Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2015-12-29 09:06:22

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Some unrelated questions

A few question,

(1)A binary operation is defined on the set of real numbers by a*b = 3ab + a - 2b
Find the value of K which satisfies the equation K * 3 = 14
How would you do this?

(2)Find the next four terms of the sequence given by Un = 3 + 2n for n = 1, 2 ,3 ,4
So is the following solution correct? 3 + 2(1) = 5
3 + 2(2) = 7
3 + 2(3) = 9
3 + 2(4) = 11.

Thank you all


I know only one thing - that is that I know nothing

Offline

#2 2015-12-29 09:11:36

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Some unrelated questions

Hi;

2) Is correct.


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.

Offline

#3 2015-12-29 09:22:42

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,432
Website

Re: Some unrelated questions

For (1), you'll want to look at what happens if you let a = K, b = 3, then set ab equal to 14.

Offline

#4 2015-12-29 09:37:34

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Some unrelated questions

I'm getting K = 4.666666667 correct?


I know only one thing - that is that I know nothing

Offline

#5 2015-12-29 09:40:53

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,432
Website

Re: Some unrelated questions

No: remember that a*b is not ab. We have defined * so that a*b = 3ab + a - 2b.

In other words, K*3 = ...

Offline

#6 2015-12-29 09:43:58

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Some unrelated questions

My final answer is 12.666666 correct?


I know only one thing - that is that I know nothing

Offline

#7 2015-12-29 09:45:23

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,432
Website

Re: Some unrelated questions

I'm not getting that answer -- could you post your working?

Offline

#8 2015-12-29 09:51:26

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Some unrelated questions

I go like this 14/3 = 4.666 then had k = 4.66.. then I plugged it into 3ab + a - 2b.


I know only one thing - that is that I know nothing

Offline

#9 2015-12-29 09:59:00

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,432
Website

Re: Some unrelated questions

Remember that you cannot simply divide both sides by 3. Multiplication here is not being defined in the usual sense: therefore, the division operation will not be defined in the usual sense, either. What you should do is this:

a*b = 3ab + a - 2b, so that

K*3 = 3(K)(3) + K - 2(3) = 9K + K - 6 = 10K - 6

We want to find the value of K such that K*3 = 14. Therefore, we want to solve:

K*3 = 10K - 6 = 14.

For which value of K is it true that 10K - 6 = 14?

Offline

#10 2015-12-29 10:09:00

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Some unrelated questions

2 right?


I know only one thing - that is that I know nothing

Offline

#11 2015-12-29 10:10:52

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,432
Website

Re: Some unrelated questions

Yes, that's correct. Is the method clear?

Offline

#12 2015-12-29 10:13:32

EbenezerSon
Member
Registered: 2013-07-04
Posts: 554

Re: Some unrelated questions

Yes sirrrrr!

Thank you!


I know only one thing - that is that I know nothing

Offline

Board footer

Powered by FluxBB