# Hard thinking questions

1. Oct 21, 2010

### I Like Pi

1. The problem statement, all variables and given/known data

a) given, a + 5 and 2a-1, one is 40% greater than the other one, solve for a.

b) given, 5x$$^{4}$$ + 4x$$^{3}$$ + 3x$$^{2}$$ + Px + Q. When divided by x$$^{2}$$ - 1, you get a remainder of 0, solve for p and q.

c) given csc(6b + $$\frac{pi}{8}$$) = sec(2b - $$\frac{pi}{8}$$), solve for b.

2. Relevant equations

3. The attempt at a solution

please help, i can't get started on these three at all...

edit:

c) i know that cscx = 1/sinx and secx = 1/cosx, i then cross multiplied to get $$cos(2b-pi/8) = sin(6b+pi/8)... Last edited: Oct 21, 2010 2. Oct 21, 2010 ### Quinzio Question a) shouldn't be a problem at all. Any attempt by you ? 3. Oct 21, 2010 ### I Like Pi Would it be (a+5) = .4(2a-1) + 2a-1 ? or .4(a+5) + (a+5) = 2a - 1 ? 4. Oct 21, 2010 ### Quinzio It's not clear from the text. Choose one and go on, or solve both in sequence. 5. Oct 21, 2010 ### I Like Pi well then you get a+5 = 0.8a - 0.4 + 2a -1 a+5 = 2.8a - 1.4 1.8a - 6.4 = 0 1.8a = 6.4 a = 3.55555556 or 2a - 1 = .4a + 2 + a + 5 2a - 1 = 1.4a + 7 0.6a - 8 = 0 0.6a = 8 a = 13.3333333 therefore a can be 13.333 or 3.555 ? 6. Oct 21, 2010 ### Quinzio yes. 7. Oct 21, 2010 ### I Like Pi thanks could you help me get started on b) ? Thanks for your time! 8. Oct 21, 2010 ### Quinzio b) Make this multiplication [tex] (x^2-1)(Ax^2+Bx+C)$$

9. Oct 21, 2010

### I Like Pi

that would give you $$ax^4 + bx^3 + (c - a)x^2 - bx - c$$. Is that what you mean?

10. Oct 21, 2010

### Quinzio

Ok, so now give the solution. It's really easy.

11. Oct 21, 2010

### I Like Pi

do you use the original equation? so a = 5, b = 4, and c = 3?

but that doesn't work... cause then you get:$$5x^4 + 4x^3 + (3 - 5)x^2 - 4x - 3$$

12. Oct 21, 2010

### Quinzio

You realize by yourself there's something wrong. Ok.

You should come alone to the solution. The next step would be giving you the solution.

13. Oct 21, 2010

### I Like Pi

I don't see what I could possibly do to get the answer I know that c - a = 3, that's all... but c itself is 3

14. Oct 21, 2010

### Quinzio

Why you say "c itself is 3"... ???
Tell me where is written that ?

15. Oct 21, 2010

### I Like Pi

oh, well i based it on the original... a = 5, b = 4, c = 3...

well, then if that's the case,

$$ax^4 + bx^3 + (c - a)x^2 - bx - c$$
$$=5x^4 + 4x^3 + (c - 5)x^2 - 4x - c$$
therefore
$$c = 8$$?
and therefore:
$$P = -4$$
$$Q = -8$$

is that what you meant?

Thanks for your help! Means a lot!

Last edited: Oct 21, 2010
16. Oct 21, 2010

### zgozvrm

Not quite....
You solve for the cases where one term is 40% of the other, not 40% greater then the other, as the question asked!

In other words, suppose you have a number (let's say 20) and you want to find the value that is 40% greater.
0.4 * 20 = 8 which is clearly not 40% greater. In fact, it is less!

What would you do to determine the value that is 40% greater than 20?

17. Oct 21, 2010

### I Like Pi

Well you would do .4 * 20 + 20, a value 40% greater then 20 is 28?

18. Oct 21, 2010

### zgozvrm

Yes, but that simplifies...

0.4 * 20 + 20 = (0.4 + 1) * 20 = 1.4 * 20

Therefore, a number that is 40% larger than x is 1.4 * x

19. Oct 21, 2010

### 94JZA80

well at first glance (and i do mean i only "glanced" at it for a split second), i thought the same thing...here are the equations he set up:
look closer at the right-hand side of the first equation. 0.4(2a-1) + 2a-1 = 1.4(2a-1), and the original equation becomes a+5 = 1.4(2a-1), which certainly implies that a+5 is 40% larger than 2a-1. likewise, we can see that the left-hand side of the 2nd equation, 0.4(a+5) + (a+5), equals 1.4(a+5). and so equation 2 becomes 1.4(a+5) = 2a-1, which certainly implies that 2a-1 is 40% greater than a+5.

your calculations are correct - you just chose to represent the quantity on one side ofthe equation as 0.4x + x instead of 1.4x.

20. Oct 21, 2010

### tiny-tim

Hi I Like Pi!!

(since you like them so much, have a pi: π )
Yes, and now use cosθ = sin(π/2 - θ) to get that in the form sinA = sinB.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
The text passage contains a series of mathematical questions and some attempts at solving them, but no complete answers are provided for all questions.
multiple_questions

1. the content structure includes a list of mathematical problems (a, b, c) with some initial attempts at solving them, followed by a discussion where the user and another participant (quinzio) work through the solutions.
2. the passage contains multiple mathematical questions, and partial solutions are provided for some of them, but not all questions are fully answered.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Hard thinking questions

1. Oct 21, 2010

### I Like Pi

1. The problem statement, all variables and given/known data

a) given, a + 5 and 2a-1, one is 40% greater than the other one, solve for a.

b) given, 5x$$^{4}$$ + 4x$$^{3}$$ + 3x$$^{2}$$ + Px + Q. When divided by x$$^{2}$$ - 1, you get a remainder of 0, solve for p and q.

c) given csc(6b + $$\frac{pi}{8}$$) = sec(2b - $$\frac{pi}{8}$$), solve for b.

2. Relevant equations

3. The attempt at a solution

please help, i can't get started on these three at all...

edit:

c) i know that cscx = 1/sinx and secx = 1/cosx, i then cross multiplied to get $$cos(2b-pi/8) = sin(6b+pi/8)... Last edited: Oct 21, 2010 2. Oct 21, 2010 ### Quinzio Question a) shouldn't be a problem at all. Any attempt by you ? 3. Oct 21, 2010 ### I Like Pi Would it be (a+5) = .4(2a-1) + 2a-1 ? or .4(a+5) + (a+5) = 2a - 1 ? 4. Oct 21, 2010 ### Quinzio It's not clear from the text. Choose one and go on, or solve both in sequence. 5. Oct 21, 2010 ### I Like Pi well then you get a+5 = 0.8a - 0.4 + 2a -1 a+5 = 2.8a - 1.4 1.8a - 6.4 = 0 1.8a = 6.4 a = 3.55555556 or 2a - 1 = .4a + 2 + a + 5 2a - 1 = 1.4a + 7 0.6a - 8 = 0 0.6a = 8 a = 13.3333333 therefore a can be 13.333 or 3.555 ? 6. Oct 21, 2010 ### Quinzio yes. 7. Oct 21, 2010 ### I Like Pi thanks could you help me get started on b) ? Thanks for your time! 8. Oct 21, 2010 ### Quinzio b) Make this multiplication [tex] (x^2-1)(Ax^2+Bx+C)$$

9. Oct 21, 2010

### I Like Pi

that would give you $$ax^4 + bx^3 + (c - a)x^2 - bx - c$$. Is that what you mean?

10. Oct 21, 2010

### Quinzio

Ok, so now give the solution. It's really easy.

11. Oct 21, 2010

### I Like Pi

do you use the original equation? so a = 5, b = 4, and c = 3?

but that doesn't work... cause then you get:$$5x^4 + 4x^3 + (3 - 5)x^2 - 4x - 3$$

12. Oct 21, 2010

### Quinzio

You realize by yourself there's something wrong. Ok.

You should come alone to the solution. The next step would be giving you the solution.

13. Oct 21, 2010

### I Like Pi

I don't see what I could possibly do to get the answer I know that c - a = 3, that's all... but c itself is 3

14. Oct 21, 2010

### Quinzio

Why you say "c itself is 3"... ???
Tell me where is written that ?

15. Oct 21, 2010

### I Like Pi

oh, well i based it on the original... a = 5, b = 4, c = 3...

well, then if that's the case,

$$ax^4 + bx^3 + (c - a)x^2 - bx - c$$
$$=5x^4 + 4x^3 + (c - 5)x^2 - 4x - c$$
therefore
$$c = 8$$?
and therefore:
$$P = -4$$
$$Q = -8$$

is that what you meant?

Thanks for your help! Means a lot!

Last edited: Oct 21, 2010
16. Oct 21, 2010

### zgozvrm

Not quite....
You solve for the cases where one term is 40% of the other, not 40% greater then the other, as the question asked!

In other words, suppose you have a number (let's say 20) and you want to find the value that is 40% greater.
0.4 * 20 = 8 which is clearly not 40% greater. In fact, it is less!

What would you do to determine the value that is 40% greater than 20?

17. Oct 21, 2010

### I Like Pi

Well you would do .4 * 20 + 20, a value 40% greater then 20 is 28?

18. Oct 21, 2010

### zgozvrm

Yes, but that simplifies...

0.4 * 20 + 20 = (0.4 + 1) * 20 = 1.4 * 20

Therefore, a number that is 40% larger than x is 1.4 * x

19. Oct 21, 2010

### 94JZA80

well at first glance (and i do mean i only "glanced" at it for a split second), i thought the same thing...here are the equations he set up:
look closer at the right-hand side of the first equation. 0.4(2a-1) + 2a-1 = 1.4(2a-1), and the original equation becomes a+5 = 1.4(2a-1), which certainly implies that a+5 is 40% larger than 2a-1. likewise, we can see that the left-hand side of the 2nd equation, 0.4(a+5) + (a+5), equals 1.4(a+5). and so equation 2 becomes 1.4(a+5) = 2a-1, which certainly implies that 2a-1 is 40% greater than a+5.

your calculations are correct - you just chose to represent the quantity on one side ofthe equation as 0.4x + x instead of 1.4x.

20. Oct 21, 2010

### tiny-tim

Hi I Like Pi!!

(since you like them so much, have a pi: π )
Yes, and now use cosθ = sin(π/2 - θ) to get that in the form sinA = sinB.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
user
The text passage contains a series of mathematical questions and some attempts at solving them, but no complete answers are provided for all questions.

TYPE: MULTIPLE_QUESTIONS

1. The content structure includes a list of mathematical problems (a, b, c) with some initial attempts at solving them, followed by a discussion where the user and another participant (Quinzio) work through the solutions.
2. The passage contains multiple mathematical questions, and partial solutions are provided for some of them, but not all questions are fully answered.