 - (2+9y)/4x 2) L.C.M. of 2-b , 4-b^2, 8-b^3 4-b^2 = (2-b)(2+b) ......because a^2-b^2 = (a-b)(a+b) 8-b^3 = (2-b)(4+2b+b^2) ........because a^3-b^3 = (a-b)(a^2+ab+b^2) hence, L.C.M. = (2-b)(2+b)(4+2b+b^2) = (4-b^2)(4+2b+b^2) = 16+6b-2b^3-b^4 3) (2x+3)(x-a) = 2x^2+b(x+1) 2x^2+(3-2a)x-3a = 2x^2 +bx +b hence 3-2a =b ......(1) & b=-3a .......(2) put (2) into (1) 3-2a=-3a ===> -a=3 , hence a=-3 & b=-3a =9 4) let x be the original hourly pay, hence original daily income is 8x, the daily income after deduction will be 10 [x * (1-25%)] = 7.5x hence, the % change will be: (8x-7.5x)/8x * 100% = 6.25% i.e. the daily income is decreased by 6.25% 5) if the scale of a map is 1:4000, the ratio of the area on map to the actual area will be 1: 16 000 000 hence area on map = 8000/16000000 m^2= 1/2000 m^2 = 5cm^2 2007-08-22 02:14:26 補充： 6) draw a square around the 8side polygon4 equal triangles is formed interior angles are 90-45-45 resp.(since the interior angles of regular 8 side polygon is 135)then the base & height of the triangle will be(6^2 / 2)^(-2) = 3root2 ........ root2 = 2既開方 2007-08-22 02:14:53 補充： length of square = 6 6root2area of square = 36(1 root2)^2 = 108 72root2area of 8side polygon108 72root2 - 4 * ( 1/2 * 3root2 * 3root2)=108 72root2 - 36= 72(1 root2) ................root2 ~ 1.4142=173.822 corr to the 3 sig fig 2007-08-22 02:17:40 補充： 唔知點解上面冇左d 號length of square = 6 6root2area of square = 36(1 root2)^2 = 108 72root2area of 8side polygon108 72root2 - 4 * ( 1/2 * 3root2 * 3root2)=108 72root2 - 36= 72(1 root2) ................root2 ~ 1.4142=173.822 corr to the 3 sig fig 2007-08-23 10:45:12 補充： 更正~~1) (3/x - 2/y) / (4x/y - 9y/x)= [(3y-2x)/xy] / [(4x^2-9y^2)/xy]=[(3y-2x)/xy] [ xy/(4x^2-9y^2)]=(3y-2x) / [ (2x)^2 - (3y)^2]= (3y-2x) / [(2x-3y)(2x 3y)]= -1/ (2x 3y) 2007-08-23 10:45:39 補充： 更正6) length & height of the triangles are: 3√2length of square = 6(1 √2)area of octagon:[6(1 √2)]^2 - 4[ (1/2)(3√2)^2]= 36(1 2√2 2) - 36= 72 72√2= 173.823 ..........corr. to the 3 sig fig. 2007-08-23 10:50:40 補充： 唔知點解 出唔到架~~6(1 √2) ...length of square36(1 2√2 2)-36 ...area of octagon=72 72√2=173.823 .. 2007-08-23 10:52:58 補充： 更正6) length & height of the triangles are: 3√2length of square = 6(1 + √2)area of octagon:[6(1 + √2)]^2 - 4[ (1/2)(3√2)^2]= 36(1 + 2√2 + 2) - 36= 72 + 72√2= 173.823 ..........corr. to the 3 sig fig.
有 Simplify、L.C.M.、恒等式、Percentage、Map、Polygon area 英文 20 分
發問:
( / = 份線 ) 所有問題要 show step 同答案，唔該晒 =]1. 3/2 - 2/y / 4x/y - 9y/4x =2. The L.C.M. of 2-b , 4-b^2 and 8-b^3 is3. If (2x+3)(x-a) ≡ 2x^2+b(x+1) , find a and b.4. John's daily working hours have increased from 8 hours to 10 hours but his hourly pay has decreased by 25%. Find the percentage change in... 顯示更多 ( / = 份線 ) 所有問題要 show step 同答案，唔該晒 =] 1. 3/2 - 2/y / 4x/y - 9y/4x = 2. The L.C.M. of 2-b , 4-b^2 and 8-b^3 is 3. If (2x+3)(x-a) ≡ 2x^2+b(x+1) , find a and b. 4. John's daily working hours have increased from 8 hours to 10 hours but his hourly pay has decreased by 25%. Find the percentage change in John's daily income. 5. The scale of a map is 1:4 000. If the actual area of a sports field is 8 000m^2, find its area on the map. 更新: 6. The length of a side of a regular 8-sided polygon is 6 cm. Find its area, correct to 3 significant figures.
最佳解答:
1) 3/2 - 2/y / 4x/y - 9y/4x =3/2 - 2/y (y/4x) - 9y/4x =3/2 - 1/2x-9y/4x = 3/2 - (2+9y)/4x 2) L.C.M. of 2-b , 4-b^2, 8-b^3 4-b^2 = (2-b)(2+b) ......because a^2-b^2 = (a-b)(a+b) 8-b^3 = (2-b)(4+2b+b^2) ........because a^3-b^3 = (a-b)(a^2+ab+b^2) hence, L.C.M. = (2-b)(2+b)(4+2b+b^2) = (4-b^2)(4+2b+b^2) = 16+6b-2b^3-b^4 3) (2x+3)(x-a) = 2x^2+b(x+1) 2x^2+(3-2a)x-3a = 2x^2 +bx +b hence 3-2a =b ......(1) & b=-3a .......(2) put (2) into (1) 3-2a=-3a ===> -a=3 , hence a=-3 & b=-3a =9 4) let x be the original hourly pay, hence original daily income is 8x, the daily income after deduction will be 10 [x * (1-25%)] = 7.5x hence, the % change will be: (8x-7.5x)/8x * 100% = 6.25% i.e. the daily income is decreased by 6.25% 5) if the scale of a map is 1:4000, the ratio of the area on map to the actual area will be 1: 16 000 000 hence area on map = 8000/16000000 m^2= 1/2000 m^2 = 5cm^2 2007-08-22 02:14:26 補充： 6) draw a square around the 8side polygon4 equal triangles is formed interior angles are 90-45-45 resp.(since the interior angles of regular 8 side polygon is 135)then the base & height of the triangle will be(6^2 / 2)^(-2) = 3root2 ........ root2 = 2既開方 2007-08-22 02:14:53 補充： length of square = 6 6root2area of square = 36(1 root2)^2 = 108 72root2area of 8side polygon108 72root2 - 4 * ( 1/2 * 3root2 * 3root2)=108 72root2 - 36= 72(1 root2) ................root2 ~ 1.4142=173.822 corr to the 3 sig fig 2007-08-22 02:17:40 補充： 唔知點解上面冇左d 號length of square = 6 6root2area of square = 36(1 root2)^2 = 108 72root2area of 8side polygon108 72root2 - 4 * ( 1/2 * 3root2 * 3root2)=108 72root2 - 36= 72(1 root2) ................root2 ~ 1.4142=173.822 corr to the 3 sig fig 2007-08-23 10:45:12 補充： 更正~~1) (3/x - 2/y) / (4x/y - 9y/x)= [(3y-2x)/xy] / [(4x^2-9y^2)/xy]=[(3y-2x)/xy] [ xy/(4x^2-9y^2)]=(3y-2x) / [ (2x)^2 - (3y)^2]= (3y-2x) / [(2x-3y)(2x 3y)]= -1/ (2x 3y) 2007-08-23 10:45:39 補充： 更正6) length & height of the triangles are: 3√2length of square = 6(1 √2)area of octagon:[6(1 √2)]^2 - 4[ (1/2)(3√2)^2]= 36(1 2√2 2) - 36= 72 72√2= 173.823 ..........corr. to the 3 sig fig. 2007-08-23 10:50:40 補充： 唔知點解 出唔到架~~6(1 √2) ...length of square36(1 2√2 2)-36 ...area of octagon=72 72√2=173.823 .. 2007-08-23 10:52:58 補充： 更正6) length & height of the triangles are: 3√2length of square = 6(1 + √2)area of octagon:[6(1 + √2)]^2 - 4[ (1/2)(3√2)^2]= 36(1 + 2√2 + 2) - 36= 72 + 72√2= 173.823 ..........corr. to the 3 sig fig.
此文章來自奇摩知識+如有不便請留言告知
其他解答:
文章標籤
全站熱搜
留言列表
