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Non-Linear, SMB-024

The volume of a sphere is given by  `V = 4/3 pi r^3`  where  `r`  is the radius of the sphere.

If the volume of a sphere is  `220\ text(cm)^3`, find the radius, to 1 decimal place.  (3 marks)

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`3.7\ \ text{cm  (to 1 d.p.)}`

Show Worked Solution
`V` `= 4/3 pi r^3`
`3V` `= 4 pi r^3`
`r^3` `= (3V)/(4 pi)`

 

`text(When)\ \ V = 220`

`r^3` `= (3 xx 220)/(4 pi)`
  `= 52.521…`
`:. r` `=root3 (52.521…)`
  `= 3.744…\ \ \ text{(by calc)}`
  `= 3.7\ \ text{cm   (to 1 d.p.)}`

Algebra, STD2 A1 2005 HSC 24c

Make  `L`  the subject of the equation  `T = 2piL^2`.   (2 marks)

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`± sqrt(T/(2pi))`

Show Worked Solution
`T` `= 2piL^2`
`L^2` `= T/(2pi)`
`:.L` `= ±sqrt(T/(2pi))`

Algebra, STD2 A1 2004 HSC 11 MC

If  `d = 6t^2`, what is a possible value of `t` when  `d = 2400`?

  1. `0.05`
  2. `20`
  3. `120`
  4. `400`
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`B`

Show Worked Solution
`d` `= 6t^2`
`t^2` `= d/6`
`t` `= +- sqrt(d/6)`

 
`text(When)\ \ d = 2400:`

`t` `= +- sqrt(2400/6)`
  `= +- 20`

 
`=> B`

Algebra, STD2 A1 2011 HSC 18 MC

Which of the following correctly expresses  `a`  as the subject of  `s= ut+1/2at^2 `?

  1. `a=(2(s-ut))/t^2`
  2. `a=(2s-ut)/t^2`
  3. `a=(1/2(s-ut))/t^2`
  4. `a=(1/2s-ut)/t^2`
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`A`

Show Worked Solution
`s` `=ut+1/2at^2`
`1/2at^2` `=s-ut`
`at^2` `=2(s-ut)`
`a` `=(2(s-ut))/t^2`

 
`=>A`