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Chapter 2: Problem 40

What does it mean if two quantities vary directly?

Short Answer

Expert verified
Two quantities are said to vary directly if an increase or decrease in one quantity causes a corresponding increase or decrease in the other quantity. This is often represented as y = kx, where y and x are the two quantities, and k is a constant factor.

Step by step solution

01

Title

Understanding Direct Variation
02

Title

Identifying Direct Variation
03

Title

Practical Example of Direct Variation

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Most popular questions from this chapter

Solve each inequality using a graphing utility. $$\frac{x-4}{x-1} \leq 0$$

Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$h(x)=\frac{1}{(x-3)^{2}}+1$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The inequality \(\frac{x-2}{x+3}<2\) can be solved by multiplying both sides by \((x+3)^{2}, x \neq-3,\) resulting in the equivalent inequality \((x-2)(x+3)<2(x+3)^{2}\).

Write the equation of a rational function \(f(x)=\frac{p(x)}{q(x)}\) having the indicated properties, in which the degrees of p and q are as small as possible. More than one correct function may be possible. Graph your function using a graphing utility to verify that it has the required properties. \(f\) has a vertical asymptote given by \(x=3,\) a horizontal asymptote \(y=0, y\) -intercept at \(-1,\) and no \(x\) -intercept.

Use long division to rewrite the equation for \(g\) in the form $$\text {quotient }+\frac{\text {remainder}}{\text {divisor}}$$ Then use this form of the function's equation and transformations of \(f(x)=\frac{1}{x}\) to graph \(g.\) $$g(x)=\frac{2 x-9}{x-4}$$
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