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Mathematics 20 Online
OpenStudy (angela210793):

@amistre64 will u help me in smth pls?

OpenStudy (amistre64):

depends on what I have to do with smth :)

OpenStudy (angela210793):

O.o..let me attach the problem pls...

OpenStudy (angela210793):

U have to find the area of the circle...

OpenStudy (angela210793):

it is a rhomb ***

OpenStudy (amistre64):

i could see this as looking for the radius; which would indicate the a triangle in Q1

OpenStudy (amistre64):

its a 3-4-5 right triangle

OpenStudy (amistre64):

we then find the max area of a square that fits in it...maybe; or the max part of the circle to fit it

OpenStudy (angela210793):

w8..i think i got how to solve it....all we have to do is find the height at ODC triangle and that=r :)

OpenStudy (angela210793):

And then S=pi*r^2

OpenStudy (angela210793):

Right?

OpenStudy (amistre64):

OpenStudy (angela210793):

this was what u were talking abt 2? Thnx a loot :)

OpenStudy (amistre64):

the equation of the line that we want is: (0,3) ; (4,0) ; the slope then being 3/4 or.... y = -(3/4)x + 3 right? that is the equation for the hyp ... that line of 5

OpenStudy (amistre64):

we want a perp line to this that goes thru the origin (0,0) if anything

OpenStudy (amistre64):

y = (4/3)x

OpenStudy (amistre64):

the distance R is the distance from the origin to the point where these 2 lines meet right?

OpenStudy (angela210793):

ehe...

OpenStudy (angela210793):

r=12/5?

OpenStudy (amistre64):

(4/3)x = (3/4)x +3 dunno yet still figuring this out the hard way lol

OpenStudy (watchmath):

I think it should be -(3/4)x=(4/3)x+4 Amistre...

OpenStudy (angela210793):

w8 is easy...S(odc)= B*H/2=3*4/2=6 S(odc) is also=OE*DC/2=6----> OE=12/DC=12/5

OpenStudy (amistre64):

the slope of the hyp I drew is -3/4 with a y int at (0,3) right?

OpenStudy (angela210793):

I didn't get ur way......:(:(:( why with coordinates? O.o :(

OpenStudy (amistre64):

my way is sound to me; i understand graphs and lines better than drawings

OpenStudy (watchmath):

Your solution is nice angela :)

OpenStudy (angela210793):

Wht abt my way? is it wrong?

OpenStudy (angela210793):

Oh thnx :) :)

OpenStudy (amistre64):

4 up and 3 over is the same region as 3 up and 4 over, ...

OpenStudy (amistre64):

i dont really know if your way is right or wrong yet ;)

OpenStudy (angela210793):

hmmmm.....

OpenStudy (watchmath):

Her solution based on computing the area of ODC in two ways. First: 1/2*3*4 Second* 1/2*CD*r = 1/2*5*r

OpenStudy (angela210793):

Ehe...

OpenStudy (amistre64):

(4/3)x = (-3/4)x + 3 [3] 4x = (-9/4)x +9 [4] 16x = -9x + 36 25x = 36 x = 36/25 did I get that right?

OpenStudy (angela210793):

I didn't get ur way so i can't tell it if it is right or not.... Thank u very much anyway :):):):)

OpenStudy (watchmath):

Amistre, the y-intercept is at (0,4)

OpenStudy (amistre64):

4 36 -- * --- = y 3 25 4 12 -- * --- = y = 48/25 1 25 R = sqrt(x^2 + y^2) R = sqrt((36/25)^2+(48/25)^2)

OpenStudy (amistre64):

watch; it can be; but im actually using the other side; even tho I inadvertantly flipped it; it doesnt matter if we have 4 over and 3; or 3 over and 4 up; its the same triangle just flipped on itself with the same amount of circle it it ...

OpenStudy (amistre64):

its the point of tangency that is important; in my figuring

OpenStudy (angela210793):

let me read it from the start once again...

OpenStudy (amistre64):

like this

OpenStudy (watchmath):

Yes, your computation gives the same r :)

OpenStudy (angela210793):

thank u both :)

OpenStudy (amistre64):

R = 12/5 yay!! lol

OpenStudy (angela210793):

:D ^_^

OpenStudy (amistre64):

so that verifies your answer angela :) I know my way is solid, which is why I went that route

OpenStudy (angela210793):

Will u see another 1 with inflexion points? (Is this how u call it?)

OpenStudy (amistre64):

inflection points are where the graph stays along a course in a general direction.. sure

OpenStudy (angela210793):

^_^ ok w8 :)

OpenStudy (angela210793):

f(x)=x^4+c*x^3+x^2 what should b X so it will have 2 inflect. points? and then 1?

OpenStudy (amistre64):

'X' or 'c' ?

OpenStudy (amistre64):

f'= 4x^3 +3cx^2 +2x f'' = 12x^2 +6cx +2 = 0 for inflection points

OpenStudy (angela210793):

it says x...

OpenStudy (amistre64):

x, as far as I can tell, is an input and has no real effect on the graph of this thing; the constants describe the path it takes

OpenStudy (amistre64):

how are they defining inflection?

OpenStudy (angela210793):

they who? O.o

OpenStudy (amistre64):

they as in the people who designed the question, the authors of the material that you are using .... those guys

OpenStudy (amistre64):

I see the answers; but the question should be what value should 'c' be...

OpenStudy (angela210793):

C'mon...idk the words in english...............:S

OpenStudy (angela210793):

ok u solve it 4 c...

OpenStudy (amistre64):

f'' = 12x^2 +6cx +2 = 0 in order for this to have 2 real roots; we have to manipulate the discriminate of the quadratic formula....

OpenStudy (amistre64):

36c^2 -4(2)(12) > 0 for 2 inflections 36c^2 -4(2)(12) = 0 for 1 inflection

OpenStudy (amistre64):

36c^2 -96 = 0 36c^2 = 96 c^2 = 96/36 c = +- sqrt(96)/6 for one inflection

OpenStudy (amistre64):

and greater than that for 2 inflections

OpenStudy (angela210793):

whr did tht 36c^2 come from?O.o Florida? :P

OpenStudy (amistre64):

it comes from taking the 1st and 2nd derivatives of the given equation

OpenStudy (amistre64):

youd have to understand a little calculus to get the idea of it; but basically I used proven methods to find when the 2nd derivative = 0

OpenStudy (amistre64):

y = x^4+c*x^3+x^2 y' = 4x^3 +3cx^2 +2x y'' = 12x^2 +6cx +2 ; when y'' = 0 we have a point of inflection

OpenStudy (amistre64):

y'' is a quadratic that can have its roots figured out by the quadratic formula; the discriminant of the quad formula tells us how many roots we will have

OpenStudy (amistre64):

b^2 -4ac (6c)^2 - 4(2)(12) 36c^2 -96 has to be greater than 0 for it to have 2 points for inflection 36c^2 -96 has to equal 0 for it to only have 1 point of inflection

OpenStudy (amistre64):

so you solve the equations of the discriminate for c..

OpenStudy (amistre64):

if we know what c is ro get the discriminate to = 0; then we should assume that larger values of c will make it greater then 0 for 2 roots

OpenStudy (angela210793):

ahaaa.....i got it....Thnx ^_^

OpenStudy (angela210793):

Will u help me in smth else?..... if u don't mind ofc...

OpenStudy (amistre64):

i gotta finish my international business homework; its due today..

OpenStudy (angela210793):

Oh..Ok..I'm sorry...didn't know tht.... Thnx a lot 4 helping me and good luck with ur hw :)

OpenStudy (amistre64):

thnx :) and good luck with yours :)

OpenStudy (angela210793):

^_^

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