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Chapter 1: Problem 68
Determine whether the lines are parallel, perpendicular, or neither. $$\begin{aligned} &L_{1}: y=4 x-1\\\ &L_{2}: y=4 x+7 \end{aligned}$$
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Find the difference quotient and simplify your Answer: $$f(x)=4 x^{2}-2 x, \quad \frac{f(x+h)-f(x)}{h}, \quad h \neq 0$$
Write a sentence using the variation terminology of this section to describe the formula. Surface area of a sphere: \(S=4 \pi r^{2}\)
(a) use a graphing utility to graph the function and (b) state the domain and range of the function. $$s(x)=2\left(\frac{1}{4} x-\left[\frac{1}{4} x\right]\right)$$
Finding a Mathematical Model In Exercises \(41-50\), find a mathematical model for the verbal statement. Newton's Law of Cooling: The rate of change \(R\) of the temperature of an object is directly proportional to the difference between the temperature \(T\) of the object and the temperature \(T_{e}\) of the environment in which the object is placed.
Find a mathematical model that represents the statement. (Determine the constant of proportionality.) Use the fact that 14 gallons is approximately the same amount as 53 liters to find a mathematical model that relates liters \(y\) to gallons \(x\) Then use the model to find the numbers of liters in 5 gallons and 25 gallons.
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