Aussie Maths & Science Teachers: Save your time with SmarterEd
Jacques is a marine biologist and finds that the mass of a crab is directly proportional to the cube of the diameter of its shell.
If a crab with a shell diameter of 15 cm weighs 680 grams, what will be the diameter of a crab that weighs 1.1 kilograms? Give your answer to 1 decimal place. (2 marks)
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`17.6\ text(cm)`
| `M` | `prop d^3` | |
| `M` | `= kd^3` |
`text(When)\ \ M=680, \ d=15`
| `680` | `=k xx 15^3` | |
| `k` | `=0.201481…` |
`text(Find)\ \ d\ \ text(when)\ \ M=1100:`
| `1100` | `=0.20148… xx d^3` | |
| `d` | `=root3(1100/(0.20148…))` | |
| `=17.608…` | ||
| `=17.6\ text{cm (to 1 d.p.)}` |
The stopping distance of a car on a certain road, once the brakes are applied, is directly proportional to the square of the speed of the car when the brakes are first applied.
A car travelling at 70 km/h takes 58.8 metres to stop.
How far does it take to stop if it is travelling at 105 km/h? (3 marks)
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`132.3\ text(metres)`
`text(Let)\ \ d\ text(= stopping distance)`
`d \prop s^2\ \ =>\ \ d = ks^2`
`text(Find)\ k,`
| `58.8` | `= k xx 70^2` |
| `k` | `= 58.8/(70^2)= 0.012` |
`text(Find)\ \ d\ \ text(when)\ \ s = 105:`
| `d` | `= 0.012 xx 105^2` |
| `= 132.3\ text(metres)` |
Fuifui finds that for Giant moray eels, the mass of an eel is directly proportional to the cube of its length.
An eel of this species has a length of 25 cm and a mass of 4350 grams.
What is the expected length of a Giant moray eel with a mass of 6.2 kg? Give your answer to one decimal place. (3 marks)
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`28.1\ text{cm}`
`text(Mass) prop text(length)^3`
`m = kl^3`
`text(Find)\ k:`
| `4350` | `= k xx 25^3` |
| `k` | `= 4350/25^3` |
| `= 0.2784` |
`text(Find)\ \ l\ \ text(when)\ \ m = 6200:`
| `6200` | `= 0.2784 xx l^3` |
| `l^3` | `= 6200/0.2784` |
| `:. l` | `= 28.13…` |
| `= 28.1\ text{cm (to 1 d.p.)}` |