Aussie Maths & Science Teachers: Save your time with SmarterEd
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.
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It is known that a quantity `P` kgs is proportional to the reciprocal of another quantity `Q` kgs such that `P prop 1/Q`.
If `P=12` when `Q=20`, calculate the estimated quantity of `Q` when `P=45` kgs, to the nearest gram. (3 marks)
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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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It is known that a quantity `y` is inversely proportional to another quantity `x`.
If `y=3` when `x=1.8`, calculate the constant of variation `k`. (2 marks)
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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.
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\begin{array} {|c|c|c|c|}
\hline \ \ T\ \ & \ \ 5\ \ & \ 15\ & \ 30\ \\
\hline M & & & \\
\hline \end{array}
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a. `M=180/T`
b.
\begin{array} {|c|c|c|c|}
\hline \ \ T\ \ & \ \ 5\ \ & \ 15\ & \ 30\ \\
\hline M & 36 & 12 & 6 \\
\hline \end{array}
a. `M prop 1/T\ \ =>\ \ M=k/T`
`\text{Find}\ k:`
| `12` | `=k/15` | |
| `k` | `=12 xx 15=180` |
`:.M=180/T`
b.
\begin{array} {|c|c|c|c|}
\hline \ \ T\ \ & \ \ 5\ \ & \ 15\ & \ 30\ \\
\hline M & 36 & 12 & 6 \\
\hline \end{array}
The time taken for a car to travel between two towns at a constant speed varies inversely with its speed.
It takes 1.5 hours for the car to travel between the two towns at a constant speed of 80 km/h.
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a. `120\ text(km)`
b.
a. `D= S xx T= 80 xx 1.5= 120\ text(km)`
b.
\begin{array} {|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ S\ \ \rule[-1ex]{0pt}{0pt} & 20 & 40 & 60 & 80 \\
\hline
\rule{0pt}{2.5ex} T \rule[-1ex]{0pt}{0pt} & 6 & 3 & 2 & 1.5 \\
\hline
\end{array}
If pressure `(p)` varies inversely with volume `(V)`, which formula correctly expresses `p` in terms of `V` and `k`, where `k` is a constant?
The air pressure, `P`, in a bubble varies inversely with the volume, `V`, of the bubble.
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a. `P = a/V`
b. `P = 1 1/2`
c.
a. `P prop 1/V\ \ =>\ \ P= a/V`
b. `text(When)\ P=3,\ V=2:`
`3= a/2\ \ =>\ \ a=6`
`text(Find)\ P\ text(when)\ V = 4:`
`P=6/4=3/2`
| c. | |
The time for a car to travel a certain distance varies inversely with its speed.
Which of the following graphs shows this relationship?
The number of hours that it takes for a block of ice to melt varies inversely with the temperature. At 30°C it takes 8 hours for a block of ice to melt.
How long will it take the same size block of ice to melt at 12°C?