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### Summer-1 2024 (Part II)

Question 9, 2.6.107

HW Score: [tex]$41.33\%$[/tex], 4.13 of 10 points

Part 1 of 3

Points: 0 of 1

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A common air pollutant responsible for acid rain is sulfur dioxide ([tex]$SO_2$[/tex]). Emissions of ([tex]$SO_2$[/tex]) from burning coal during year [tex]$x$[/tex] are computed by [tex]$f(x)$[/tex] in the table. Emissions of ([tex]$SO_2$[/tex]) from burning oil are computed by [tex]$g(x)$[/tex]. Amounts are given in millions of tons.

[tex]\[
\begin{tabular}{|c|c|c|c|c|c|}
\hline
$x$ & 1860 & 1900 & 1940 & 1970 & 2000 \\
\hline
$f(x)$ & 23 & 12.5 & 24.3 & 38.2 & 54.0 \\
\hline
$g(x)$ & 0 & 0.1 & 24 & 21.8 & 23.0 \\
\hline
\end{tabular}
\][/tex]

Answer questions (a) through (c)

(a) Evaluate [tex]$(f + g)(1970)$[/tex]
[tex]\[
(f + g)(1970) = \square
\][/tex]
(Simplify your answer. Type an integer or a decimal)



Answer :

GinnyAnswer
Let's solve the problem step by step.

We are given two functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] which represent the emissions of [tex]\( \text{SO}_2 \)[/tex] in millions of tons from burning coal and oil respectively during different years. We need to evaluate [tex]\( (f + g)(1970) \)[/tex].

Here's how we do it:

1. Identify the values of [tex]\( f(1970) \)[/tex] and [tex]\( g(1970) \)[/tex] from the table:

- From the table, for the year 1970:
[tex]\[ f(1970) = 38.2 \][/tex]
[tex]\[ g(1970) = 21.8 \][/tex]

2. Add these values together to find [tex]\( (f + g)(1970) \)[/tex]:

- Sum the emissions from burning coal and oil for the year 1970.
[tex]\[ (f + g)(1970) = f(1970) + g(1970) \][/tex]
[tex]\[ (f + g)(1970) = 38.2 + 21.8 \][/tex]

3. Compute the result:

[tex]\[ 38.2 + 21.8 = 60.0 \][/tex]

So, the value of [tex]\( (f + g)(1970) \)[/tex] is:

[tex]\[ (f + g)(1970) = 60.0 \][/tex]

Thus, the solution to the problem is [tex]\( \boxed{60.0} \)[/tex].