Math Is Fun Forum

NadineSch

Member

Registered: 2016-04-24

Posts: 13

Maths Exam and no clue

Dear maths geeks (and I mean that as a compliment!!!)

I am in the middle of the preparation of my maths exam which is the final chance to succeed my studies. Whilst I successfully solve many exercise questions, there is a list of exercises that I know will be part of the exam, that I just CANNOT get to grips to

The general topics are Integrals, Differentials and Matrix calculations.

Is there anywhere where I can find help, maybe submit the exercises and find someone that actually enjoys solving them and sharing with me how to get there?

Thank you so very much in advance for anything. Tips, advice, contacts?

A very desperate Nadine

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Maths Exam and no clue

Hi;

Welcome to the forum. Post the ones that are giving you trouble.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

NadineSch

Member

Registered: 2016-04-24

Posts: 13

Re: Maths Exam and no clue

Thank you! Here they come

1. Compute (by hand) the area of the planar region enclosed by the graph of the function
f(x)= (6x-18)/(6x-x^2-5), the x-axis and the vertical lines x=2 and x=4

2. General solution (in implicit form) of the differential equation (1-y^3) y' - x^3 (lnx)^2 sqrt(4y-y^4) = 0

3. Consider the matrices
A= ( k 3 0
       8 2  -1
      0  k  1)
and

B= (1  4  2
      2  0  -2)

k is a parameter, element of IR

a) For which value(s) of k, if any, is A an invertible matrix?
b) For which value(s) of k, if any, does the matrix equation AM=A+M have a unique solution for M?
c) let k=5. Find all solutions M, if any, of the matrix equation AM=B, respectively MA=B

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Maths Exam and no clue

Hi;

1) I would say 0.

3a) That matrix is invertible for all values of k other than k = -6 or k = 4, by the way what is IR?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

NadineSch

Member

Registered: 2016-04-24

Posts: 13

Re: Maths Exam and no clue

Hi bobbym. Thank you! IR was my attempt to write out the sign for real numbers

Is there any way you could get the way to your answers to me? As that is where I struggle. I find exercises with solutions but it doesn't help me because I am insecure about the steps to reach it...

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Maths Exam and no clue

for Q.2 Use variables separable method bringing all terms of y to left hand side and x terms to r.h.s. and integrate each side. Substitute

and solve l.h.s for r.h.s. use integration by parts. IR I thought integer regime.

I am not sure but I have a hunch for 3.(b)
AM=A+M Premultiply by

now in order for M  to be unique  I-A^-1 must be invertible.

Last edited by thickhead (2016-04-26 02:39:36)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Maths Exam and no clue

Last edited by thickhead (2016-04-26 17:03:39)

---

{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Maths Exam and no clue

HI;

For 1) If you graph the function you can get the idea that it is symmetrical.

3a) Get the determinant and solve the quadratic.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

NadineSch

Member

Registered: 2016-04-24

Posts: 13

Re: Maths Exam and no clue

Thank you very much! That was very helpful indeed. I had 0 as a solution for the first one, but I simply could not make sense of it...

bobbym (or anyone else), could you write out how you got the determinant and with that found the solution? I end up with -k^2+2k-24 and don't see how I can expand that to have the answer visual

NadineSch

Member

Registered: 2016-04-24

Posts: 13

Re: Maths Exam and no clue

I think I've got it, sorry, I was desperately trying to expand the quadratic to have the solution jump at me, but it worked by taking the discriminant

NadineSch

Member

Registered: 2016-04-24

Posts: 13

Re: Maths Exam and no clue

For everyone that helped: I have passed my exam!! Thank you very much. I only found it polite to come back to you with this.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Maths Exam and no clue

Congrats.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Maths Exam and no clue

Was it hard or did you just breeze right through it?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.