SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Rates of Change, SMB-008

It is known that the quantity of steel produced in tonnes `(S)`, is directly proportional to the tonnes of iron ore used in the process `(I)`.

If 16 tonnes or iron ore produces 10 tonnes of steel, calculate the tonnes of iron ore required to produce 48 tonnes of steel.  (3 marks)

Show Answers Only

`76.8\ text{tonnes}`

Show Worked Solutions

`S prop I\ \ =>\ \ S=kI`

`text(Find)\ k\ text{given}\ S=10\ text{when}\ I=16:`

`10` `=k xx 16`
`k` `=10/16`
  `=0.625`

 
`text{Find}\ I\ text{when}\ S=48:`

`48` `=0.625 xx I`
`:. I` `=48/0.625`
  `=76.8\ text{tonnes}`

Rates of Change, SMB-002

It is known that at a constant speed, the distance travelled in kilometres `(d)` is directly proportional to the time of travel in hours `(t)`, or  `d prop t`.

  1. If `d=75` when `t=5`, calculate the constant of variation `k`.  (2 marks)

  2. In the context of this question, what does the value of `k` represent?  (1 mark)

Show Answers Only

i.    `k=15`

ii.   `text{Speed}`

Show Worked Solutions

i.    `d prop t`

`d=kt`

`text(Find)\ k\ text{given}\ d=75\ text{when}\ t=5:`

`75` `=k xx 5`
`:. k` `=75/5`
  `=15`

 
ii.   `k\ text{represents the speed.}`

Algebra, STD2 A2 2014 HSC 26f

The weight of an object on the moon varies directly with its weight on Earth.  An astronaut who weighs 84 kg on Earth weighs only 14 kg on the moon.

A lunar landing craft weighs 2449 kg when on the moon. Calculate the weight of this landing craft when on Earth.   (2 marks)

Show Answers Only

 `14\ 694\ text(kg)`

Show Worked Solution

`W_text(moon) prop W_text(earth)`

`=> W_text(m) = k xx W_text(e)`

`text(Find)\ k\ text{given}\  W_text(e) = 84\ text{when}\ W_text(m) = 14`

`14` `= k xx 84`
`k` `= 14/84 = 1/6`

 

`text(If)\ W_text(m) = 2449\ text(kg),\ text(find)\ W_text(e):`

`2449` `= 1/6  xx W_text(e)`
`W_text(e)` `= 14\ 694\ text(kg)`

 

`:.\ text(Landing craft weighs)\ 14\ 694\ text(kg on earth)`