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|dw:1345995812545:dw|

Nobody knows what to do?:#

a) (12-y)x
b) 12(x-0.1x^2)
c) 30 sq units

...How?

Is "How" for all of it?

Just b and c

especially b... :O

Okay. Makes sense I guess:p thanks!

small catch

triangle ACE is similar to triangle BCD
=>
height1/height2 = base1/base2

12/y = 20/x
y = (3/5)x

this would give you max area 60

o.O But y needs to be written as a function of x.

y = (3/5)x

its a function of x

linear

Oh yeah :3. So why did you use the entire base and @Zekarias used 1/2?

since both are similar triangles,
"ratio of bases" equals "ratio of heights"

Okay, that makes sense. :3
Can you explain how you got 60 though?

write the area equation in x and optimize

this q from conics, or calculus ?

calculus. Going into calculus next year and they gave us some prep stuff*.*

oh ok,
so we have this so far :
A = x(12-y) -------(1)
y = (3/5)x --------(2)

Okay, true.

hmm which one moves ?

ohhk yeah as we go down its moving a lot it seems...

substitute (2) in (1)

x(12-(3/5)x)

\(A = x(12 - \frac{3}{5}x)\)
\(A = 12x- \frac{3}{5}x^2)\)

Okayy and solve for x

nope we need to optimize A

find maximum possible value of A, right ?

Oh.

Ya

theres a process for finding maximum/minimum values of any funcitons

you familiar with differentiation ?

... I guess I havenet learned that yet..

its simple... if you knw differentiation already

I think we are learning that next year :( (monday)

just if you knw derivative of x, and x^2, its enough

oh ok then you cannot use calculus, lets switch to conics. you knw parabolas, right

Yes.

You said f(-b/2a)

yes

A = 12x - (3/5) x^2

\(A = \frac{-3}{5}x^2 + 12x\)

Yes

a = -3/5
b = 12

Cool, thanks, just plug and chug now:D

f(-b/2a) gives the vertex y co-ordinate, which is the maximum value

y=10

|dw:1345999525420:dw|

-b/2a = 10
f(-b/2a) = ?

put x = -b/2a = 10, in area function

Okay.

60!:D

great !!

Thank you so much! Now I can do the rest of these problems:D

glad to hear ! calculus wud be much fun :) good luck !!