F. 3 Variations

2007-04-14 2:47 am

1) It is known that the interest ($I) received from an investment varies jointly as the interest rate per annum(r %) and the period of investment (T years). If an amount of money is invested obtained will be$1200.
(a) Express I in terms of r and T.
(b) If the same amount of money is invested for 3years and the interest rate is14% p.a., what will be the interest obtained
更新1:

2) The resistance (R units) of a metal wire varies inversely as the square of the diameter (d m) of the metal wire and directly as its length (l m). If the length of a metal wire is10m and its diameter is 4mm, then resistance is 75 units.

更新2:

(a) Express R in terms of d and l. (b) Find the resistance of a metal wire of length 40m and diameter 1 cm

更新3:

Answer : 1a) I = 50rT ; b) $2100 ; 2a) R = 3l / 25000d^2 ; b) 48 units

回答 (1)

2007-04-14 7:22 am
✔ 最佳答案
1)

Principal = 1200 - I

under Compound interest rate : 1200 = (1200 - I)*(1 + r)^T

(a)
1200 = (1200 - I)*(1 + r)^T
1200 - I = 1200*(1 + r)^(-T)

I = 1200 - 1200*(1 + r)^(-T) = 1200 * [ 1 - (1 + r)^(-T) ]

(b) Hence, using the result by part (a),
the interest obtained I = 1200 * [ 1 - (1 + 14%)^(-3) ] = $390.03

2007-04-13 23:25:20 補充:
sorry, misunderstand your question, then give you wrong anwser.
參考: me


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