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1.It is give that r is a root of the quadratic equation x^2-3x-5=0,find the value of r^5-3r^4-5r^3+2r^2-6r2.Tom and Mary are due south and aue east of a bus stop respectively,and the distance between them is 60m.They walk towards the bus stop at the same time with their own constant speeds.After 6 seconds,they... 顯示更多 1.It is give that r is a root of the quadratic equation x^2-3x-5=0,find the value of r^5-3r^4-5r^3+2r^2-6r 2.Tom and Mary are due south and aue east of a bus stop respectively,and the distance between them is 60m.They walk towards the bus stop at the same time with their own constant speeds.After 6 seconds,they are both 27m away from the bus stop.If Mary walks slower than Tom by 2m/s,find their speeds.
最佳解答:
1. r^2 - 3r - 5 = 0 r^2 - 3r = 5 r^5 - 3r^4 - 5r^3 + 2r^2 - 6r = r^3(r^2 - 3r - 5) + 2(r^2 - 3r) = r^3(0) + 2(5) = 10 2. Let the speed of Tom be x m/s, then speed of Mary is (x - 2)m/s. Setting up the equation: (6x)^2 + [6(x-2)]^2 = 60^2 (Pyth.theorem) 36x^2 + 36(x^2 - 4x + 4) = 3600 x^2 + x^2 - 4x + 4 = 100 2x^2 - 4x - 96 = 0 x^2 - 2x - 48 = 0 (x - 8)(x + 6) = 0 x = 8 or x = -6(rejected) The speed of Tom is 8 m/s and the speed of Mary is 6 m/s. 2010-12-30 20:46:47 補充： Sorry I hv made a mistake in question 2. The distance of Tom from the bus stop = 6x + 27 The distance of Mary from the bus stop = 6(x - 2) + 27 By Pyth. theorem, (6x + 27)^2 + [6(x-2) + 27]^2 = 60^2 36x^2 + 324x + 729 + 36(x^2 - 4x + 4) + 324(x-2) + 729 = 3600 2010-12-30 20:46:50 補充： 72x^2 + 504x - 2646 = 0 4x^2 + 28x - 147 = 0 (2x - 7)(2x + 21) = 0 x = 7/2 or x = -21/2 (rejected) So, speed of Tom is 7/2 m/s and that of Mary is 3/2 m/s
其他解答:1C924F1C0172E337
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有兩條數唔識發問:
1.It is give that r is a root of the quadratic equation x^2-3x-5=0,find the value of r^5-3r^4-5r^3+2r^2-6r2.Tom and Mary are due south and aue east of a bus stop respectively,and the distance between them is 60m.They walk towards the bus stop at the same time with their own constant speeds.After 6 seconds,they... 顯示更多 1.It is give that r is a root of the quadratic equation x^2-3x-5=0,find the value of r^5-3r^4-5r^3+2r^2-6r 2.Tom and Mary are due south and aue east of a bus stop respectively,and the distance between them is 60m.They walk towards the bus stop at the same time with their own constant speeds.After 6 seconds,they are both 27m away from the bus stop.If Mary walks slower than Tom by 2m/s,find their speeds.
最佳解答:
1. r^2 - 3r - 5 = 0 r^2 - 3r = 5 r^5 - 3r^4 - 5r^3 + 2r^2 - 6r = r^3(r^2 - 3r - 5) + 2(r^2 - 3r) = r^3(0) + 2(5) = 10 2. Let the speed of Tom be x m/s, then speed of Mary is (x - 2)m/s. Setting up the equation: (6x)^2 + [6(x-2)]^2 = 60^2 (Pyth.theorem) 36x^2 + 36(x^2 - 4x + 4) = 3600 x^2 + x^2 - 4x + 4 = 100 2x^2 - 4x - 96 = 0 x^2 - 2x - 48 = 0 (x - 8)(x + 6) = 0 x = 8 or x = -6(rejected) The speed of Tom is 8 m/s and the speed of Mary is 6 m/s. 2010-12-30 20:46:47 補充： Sorry I hv made a mistake in question 2. The distance of Tom from the bus stop = 6x + 27 The distance of Mary from the bus stop = 6(x - 2) + 27 By Pyth. theorem, (6x + 27)^2 + [6(x-2) + 27]^2 = 60^2 36x^2 + 324x + 729 + 36(x^2 - 4x + 4) + 324(x-2) + 729 = 3600 2010-12-30 20:46:50 補充： 72x^2 + 504x - 2646 = 0 4x^2 + 28x - 147 = 0 (2x - 7)(2x + 21) = 0 x = 7/2 or x = -21/2 (rejected) So, speed of Tom is 7/2 m/s and that of Mary is 3/2 m/s
其他解答:1C924F1C0172E337
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