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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: Yacoubb on June 05, 2013, 10:32:08 pm

Title: URGENT - SAC HELP!
Post by: Yacoubb on June 05, 2013, 10:32:08 pm: Help with this question please:

A cuboid of a rectangular prism has a length of 4x m, a width of x m and a height of h m. The cuboid is made up of 640 m of wire.

a) Find h in terms of x
b) Find the volume, Vm³, of the cuboid in terms of x

These two questions are screwing with my brain and at the moment I'm cramming for this Methods 1+2 SAC.

Thanks for your help!
Title: Re: URGENT - SAC HELP!
Post by: b^3 on June 05, 2013, 10:35:33 pm: Hint:
a) What will the perimeter of the wires that make up the shape be? (2 lengths of $x$ , 2 lengths of $4x$ and two lengths of $h$ ). You know that they will add up to 640, so you can rearrange the equation for $h$ in terms of $x$ .
b) V=lwh, substitute the expressions in, and for $h$ use the expression you found in a.
Title: Re: URGENT - SAC HELP!
Post by: Yacoubb on June 05, 2013, 10:41:44 pm: Quote from: b^3 on June 05, 2013, 10:35:33 pm
Hint:
a) What will the perimeter of the wires that make up the shape be? (2 lengths of $x$ , 2 lengths of $4x$ and two lengths of $h$ ). You know that they will add up to 640, so you can rearrange the equation for $h$ in terms of $x$ .
b) V=lwh, substitute the expressions in, and for $h$ use the expression you found in a.

Thanks so much! Got it, so (1.) Find the perimeter as you are given the overall wire and (2.) make h the subject + simplify.

Then go 4x * x * h = V, and substitute the value of h found in the previous equation. Honestly you just saved me life!
Title: Re: URGENT - SAC HELP!
Post by: Yacoubb on June 05, 2013, 11:20:55 pm: One more question:

A possible sequence of transformations which transforms the graph of y = x³ to the graph of y = x³ + 3x²+ 3x + 7??
Title: Re: URGENT - SAC HELP!
Post by: b^3 on June 05, 2013, 11:24:38 pm: We can factorise $y=x^{3}+3x^{2}+3x+7$ into turning point form.
$\begin{alignedat}{1}y & =x^{3}+3x^{2}+3x+7<br />\\ & =\left(x^{3}+3x^{2}+3x+1\right)+6<br />\\ y & =\left(x+1\right)^{3}+6<br />\end{alignedat}$
Now see if you can work out the transformations (in this case translations) that will take $y=x^{3}$ to $y=\left(x+1\right)^{3}+6$ . (Remember, an $x$ shift to the right will be $x-a$ in the equation, and a $y$ shift upwards will be a positive constant in the equation).