Answer :
Answer:
a
[tex]A = \$66 \foot [/tex]
b
tex]C(10)' = \$60 / feet[/tex]
c
[tex]C(10)' = \$79.696 \ feet [/tex]
Step-by-step explanation:
From the question we are told that
The price per square foot of a floor tile is [tex]p = \$ 3[/tex]
The cost of shipping is [tex]s = \$ 20[/tex]
The current length of the square bathroom is x = 10 ft
The new length is [tex]x_ 1 = 12 \ ft[/tex]
Generally the equation representing the cost of the square tile is mathematically represented as
[tex]C(x) = 3x^2 + 20[/tex]
Generally the average rate of change of cost is mathematically represented as
[tex]A = \frac{ cost \ for\ a \ 12 feet \ bathroom - cost \ for\ a \ 10 feet \ bathroom }{12 feet - 10 feet}[/tex]
Generally the cost for flooring a 12 feet square bathroom is mathematically represented as
[tex]C(12) = 3(12)^2 + 20[/tex]
=> [tex]C(12) = \$ 452 [/tex]
Generally the cost for flooring a 10 feet square bathroom is mathematically represented as
[tex]C(10) = 3(10)^2 + 20[/tex]
=> [tex]C(10) = \$320[/tex]
So
[tex]A = \frac{ 452- 320 }{12 feet - 10 feet}[/tex]
=> [tex]A = \$66 \foot [/tex]
Generally the instantaneous rate of change of cost is obtained by the differentiating the cost function as follows
[tex]C(x) = 3x^2 + 20[/tex]
[tex]C(x)' = \frac{dC(x)}{dx} = 6x[/tex]
So the instantaneous rate of change of cost at length 10 feet is mathematically represented as
[tex]C(10)' = 6(10)[/tex]
=> [tex]C(10)' = \$60 / feet[/tex]
Generally given that the new cost function is
[tex]C(x) = 20(1 + sinx) + 3x^2[/tex]
Now the instantaneous rate of change of cost will now be
[tex]C(x)' = 20cos(x) + 6x[/tex]
So the instantaneous rate of change of cost at length 10 feet is mathematically represented as
[tex]C(10)' = 20cos(10) + 6* 10 [/tex]
=> [tex]C(10)' = \$79.696 \ feet [/tex]