Post by: Tutu_93 on October 17, 2009, 01:18:15 pm
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 ??
Post by: Tutu_93 on October 17, 2009, 01:24:46 pm
Post by: Ghost Of Highbury on October 17, 2009, 01:25:16 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)
Post by: Tutu_93 on October 17, 2009, 01:28:36 pm
Anywayz thnnx ;D
Post by: Ghost Of Highbury on October 17, 2009, 01:29:12 pm
Dint understand ..
Anywayz thnnx ;D
refer to ur book!
Post by: Tutu_93 on October 17, 2009, 01:31:06 pm
but we have this teacher who doesnt knw how to explaain so im really fed up :'(
Post by: Ghost Of Highbury on October 17, 2009, 01:33:11 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 ....
Post by: astarmathsandphysics on October 17, 2009, 02:33:41 pm
Post by: Tutu_93 on October 17, 2009, 03:12:17 pm
Thnnx By the way
Post by: slvri on October 17, 2009, 04:14:21 pm
I have a question in math slok.........y=x2+4x+6
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=((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 :)
Post by: astarmathsandphysics on October 17, 2009, 05:02:35 pm
Post by: sameer210394 on October 17, 2009, 06:42:54 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 ..
Post by: IGSTUDENT on November 10, 2009, 03:47:21 pm
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.
Post by: astarmathsandphysics on November 10, 2009, 09:58:30 pm
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.
SO p(1) is true. Suppose p(k) is true, prove p(k+1) trues
2.
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
Post by: falafail on November 10, 2009, 10:21:56 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
Post by: IGSTUDENT on November 14, 2009, 04:36:35 am
Thanks a lot for the help. I still do not really understand Q2.
For Q1. It was actually show that an=3^(n-1) for all positive integers. sorry for they typo.
I also had another question.
how do you solve 5logx +2 is greater than 0. where x is the base
and 3+lnx is greater than e^x?
Thanks.
. 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.
SO p(1) is true. Suppose p(k) is true, prove p(k+1) truesAre you sure this question is right?
2.
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
Post by: astarmathsandphysics on November 14, 2009, 09:37:48 am
Post by: IGSTUDENT on March 20, 2010, 02:47:00 pm
1. The quadratic equation ax^2+bx+c=0 has roots x=alpha and x=beta
a) Express the product of roots, alpha*beta in terms of a and c
2. Find a quadratic function in the form y=x^2+bx+c the satisfies the given functions:
The function has zeros of x=1/2 and x=3 and its graph passes through the point (-1,4)
Thanks
Post by: nid404 on March 20, 2010, 03:05:54 pm
y=0 when x=1/2 or x=3
3eqns 3 variables...solve simultaneously
x=3
9y+3b+c=0
x=1/2
0.25y+0.5b+c=0
x=-1
1y-1b+c=4
y=2/3 b=-7/3 c=1
y=2/3x2-7/3x+1
Post by: IGSTUDENT on March 20, 2010, 03:55:55 pm
I didn't quite get the first question...but i got the second one...so here it is
y=0 when x=1/2 or x=3
3eqns 3 variables...solve simultaneously
x=3
9y+3b+c=0
x=1/2
0.25y+0.5b+c=0
x=-1
1y-1b+c=4
y=2/3 b=-7/3 c=1
y=2/3x2-7/3x+1
Thanks, i made a mistake in the 1st Q. it is alpha *beta and not delta will that help?
Post by: IGSTUDENT on March 27, 2010, 06:55:52 am
1. Given that the roots of the equation x^3-9x^2+bx-216=0 are consecutive terms in a geometric sequence, find the value of b and solve the equation
2. The polynomial p(x)=(ax+b)^3 leaves a remainder of -1 when divide by x+1 and a remainder of 27 when divided by x-2. Find the values of the real numbers a and b.
3. Prove that when a polynomial p(x) is divided by ax-b the remainder if p(b/a)
Thanks
Post by: astarmathsandphysics on March 27, 2010, 07:34:38 am
Multiply this to givex^3-x^2(ab+bc+ac)+x(a+b+c)-216 (1)
If the smallest root is t then the other roots are rt and r^2t so product of roots r^3t^3=216
rt=6 so r=1,t=6 or r=6,t=1 or r=2,t=3 or some variation of these with plus or minus too.
I think a typo x^3-90x^2+bx-216=0 I get (x+3)(x+6)(x-12) b=-3
2.(-a+b)^3=-1 so -a+b=-1
(2a+b)^3=27 so 2a+b=3
a=4/3 b=1/3
will have to wait for q3
Post by: IGSTUDENT on March 27, 2010, 09:40:46 am
Post by: IGSTUDENT on April 14, 2010, 03:45:56 pm
1. Consider the trigonometric curve y=sin(2x-pi/2)
a) Find dy/dx and d2y/dx2
2. Find an equation for a line that is tangent to the graph of y=e^x that passes through the origin
3. Find the derivatice of y with repect to x, dy/dx by implicity differentiation: xy(x+y)^1/2=1
4. Find the derivative of y with repect to x, dy/dx: ln(1+x^2)^1/2=xarctanx
Thanks!
Post by: astarmathsandphysics on April 14, 2010, 03:57:21 pm
Post by: astarmathsandphysics on April 14, 2010, 04:10:49 pm
1. Consider the trigonometric curve y=sin(2x-pi/2)
a) Find dy/dx and d2y/dx2
2. Find an equation for a line that is tangent to the graph of y=e^x that passes through the origin
3. Find the derivatice of y with repect to x, dy/dx by implicity differentiation: xy(x+y)^1/2=1
4. Find the derivative of y with repect to x, dy/dx: ln(1+x^2)^1/2=xarctanx
Thanks!
a)dy/dx=2cos(2x-pi/2) and d2y/d2x =-4sin(2x-pi/2)
b)dy/dx =e^x so at x=0 gradient is e^0 =1 and y=1
y-1=1(x-0) so y=x+1
c)o sh*t
y(x+y)^1/2 +x(x+y)^1/2 dy/dx +1/2xy(x+y)^-1/2 (1+dy/dx) =0
dy/dx(x(x+y)^1/2+1/2xy(x+y)^-1/2 )=-y(x+y)^1/2 -1/2xy(x+y)^-1/2
dy/dx =(-y(x+y)^1/2 -1/2xy(x+y)^-1/2)/(x(x+y)^1/2+1/2xy(x+y)^-1/2 ) =(-y(x+y)-1/2xy)/(x(x+y)+1/2xy) =(-y^2-3/2xy)/(x^2 +3/2xy)
4. Where is y here
Post by: IGSTUDENT on April 15, 2010, 01:53:45 am