Respuesta :
Answer:
$520
Explanation:
Using information provided in the question, equations can be formed to determine the unknown proportionality factors.
[tex]C=AT + BL^2[/tex] , where C is the cost, T is the thickness, L is the length and A and B are the proportionality factors
Equation 1:
Slab 1: [tex]C_1=0.2A + 2^2B=0.2A+4B[/tex]
Slab 2: [tex]C_2=0.1A + 2^2B=0.1A+4B[/tex]
[tex]C_1=C_2+160[/tex]
[tex]0.2A+4B=0.1A+4B+160[/tex]
[tex]0.1A=160[/tex]
[tex]A=1600[/tex]
Equation 2:
Slab 2: [tex]C_2=0.1A + 3^2B=0.1A+9B[/tex]
Slab 3: [tex]C_3=0.1A + 2^2B=0.1A+4B[/tex]
[tex]C_2=C_3+200[/tex]
[tex]0.1A+9B=0.1A+4B+200[/tex]
[tex]5B=200[/tex]
[tex]B=40[/tex]
After determining unknowns A=1600 and B=40, these can be substituted into [tex]C=AT + BL^2[/tex] to give below
[tex]C=1600T + 40L^2[/tex]
Cost is to be determined for T=0.1m and L=3m
[tex]C=1600T + 40L^2[/tex]
[tex]C=1600(0.1) + 40(3)^2[/tex]
[tex]C=160 + 360[/tex]
[tex]C=520[/tex]
The cost of a square slab of 3 meter length and 0.1 meter thickness is $520
Answer:
(1) The cost of the square slab is $360
(2) The cost of the square slab is $360
Explanation:
Cost (C) varies as thickness (t) and square of length (L^2)
Therefore, C = ktL^2
Case 1
C1 = 160 + C2
C1 - C2 = 160
C1 = ktL^2 (t = 0.2, L = 2)
C1 = k×0.2×2^2 = 0.8k
C2 = ktL^2 (t = 0.1, L = 2)
C2 = k×0.1×2^2 = 0.4k
C1 - C2 = 0.8k - 0.4k = 0.4k
C1 - C2 = 0.4k
160 = 0.4k
k = 160/0.4 = 400
C = ktL^2 (t = 0.1, t = 3)
C = 400×0.1×3^2 = $360
Case 2
C1 = 200 + C2
C1 - C2 = 200
C1 = ktL^2 (t = 0.1, L = 3)
C1 = k×0.1×3^2 = 0.9k
C2 = ktL^2 (t = 0.1, L = 2)
C2 = k×0.1×2^2 = 0.4k
C1 - C2 = 0.9k - 0.4k = 0.5k
C1 - C2 = 0.5k
200 = 0.5k
k = 200/0.5 = 400
C = ktL^2 (t = 0.1, L = 3)
C = 400×0.1×3^2 = $360
