Algebra, NAPX-F4-CA29 SA

Question

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Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

702

Question

The mass of a trout fish is 16.9 kilograms.

Its length is 1.24 metres.

A rule that can be used to approximately predict the length of a trout from its mass is


l\large l = m10\sqrt{ \dfrac{m}{10}}


where l\large l is the length of the trout in metres and m\large m is the mass in kilograms.

What is the difference in centimetres between the trout's actual length and the length predicted by the rule?

Worked Solution

Actual length = 1.24 m = 124 cm

Predicted length

= 16.910\sqrt{\dfrac{16.9}{10}}

= 1.69\sqrt{1.69}

= 1.3 m

= 130 cm
∴\therefore Difference = 130 −- 124
= 6 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
The mass of a trout fish is 16.9 kilograms. Its length is 1.24 metres. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2018/07/NAPX-F4-CA29-SA_1.svg 330 indent3 vpad A rule that can be used to approximately predict the length of a trout from its mass is
>>$\large l$ = $\sqrt{ \dfrac{m}{10}}$
where $\large l$ is the length of the trout in metres and $\large m$ is the mass in kilograms. What is the difference in centimetres between the trout's actual length and the length predicted by the rule?
workedSolution
Actual length = 1.24 m = 124 cm Predicted length >> = $\sqrt{\dfrac{16.9}{10}}$ >> = $\sqrt{1.69}$ >>= 1.3 m >>= 130 cm
| | | | ------------: | ---------- | | $\therefore$ Difference | \= 130 $-$ 124 | | | \= {{{correctAnswer0}}} {{{suffix0}}} |
correctAnswer0
6
prefix0
suffix0
cm

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer06

cm

Variant 1

DifficultyLevel

702

Question

The mass of a trout fish is 12.1 kilograms.

Its length is 1.05 metres.

A rule that can be used to approximately predict the length of a trout from its mass is


l\large l = m10\sqrt{ \dfrac{m}{10}}


where l\large l is the length of the trout in metres and m\large m is the mass in kilograms.

What is the difference in centimetres between the trout's actual length and the length predicted by the rule?

Worked Solution

Actual length = 1.05 m = 105 cm

Predicted length

= 12.110\sqrt{\dfrac{12.1}{10}}

= 1.21\sqrt{1.21}

= 1.1 m

= 110 cm
∴\therefore Difference = 110 −- 105
= 5 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
The mass of a trout fish is 12.1 kilograms. Its length is 1.05 metres. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/NAPX-F4-CA29-SA_var1.svg 330 indent3 vpad A rule that can be used to approximately predict the length of a trout from its mass is
>>$\large l$ = $\sqrt{ \dfrac{m}{10}}$
where $\large l$ is the length of the trout in metres and $\large m$ is the mass in kilograms. What is the difference in centimetres between the trout's actual length and the length predicted by the rule?
workedSolution
Actual length = 1.05 m = 105 cm Predicted length >> = $\sqrt{\dfrac{12.1}{10}}$ >> = $\sqrt{1.21}$ >>= 1.1 m >>= 110 cm
| | | | ------------: | ---------- | | $\therefore$ Difference | \= 110 $-$ 105 | | | \= {{{correctAnswer0}}} {{{suffix0}}} |
correctAnswer0
5
prefix0
suffix0
cm

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer05

cm

Variant 2

DifficultyLevel

702

Question

The mass of a trout fish is 6.4 kilograms.

Its length is 0.87 metres.

A rule that can be used to approximately predict the length of a trout from its mass is


l\large l = m10\sqrt{ \dfrac{m}{10}}


where l\large l is the length of the trout in metres and m\large m is the mass in kilograms.

What is the difference in centimetres between the trout's actual length and the length predicted by the rule?

Worked Solution

Actual length = 0.87 m = 87 cm

Predicted length

= 6.410\sqrt{\dfrac{6.4}{10}}

= 0.64\sqrt{0.64}

= 0.80 m

= 80 cm
∴\therefore Difference = 87 −- 80
= 7 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
The mass of a trout fish is 6.4 kilograms. Its length is 0.87 metres. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/NAPX-F4-CA29-SA_var2.svg 330 indent3 vpad A rule that can be used to approximately predict the length of a trout from its mass is
>>$\large l$ = $\sqrt{ \dfrac{m}{10}}$
where $\large l$ is the length of the trout in metres and $\large m$ is the mass in kilograms. What is the difference in centimetres between the trout's actual length and the length predicted by the rule?
workedSolution
Actual length = 0.87 m = 87 cm Predicted length >> = $\sqrt{\dfrac{6.4}{10}}$ >> = $\sqrt{0.64}$ >>= 0.80 m >>= 80 cm
| | | | ------------: | ---------- | | $\therefore$ Difference | \= 87 $-$ 80 | | | \= {{{correctAnswer0}}} {{{suffix0}}} |
correctAnswer0
7
prefix0
suffix0
cm

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer07

cm

Variant 3

DifficultyLevel

702

Question

The mass of a trout fish is 14.4 kilograms.

Its length is 1.18 metres.

A rule that can be used to approximately predict the length of a trout from its mass is


l\large l = m10\sqrt{ \dfrac{m}{10}}


where l\large l is the length of the trout in metres and m\large m is the mass in kilograms.

What is the difference in centimetres between the trout's actual length and the length predicted by the rule?

Worked Solution

Actual length = 1.18 m = 118 cm

Predicted length

= 14.410\sqrt{\dfrac{14.4}{10}}

= 1.44\sqrt{1.44}

= 1.20 m

= 120 cm
∴\therefore Difference = 120 −- 118
= 2 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
The mass of a trout fish is 14.4 kilograms. Its length is 1.18 metres. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/NAPX-F4-CA29-SA_var3.svg 330 indent3 vpad A rule that can be used to approximately predict the length of a trout from its mass is
>>$\large l$ = $\sqrt{ \dfrac{m}{10}}$
where $\large l$ is the length of the trout in metres and $\large m$ is the mass in kilograms. What is the difference in centimetres between the trout's actual length and the length predicted by the rule?
workedSolution
Actual length = 1.18 m = 118 cm Predicted length >> = $\sqrt{\dfrac{14.4}{10}}$ >> = $\sqrt{1.44}$ >>= 1.20 m >>= 120 cm
| | | | ------------: | ---------- | | $\therefore$ Difference | \= 120 $-$ 118 | | | \= {{{correctAnswer0}}} {{{suffix0}}} |
correctAnswer0
2
prefix0
suffix0
cm

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer02

cm

Variant 4

DifficultyLevel

705

Question

The mass of a trout fish is 8.1 kilograms.

Its length is 0.87 metres.

A rule that can be used to approximately predict the length of a trout from its mass is


l\large l = m10\sqrt{ \dfrac{m}{10}}


where l\large l is the length of the trout in metres and m\large m is the mass in kilograms.

What is the difference in centimetres between the trout's actual length and the length predicted by the rule?

Worked Solution

Actual length = 0.87 m = 87 cm

Predicted length

= 8.110\sqrt{\dfrac{8.1}{10}}

= 0.81\sqrt{0.81}

= 0.90 m

= 90 cm
∴\therefore Difference = 90 −- 87
= 3 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
The mass of a trout fish is 8.1 kilograms. Its length is 0.87 metres. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/NAPX-F4-CA29-SA_var4.svg 330 indent3 vpad A rule that can be used to approximately predict the length of a trout from its mass is
>>$\large l$ = $\sqrt{ \dfrac{m}{10}}$
where $\large l$ is the length of the trout in metres and $\large m$ is the mass in kilograms. What is the difference in centimetres between the trout's actual length and the length predicted by the rule?
workedSolution
Actual length = 0.87 m = 87 cm Predicted length >> = $\sqrt{\dfrac{8.1}{10}}$ >> = $\sqrt{0.81}$ >>= 0.90 m >>= 90 cm
| | | | ------------: | ---------- | | $\therefore$ Difference | \= 90 $-$ 87 | | | \= {{{correctAnswer0}}} {{{suffix0}}} |
correctAnswer0
3
prefix0
suffix0
cm

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer03

cm

Variant 5

DifficultyLevel

705

Question

The mass of a trout fish is 4.9 kilograms.

Its length is 0.64 metres.

A rule that can be used to approximately predict the length of a trout from its mass is


l\large l = m10\sqrt{ \dfrac{m}{10}}


where l\large l is the length of the trout in metres and m\large m is the mass in kilograms.

What is the difference in centimetres between the trout's actual length and the length predicted by the rule?

Worked Solution

Actual length = 0.64 m = 64 cm

Predicted length

= 4.910\sqrt{\dfrac{4.9}{10}}

= 0.49\sqrt{0.49}

= 0.70 m

= 70 cm
∴\therefore Difference = 70 −- 64
= 6 cm

Question Type

Answer Box

Variables

Variable nameVariable value
question
The mass of a trout fish is 4.9 kilograms. Its length is 0.64 metres. sm_img https://teacher.smartermaths.com.au/wp-content/uploads/2022/08/NAPX-F4-CA29-SA_var5.svg 330 indent3 vpad A rule that can be used to approximately predict the length of a trout from its mass is
>>$\large l$ = $\sqrt{ \dfrac{m}{10}}$
where $\large l$ is the length of the trout in metres and $\large m$ is the mass in kilograms. What is the difference in centimetres between the trout's actual length and the length predicted by the rule?
workedSolution
Actual length = 0.64 m = 64 cm Predicted length >> = $\sqrt{\dfrac{4.9}{10}}$ >> = $\sqrt{0.49}$ >>= 0.70 m >>= 70 cm
| | | | ------------: | ---------- | | $\therefore$ Difference | \= 70 $-$ 64 | | | \= {{{correctAnswer0}}} {{{suffix0}}} |
correctAnswer0
6
prefix0
suffix0
cm

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer06

cm

Tags

  • ms_ca