another diff minimum prob :/ (1 Viewer)

[MrBrightside]

Show that V = 125x - x^3 / 2

rectangular prism with a square base..with a SA of 250 cm^2


____________________________________________________________

what I've done so far:

SA: x^2 + 4xh + x^2

= 2x^2 + 4xh = 250 (divide 250 by 2x^2 + 4x)

h = 250 / 2x^2 + 4x


V = Ah

= x^2h

V = x^2 (250/2x^2 + 4x) (sub in h)

now what??

 

[hscmathstutor10]

Show that V = 125x - x^3 / 2

rectangular prism with a square base..with a SA of 250 cm^2


____________________________________________________________

what I've done so far:

SA: x^2 + 4xh + x^2

= 2x^2 + 4xh = 250 (divide 250 by 2x^2 + 4x)
h = 250 / 2x^2 + 4x


V = Ah

= x^2h

V = x^2 (250/2x^2 + 4x) (sub in h)

now what??

what u doing man lol!, isolate the h before dividing

 

[hscmathstutor10]

so we have S= 2x^2 +4xh=250 ( this is correct ! )

and V= Ah = x^2h

now we have to rearrange the first for h,

so 4xh = 250 - 2x^2
h = (250-2x^2 ) / 4x


then subing into volume formula

V= x^2 [ (250-2x^2) /4x ]
= x(250-2x^2) / 4
= x * 2 ( 125 -x^2) / (2 *2)
= x (125-x^2) /2
= (125x -x^3 ) /2

 

[hscmathstutor10]

very important you know your basic algebra manipulation skills inside out and back to front if you want to do any good at the hsc, thats kinda what yr11 was for, but that doesnt mean you cant turn it around in yr12 !

 

[MrBrightside]

so we have S= 2x^2 +4xh=250 ( this is correct ! )

and V= Ah = x^2h

now we have to rearrange the first for h,

so 4xh = 250 - 2x^2
h = (250-2x^2 ) / 4x


then subing into volume formula

V= x^2 [ (250-2x^2) /4x ]
= x(250-2x^2) / 4
= x * 2 ( 125 -x^2) / (2 *2)
= x (125-x^2) /2
= (125x -x^3 ) /2

why 2 * 2? can you do that?

 

[Alkanes]

LOL this from the maths in focus book 2? i remember doing this question.. was it from test yourself page? if memory serves me right :L

 

[hscmathstutor10]

why 2 * 2? can you do that?

2 *2 = 4 doesnt it ??, then I can cancel a factor of 2 from the top and from the bottom

i just did it like that because i thought that if I went straight from x(250-2x^2) / 4 to x (125-x^2) /2 you might not follow

 

[MrBrightside]

@ Alkanes yes it is


@mathstutor well you see all these little things no one ever taught me. So I find like every little thing difficult, or have to do it a longer way instead. IF someone explained to me what all the little things did then I would be flash.


for e.g. say for this qs..... 250x^2 - 2x^4 / 4x

that one x at the bottom can it only cancel out one x at the top? ORR can in cancel out multiple one x from the 250 and one x from the 2 ?

 

[Alkanes]

h = 250 - 2x^2 / 4x yea? divide everything by 2.. h = 125-x^2/2x
V = x^2 x h ==> V = x^2 x (125 - x^)/2x
cross out the power 2 from x^2 and the x from the fraction 2x
Leaving u with x(125-x^2)/2
Expand: 125x-x^3 / 2 =)

 

[MrBrightside]

another tip I learnt from this site: 2x * 2x is just 2x^2 ....it's NOT 4x^2 (which i would presume a lot of people would make as a mistake)

 

[hscmathstutor10]

@ Alkanes yes it is


@mathstutor well you see all these little things no one ever taught me. So I find like every little thing difficult, or have to do it a longer way instead. IF someone explained to me what all the little things did then I would be flash.


for e.g. say for this qs..... 250x^2 - 2x^4 / 4x

that one x at the bottom can it only cancel out one x at the top? ORR can in cancel out multiple one x from the 250 and one x from the 2 ?

always factor before cancelling anything

so 2x[ 125x-x^3] / 4x or 2x[125x-x^3]/ (2*2 x)

whatever form you are happy with

thn cancel WHOLE factors from the top and bottom

so we cancel of a 2 and an x

to get [125x -x^3 ] / 2

 

[hscmathstutor10]

another tip I learnt from this site: 2x * 2x is just 2x^2 ....it's NOT 4x^2 (which i would presume a lot of people would make as a mistake)

excuse me lol

 

[hscmathstutor10]

Math teachers need to spend alot more time on basic algebraic manipulations far too many simple mistakes are made.

 

[MrBrightside]

excuse me lol

lol whats wrong with it? :/ plz dont say its wrong

 

[hscmathstutor10]

quick quiz: just a little test

simplify ( 12x+7) / 5x

 

[hscmathstutor10]

lol whats wrong with it? :/ plz dont say its wrong

2x *2x IS 4x^2

 

[Alkanes]

quick quiz: just a little test

simplify ( 12x+7) / 5x

no solution LOL na wat is it?

 

[hscmathstutor10]

no solution LOL na wat is it?

its kinda a trick question , you could write it as ( 12x/ 5x) + 7/ (5x) = 12/5 + 7/ (5x)

but if you gave that in an hsc I would be willing to bet atleast 40% of people would incorrectly cancel the x and say ( 12 +7) / 5 = 19/5 { well maybe they wouldnt as you WOULD think that just a constant as the final answer would set off warning bells, but you get the idea } , it is not a WHOLE factor

 

[Ishynooshy]

2x*2x
=(2x)^2
=4x^2

Be careful!

 

[Absolutezero]

2x * 2x is just 2x^2 ....it's NOT 4x^2

Do you mean:

(2x)^2

EDIT: I see Ishnooshy got in before me.