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數學問題!!!Thank
1.) Factorize a2次b+ab2次2.Round off 405.504 to(a) the nearest integer(b)2 decimal places(c)2 significant figures3.The total number of stamps owned by John and Mary is 300.If Mary buys 20 stamps from a post office,the number owned by her will be 4 times that owned by John>Find the number of stamps... 顯示更多 1.) Factorize a2次b+ab2次 2.Round off 405.504 to (a) the nearest integer (b)2 decimal places (c)2 significant figures 3.The total number of stamps owned by John and Mary is 300.If Mary buys 20 stamps from a post office,the number owned by her will be 4 times that owned by John>Find the number of stamps owned by John. 4.In a polar coordinate system,O is the pole. The polar coordinates of the points P and Q are (k,123度) and (24,213度)respectively,where k is a positive constant.It is given that PQ=25. (a) Is △OPQ a right-angled triangle? (b)Find the perimeter of △OPQ Please HELP!!Thank so muych!!!!
最佳解答:
1) a2b + ab2 ab*a + ab*b = ab(a + b) ===== 2. (a) 406 (b) 405.50 (c) 410 ===== 3. Method 1 : Let n be the number of stamps owned by John. Then, the number of stamps owned by Mary = 300 - n (300 - n) + 20 = 4n 320 - n = 4n 5n = 320 n = 64 Hence, John owns 64 stamp. Method 2 : Let j be the number of stamps owned by John, and m be that owned by Mary. j + m = 300 ..... [1] m + 20 = 4j ..... [2] [1] - [2] : j - 20 = 300 - 4j 5j = 320 j = 64 Hence, John owns 64 stamp. ===== 4. (a) ∠QOP = 213° - 123° = 90° Hence, ΔOPQ is a right-angled triangle. (b) OP = k OQ = 24 PQ = 25 In right-angled ΔOPQ : OP2 + OQ2 = PQ2 k2 + 242 = 252 k2 = 252 - 242 k2 = 49 k = 7 or k = -7 (rejected) Perimeter of ΔOPQ = OP + OQ + PQ = 7 + 24 + 25 = 56 2012-09-08 19:43:32 補充： The reason of OP2 + OQ2 = PQ2 is Pythagoras' theorem.
其他解答:
1)a^2*b+a*b^2 =ab(a+b) 2a)406 2b)405.50 2c)410 3) Let the number of stamp John own to be x, then (300-x) is the number of stamp Mary originally own. (300-x)+20 = 4x 300-x+20 = 4x 320-x=4x 320=5x x=64 So, John own 64 stamps.|||||2) a) 406 b) 405.50 c) 400 3) 760D7DAC4E6DF60DFA
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發問:1.) Factorize a2次b+ab2次2.Round off 405.504 to(a) the nearest integer(b)2 decimal places(c)2 significant figures3.The total number of stamps owned by John and Mary is 300.If Mary buys 20 stamps from a post office,the number owned by her will be 4 times that owned by John>Find the number of stamps... 顯示更多 1.) Factorize a2次b+ab2次 2.Round off 405.504 to (a) the nearest integer (b)2 decimal places (c)2 significant figures 3.The total number of stamps owned by John and Mary is 300.If Mary buys 20 stamps from a post office,the number owned by her will be 4 times that owned by John>Find the number of stamps owned by John. 4.In a polar coordinate system,O is the pole. The polar coordinates of the points P and Q are (k,123度) and (24,213度)respectively,where k is a positive constant.It is given that PQ=25. (a) Is △OPQ a right-angled triangle? (b)Find the perimeter of △OPQ Please HELP!!Thank so muych!!!!
最佳解答:
1) a2b + ab2 ab*a + ab*b = ab(a + b) ===== 2. (a) 406 (b) 405.50 (c) 410 ===== 3. Method 1 : Let n be the number of stamps owned by John. Then, the number of stamps owned by Mary = 300 - n (300 - n) + 20 = 4n 320 - n = 4n 5n = 320 n = 64 Hence, John owns 64 stamp. Method 2 : Let j be the number of stamps owned by John, and m be that owned by Mary. j + m = 300 ..... [1] m + 20 = 4j ..... [2] [1] - [2] : j - 20 = 300 - 4j 5j = 320 j = 64 Hence, John owns 64 stamp. ===== 4. (a) ∠QOP = 213° - 123° = 90° Hence, ΔOPQ is a right-angled triangle. (b) OP = k OQ = 24 PQ = 25 In right-angled ΔOPQ : OP2 + OQ2 = PQ2 k2 + 242 = 252 k2 = 252 - 242 k2 = 49 k = 7 or k = -7 (rejected) Perimeter of ΔOPQ = OP + OQ + PQ = 7 + 24 + 25 = 56 2012-09-08 19:43:32 補充： The reason of OP2 + OQ2 = PQ2 is Pythagoras' theorem.
其他解答:
1)a^2*b+a*b^2 =ab(a+b) 2a)406 2b)405.50 2c)410 3) Let the number of stamp John own to be x, then (300-x) is the number of stamp Mary originally own. (300-x)+20 = 4x 300-x+20 = 4x 320-x=4x 320=5x x=64 So, John own 64 stamps.|||||2) a) 406 b) 405.50 c) 400 3) 760D7DAC4E6DF60DFA
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