Question

the cost c of operating a certain car that gets 32 miles per gallon is a function of the price g, in dollars per gallon, of gasoline and the distance d, in miles, that you drive. the formula for c = c(g, d) is given below. c = \frac{gd}{32} dollars. (a) use functional notation to express the cost of operation if gasoline costs 98 cents per gallon and you drive 220 miles. calculate the cost. (round the cost to two decimal places.) c( , ) = $ (b) calculate c(1.07, 177). (round your answer to two decimal places.) $. explain the meaning of the number you have calculated in (b). this represents the cost of driving 98 miles if gas costs $2.20 per gallon. this represents the cost of driving 107 miles if gas costs $1.77 per gallon. this represents the cost of driving 177 miles if gas costs $1.07 per gallon. this represents the cost of driving 220 miles if gas costs $0.98 per gallon.

Explanation:

Step1: Identify values for part (a)

Given $g = 0.98$ (98 cents in dollars) and $d=220$.

Step2: Substitute into formula for part (a)

$C(g,d)=\frac{gd}{32}$, so $C(0.98,220)=\frac{0.98\times220}{32}$
$=\frac{215.6}{32}=6.7375\approx6.74$

Step3: Identify values for part (b)

Given $g = 1.07$ and $d = 177$.

Step4: Substitute into formula for part (b)

$C(1.07,177)=\frac{1.07\times177}{32}$
$=\frac{189.39}{32}=5.9184375\approx5.92$

Step5: Interpret part (b) result

In $C(1.07,177)$, $g = 1.07$ is the price per - gallon and $d = 177$ is the distance driven. So it represents the cost of driving 177 miles if gas costs $1.07$ per gallon.

Answer:

(a) $C(0.98,220)=\$6.74$
(b) $\$5.92$
This represents the cost of driving 177 miles if gas costs $1.07$ per gallon.