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The cost($C) for making a colour cube consists of two parts. One part varies directly as its volume (Vm^3) and the other part varies directly as its total surface area(A m^2). If the cost for making a cube of length 3 mis $324 and the cost for making a cube of length 4m is $608,(a) express C in terms of V and... 顯示更多 The cost($C) for making a colour cube consists of two parts. One part varies directly as its volume (Vm^3) and the other part varies directly as its total surface area(A m^2). If the cost for making a cube of length 3 mis $324 and the cost for making a cube of length 4m is $608, (a) express C in terms of V and A (b) find the cost for making a cube of length 5m.

最佳解答:

(a) Let C = K1V + K2A where K's are constants Then: C = K1x3 + K2x2 When x = 3: 324 = 27K1 + 9K2 When x = 4: 608 = 64K1 + 16K2 Solving, we have: K1 = 2 K2 = 30 Therefore, C = 2x3 + 30x2 (b) Sub x = 5 into the expression: C = 2(5)3 + 30(5)2 = 1000 So the cost for making a cube of length 5m is $1000.

其他解答:

(a) C = xV + yA 324 = x*(3*3*3) + y*[(3*3)*6] 324 = 27x + 54y 12 = x + 2y x = 12 - 2y 608 = x*(4*4*4) + y*[(4*4)*6] 608 = 64x + 96y 608 = 64(12 - 2y) + 96y 608 = 768 - 128y + 96y -160 = -32y y = 5 if y=5, x = 12 - 2(5) x = 2 C = 2V + 5A (b) C = 2(5*5*5) + 5*[(5*5)*6] = 1000|||||a) 324=3X3X3V+6X3X3A 12=V+2A-----------------1 608=4X4X4V+6X4X4A 608=64V+96A 19=2V+3A-----------------2 b) 24=2V+4A-------------1 19=2V+3A-------------2 1-2 A=5 V=2 C=5X5X5V+6X5X5A C=250+750 C=1000|||||(a) C = k?V + k?A For a cube of length 3 m, A = 6 x 32 = 54 m2, V = 33 = 27 m3, C = 324 324 = 27 k?+ 54 k? ---- (1) For a cube of length 4 m, A = 6 x 42 = 96 m2, V = 43 = 64 m3, C = 608 608 = 64 k?+ 96 k? ---- (2) (1) x 64 - (2) x 27, 4320 = 864k? k?= 5 Put k?= 5 into (1), we get k?= 2 Hence, C = 2V + 5A (b) the cost for making a cube of length 5 m = 2 x 53 + 5 x (6 x 52) = $ 1000A9A3995907B431A4