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Quadratics and Cubics, SMB-044

Solve for `a` given  `8a^3+21=0.`

Round your answer to two decimal places.  (2 marks)

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`a=-1.38`

Show Worked Solution
`8a^3+21` `=0`
`8a^3` `=-21`
`a^3` `=-21/8`
`a` `=-root3(21/8)`
  `=-1.379…`
  `= -1.38`

Filed Under: Quadratics and Cubics Tagged With: num-title-ct-pathb, smc-4386-50-Cubics

Quadratics and Cubics, SMB-043

Solve for `p` given  `64p^3+125=0.`  (2 marks)

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`p=-5/4`

Show Worked Solution
`64p^3+125` `=0`
`64p^3` `=-125`
`p^3` `=-125/64`
`p` `=-root3(125/64)`
  `=-(root3(125))/(root3(64))`
  `= -5/4`

Filed Under: Quadratics and Cubics Tagged With: num-title-ct-pathb, smc-4386-50-Cubics

Quadratics and Cubics, SMB-042

Solve for `x` given  `8x^3=27`.  (2 marks)

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`x=3/2`

Show Worked Solution
`8x^3` `=27`
`x^3` `=27/8`
`x` `=root3(27/8)`
  `=(root3(27))/(root3(8))`
  `= 3/2`

Filed Under: Quadratics and Cubics Tagged With: num-title-ct-pathb, smc-4386-50-Cubics

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.)}`

Filed Under: Quadratics and Cubics Tagged With: num-title-ct-pathc, smc-4386-10-Rearrange equation, smc-4386-15-Substitution, smc-4386-50-Cubics

Non-Linear, SMB-023

Make  `r`  the subject of the equation  `V = 4/3 pir^3`.  (3 marks)

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`r = root(3)((3V)/(4pi))`

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

Filed Under: Quadratics and Cubics Tagged With: num-title-ct-pathc, smc-4386-10-Rearrange equation, smc-4386-50-Cubics

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