# Math Lesson 8.1.6 - Finding the Inverse Formula

Welcome to our Math lesson on Finding the Inverse Formula, this is the sixth lesson of our suite of math lessons covering the topic of Writing Formulas and Substituting in a Formula, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

## Finding the Inverse Formula

Sometimes, the independent variable in a formula is known and the value of one of dependent variables is required. In this case, we need to find a new formula based on the original one but which expresses the new unknown quantity in terms of the known ones. This is known as the inverse formula. For example, in the formula

y = 3x - 5

we may have the y known and berequired to calculate x. In this case, we isolate x (as unknown) and write the rest of formula in terms of y. Thus, we have

y = 3x - 5
y + 5 = 3x
x = y + 5/3

For example, if y = 7 and we need to find x, we obtain

x = y + 5/3
= 12/3
= 4

### Example 8

The number N of dust particles per cubic centimetre present in the environment at an industrial site in terms of the raining time t (in minutes) is given by the formula

N = 80,000/t2

Calculate the raining time necessary to reduce the air pollution to 8 particles per cubic centimetre.

### Solution 8

We already know N but we need to calculate the time t. Thus, we isolate t to express it in terms of N. We have

N = 80,000/t2
t2 = 80,000/N
t = √80,000/N

Given that N = 8, we obtain

t = √80,000/8
= √10,000
= 100

Hence, if it rains ceaselessly for 100 minutes in the given site, the air pollution reduces to 8 particles per cubic centimetre.

## More Writing Formulas and Substituting in a Formula Lessons and Learning Resources

Formulas Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
8.1Writing Formulas and Substituting in a Formula
Lesson IDMath Lesson TitleLessonVideo
Lesson
8.1.1Mathematical vs Word Sentences
8.1.2What is a Formula? How do we Write Formulas?
8.1.3Expressing Events in a Shorter Way using Formulas
8.1.4Substituting into a Formula
8.1.5Substituting in Formulas derived from Wordy Problems
8.1.6Finding the Inverse Formula

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7. Continuing learning formulas - read our next math tutorial: Types of Formulas. Rearranging Formulas