Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 7: Q. 326 (page 720)

If $a$ varies inversely with $b$ and $a = 12$ when $b = \frac{1}{3}$ , find the equation that relates $a$ and $b$ .

Short Answer

Expert verified

The equation that relates $a$ and $b$ is $a = \frac{4}{b}$ .

Step by step solution

Step 1. Given information

Given that $a$ varies inversely as $b$ and $a = 12$ and $b = \frac{1}{3}$ .

Step 2. Determine the equation relating a and b.

As $a$ varies inversely as $b$ so, for some constant $a = \frac{k}{b}$ .

Label the obtained equation.

$a = \frac{k}{b} (1)$

Substitute the given values and solve for $k$ .

$\begin{array}{rcl} 12 & = & \frac{k}{\frac{1}{3}} \\ 12 & = & 3 k \\ \frac{12}{3} & = & k \\ 4 & = & k \end{array}$

Substitute 4 for $k$ into equation $(1)$ .

$a = \frac{4}{b}$

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91影视

If $a$ varies inversely with $b$ and $a = 12$ when $b = \frac{1}{3}$ , find the equation that relates $a$ and $b$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determine the equation relating a and b.

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91影视

Ifavaries inversely withbanda=12whenb=13, find the equation that relatesaandb.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determine the equation relating a and b.

One App. One Place for Learning.

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If $a$ varies inversely with $b$ and $a = 12$ when $b = \frac{1}{3}$ , find the equation that relates $a$ and $b$ .