Math help (1 Viewer)

[Sy123]

Do you always have to do both sum and products? and How come you have two unknowns in the equation? aren't you suppose to have one?

We are doing mathematics here, although you want to take a non-rote approach to maths, asking yourself these kinds of questions will lead to you roting everything (if thats what you want thats your choice). In mathematics sometimes you need to do something different, with enough practise and exposure to different types of questions you gain experience in these sort of matters. We cant always ask ourselves 'I have to ALWAYS do X, then I ALWAYS have to do Y'
It doesnt work like that. We have to observe the question and see where it takes us. We test both because having only ONE equation doesnt do us any good. So hence we go for a second equation. If we found that the first equation was ENOUGH, then we stop and solve.

Why don't you find alpha by square rooting the RHS? instead of keeping it as alpha squared?

You can take whatever path you like as long as you find a way to eliminate alpha. Square rooting it is pretty much leading you to the same thing since in the end you must square both sides to eliminate the square root, try your own algebraic approach you end up doing the same thing.

Why alpha squared and not alpha?

Note how one equation has alpha and one has alpha squared (because we multiplied alpha by alpha). So to eliminate alpha we must make it such that the LHS of BOTH equations are the same, then we can eliminate LHS and solve for the RHS (this is in essence what solving simultaneously by elimination is) Feel free to take whatever algebraic approach you are comfortable with as long as it leads you to the answer (and its short)

What lol. How is the (k+1)² the numerator?

I didnt want to write the whole fraction for the 0.5 one since its tedious:

How does the whole thing equal to 0... One line it's a fraction with squares and the next line it's 0...

I just skipped the algebraic mishap, disregard it though, I divided both sides by 1/4, then by (k+1) (which is incorrect). Look at my above post

 

[awstarr]

Hi Fawun,

Spiral tells me that you need a bit of maths help and that you are quite shy in asking people. I will be here patrolling this thread the whole of the night, you don't have to feel anxious - asking questions is a natural part of the human condition. If you need any help throughout the night feel free to leave your question here or alternatively you can reach me through the messaging system.

awstarr

 

[Fawun]

That's a polynomial of degree two, just like your question. This polynomial has two equal roots. It's the same as (x-ß)(x-ß) = 0, where 'a' are the roots. It is in the same 'form' as the polynomial in the question. If you expand it, you get x²-2ßx+ß². (I changed it to beta to avoid confusion)

I'm trying to show you a situation where the 'roots are equal'. You have to know what it means before attempting the question. Do you even know what it means now? Also, thank you for taking the time to help me.

Two equal roots are essentially saying the roots or the solutions of the polynomial are the same/equal/identical.

So what you're trying to say is that two equal roots are basically two roots that are the same? like in (x-a)(x-a), the roots are 'a' which are equal?

We are doing mathematics here, although you want to take a non-rote approach to maths, asking yourself these kinds of questions will lead to you roting everything (if thats what you want thats your choice). In mathematics sometimes you need to do something different, with enough practise and exposure to different types of questions you gain experience in these sort of matters. We cant always ask ourselves 'I have to ALWAYS do X, then I ALWAYS have to do Y'
It doesnt work like that. We have to observe the question and see where it takes us. We test both because having only ONE equation doesnt do us any good. So hence we go for a second equation. If we found that the first equation was ENOUGH, then we stop and solve.

How will a question 'lead' or 'take' us if we don't know what to do? Isn't that why i'm suppose to ask questions to know what to do?

Note how one equation has alpha and one has alpha squared (because we multiplied alpha by alpha). So to eliminate alpha we must make it such that the LHS of BOTH equations are the same, then we can eliminate LHS and solve for the RHS (this is in essence what solving simultaneously by elimination is) Feel free to take whatever algebraic approach you are comfortable with as long as it leads you to the answer (and its short)

But the LHS of BOTH equations aren't the same? One equation is non-squared and the other is squared. I don't get what you mean in this paragraph :S Thanks for taking the time to help

Hi Fawun,

Spiral tells me that you need a bit of maths help and that you are quite shy in asking people. I will be here patrolling this thread the whole of the night, you don't have to feel anxious - asking questions is a natural part of the human condition. If you need any help throughout the night feel free to leave your question here or alternatively you can reach me through the messaging system.

awstarr

Haha yeah I must admit. I sometimes say that "I get it" when I actually don't (Carrot can confirm) and I tend not to ask questions because i'm scared that I will annoy people lol but thank you

 

[Sy123]

How will a question 'lead' or 'take' us if we don't know what to do? Isn't that why i'm suppose to ask questions to know what to do?

Well in general, we need to get straight down to earth about what the question is asking. The question asks us to find k and nothing else with the given equation and the condition that roots are equal. So the objective is to find k. Well since its a quadratic we know we can use sum and products of roots in order to get 2 equations. We solve simultaneously to get k. For these questions you just need to find the sum and product of the roots with the given conditions in order to get what we want.

But the LHS of BOTH equations aren't the same? One equation is non-squared and the other is squared. I don't get what you mean in this paragraph :S Thanks for taking the time to help

]

Yes initially the LHS are not the same, but I square both sides of ONE of them to get alpha squared on BOTH the LHS. Which in turn makes them equal hence elimination.

 

[awstarr]

Fawun,

Here is something I always tell younger kids: If you don't ask questions - you won't know something.

A few weeks later, you will be behind in your grade. It really does pay off to ask questions and the HSC shouldn't be something you should 'solo'. Also, if you are considering getting a tutor then make sure he/she places you in an environment that isn't condescending. You'll get discouraged and not turn up to class.

Just raising your hand and asking questions will help at least 2 other people in your classroom as they are likely to not know as well. Plus you will be miles ahead of another kid who doesn't ask.

If you bottle it away, you realise once you get home, it can take up to hours to figure out concepts yourself.

 

[SpiralFlex]

Fawun,

Here is something I always tell younger kids: If you don't ask questions - you won't know something.

A few weeks later, you will be behind in your grade. It really does pay off to ask questions and the HSC shouldn't be something you should 'solo'. Also, if you are considering getting a tutor then make sure he/she places you in an environment that isn't condescending. You'll get discouraged and not turn up to class.

Just raising your hand and asking questions will help at least 2 other people in your classroom as they are likely to not know as well. Plus you will be miles ahead of another kid who doesn't ask.

If you bottle it away, you realise once you get home, it can take up to hours to figure out concepts yourself.

This.

Young Fawn you're not annoying anyone, imo if teachers can't stand students asking questions they shouldn't be teaching.

 

[Fawun]

The numbers 3, x, y are in arithmetic progression and x, y 25 are in geometric progression. Find x and y.

Lolwat

 

[SpiralFlex]

The numbers 3, x, y are in arithmetic progression and x, y 25 are in geometric progression. Find x and y.

Lolwat

Have you learnt those terms before? You need to know what they are first.

 

[deswa1]

The numbers 3, x, y are in arithmetic progression and x, y 25 are in geometric progression. Find x and y.

Lolwat

x-3=y-x (arithmetic progression)
2x=y+3 (Piece of info 1)

y/x=25/y (geometric progression)
25x=y^2 (Piece of info 2)

Now solve 1 and 2 simultanously

 

[SpiralFlex]

Blergh, Fawn how are you learning this?

 

[Fawun]

x-3=y-x (arithmetic progression)
2x=y+3 (Piece of info 1)

y/x=25/y (geometric progression)
25x=y^2 (Piece of info 2)

Now solve 1 and 2 simultanously

Thank you

Blergh, Fawn how are you learning this?

Tutor

I am behind. Trying to catch up.

 

[enoilgam]

Stay on topic guys.

 

[Fawun]

Can someone please tell me if i'm doing this question right?









Is that right? I've checked it a million times yet the answer says that it's 87376

Did I do something wrong in my working out? Thanks

 

[SpiralFlex]

Can someone please tell me if i'm doing this question right?









Is that right? I've checked it a million times yet the answer says that it's 87376

Did I do something wrong in my working out? Thanks

You are correct.

 

[Carrotsticks]

For the record, Fawun, best to write down the last 2 terms as well, so you can see the pattern distinctly.

 

[SpiralFlex]

I'm impressed Fawn learnt LaTeX at a rapid rate.

 

[deswa1]

A simple way Fawun to check that the answer in the book is wrong is notice that 5 to the power of any integer is a whole number so you're adding 0.2 (the initial term) to a bunch of whole numbers. Therefore any correct answer has to end in .2, but the answer didn't -> therefore its wrong

 

[Parvee]

I got the same answer.

 

[Fawun]

For the record, Fawun, best to write down the last 2 terms as well, so you can see the pattern distinctly.

What last two terms?

A simple way Fawun to check that the answer in the book is wrong is notice that 5 to the power of any integer is a whole number so you're adding 0.2 (the initial term) to a bunch of whole numbers. Therefore any correct answer has to end in .2, but the answer didn't -> therefore its wrong

So what you're saying is, is that any whole number to the power of 5 will have a .2 in the end? lol

I got the same answer.

Glad to know that I wasn't wrong.

 

[Carrotsticks]

What last two terms?

When you wrote the summation, you only wrote the first 3 terms, then the "..." (ellipsis, or should I say ... ellipses)

But you should write the first 3 terms, then ..., then the last 2 terms.

So for example:



An ellipsis after a series generally implies an infinite series, for example: