Problem 1
Question
Write an equation that expresses each relationship. Use \(k\) as the constant of variation. \(g\) varies directly as \(h\)
Step-by-Step Solution
Verified Answer
The equation that expresses the relationship is \(g = kh\).
1Step 1: Understanding direct variation
Firstly, get familiar with the concept of direct variation. If one quantity varies directly as another, it means they increase or decrease at a constant rate. The equation representing a direct variation is usually written in the form \(y = kx\), where \(k\) is the constant of variation.
2Step 2: Writing the equation for the given quantities
Knowing that the rule for direct variation is \(y = kx\), we can use this to form an equation using our variables \(g\) and \(h\). In this case, let \(g\) be the \(y\) variable and \(h\) be the \(x\) variable, with \(k\) remaining the constant of variation. Thus the equation that expresses the relationship is \(g = kh\).
Other exercises in this chapter
Problem 1
In Exercises \(1-10\), determine which functions are polynomial functions. For those that are, identify the degree. $$f(x)=5 x^{2}+6 x^{3}$$
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In Exercises \(1-8,\) find the domain of each rational function. $$f(x)=\frac{5 x}{x-4}$$
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Use the Rational Zero Theorem to list all possible rational zeros for each given function. $$ f(x)=x^{3}+x^{2}-4 x-4 $$
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Use the Upper and Lower Bound Theorem to solve Exercises \(1-4\). Show that all the real roots of the equation \(x^{4}-5 x^{3}+11 x^{2}+33 x-18=0\) lie between
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