標題:
初中數學問題+排列與組合求解答!要詳細步驟PLZ
發問:
若N是正指數,簡化:Q1) ((a^n+4)-a^3n)/((a^3n+3)-a^n+7)Q2) (2^3x(-2)^2n-1)/2(-2)^4nQ3) the base of a solid metal pyramid is a rectangle with dimensions of 5cm x 9 cm. if it is melted and recast into a square-based solid metal pyramid with the height 1.25 times of the original height, find the length of each side of the... 顯示更多 若N是正指數,簡化: Q1) ((a^n+4)-a^3n)/((a^3n+3)-a^n+7) Q2) (2^3x(-2)^2n-1)/2(-2)^4n Q3) the base of a solid metal pyramid is a rectangle with dimensions of 5cm x 9 cm. if it is melted and recast into a square-based solid metal pyramid with the height 1.25 times of the original height, find the length of each side of the square. Q4) the base of a warning sign is a frustum. the height of the frustum is 42 cm, and its upper and lower bases are squares of side 20 cm and 30 cm respectively. if the height of the original pyramid is 126 cm, find the volume of the base of the warning sign. Q5)心悅以4:1之比把酒精和水混合.過了一會兒,這混合物中的15%的酒精蒸發了.若心悅其後在混合物中加入水,其體積相等於原來水的體積的30% (a)求新混合物中酒精和水的體積之比 (b)求混合物總體積的百分變化 q6)若某平行四邊形的底邊長增加了25%，問其高應減少百分之幾先可以令面積維持不變? q7)兄弟二人共有20枝棒棒糖。若哥哥把他1/3的棒棒糖送給弟弟，則哥哥和弟弟的棒棒糖數量之比為2:3 a) 在哥哥送棒棒糖給弟弟後，弟弟有棒棒糖多少枝？ b)在哥哥送棒棒糖給弟弟前，哥哥有棒棒糖多少枝？ q8 a)因式分解x^3 - x^2y + xy^2 b)因式分解 x^2y - xy^2 + y^3 C)運用a和b的結果，因式分解 x^3 + y^3 Q9)在folk和dance兩個英文字母中，每次分別抽出3個不同的字母，共有多少個不同的組合? Q10)哥哥飼養了一隻貓和一隻狗，求牠們在不同月份出生的概率
最佳解答:
Q1) [a^(n+4) - a^(3n)] / [a^(3n+3) - a^(n+7)] = [a^(n+4) - a^(3n)] / [a^3?a^(3n) - a^3?a^(n+4)] = -[a^(3n) - a^(n+4)] / (a^3)[ a^(3n) - a^(n+4)] = -1/a^3 ===== Q2) [2^3 ? (-2)^(2n - 1)] / 2(-2)^4n = [-(-2)^3 ? (-2)^(2n - 1)] / 2(2)^4n = -(-2)^(3+2n-1) / 2^(4n+1) = -(-2)^(2n+2) / 2^(4n+1) = -2^(2n+2) / 2^(4n+1) = -2^(2n+2-4n-1) = -2^[-(2n-1)] = -1/2^(2n-1) ===== Q3) Let y cm the length of each side of the square. Let h cm be the length of the original height. (1/3) x 5 x 9 x h = (1/3) x y2 x (1.25h) 1.25y = 45 y = 36 y = 6 or y = -6 (rejected) The length of each side of the square = 6 cm ===== Q4) The frustum is made by cutting off a small pyramid from the original pyramid. The upper base is the base of the small pyramid, while the lower base is thebase of the original pyramid. Height of the small pyramid = 126 - 42 cm = 84 Volume of the frustum = (Volume of the original pyramid) - (Volume of the small pyramid) = (1/3) x 302 x 126 - (1/3) x 202 x 84 cm3 = 26600 cm3 ===== Q5) (a) 設原有酒精的體積為 4 單位，則原有水的體積為 1 單位。 新混合物中，酒精體積 : 水體積 = 4(1 - 15%) : 1(1 + 30%) = 3.4 : 1.3 = 34 : 13 (b) 總體積的百分變化 = {[(3.4 + 1.3) - (4 + 1)] / (4 + 1)} x 100% = -(0.3/5) x 100% = -6% (減少 6%) ===== Q6) 設高應減少 R%。 (1 + 25%) x (1 - R%) = 1 1.25(1 - R%) = 1 1 - R% = 0.8 R% = 0.2 R = 20 高應減少 20%。 ===== Q7) (a) 在哥哥送棒棒糖給弟弟後，弟弟的棒棒糖數目 = 20 x [3/(2+3)] 枝 = 20 x (3/5) 枝 = 12 枝 (b) 設哥哥原有棒棒糖 n 枝。 則弟弟原有棒棒糖 (20 - n) 枝。 (20 - n) + (1/3)n = 12 20 - n + (1/3)n = 12 (2/3)n = 8 n = 12 在哥哥送棒棒糖給弟弟前，哥哥的棒棒糖數目 = 12 枝 ===== Q8) (a) x3 - x2y + xy2 = x(x2 - xy + y2) (b) x2y - xy2 + y3 = y(x2 - xy + y2) (c) x3 + y3 = (x3 - x2y + xy2) + (x2y - xy2 + y3) = x(x2 - xy + y2) + y(x2 - xy + y2) = (x + y)(x2 - xy + y2) ===== Q9) 在 11 個字母中抽出 3 個不同的字母，不同的組合數目 = 11C3 個 = 11! / 3!8! = 165 個 ===== Q10) 牠們在相同月份出生的概率 = 1 x (1/12) = 1/12 牠們在不同月份出生的概率 = 1 - (1/12) = 11/12
初中數學問題+排列與組合求解答!要詳細步驟PLZ
發問:
若N是正指數,簡化:Q1) ((a^n+4)-a^3n)/((a^3n+3)-a^n+7)Q2) (2^3x(-2)^2n-1)/2(-2)^4nQ3) the base of a solid metal pyramid is a rectangle with dimensions of 5cm x 9 cm. if it is melted and recast into a square-based solid metal pyramid with the height 1.25 times of the original height, find the length of each side of the... 顯示更多 若N是正指數,簡化: Q1) ((a^n+4)-a^3n)/((a^3n+3)-a^n+7) Q2) (2^3x(-2)^2n-1)/2(-2)^4n Q3) the base of a solid metal pyramid is a rectangle with dimensions of 5cm x 9 cm. if it is melted and recast into a square-based solid metal pyramid with the height 1.25 times of the original height, find the length of each side of the square. Q4) the base of a warning sign is a frustum. the height of the frustum is 42 cm, and its upper and lower bases are squares of side 20 cm and 30 cm respectively. if the height of the original pyramid is 126 cm, find the volume of the base of the warning sign. Q5)心悅以4:1之比把酒精和水混合.過了一會兒,這混合物中的15%的酒精蒸發了.若心悅其後在混合物中加入水,其體積相等於原來水的體積的30% (a)求新混合物中酒精和水的體積之比 (b)求混合物總體積的百分變化 q6)若某平行四邊形的底邊長增加了25%，問其高應減少百分之幾先可以令面積維持不變? q7)兄弟二人共有20枝棒棒糖。若哥哥把他1/3的棒棒糖送給弟弟，則哥哥和弟弟的棒棒糖數量之比為2:3 a) 在哥哥送棒棒糖給弟弟後，弟弟有棒棒糖多少枝？ b)在哥哥送棒棒糖給弟弟前，哥哥有棒棒糖多少枝？ q8 a)因式分解x^3 - x^2y + xy^2 b)因式分解 x^2y - xy^2 + y^3 C)運用a和b的結果，因式分解 x^3 + y^3 Q9)在folk和dance兩個英文字母中，每次分別抽出3個不同的字母，共有多少個不同的組合? Q10)哥哥飼養了一隻貓和一隻狗，求牠們在不同月份出生的概率
最佳解答:
Q1) [a^(n+4) - a^(3n)] / [a^(3n+3) - a^(n+7)] = [a^(n+4) - a^(3n)] / [a^3?a^(3n) - a^3?a^(n+4)] = -[a^(3n) - a^(n+4)] / (a^3)[ a^(3n) - a^(n+4)] = -1/a^3 ===== Q2) [2^3 ? (-2)^(2n - 1)] / 2(-2)^4n = [-(-2)^3 ? (-2)^(2n - 1)] / 2(2)^4n = -(-2)^(3+2n-1) / 2^(4n+1) = -(-2)^(2n+2) / 2^(4n+1) = -2^(2n+2) / 2^(4n+1) = -2^(2n+2-4n-1) = -2^[-(2n-1)] = -1/2^(2n-1) ===== Q3) Let y cm the length of each side of the square. Let h cm be the length of the original height. (1/3) x 5 x 9 x h = (1/3) x y2 x (1.25h) 1.25y = 45 y = 36 y = 6 or y = -6 (rejected) The length of each side of the square = 6 cm ===== Q4) The frustum is made by cutting off a small pyramid from the original pyramid. The upper base is the base of the small pyramid, while the lower base is thebase of the original pyramid. Height of the small pyramid = 126 - 42 cm = 84 Volume of the frustum = (Volume of the original pyramid) - (Volume of the small pyramid) = (1/3) x 302 x 126 - (1/3) x 202 x 84 cm3 = 26600 cm3 ===== Q5) (a) 設原有酒精的體積為 4 單位，則原有水的體積為 1 單位。 新混合物中，酒精體積 : 水體積 = 4(1 - 15%) : 1(1 + 30%) = 3.4 : 1.3 = 34 : 13 (b) 總體積的百分變化 = {[(3.4 + 1.3) - (4 + 1)] / (4 + 1)} x 100% = -(0.3/5) x 100% = -6% (減少 6%) ===== Q6) 設高應減少 R%。 (1 + 25%) x (1 - R%) = 1 1.25(1 - R%) = 1 1 - R% = 0.8 R% = 0.2 R = 20 高應減少 20%。 ===== Q7) (a) 在哥哥送棒棒糖給弟弟後，弟弟的棒棒糖數目 = 20 x [3/(2+3)] 枝 = 20 x (3/5) 枝 = 12 枝 (b) 設哥哥原有棒棒糖 n 枝。 則弟弟原有棒棒糖 (20 - n) 枝。 (20 - n) + (1/3)n = 12 20 - n + (1/3)n = 12 (2/3)n = 8 n = 12 在哥哥送棒棒糖給弟弟前，哥哥的棒棒糖數目 = 12 枝 ===== Q8) (a) x3 - x2y + xy2 = x(x2 - xy + y2) (b) x2y - xy2 + y3 = y(x2 - xy + y2) (c) x3 + y3 = (x3 - x2y + xy2) + (x2y - xy2 + y3) = x(x2 - xy + y2) + y(x2 - xy + y2) = (x + y)(x2 - xy + y2) ===== Q9) 在 11 個字母中抽出 3 個不同的字母，不同的組合數目 = 11C3 個 = 11! / 3!8! = 165 個 ===== Q10) 牠們在相同月份出生的概率 = 1 x (1/12) = 1/12 牠們在不同月份出生的概率 = 1 - (1/12) = 11/12
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