Math Is Fun Forum

coolbee

Member

Registered: 2016-04-05

Posts: 19

random questions by coolbee

If

has two factors (2x+1) and (3x-1), then what must be the value of p?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: random questions by coolbee

HI;

I am getting p = - 2

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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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: random questions by coolbee

hi coolbee

There is a method using the remainder theorem but, in case you've not heard of that. here's a way that just uses factors.

There must be a third factor.  As I want 24x^3 I'll assume this factor is (4x + r)

By comparing coefficients with the original expression you can find r and hence p.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

coolbee

Member

Registered: 2016-04-05

Posts: 19

Re: random questions by coolbee

The sum of series

Last edited by coolbee (2016-04-24 21:53:33)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: random questions by coolbee

Hi;

Is the last term 25 choose 3?

---

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.

coolbee

Member

Registered: 2016-04-05

Posts: 19

Re: random questions by coolbee

yes. corrected.

coolbee

Member

Registered: 2016-04-05

Posts: 19

Re: random questions by coolbee

the answer is:

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: random questions by coolbee

I think the summation has something to do with splitting the denominator say 1/(4*5) into (1/4-1/5) and combining first part with the previous term and the other with the later term.I can't figure out right now.

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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: random questions by coolbee

Hi coolbee;

By direct computation I am getting

---

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.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: random questions by coolbee

My calculation agrees with bobbym. I calculated the sum on excel sheet.My value is 226494. coolbee's value comes to 191193.3048. coolbee, please check the formula.

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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: random questions by coolbee

Last edited by thickhead (2016-05-02 05:08:19)

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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.}

ElainaVW

Member

Registered: 2013-04-29

Posts: 580

Re: random questions by coolbee

Hello thickhead:

You mean

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: random questions by coolbee

Hi EVW;

Direct computation and then my propfrac routine? Yes?

I was wondering if you could offer a closed form using the snake oil method? I am aware of the closed form given by M.

---

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.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: random questions by coolbee

It seems i put some junk value in the numerator of the fraction by mistake.It can not end with 5.

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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: random questions by coolbee

I confirm Elainavw's  values. coolbee's value can not be correct since both of us used integer mathematics and the denominator can not vanish into thin air.

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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.}

coolbee

Member

Registered: 2016-04-05

Posts: 19

Re: random questions by coolbee

well this question was asked in one of the engg. entrance exams in India so it is difficult to doubt in the answer key.

let's leave it for now and see some other questions:

If

,

and

,

then

is equal to what?

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: random questions by coolbee

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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: random questions by coolbee

well this question was asked in one of the engg. entrance exams in India so it is difficult to doubt in the answer key.

It is not to doubt the source but from objective point of view. Three of us got same denominator of proper fraction with a large denominator and the  answer suggested conatains only denominator 26x27. Our denominator is still not divisible by 27.

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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: random questions by coolbee

well this question was asked in one of the engg. entrance exams in India so it is difficult to doubt in the answer key.

There are tons of mistakes in all kinds of manuscripts, regardless of the source.

---

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.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: random questions by coolbee

If we can't go from left to right let us go from right to left.

Last edited by thickhead (2016-05-05 17:24:59)

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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: random questions by coolbee

The terms shown in the above comment are asymmetric. They can be recast in symmetric way.

On R.H.S. the numerators are same as given by "coolbee" but denominators are different.

Last edited by thickhead (2016-05-07 03:52:40)

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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.}

coolbee

Member

Registered: 2016-04-05

Posts: 19

Re: random questions by coolbee

Suppose f,f',f" are continuous on [0,e] and that f'(e)=f(e)=f(1)=1 and

,then find the value of

.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: random questions by coolbee

Suppose f,f',f" are continuous on [0,e] and that f'(e)=f(e)=f(1)=1 and

,then find the value of

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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.}