Question

1. the inductive reactance of a 0.75 h coil is given by \\(x_l = 4.712f\\), where \\(f\\) is the frequency in hertz and \\(x_l\\) is in ohms.

(a) what is the slope of this line?
(b) what is the \\(y\\)-intercept?

1. an electronics store purchased a panel truck for \\$29,625. they figure that the truck will require an average of \\$19.65 per day in maintenance and operating costs. the total cost of owning this truck on any given day, \\(t\\), can be represented by a straight line.

(a) what is the slope of this line?
(b) what is the \\(y\\)-intercept?
(c) find the linear function for the total costs, \\(c\\), of owning the truck after \\(t\\) days.

Explanation:

Analyze the inductive reactance equation

Using the Inductive Reactance Modeling and Slope-Intercept Form knowledge points

$$
LATEXBLOCK0
$$

Determine the y-intercept of the reactance line

Using the y-intercept knowledge point

$$ \text{When } f = 0,\ X_L = 4.712(0) = 0 \implies (0, 0) $$

Analyze the truck cost parameters

Using the Cost Function Modeling knowledge point

$$
LATEXBLOCK1
$$

Formulate the linear cost function

Using the Slope-Intercept Form and Cost Function Modeling knowledge points

$$ C(t) = 19.65t + 29625 $$

Answer:

Question 4

(a) The slope of the line is \(4.712\).
(b) The \(y\)-intercept is \(0\) (or the point \((0, 0)\)).

Question 5

(a) The slope of the line is \(19.65\).
(b) The \(y\)-intercept is \(29,625\) (or the point \((0, 29625)\)).
(c) The linear function is \(C = 19.65t + 29,625\).