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標題:
F4 數學問題 ( 2 )
發問:
1 .http://img707.imageshack.us/img707/8128/questionpics02.pngThe figure shows a right-angled triangle PQR , where ∠PQR = 90 ° , PQ = 16 cm and QR = 12 cm . S and T are points on PQ and PR respectively such that ST // QR and SQ = x cm .( a ) . Express the lengths of PS and ST in terms of x .(... 顯示更多 1 . http://img707.imageshack.us/img707/8128/questionpics02.png The figure shows a right-angled triangle PQR , where ∠PQR = 90 ° , PQ = 16 cm and QR = 12 cm . S and T are points on PQ and PR respectively such that ST // QR and SQ = x cm . ( a ) . Express the lengths of PS and ST in terms of x . ( b ) If the area of trapezium TSQR is 72 cm cube , find the value of x . 2 . Given the quadratic equation ax ^ 2 + bx + c = 0 , where a , b and c are positive , does the equation have a positive root ? Explain your answer . 3 . The cost price of a diamond is $ 120000 . Mary sold it to Helen at a profit of r % . After one year , Helen sold the diamond back to Mary at a profit of r % . As a result , Mary lost $ 28800 . Find the value of r . 答的時候請給予 Step , 謝 ! !
最佳解答:
1a) ∠ PTS = ∠ PRQ ( corr ∠ , ST//QR) ∠ TPS = ∠ RPQ ( common angle ) ∴ △ TPS ~ △ RPQ ( AAA ) PS = 16 - x ST / 12 = ( 16 - x ) / 16 ( corr. sides, ~△ ) 12(16-x) = 16ST ST = 3(16-X)/4 1b) (1/2)( ST + RQ) x = 72 (1/2)( 96 - 3x / 4) x = 72 X ( 96 - 3x /4 ) = 144 96X - 3x^2 = 576 3x^2 - 96x + 576 = 0 (x - 24)(3x-24) = 0 x = 24 OR x = 8 since x < 16 , x = 8 2) let the roots be α and β , α + β = -b / a since b > 0 and a > 0 α + β < 0 The roots may 1 positive 1 negative or 2 negative αβ = c / a since c > 0 and a > 0, αβ > 0 The roots may 2 negative or 2 positive so the roots must by both negative, The equation doesn't have a positive root. 2010-09-18 00:04:59 補充： 120000(1 + r%)(1 + r%) - $120000(1 + r%) = $28800 (1+r%)^2 - (1+r%) = 6 / 25 (r%)^2 + 2(r%) +1 - 1 - r% = 6/25 25(r%)^2 + 25(r%) - 6 = 0 (5r%-1)(5r%+6)=0 r% = 0.2 or r%= - 6/5 ( reject) r% = 0.2 r = 20
其他解答:
F4 數學問題 ( 2 )
發問:
1 .http://img707.imageshack.us/img707/8128/questionpics02.pngThe figure shows a right-angled triangle PQR , where ∠PQR = 90 ° , PQ = 16 cm and QR = 12 cm . S and T are points on PQ and PR respectively such that ST // QR and SQ = x cm .( a ) . Express the lengths of PS and ST in terms of x .(... 顯示更多 1 . http://img707.imageshack.us/img707/8128/questionpics02.png The figure shows a right-angled triangle PQR , where ∠PQR = 90 ° , PQ = 16 cm and QR = 12 cm . S and T are points on PQ and PR respectively such that ST // QR and SQ = x cm . ( a ) . Express the lengths of PS and ST in terms of x . ( b ) If the area of trapezium TSQR is 72 cm cube , find the value of x . 2 . Given the quadratic equation ax ^ 2 + bx + c = 0 , where a , b and c are positive , does the equation have a positive root ? Explain your answer . 3 . The cost price of a diamond is $ 120000 . Mary sold it to Helen at a profit of r % . After one year , Helen sold the diamond back to Mary at a profit of r % . As a result , Mary lost $ 28800 . Find the value of r . 答的時候請給予 Step , 謝 ! !
最佳解答:
1a) ∠ PTS = ∠ PRQ ( corr ∠ , ST//QR) ∠ TPS = ∠ RPQ ( common angle ) ∴ △ TPS ~ △ RPQ ( AAA ) PS = 16 - x ST / 12 = ( 16 - x ) / 16 ( corr. sides, ~△ ) 12(16-x) = 16ST ST = 3(16-X)/4 1b) (1/2)( ST + RQ) x = 72 (1/2)( 96 - 3x / 4) x = 72 X ( 96 - 3x /4 ) = 144 96X - 3x^2 = 576 3x^2 - 96x + 576 = 0 (x - 24)(3x-24) = 0 x = 24 OR x = 8 since x < 16 , x = 8 2) let the roots be α and β , α + β = -b / a since b > 0 and a > 0 α + β < 0 The roots may 1 positive 1 negative or 2 negative αβ = c / a since c > 0 and a > 0, αβ > 0 The roots may 2 negative or 2 positive so the roots must by both negative, The equation doesn't have a positive root. 2010-09-18 00:04:59 補充： 120000(1 + r%)(1 + r%) - $120000(1 + r%) = $28800 (1+r%)^2 - (1+r%) = 6 / 25 (r%)^2 + 2(r%) +1 - 1 - r% = 6/25 25(r%)^2 + 25(r%) - 6 = 0 (5r%-1)(5r%+6)=0 r% = 0.2 or r%= - 6/5 ( reject) r% = 0.2 r = 20
其他解答:
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