Let where and are integers and
Let
Let
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Let where and are integers and
Let
Let
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Let and . Write down the following expressions in terms of and .
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Let and Write down the following expressions in terms of and .
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Simplify the following:
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Solve the equation giving your answer in the form where and are integers.
State the values of and
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Given that
Find the value of
Find the value of
Find the value of
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Let and
Find an expression for in terms of
Find an expression for in terms of
Find an expression for in terms of and
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Show that can be written as
Given that find the value of
Show that can be written as where and rational numbers. State the value of and
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Solve the equation Write your answer in the form where and are integers.
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can be written in the form Find the values of and Show all of your working.
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The expression can be expressed in the form
Find the value of
Let
Find the value of
The expression can be written in the form
Find the value of
Let
Find the value of
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Let
Find the values of for which is undefined.
Given that point has coordinates , find the value of .
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Given that and write down the value of and of
Hence or otherwise solve
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Write the expression in the form , where
Hence, or otherwise, solve
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Solve the equation for Express your answer in terms of and
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Solve the equation
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Simplify the following expressions, giving your answers in the form where and are rational numbers and any fractions are in lowest terms.
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Given that express each of the following in the form where and are constants.
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A block of ice cream in the shape of a cuboid that has been taken out of the freezer and left at room temperature. The rate of decrease of the volume of the block of ice cream can be modelled by the formula
where and are constants and is the time in minutes after the ice cream was removed from the freezer.
Before it was taken out of the freezer the block of ice cream measured 12 cm by 9 cm by 7 cm. Eight minutes later the block of ice cream measured 8.4 cm by 7.1 cm by 5.8 cm.
By taking logarithms of both sides, show that the rate of decrease of the volume of the block of ice cream can be rewritten as
Find the value of and .
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A zoologist is researching the connection between the mass of a particular breed of mouse, g, and its heartrate, bpm. It is suggested that the relationship can be modelled by the equation
where
The zoologist takes measurements from two different mice and records the data as follows.
Measurement |
||
1 |
17.12 |
513 |
2 |
24.51 |
401 |
Find the values of and .
Use the model to predict
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Let
Find the values of for which is undefined.
Given that point has coordinates , find the value of
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Solve
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Solve
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Solve the equation for . Express your answer in terms of and
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Solve the equation
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Given that express each of the following in the form where and are constants.
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A company has conducted some product research and believes that their profit () made over time ( weeks after opening) can be modelled by the equation
where
and
The company collects data on their revenue, , and costs, , at the end of each week. After exactly one week the company’s costs are $3000 and they make a loss of $1000.
Find the values of and
Find the week in which the company first makes a positive profit.
Suggest a limitation to the company’s model.
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The rate, , of increase of the volume of a cloud created in a science lab is related to the change in air temperature, , and air pressure, , by the equation
, where .
A meteorologist takes measurements at three intervals and records the data as follows.
Measurement |
|||
1 |
48.75 |
17.1 |
101.2 |
2 |
46.13 |
15.9 |
101.8 |
3 |
43.47 |
14.7 |
102.5 |
Find and .
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