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\(\int_4^6 2\pi(6-x)\sqrt{x}\,dx\)

the book says 0 to 4, must be a mistake

well if the problem is written exactly what you wrote above the integral should be from x=4 to x=6.

contrasat can u help me

please

4x^2-6y^2+32x-24y+16=0
give the exact coordinated of an four points

i will give u a medal

whats the question

4x^2-6y^2+32x-24y+16=0
give the exact coordinated of an four points

coordinated is not a word

of an 4 points? thats not proper english grammar

ok

can u help me

please i need better english

4x^2-6y^2+32x-24y+16=0
give the exact coordinates of any four points

on the hyperbola

ok first change that to a standard hyperbola

4 ( x^2 - 8x + ? ) - 6 ( y^2 +4 + ? ) + 16 = 0

ok

mistake
4 ( x^2 +
8x + ? ) - 6 ( y^2 +4 + ? ) + 16 = 0

ok

4 ( x^2 + 8x + (8/2)^2 - (8/2)^2 ) - 6..

theres an easier way to do this

just plug in x = 0, and see what you get for y , then x = 1, etc

4x^2-6y^2+32x-24y+16=0
so if x = 0, we have 0 - 6y^2 + 0 - 24 y + 16 = 0

ok

then solve that quadratic

ok so this is the quadractic -6y^2-24y+16=0

is that right

yes

ok these are not easy coordinates this way

can i use foil

you can use quadratic formula, but this is not an easy approach to find 4 coordinates

can u help me

YES!!!!!!!!!!!!!!!!!

where is my medal

i got 92 and 68 but i think i did it wrong can u help me

where is my medal

i gave u it

YAYYYYYYYYYYYYYYYYY!!!!!!

can u help me

do the quadractic

please

its pretty bad

what

i get y = funny bananas

too much work man

can u help me

here, lets do it anothe rway

YYYYYYYYYYYEEEEESSSSSSSS!!!!!

can u please help me with the question

are u going to help me or no casue it is rude

4( x^2 + 8x + (8/2)^2 - (8/2)^2 -

one moment, stand by

4( x^2 + 8x + (8/2)^2 - (8/2)^2) - 6 ( y^2 + 4y +(4/2)^2 - (4/2)^2 ) + 16 = 0

ok

ok

i dont mean to rush u but can u hurry up

im trying my best

are you girl or boy

a boy

4 ( (x + 4)^2 - 4^2 ) - 16 ( (y+2)^2 - 4 ) + 16 = 0 , agreed?

i completed the square

yes

can u help me now finding the four pointd

points

YYYYYYYYYYYYYYYYYYYYEEEEEEEEEEEESSSSSSSSSSSSSSS

4 ( (x + 4)^2 - 4^2 ) - 16 ( (y+2)^2 - 4 ) + 16 = 0
4 ( x+4)^2 - 4^3 - 16 ( y+2)^2 + 16*4 + 16 = 0

ok

4 ( x + 4) ^2 - 16 ( y+2)^2 = 4^3 -16*4 - 16

4 ( x+4)^2 - 16 (y+2))^2 = -16

-(x+4)^2 / 4 + (y+2)^2 / 1 = 1

now solve for y

(y+2)^2 = ( x+4)^2/4 , square root both sides

so abs (y+2) = abs(x+4)/2

+ - (y+2) = + - (x + 4)/2

so what are the points

u making me cry

we're almost there

what are the points

please

i made a mistak,e one sec

YOURE MAKING ME CRY< lol

dont cry, just take a deep breath , drink some water

ok

ok, i have to go back and find the mistake one sec

fresh piece of paper

ok

i postef a new post

ok
NOOOOOOOOOOOOOOOOOOOOOOOOOOO!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

what

nevermind

ok

(y+2)^2 /1^2 - (x+4)^2 / 4 = 1

(y+2)^2 = 1 + (x+4)^2 /4

y = + - sqrt ( 1 + (x+4)^2/4)

typo
y+2 = + - sqrt ( 1 + (x+4)^2/4)

y = -2 + - sqrt ( 1 + (x+4)^2/4 )

now we can plug in calculator and find nice points

can u help me

(-4,-1) , thats one point

not many nice integer points

oh

ok i did it again, got a diferent answer

4( x+4)^2 - 6 ( y + 2)^2 = 24

ok

(y+2)^2 = 4 [ (x+4)^2/6 - 1 ]

y = -2 + - 2 *sqrt [ (x+4)^2 /6 -1 ]

ok

can u help

further

ok

ok then i will go to bed good night
thanks for the help buddy

ok then help me

who gave you this question

the school

its a homework question but it is okay
good night

i am going to bed i am tired

im almost done

ok

ok here is one point ( 5, 5sqrt 2 -2 )

( 1, sqrt 114 /3 - 2 )

toxic, let me work on this , and i will tell you tomorrow , ok?

okk then good night

oh wait it does work

ok im confident i found the right equation

yay!!!

good

ok let me give you two other points

oh by symmetry we can just take the negative of the two points we have
( 5, + - [5sqrt(2) -2 )

oh wait, we cant , i take that back

ok so 4 points are ( 5 , 5 sqrt (2) -2 ) , ( 5 , -5sqrt (2) - 2 )

( 1, sqrt(114)/3 -2 ) , ( 1, -sqrt(114)/3 - 2 )

took me a litle while, but i got the answer , :)

oh man, theres a much easier way to solve this, woops

its much faster than actually finding the hyperbola. but this works as well.

ok can u tell me tommorow im tired

so if you set x = 0 , we have -6y^2 -24y + 16 = 0 ,
if you set y = 0 you have 4x^2 +32x + 16 = 0

so you get ( 0, y1) (0,y2) and then ( x1, 0) (x2,0) for the second part

im tired

one sec, i have it , 4 nice solutions

where is the fraction bar

hurry up

i want to use latex, i cant find the fraction bar

y = -(-2) + - sqrt ( 24^2 - 4 (-6)*16) / ( 2*-6)

y =[ -(-2) + - sqrt ( 24^2 - 4 *-6*16) ] / ( 2*-6)

tell me tommorow please

wait

( 0 , 8/3 -2/3 sqrt 22) ( 0 , 8/3 +2/3 sqrt 22)

scratch that