The time taken to clean a warehouse varies inversely with the number of cleaners employed.
It takes 8 cleaners 60 hours to clean a warehouse.
Working at the same rate, how many hours would it take 10 cleaners to clean the same warehouse.
- 45
- 48
- 62
- 75
Functions, 2ADV EQ-Bank 10
The number of trees that can be planted along the fence line of a paddock varies inversely with the distance between each tree.
There will be 108 trees if the distance between them is 5 metres.
- How many trees can be planted if the distance between them is 6 metres? (2 marks)
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- What is the distance between the trees if 120 trees are planted. (1 mark)
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Functions, 2ADV EQ-Bank 8
The intensity of light \((I)\), measured in lux, from a lamp varies inversely with the square of the distance from the lamp \((d)\), measured in metres.
At a distance of 2.2 metres from the lamp, the light intensity is 400 lux.
What is the light intensity at a distance of 5.0 metres from the lamp? (2 marks)
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Functions, 2ADV EQ-Bank 9
The quantity \(y\) varies inversely with the square of \(x\).
When \(x = 4, \ y = 10\).
Find the value of \(y\) when \(x = 8\). (2 marks)
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Functions, 2ADV F1 2022 HSC 12
A student believes that the time it takes for an ice cube to melt (`M` minutes) varies inversely with the room temperature `(T^@ text{C})`. The student observes that at a room temperature of `15^@text{C}` it takes 12 minutes for an ice cube to melt.
- Find the equation relating `M` and `T`. (2 marks)
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- By first completing this table of values, graph the relationship between temperature and time from `T=5^@C` to `T=30^@ text{C}`. (2 marks)
\begin{array} {|c|c|c|c|}
\hline \ \ T\ \ & \ \ 5\ \ & \ 15\ & \ 30\ \\
\hline M & & & \\
\hline \end{array}
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Show Answers Only
a. `M=180/T`
b.
\begin{array} {|c|c|c|c|}
\hline \ \ T\ \ & \ \ 5\ \ & \ 15\ & \ 30\ \\
\hline M & 36 & 12 & 6 \\
\hline \end{array}
Show Worked Solution
| a. | `M` | `prop 1/T` |
| `M` | `=k/T` | |
| `12` | `=k/15` | |
| `k` | `=15 xx 12` | |
| `=180` |
`:.M=180/T`
♦ Mean mark (a) 49%.
b.
\begin{array} {|c|c|c|c|}
\hline \ \ T\ \ & \ \ 5\ \ & \ 15\ & \ 30\ \\
\hline M & 36 & 12 & 6 \\
\hline \end{array}
Functions, 2ADV F1 EQ-Bank 7
The current of an electrical circuit, measured in amps `(A)`, varies inversely with its resistance, measured in ohms `(R)`.
When the resistance of a circuit is 28 ohms, the current is 3 amps.
What is the current when the resistance is 8 ohms? (2 marks)
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