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Offline Tutu_93

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Math
« on: October 17, 2009, 01:18:15 pm »
I have a question in math sl
emm USe the method of completing the square to find the minimum value of y and and x at which it occurs

eg : y=x2 + 4x + 6

Waat do they mean ??

And i have texas Ti-84 silver edition .. how can i use it to graph and that stuff ??
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Offline Tutu_93

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Re: Math
« Reply #1 on: October 17, 2009, 01:24:46 pm »
Some 1 ??? :-\
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Offline Ghost Of Highbury

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Re: Math
« Reply #2 on: October 17, 2009, 01:25:16 pm »
Quote from: Tutu_93 on October 17, 2009, 01:18:15 pm
I have a question in math sl
emm USe the method of completing the square to find the minimum value of y and and x at which it occurs

eg : y=x2 + 4x + 6

Waat do they mean ??

And i have texas Ti-84 silver edition .. how can i use it to graph and that stuff ??

(x+2)2 + 2

dy/dx of x2 + 4x + 6 = 2x+4

equate it to 0

2x = -4

x=-2

when x=-2

y = 2

thus the minimum point is (-2,2)
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Offline Tutu_93

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Re: Math
« Reply #3 on: October 17, 2009, 01:28:36 pm »
Dint understand ..
Anywayz thnnx  ;D
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Offline Ghost Of Highbury

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Re: Math
« Reply #4 on: October 17, 2009, 01:29:12 pm »
Quote from: Tutu_93 on October 17, 2009, 01:28:36 pm
Dint understand ..
Anywayz thnnx  ;D

refer to ur book!
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Offline Tutu_93

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Re: Math
« Reply #5 on: October 17, 2009, 01:31:06 pm »
its infront of me ..
but we have this teacher who doesnt knw how to explaain so im really fed up :'(
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Offline Ghost Of Highbury

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Re: Math
« Reply #6 on: October 17, 2009, 01:33:11 pm »
Quote from: Tutu_93 on October 17, 2009, 01:31:06 pm
its infront of me ..
but we have this teacher who doesnt knw how to explaain so im really fed up :'(


completeing the square is a very easy method...chk google.com to find a resource on that..

and the later part...is just differentiating it..and equating it to 0 to find the stationary point ....

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Offline astarmathsandphysics

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Re: Math
« Reply #7 on: October 17, 2009, 02:33:41 pm »
Completing the square is writing a quadratic in the form (x+a)^2 +b. In the example you gave both a and b equal 2. I will post a link when i get home
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Offline Tutu_93

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Re: Math
« Reply #8 on: October 17, 2009, 03:12:17 pm »
Okaay :D ..
Thnnx By the way
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Offline slvri

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Re: Math
« Reply #9 on: October 17, 2009, 04:14:21 pm »
Quote from: Tutu_93 on October 17, 2009, 01:18:15 pm
I have a question in math sl
emm USe the method of completing the square to find the minimum value of y and and x at which it occurs

eg : y=x2 + 4x + 6

Waat do they mean ??

And i have texas Ti-84 silver edition .. how can i use it to graph and that stuff ??
ok.........y=x2+4x+6
y=(x2+4x)+6
y=((x)2+2(x)(2)+(2)2)+6-(2)2
y=(x+2)2+6-4
y=(x+2)2+2
Now the minimum value will occur when (x+2)2=0(remember this as a rule)
(x+2)2=0
x+2=0
x=-2
and the corresponding minimum value of y is
y=(-2+2)2+2
y=2
hope this helped :)
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Offline astarmathsandphysics

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Re: Math
« Reply #10 on: October 17, 2009, 05:02:35 pm »
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Offline sameer210394

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Re: Math
« Reply #11 on: October 17, 2009, 06:42:54 pm »
Quote from: Tutu_93 on October 17, 2009, 01:18:15 pm
I have a question in math sl
emm USe the method of completing the square to find the minimum value of y and and x at which it occurs

eg : y=x2 + 4x + 6

Waat do they mean ??

And i have texas Ti-84 silver edition .. how can i use it to graph and that stuff ??

one simplest method....

this equation is written in the form of Ax2 + Bx + C

in such cases to find the turning point. use the following equations...

x = -B/2A

then solve for
y(x).

done...

if you want the proving part, plz ask ..
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Offline IGSTUDENT

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Re: Math
« Reply #12 on: November 10, 2009, 03:47:21 pm »
I have some questions in mathematical induction.

1. let a1,a2,a3,...be a sequence defined by
    a1=1,an=3an-1; n?1

    Show that an=3^n-1 for all positive integers n.


 Prove the following statement.
    n
2. ? 1/(2i-1)(2i+1)=n/2n+1       for each positive integer n.
    1

3. Use mathematical induction to prove that (5^n)+(9^n)+2 is divisible by 4,for n?Z+.

Thanks.
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Offline astarmathsandphysics

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Re: Math
« Reply #13 on: November 10, 2009, 09:58:30 pm »
. let a1,a2,a3,...be a sequence defined by
    a1=1,an=3an-1; n?1

    Show that an=3^n-1 for all positive integers n.


 Prove the following statement.
    n
2. ? 1/(2i-1)(2i+1)=n/2n+1       for each positive integer n.
    1

3. Use mathematical induction to prove that (5^n)+(9^n)+2 is divisible by 4,for n?Z+.

Thanks.
1. a_1=3*1-1=3^1 -1=2

SO p(1) is true. Suppose p(k) is true, prove p(k+1) trues
a_{n+1} =3(3^{k} -1) -1=3*3^k-3-1=3^{k+1} -4 Are you sure this question is right?

2.\sum_1^n 1/(2i-1)(2i+1) =1/2 \sum_1^n 1/(2i-1) -1/(2i+1)=1-1/(2n+1)=1/2(2n/(2n+1))=n/(2n+1)

3.p(1) 5+9+2=16 hence p(1) is true
suppoose p(k) is true then (5^k)+(9^k)+2 is divisible by 4
p(k+1)-p(k) (5^(k+1))+(9^(k+1))+2-(5^k)-(9^n)-2  =5^k(5-1) +9^k(9-1)=4*5^k +8*9^k which is divisible by 4
« Last Edit: November 10, 2009, 10:12:13 pm by astarmathsandphysics »
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Offline falafail

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Re: Math
« Reply #14 on: November 10, 2009, 10:21:56 pm »
Quote from: Tutu_93 on October 17, 2009, 01:18:15 pm
I have a question in math sl
emm USe the method of completing the square to find the minimum value of y and and x at which it occurs

eg : y=x2 + 4x + 6

Waat do they mean ??

And i have texas Ti-84 silver edition .. how can i use it to graph and that stuff ??

y = x2 + 4x + 6
y = x2 + 4x + 22 - 22 + 6
y = (x + 2)2 - 4 + 6
y = (x + 2)2 + 2
the least value of y will be when (x + 2)2 = 0, so x = -2
substitute for y.

so when you're asked to "complete the square" basically this is what you do:
x2 + bx + c
x2 + bx + (b/2)2 - (b/2)2 + c
(x + b/2)2 - (b/2)2 + c
;D
« Last Edit: November 10, 2009, 10:24:44 pm by falafail »
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