ZachCharge's Year 11 (easy) GMA Questions

[dcc]

Something interesting which I learnt about <just the other day!>.

Some conics can be described as , where is some constant, and is a symmetric matrix.

For example, if we take , and , we find:

.  Clearly this describes a circle.


If we take , we gather the relationship , which describes an ellipse.


If we take , with our other values unchanged, we gain the relationship , which describes a hyperbola.


If we use another matrix , we gather the relationship , or equivalently .

It's a strange world out there.

[ZachCharge]

Tbh don't understand that lol (havn't done matrix yet , hmmm this is a REALLY belated reply lol)

Eh, I am having trouble with creating formula, I've tried my best over holidays but I just...can't get it. Can someone please show me how to solve this and hopefully I will get an idea on the rest ;

Old lady wants to enclose a rectangular piece of land for her garden, using the existing fence as one side of the rectangle. She has 30m of wire to do the job. If l is the length of the garden parallel to the fence, establish formula for area in terms of l.

Thanks

[kamil9876]

so l is the length, w is the width of our rectangle:





which implies:

[ZachCharge]

Bah I am seriously having trouble with constructing formula...err...heres another I can't do (actually easier one then last)...

Jewellry box has , and P of base is , write formula for TSA of box in terms of length.

Heres how my train of thought goes (I think I am about to type just how stupid I am...oh well I got test on this soon and am getting panicky due to not being able to get it over holidays lol...thank fod test is only on this and transposing...and using CAS spreadsheets with this);

"Ok in terms of w...so thats means I should find w...right? Ok lets see... Since the P is a box then
so
meaning
....I hope.

Hmm...next step....ok I'm lost, lets see what has been given. Since V is maybe I can find what either w or l is...wait how the hell do i do that...ok I am lost again...thinking thinking....err...Well since TSA of a rectangular prism (assuming jewelry box isn't literally a box that is...) is ...I think. Ok, so if I just sub in w into that I should get something close to the answer......Oh god I am screwed....Eh I will try anyway...(5 minutes later, ends up with)

ARGH WRONG I TO FRUSTRATED RAWR! MUST GET MORE HELP!!!"

So yeah thats what I did and...yeah I know I totally screwed up and it has something to do with V but...I just don't know what to do lol. Answer is

[/0]

I would start by writing down what we need to find first:

Total surface area =

Now we want this in terms of , so somehow we have to 'sub out' and .

You got which is on the right track.

Now just:





And just sub in!

[ZachCharge]

Thanks for the help

I guess I'll try last question in exercise and some from chapter review and see how I go lol.

[ZachCharge]

Any last minute tips or tricks I should know about transposing and making formula?

(yay I just done formula question right by myself...)

Thanks