vwinnie8's math help thread

[vwinnie8]

Does anyone know how to do this?

"Find two positive numbers whose sum is 4 and such that the sum of the cube of the first and the square of the second is as small as possible."

[vea]

Let x and y be the two numbers.

x+y=4
y=4-x...(1)

x^3+y^2
sub (1) into the above,
x^3+(4-x)^2
x^3+x^2-8x+16
deriving...
3x^2+2x-8
Let the derivative equal zero for stationary points
3x^2+2x-8=0
x=-2, 4/3
the minimum occurs when x=4/3 (x=2 is unfeasible anyway as x>0)
sub into (1) we get y=8/3

so the two numbers are 4/3 and 8/3

[xZero]

let the first num = x where x>0, second num = y, where y>0

x+y=4
x^3+y^2=a number.

so you have 2 simultaneous equations so you can sub x=4-y into the second eq, then diff the second eq with respect to y and make it equal to 0. Make sure its the minimum and find the value of y, then sub y into the first eq to find x

[vwinnie8]

Let x and y be the two numbers.

x+y=4
y=4-x...(1)

x^3+y^2
sub (1) into the above,
x^3+(4-x)^2
x^3+x^2-8x+16
deriving...
3x^2+2x-8
Let the derivative equal zero for stationary points
3x^2+2x-8=0
x=-2, 4/3
the minimum occurs when x=4/3 (x=2 is unfeasible anyway as x>0)
sub into (1) we get y=8/3

so the two numbers are 4/3 and 8/3

amazing.... cheers mate

[vwinnie8]

let the first num = x where x>0, second num = y, where y>0

x+y=4
x^3+y^2=a number.

so you have 2 simultaneous equations so you can sub x=4-y into the second eq, then diff the second eq with respect to y and make it equal to 0. Make sure its the minimum and find the value of y, then sub y into the first eq to find x

thanks ur awesome!

[vwinnie8]

Hey guys... all of you guys are super-awesome on here  :angel: .... i know i've already asked a question before but I really dunno how to do this calculus stuff... chapter 10G in the cambridge essentials textbook :p

i will buy the worked solutions book sometime... hehehehe :p

BUT FOR NOW. PLEASE KINDLY HELP ME AGAIN?  :uglystupid2:

"Find the point on the parabola y = x2 that is closest to the point (3, 0)."
 
No idea how to do it... any help would be greatly appreciated

cheers
winnie 

[xZero]

I suggest that you merge this with your previous post so you can have a thread of your own for your questions.

Anyways the distance from y=x^2 to (3,0) is

sub y1 with x^2 and x_1 with x. Sub y2 with 0 and x2 with 3



differentiate that and find x when the derivative = 0. sub it back into the parabola to find y

[vwinnie8]

I suggest that you merge this with your previous post so you can have a thread of your own for your questions.

Anyways the distance from y=x^2 to (3,0) is

sub y1 with x^2 and x_1 with x. Sub y2 with 0 and x2 with 3



differentiate that and find x when the derivative = 0. sub it back into the parabola to find y

thanks so much for taking the time to type up everything. you're awesome!! and i'll remember to merge

[m@tty]

and i'll remember to merge

Done. (You can't merge topics.)

Oh, and sorry about the typo "vwinnies8's".. I fixed it in the first post, so it should be fine from now on.

[vwinnie8]

and i'll remember to merge

Done. (You can't merge topics.)

Oh, and sorry about the typo "vwinnies8's".. I fixed it in the first post, so it should be fine from now on.

nawww thankyou!!!

hahahahah soooooo cute... my own little maths thread ... lol :p