Respuesta :
Answer:
a
[tex]The \ price \ for \ Compact\ fluorescent\ bulbs \ is \ C_T = \$ 21.067\\The \ price \ for \ incandescent\ bulb \ is \ C_t = \$ 43.98[/tex]
b
[tex]The \ amount \ saved \ is \ C_S = \$ 22.913[/tex]
c
[tex]The \ resistance \ is \ R = 626.1 \Omega[/tex]
Explanation:
From the question we are told that
The power used by incandescent bulb [tex]P_r = 23.0 W[/tex]
The power used by Compact fluorescent bulb [tex]P_p = 100W[/tex]
The life span of Compact fluorescent bulb is [tex]t = 1000 \ hours[/tex]
The prices of Compact fluorescent bulb is [tex]C_c = \$ 12 [/tex]
The prices of incandescent bulb is [tex]C_i = \$ 0.76 [/tex]
The life span of incandescent bulb is [tex]t_k = 750 \ hours[/tex]
The cost of electricity is [tex]C_e = \$ 0.090/ kilowatt-hour = \frac{0.090}{1000} = \$0.00009 / W / h[/tex]
The duration of daily bulb usage is [tex]t_d = 4 \ hours[/tex]
Generally 3 years of bulb usage in hours is mathematically evaluated as
[tex]t_3 = 3 * 365 * t_d[/tex]
=> [tex]t_3 = 3 * 365 * 4[/tex]
=> [tex]t_3 = 4380 \ h [/tex]
Generally the cost to power a 23W bulb for the above duration is mathematically represented as
[tex]Z = 23 * t_3 * C_e[/tex]
=> [tex]Z = 23 * 4380 * 0.00009[/tex]
=> [tex]Z = \$ 9.0667[/tex]
The number of Compact fluorescent bulbs required to achieve this about of time is mathematically represented as
[tex]N = \frac{t_3}{ t}[/tex]
=> [tex]N = \frac{4380}{1000}[/tex]
=> [tex]N = 0.438 [/tex]
=> [tex]N \approx 1 [/tex]
The total cost of usage for the Compact fluorescent bulb is mathematically represented as
[tex]C_T = Z +C_c[/tex]
=> [tex]C_T = 9.0667 +12[/tex]
=> [tex]C_T = \$ 21.067 [/tex]
The number of incandescent bulbs required to achieve this about of time is mathematically represented as
[tex]M = \frac{t_3}{ t_k}[/tex]
=> [tex]M = \frac{4380}{750}[/tex]
=> [tex]M = 6 [/tex]
Generally the cost to power a 100W bulb for the above duration is mathematically represented as
[tex]Z = 100 * t_3 * C_e[/tex]
=> [tex]Z = 100 * 4380 * 0.00009[/tex]
=> [tex]Z = \$ 39.42[/tex]
The total cost of usage for the incandescent bulbs is mathematically represented as
[tex]C_t = C_e + [6 *C_i][/tex]
=> [tex]C_t = 39.42 + [0.76 * 6][/tex]
=> [tex]C_t = \$ 43.98[/tex]
Generally the total amount saved is mathematically represented as
[tex]C_S = C_t - C_T[/tex]
=> [tex]C_S = 43.98 - 21.067[/tex]
=> [tex]C_S = \$ 22.913[/tex]
Generally the resistance of the Compact fluorescent bulb is
[tex]R = \frac{V^2}{P}[/tex]
[tex]R = \frac{120^2}{23}[/tex]
[tex]R = 626.1 \Omega[/tex]
