calculus 30 question

[roary]

1. The solutions inProblem might look smooth, but it might not feel smooth because the piece-wisedefined function (consisting of for x < 0, for , and for x > 100) doesn’t have a continuous second derivative. So, youdecide to improve the design by using a quadratic function only on theinterval and connectingit to the linear functions by means of two cubic functions.
a) Write a system of equations in 11 unknownsthat ensure that the functions and their first two derivatives agree at thetransition points.
b) Solve theequations using a computer algebra system to find formulas for q(x), g(x), andh(x).

I've gotten pretty far or so I think, I've never been very good at matrixes and actually have never really been taught how to solve them. I understand the reduced row echlon form and how to get it "solved" on the calulator but im confused on what to do from there. I completely understant the first part and this is what i did.
Set q(x)=g(x) and plug in x=10 and setequation equal to zero
Set q(x)=h(x) and plug in x=90 " "
Set q’(x)=g’(x) and plug in x=10 and " "
Set q’(x)=h’(x) and plug in x=90 and " "
Set q’’(x)=g’’(x) and plug in x=10 and " "
set q’’(x)=h’’(x) and plug in x=90 and " "
when I did that I got my 6 equations and 11 unknowns and with the zeros that gave my matrix to be a 6x12 and when i solved for my matrix with calculator i got

1	0	0	1/1000	0	0	0	0	0	0	-1/1000	0
0	1	0	-3/100	0	0	0	0	-1	0	3/100	0
0	0	1	3/10	0	0	0	0	0	-1	-3/10	0
0	0	0	0	1	0	0	1/729000	0	0	-1/729000	0
0	0	0	0	0	1	0	-1/2700	-1	0	1/2700	0
0	0	0	0	0	0	1	1/30	0	-1	-1/30	0

i just really need help on how to go from here. I have 5 leading 1's and i dont know how to go from here.
Btw the variables are from left to right k,l,m,n,p,q,r,s,a,b,c

 

[mmm4444bot]

piece-wisedefined function (consisting of for x < 0, for , and for x > 100)

The correct hyphenation is piecewise-defined, but I'd settle for wisedefinitions, were I to see them.

We'll guess that the middle interval is 0 ≤ x ≤ 100?

I completely understant the first part

I've … never really been taught how to solve [problems involving matrices]

I understand … how to get it "solved" on the calulator

You're only asking about part (b) then, yes?

I understand that you have a clear picture of this exercise, but I don't.

I'm concerned about all of the typographical errors, missing information, and contradiction in your submission. I feel unmotivated at the prospect of having to decipher the goals.

The instructions tell you to solve using technology, and it appears that you did that part, but without knowing more about the piecewise function and functions q, g, and h, I'm not sure what to tell you to do with your calculator-generated values for the 11 variables.

Please post all of the given information. In particular, I am interested in what they said about that piecewise function (eg: is it linear?), as well as the meaning of functions q, g, and h.

(It is not good form to use the same symbol as function name and variable name simultaneously, by the way. Note: upper- and lower-case letters are different symbols, like q and Q. It would be better to say Q(x) versus q(x), as q is already used elsewhere.)

Cheers :cool:

 

[roary]

graph will look like a concurve down parabola.
the equations given are
Q(x)=ax^2+bx+c
G(x)=kx^3+lx^2+mx+n
H(x)=px^3+qx^2+rx+s
the variables that i gave at the coef. of the equations.

 

[mmm4444bot]

Hold on, while I re-read this exercise...

I was thinking that you had already solved for the coefficients...

Sorry for the preventable delay (blame Google's signal noise).

Okay, please post your equations, so that I may confirm your system and the reduced coefficient-matrix.

Please confirm the domains for G(x) and H(x), too. :cool:

 

[roary]

help soving 6x12 matrix

i have solved for 6 equations in calculus and those are:

1000k+100L+10m+n-100a-10b-c=0
72900p+8100q+90r+s-8100a-90b-c=0
300k+20L+m-20a-b=0
24300+180q+r-180a-b=0
60k+2L-2a=0
540p+2q-2a=0

i've put them into a rref matrix (to solve for the varibles that i need for the next step) with the formk, l,m,n,p,q,r,s,a,b,c

however when I solved with my calculator I only have 5 leading coeficients and im completely stuck. I've never been great at matrixs and it someone could break it down easy for me i'd be forever greatful.

 

[roary]

Hold on, while I re-read this exercise...

I was thinking that you had already solved for the coefficients...

Sorry for the preventable delay (blame Google's signal noise).

Okay, please post your equations, so that I may confirm your system and the reduced coefficient-matrix.

Please confirm the domains for G(x) and H(x), too. :cool:

the domains
g(x): 0<=x<10
q(x): 90<x<=100
h(x): 10<=x<=90

have solved for 6 equations in calculus and those are:

1000k+100L+10m+n-100a-10b-c=0
72900p+8100q+90r+s-8100a-90b-c=0
300k+20L+m-20a-b=0
24300+180q+r-180a-b=0
60k+2L-2a=0
540p+2q-2a=0

i've put them into a rref matrix (to solve for the varibles that i need for the next step) with the formk, l,m,n,p,q,r,s,a,b,c

however when I solved with my calculator I only have 5 leading coeficients and im completely stuck.

 

[mmm4444bot]

Your system has no finite solution, so either it does not correctly model the given scenario or there is some issue with your materials.

I am willing to tutor an individual, as long as they continue to answer my questions.

You are free to wait for somebody else to help you, of course, but I would require the entire scenario described (including all line segments, their slopes and endpoints, et cetera, from the prior exercise) before I could invest more effort in deciphering what you have posted.

I suspect that you are skipping over some other relationships involving equalities that would give you a larger system to solve.

Cheers :cool:

 

[roary]

infinately many solutions matrix..HELP!!!

i have a matrix with infinatly many solutions. I have never solved this type before and I need a lot of help. it will end up to be a 6x12 matrix with the row reduced echlon form. but I only have 5 leading ones....please help here are the equations

1000k+100L+10m+n-100a-10b-c=0
72900p+8100q+90r+s-8100a-90b-c=0
300k+20L+m-20a-b=0
24300+180q+r-180a-b=0
60k+2L-2a=0
540p+2q-2a=0

i've put them into a rref matrix (to solve for the varibles that i need for the next step) with the form
k,l,m,n,p,q,r,s,a,b,c

What i need to do is figure out how to solve for the variables even though there are infinately many solutions...please help

 

[HallsofIvy]

i have a matrix with infinatly many solutions. I have never solved this type before and I need a lot of help. it will end up to be a 6x12 matrix with the row reduced echlon form. but I only have 5 leading ones....please help here are the equations

1000k+100L+10m+n-100a-10b-c=0

So one thing you can do is say that c= 1000k+100L+ 10m+ n- 100a- 100b.

72900p+8100q+90r+s-8100a-90b-c=0

So you can say c= 72900p+ 8100q+ 90r+ s- 8100a- 90b and, then, 1000k+100L+ 10m+ n- 100a- 100b= 2900p+ 8100q+ 90r+ s- 8100a- 90b or 1000ik+ 1000L+ n- 2900p-n 8100q- 90r+ s+ 8000a- 10b= 0.

300k+20L+m-20a-b=0

so b= 300k+ 20L+ m- 20a.

24300+180q+r-180a-b=0

so b= 24300+ 180q+ r- 180a[/quote] and with the above 300k+ 20L+ m- 20a= 24300+ 180q+ r- 180a or 300k+ 20L+ m- 180q- r+ 160a= 24300.

60k+2L-2a=0

so a= 30k- L

540p+2q-2a=0

so a= 270p+ q and with the above 30k- L= 270p+ q so L= 30k- 270p- q.

You can replace b in the first equation above by 300k+20L+ m- 20a and then replace a in that equation and the last by 30k- L to get three equations in the variables k, L, m, n,p q, r, and s. Solve those three equations for three of those unknowns. The other 5 variables will be "free variables"- the solution space will be 5 dimensional.

i've put them into a rref matrix (to solve for the varibles that i need for the next step) with the form
k,l,m,n,p,q,r,s,a,b,c

What i need to do is figure out how to solve for the variables even though there are infinately many solutions...please help

 

[mmm4444bot]

The solutions inProblem might look smooth, but it might not feel smooth because the piece-wisedefined function

improve the design by using a quadratic function only on theinterval and connectingit to the linear functions by means of two cubic functions.

graph will look like a concurve down parabola

equations given are

Q(x)=ax^2+bx+c

G(x)=kx^3+lx^2+mx+n

H(x)=px^3+qx^2+rx+s

the domains

g(x): 0<=x<10

q(x): 90<x<=100

h(x): 10<=x<=90

Your system has no finite solution, so either it does not correctly model the given scenario or there is some issue with your materials.

I would require the entire scenario described (including all line segments, their slopes and endpoints, et cetera, from the prior exercise) before I could invest more effort in deciphering what you have posted.

You are not following our posting guidelines.

You continue to keep information secret.

You continue to contradict.

Please stop duplicating this thread on our boards. (I merged your other two threads into this one.)

If you are unwilling to provide the complete exercise, then please see your instructor for help.