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.

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*

y + 5 = 3x

x =

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

x = *y + 5**/**3*

=*12**/**3*

= 4

=

= 4

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/t^{2}

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

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**/**t*^{2}

t^{2} = *80,000**/**N*

t = √*80,000**/**N*

t

t = √

Given that N = 8, we obtain

t = √*80,000**/**8*

= √**10,000**

= 100

= √

= 100

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

Enjoy the "Finding the Inverse Formula" math lesson? People who liked the "Writing Formulas and Substituting in a Formula lesson found the following resources useful:

- Inverse Formula Feedback. Helps other - Leave a rating for this inverse formula (see below)
- Formulas Math tutorial: Writing Formulas and Substituting in a Formula. Read the Writing Formulas and Substituting in a Formula math tutorial and build your math knowledge of Formulas
- Formulas Video tutorial: Writing Formulas and Substituting in a Formula. Watch or listen to the Writing Formulas and Substituting in a Formula video tutorial, a useful way to help you revise when travelling to and from school/college
- Formulas Revision Notes: Writing Formulas and Substituting in a Formula. Print the notes so you can revise the key points covered in the math tutorial for Writing Formulas and Substituting in a Formula
- Formulas Practice Questions: Writing Formulas and Substituting in a Formula. Test and improve your knowledge of Writing Formulas and Substituting in a Formula with example questins and answers
- Check your calculations for Formulas questions with our excellent Formulas calculators which contain full equations and calculations clearly displayed line by line. See the Formulas Calculators by iCalculator™ below.
- Continuing learning formulas - read our next math tutorial: Types of Formulas. Rearranging Formulas

We hope you found this Math tutorial "Writing Formulas and Substituting in a Formula" useful. If you did it would be great if you could spare the time to rate this math tutorial (simply click on the number of stars that match your assessment of this math learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of math and other disciplines.