Respuesta :
Answer:
[tex]R = \dfrac{16}{5}t + \dfrac{1}{5}[/tex]
where R is the R-value and t is the thickness in inches.
Step-by-step explanation:
We are given the following in the question:
The R-value of fiberglass insulation and f its thickness have a linear relation.
Let R be the R-value and t be the thickness. Then, the equation can be written as:
[tex]R = at + b[/tex]
where a and b are constants.
When t = 3.5, R = 11
[tex]11 = 3.5a + b[/tex]
When t = 6, R = 19
[tex]19 = 6a + b[/tex]
Solving the two equation, using the elimination method, we have,
[tex]19-11 = 6a + b-(3.5a + b)\\8 = 2.5a\\\\\Rightarrow a = \dfrac{16}{5}\\\\11 = 6(\dfrac{16}{5}) + b\\\\\Rightarrow b = \dfrac{1}{5}[/tex]
Thus, the linear relationship is given by:
[tex]R = \dfrac{16}{5}t + \dfrac{1}{5}[/tex]
where R is the R-value and t is the thickness in inches.
