17 - Isolating Variables PDF

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17 - Isolating Variables

MPM1D – Polynomials and Equations

Date: ____________________________________________

Isolating Variables Formulae are special kinds of equations. They describe relationships between quantities of interest. You already know several formulae. Area of a rectangle:

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Perimeter of a rectangle:

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Circumference of a circle:

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Area of a circle:

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Area of a triangle:

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We can use existing/given formulae to solve a problem. When using a formula, we always: •

isolate the desired unknown variable on the left side of the equal sign

•

show our substitution of all known variables and all calculations

•

state our final answer with the appropriate units (if given)

Examples: 1) Solve each formula for the indicated variable. a)  =   for 

b)  =   ℎ for ℎ

d)  = 2 + 2 for 

e)

 

=  for 

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

c)  = ℎ for  

f)





=

 

for 

17 - Isolating Variables

MPM1D – Polynomials and Equations

2) The formula for estimating a dog’s age in equivalent human years, h, is ℎ = 5 + 12, where d is the dog’s age in actual years. Find Odie’s actual age if he is 47 in equivalent human years.



3) The formula,  = , where t is the time in seconds between the lightning flash and the  thunder, provides a convenient rule of thumb for estimating how many kilometres away a storm is. a) How far away is the storm if 15 seconds elapse between the flash of lightning and the thunder?

b) How many seconds separate the lightning and the thunder if the storm is 6 kilometres away?

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17 - Isolating Variables

MPM1D – Polynomials and Equations

Homework 1. Solve the formula for the variable indicated. You may first need to simplify the formula. !

a)  =  , 

b)  = , # "

c) $ = 2, 

h)  = 2 + , 

i) 3 = 4 + , 

f) / = 1801 − 2 , 1

e) (  = )  − 30-,.-

d) % = &' , '

g) - = 3 + 2,  j) 3 = 4 − ,

k) / = 5

67 

8 -, )

l)

9 

= , 

2. To find t for different values of u and v in an experiment, a calculator is to be used. Express t in terms of the other variables, (  = )  − 30- and then find the values of t for each of the following values of u and v. Round to one decimal place. a) ) = 28, ( = 36

b) ) = 28.5, ( = 23.2

c) ) = 146.3, ( = 189.8

Answers 1. >

a)  = ?

b) # = @

e) - =

f) 1 = G + 2

6 E 7 E

i)  =



HI J

F

j)

b) 9.1

d) ' = D



h)  = −  

C

H

= 4−K

g)  =  − 2 k) ) =

F 

2. a) –17.1

A

c)  = B

c) –487.3

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−(



l)  = 2 + 2

17 - Isolating Variables

MPM1D – Polynomials and Equations

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