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[the-pi-guy]

Can I ask what X is? It seems to be a set of numbers, but I'm not sure what we're looking at.

X is a set of 15 integers.
Don't want to share the exact set, because it's a teacher made up problem. (Probably not a good reason...)

Basically it's a set made up of numbers similar to this:
{1,7,-49,343, -117993, 17206, etc}

How would I show there's no subset that sums to 15?
Any tips or things to look for?

 

[Link1110]

Can someone help me with this math problem!
You're building a new house on the cartesian plane measured in miles. Your house is at 2,0, and the gas line is on the curve sqrt(16x^2+5x +16). WHat's the cheapest you can pay to get it hooked up to your house.
OK, so first I make an erquation. Using the point distance formula, I get sqrt(17x^2+x+20). I differentiate that to;
17x+1/2*sqrt(17x^2+x+20)
This function has one zero; -1/17. that thing in the square root has no real zeroes, so the function is never undefined. Also, I can testthe derivitive and confirm that the -1/17 is indeed a minimum, since the function is decreasing before it and increasing after.
Plugging -17 into the original equation gets me 3.970044 (i did that math in R) and then plugging all the points (0,2) and (-1/17,3.970044) into the distance formula gets me 1.970922. Times 400 is 788.37 (rounded to the nearest hundreth) but it's wrong.
I'm really stuck here!

 

[BlueLiquid]

Can someone help me with this math problem!
You're building a new house on the cartesian plane measured in miles. Your house is at 2,0, and the gas line is on the curve sqrt(16x^2+5x +16). WHat's the cheapest you can pay to get it hooked up to your house.
OK, so first I make an erquation. Using the point distance formula, I get sqrt(17x^2+x+20). I differentiate that to;
17x+1/2*sqrt(17x^2+x+20)
This function has one zero; -1/17. that thing in the square root has no real zeroes, so the function is never undefined. Also, I can testthe derivitive and confirm that the -1/17 is indeed a minimum, since the function is decreasing before it and increasing after.
Plugging -17 into the original equation gets me 3.970044 (i did that math in R) and then plugging all the points (0,2) and (-1/17,3.970044) into the distance formula gets me 1.970922. Times 400 is 788.37 (rounded to the nearest hundreth) but it's wrong.
I'm really stuck here!

A couple of things here:

1. Your derivative is wrong. The 17x term you have should also have sqrt(17x^2+x+20) as a denominator. I would just write it as (34x + 1) / (2*sqrt(17x^2+x+20)).

2. Because the square root function is strictly increasing, the greater the stuff under the root, the greater the root of that stuff. Likewise the lesser it is, the lesser the root will be. So to minimize the distance you need only minimize the function f(x) = 17x^2+x+20 and save yourself some trouble on derivatives. Note that the derivative of f here is the same as the numerator in the derivative in 1. above.

 

[Link1110]

A couple of things here:

1. Your derivative is wrong. The 17x term you have should also have sqrt(17x^2+x+20) as a denominator. I would just write it as (34x + 1) / (2*sqrt(17x^2+x+20)).

2. Because the square root function is strictly increasing, the greater the stuff under the root, the greater the root of that stuff. Likewise the lesser it is, the lesser the root will be. So to minimize the distance you need only minimize the function f(x) = 17x^2+x+20 and save yourself some trouble on derivatives. Note that the derivative of f here is the same as the numerator in the derivative in 1. above.

17x+1
------------------
2*sqrt(17x^2+x+20)

Sorry, that's my derivitive. The way I typed it may be strange. Why is it 34x +1 and not 17x?

As for the second part, gotta read that a few times and wrap my head around it. Takes me a while to process this stuff haha

 

[bidguy]

can someone explain how you get from this graph to the next ? second graph is the sampling of the first graph btw, whats bothering me is the 1/2pi multiplication of Y(w) on the second picture... apparently x axis is named W/W0 in the second pic instead of just W but how does that get rid of the 1/2pi ?

just to be clear i know whats happening here, my signal Y(w) gets convoluted with tons of dirac impulses so it gets copied at every w0 of the dirac impulse

just cant really comprehend how changing x axis from w to w/w0 enables me to ignore the 1/2pi ...

1:

2:

you can also send me a pm if youd like id really appreciate it

 

[the-pi-guy]

How can I simplify stacked exponents?

(((((2^4)^8)^16)^32)^....^k)

You use two facts:

1) When you raise something to a power you are effectively multiplying the exponents
2) When you multiply two powers of the same number, you add the exponents

Thanks! Was a huge help!

 

[FortuneFaded]

How can I simplify stacked exponents?

(((((2^4)^8)^16)^32)^....^k)

You use two facts:

1) When you raise something to a power you are effectively multiplying the exponents
2) When you multiply two powers of the same number, you add the exponents

So we have (((((((2^(2^2))^2^3)^2^4)))...

= (2^(2^(2+3+4+....

(Just start with a couple and you will see the pattern)

= 4^(2+3+4+...

= 4^((1/2)(n+1) - 1)

where k = 2^n

 

[Pau]

Nevermind, figured them out!

 

[Allonym]

Can anyone help me out with these problems from my Precalc review? I'll post the image which contains the problem...actually I posted a link because I'm now sure how to embed the image but yes, if you could follow the link and offer some explanation I'd greatly appreciate it. Question #2 please

https://imageshack.us/i/pmLPzGRij

 

[Fou-Lu]

I have no idea what I am doing with this Fisher Discriminant stuff. I am used to just running the integrated functions in R if I want stats information. I was given two sample data sets (background and signal) and asked to construct a Fisher Linear Discriminant function, which I have done, but then I was given a third data set and asked to extract the signal from it using my Fisher function. I have absolutely ZERO idea of how to do this.

 

[kgtrep]

Can anyone help me out with these problems from my Precalc review? I'll post the image which contains the problem...actually I posted a link because I'm now sure how to embed the image but yes, if you could follow the link and offer some explanation I'd greatly appreciate it. Question #2 please

https://imageshack.us/i/pmLPzGRij

The problem asks you to recall the properties of a logarithmic function and apply them to evaluate log(x) for certain values of x.

For any positive numbers x and y, and any real number n,

log(x*y) = log(x) + log
log(x/y) = log(x) - log
log(x^n) = n * log(x).

These are true in any logarithmic base, so I will omit the base a that is stated in your problem.


To evaluate log(15) using the given information, note that 15 = 5 * 3. Hence,

log(15) = log(5 * 3) = log(5) + log(3) = 2.3 + 1.6 = 3.9.

I'll leave you think about what to do for 5a and 3/a^2.

 

[Allonym]

The problem asks you to recall the properties of a logarithmic function and apply them to evaluate log(x) for certain values of x.

For any positive numbers x and y, and any real number n,

log(x*y) = log(x) + log
log(x/y) = log(x) - log
log(x^n) = n * log(x).

These are true in any logarithmic base, so I will omit the base a that is stated in your problem.


To evaluate log(15) using the given information, note that 15 = 5 * 3. Hence,

log(15) = log(5 * 3) = log(5) + log(3) = 2.3 + 1.6 = 3.9.

I'll leave you think about what to do for 5a and 3/a^2.

Thanks for the help. I really appreciate it. I understand the first three but the final two don't really make sense to me. Could you guide me through those? for the first 3 I got;

2a.)3.9, because 3*5 =15 and this let's you know that it's using the addition of logs
2b.)3.2, I assume you'll multiply the exponent 1.6 by 2
2c.)0.7, this one you subtracting the 2.3 and 1.6 which is indicated by 5/3

I know you're expecting me to think critically about the final 2 but I don't know where to even begin. Is it a combination of logarithmic properties?

 

[AntraxSuicide]

Thanks for the help. I really appreciate it. I understand the first three but the final two don't really make sense to me. Could you guide me through those? for the first 3 I got;

2a.)3.9, because 3*5 =15 and this let's you know that it's using the addition of logs
2b.)3.2, I assume you'll multiply the exponent 1.6 by 2
2c.)0.7, this one you subtracting the 2.3 and 1.6 which is indicated by 5/3

I know you're expecting me to think critically about the final 2 but I don't know where to even begin. Is it a combination of logarithmic properties?

5a=5*a so use addition of logarithms here to pull that apart.

Same for the second one. The trick is to know what log(a) is.

 

[Allonym]

5a=5*a so use addition of logarithms here to pull that apart.

Same for the second one. The trick is to know what log(a) is.

And that's where I'm stumped. I fucking hate math...well at least at this moment because this stuff isn't clicking for me. Isn't "a" the base? Yet knowing that doesn't seem to help me. Like with 5a, even though I know it's the addition property how does that get me the answer of 3.3? Like 2.3 was added with 1 but how did I get that 1? Same with the 3/a^2. This is all so confusing.

 

[kgtrep]

And that's where I'm stumped. I fucking hate math...well at least at this moment because this stuff isn't clicking for me. Isn't "a" the base? Yet knowing that doesn't seem to help me. Like with 5a, even though I know it's the addition property how does that get me the answer of 3.3? Like 2.3 was added with 1 but how did I get that 1? Same with the 3/a^2. This is all so confusing.

Don't worry. The key is that a logarithmic function is the inverse function of an exponential function, i.e. a logarithmic function "undoes" what an exponential function does.


By definition, log_a(x) is the exponent---let's call it y---such that a^y will give us x.

In other words, the equation

(1) y = log_a(x)

is equivalent to the equation,

(2) a^y = x.


Let's look at (1). If the base is a and x is a, the base, what is log_a(a)?

Well, we see from (2) that this question is equivalent to solving the equation,

a^y = a.

Clearly, we must have y = 1.


In summary, for any base a, it is true that,

log_a(a) = 1.

Use this fact along with the properties that I mentioned before to evaluate log_a(5a) and log_a(3/a^2).

 

[Psycho_Mantis]

I don't know if I'm just being ignorant here but is there an analytical way to solve this equation with pen and paper:

y = (1-x^10)/(1-x)

Of course I can use numerical methods but I feel like I'm missing something obvious?

 

[Therion]

I don't know if I'm just being ignorant here but is there an analytical way to solve this equation with pen and paper:

y = (1-x^10)/(1-x)

Of course I can use numerical methods but I feel like I'm missing something obvious?

1 - x^10 factors to (1 - x)(1 + x + x^2 + ... + x^8 + x^9), so y = 1 + x + x^2 + ... + x^8 + x^9 for x != 1.

That simplifies it; I wasn't sure what you meant by solving it. The simplification would immediately give you x = -1 as a root, but you could get that from the original anyway.

 

[Psycho_Mantis]

1 - x^10 factors to (1 - x)(1 + x + x^2 + ... + x^8 + x^9), so y = 1 + x + x^2 + ... + x^8 + x^9 for x != 1.

That simplifies it; I wasn't sure what you meant by solving it. The simplification would immediately give you x = -1 as a root, but you could get that from the original anyway.

Sorry, I should of wrote something like this:

20 = (1-x^10)/(1-x)

 

[Wollan]

I need to shorten (1-x^2) / (x^2-x-2)

The end result is supposed to be (1-x) / (x-2)

I use the quadratic formula on the divisor:
(x^2-x-2) --> (1±√(-1^2)-(4⋅1⋅-2)) / (2⋅1) --> (1±√1+8) / 2 --> x = 2 or x = -1
...and end up with (x-2)(x+1)

I'm not sure about the dividend though: 1-x^2
Whatever I factor it to should contain (x+1) so I can remove the term from the divisor and the dividend ends up as 1-x.

 

[AntraxSuicide]

Sorry, I should of wrote something like this:

20 = (1-x^10)/(1-x)

Same thing they posted above, but you'll need to solve a giant polynomial instead.

Or solve algebraically:
20-20x = (1-x^10)
(x^10)-20x+19 = 0.

Then solve that one.

I need to shorten (1-x^2) / (x^2-x-2)

The end result is supposed to be (1-x) / (x-2)

I use the quadratic formula on the divisor:
(x^2-x-2) --> (1±√(-1^2)-(4⋅1⋅-2)) / (2⋅1) --> (1±√1+8) / 2 --> x = 2 or x = -1
...and end up with (x-2)(x+1)

I'm not sure about the dividend though: 1-x^2
Whatever I factor it to should contain (x+1) so I can remove the term from the divisor and the dividend ends up as 1-x.

That numerator factors into (1+x)(1-x). It's the standard factorization for the difference of two perfect squares.

 

[Wollan]

But how can I drop the (x+1) term from the divisor(denominator)?

 

[Chilli_Axe]

But how can I drop the (x+1) term from the divisor(denominator)?

Partial fraction decomposition should be able to do this

 

[Hypertrooper]

I have to show that the generator polynom of the intersection of two cyclic codes C and D is lcm(g,h) where g is the generator polynom of C and h the generator polynom of D.

We had the following equivalence which we call Lemma in this post:
g is generator polynom of cyclic code C iff g is an element of C and for all elements b of C: g divides b.

If you do not know what cyclic code is, just imagine that C and D are principle ideals of the integers.

In the following, I is defined as the intersection of C and D.

My proof would be the following:

Let e:=lcm(g,h). Since g divides e and h divides e, it follows that e is an element of C and an element of D. Therefore e is an element of I.

Let c be an arbitrary element of I. Therefore c is a common multiple of g and h. Since e is the least common multiple of g and h, it follows that e divides c. Because c is arbitrarily chosen, it follows with the Lemma that e is the generator polynom of I.

The proof was pretty easy and that's the reason why I am distrustful. Did I miss something?

 

[myco666]

Any logic mathematicians here?

Need to show that following set isn't complete (not entirely sure if this the correct term here as I am not native english speaker)

Basically what I've done is that I say if v(a)=1 and v(b)=1 then v(A)=1. But if v(a)=1 and v(b)=0 then v(A)=0. a is the first symbol, b the latter and A is the set in question. From here I can say that you can prove A and not A meaning it is contradictory and therefore not complete.

However this feels way too easy solution so I am doubting myself.

edit. nevermind. figured it out lol.

 

[XenodudeX]

Hi. I was wondering if someone could help me with a discreet mathematics problem?

If n is a perfect square , then n + 2 is not a perfect square.

Now I originally answered this by saying: n = 4, which is a perfect square. So 4 +2 = 6 , which is not a perfect square. Would this be the correct answer?

 

[Linkstrikesback]

Hi. I was wondering if someone could help me with a discreet mathematics problem?

If n is a perfect square , then n + 2 is not a perfect square.

Now I originally answered this by saying: n = 4, which is a perfect square. So 4 +2 = 6 , which is not a perfect square. Would this be the correct answer?

I mean, if all they want is a contradiction, then sure.

You could always do it more concretely though.

edit: Person below me did it faster than I could edit it in, haha.

;(

 

[Biggest-Geek-Ever]

Hi. I was wondering if someone could help me with a discreet mathematics problem?

If n is a perfect square , then n + 2 is not a perfect square.

Now I originally answered this by saying: n = 4, which is a perfect square. So 4 +2 = 6 , which is not a perfect square. Would this be the correct answer?

Not quite. If the question was "If n is a perfect square , then n + 2 is a perfect square", your answer would be sufficient, since one contradictory example is enough. But you are being asked to show that n + 2 is not a perfect square for all n. I would prove by contradiction. (Note this holds trivially for n = 0)

Let n be a perfect square greater than 0. Assume, for sake of contradiction, that n + 2 is a perfect square. Then we have

n = k^2
n + 2 = j^2

where k and j are integers. We have that j > k which implies that j ≥ k + 1. Hence

j^2 = n + 2 ≥ (k + 1)^2 = k^2 + 2k + 1 ≥ k^2 + 3

See if you can see the contradiction here.

 

[XenodudeX]

Not quite. If the question was "If n is a perfect square , then n + 2 is a perfect square", your answer would be sufficient, since one contradictory example is enough. But you are being asked to show that n + 2 is not a perfect square for all n. I would prove by contradiction. (Note this holds trivially for n = 0)

Let n be a perfect square greater than 0. Assume, for sake of contradiction, that n + 2 is a perfect square. Then we have

n = k^2
n + 2 = j^2

where k and j are integers. We have that j > k which implies that j ≥ k + 1. Hence

j^2 = n + 2 ≥ (k + 1)^2 = k^2 + 2k + 1 ≥ k^2 + 3

See if you can see the contradiction here.

I don't understand that at all. It might was well be gibberish.

Edit: So this question is actually a proof by contradiction question?

 

[kgtrep]

I don't understand that at all. It might was well be gibberish.

Edit: So this question is actually a proof by contradiction question?

Yes, you can prove the statement by contradiction. Allow me to clarify Biggest-Geek-Ever's proof.


Suppose we can write both n (> 0) and n + 2 as perfect squares.

Then, for some integers k and j, we must have,

n = k^2, n + 2 = j^2.

From these equations, we see that,

(1) j^2 = k^2 + 2.


On the other hand, we know that |j| > |k| (since n + 2 is greater than n).

We can turn the strict inequality to an inequality because j and k are integers:

|j| >= |k| + 1

Square both sides and the inequality remains true:

j^2 >= k^2 + 2|k| + 1.

Since k is a nonzero integer (I assumed that n > 0), we know that |k| >= 1. Hence,

(2) j^2 >= k^2 + 3


Combine (1) and (2) to arrive at a contradiction, k^2 + 2 >= k^2 + 3.

Hence, our initial assumption that both n and n + 2 are perfect squares must be incorrect.

 

[Biggest-Geek-Ever]

I don't understand that at all. It might was well be gibberish.

Edit: So this question is actually a proof by contradiction question?

Yes. Whenever you're asked to show something is not true in math, a lot of times the best way is by contradiction. edit: Thanks kgtrep!


Another way to proceed with the proof would be to show that, if n = k^2 and n + 2 = j^2, then

2 = (n + 2) - n = j^2 - k^2 = (j +k)(j -k)

gives you a contradiction. Since j and k are both integers, their sum and difference are both integers. j - k < j +k, so we then have

j + k = 2
j - k = 1

since 2*1 is the only possible integer product that gives you 2. From the second equation, we get that k= j - 1. Plugging that into the first, we then have 2j = 3, ie j = 3/2. Contradiction.

 

[XenodudeX]

Yes. Whenever you're asked to show something is not true in math, a lot of times the best way is by contradiction. edit: Thanks kgtrep!


Another way to proceed with the proof would be to show that, if n = k^2 and n + 2 = j^2, then

2 = (n + 2) - n = j^2 - k^2 = (j +k)(j -k)

gives you a contradiction. Since j and k are both integers, their sum and difference are both integers. j - k < j +k, so we then have

j + k = 2
j - k = 1

since 2*1 is the only possible integer product that gives you 2. From the second equation, we get that k= j - 1. Plugging that into the first, we then have 2j = 3, ie j = 3/2. Contradiction.

Could you explain how you got this?

2 = (n + 2) - n = j^2 - k^2 = (j +k)(j -k)

 

[Biggest-Geek-Ever]

Could you explain how you got this?

That's the difference of squares identity: for any real numbers a and b, we have that

a^2 - b^2 = (a + b)(a - b)


Which is easily verified by expanding the right hand side out:

(a + b)(a - b) = a*a - a*b + b*a - b*b = a^2 - a*b + b*a - b^2 = a^2 - b^2

since - a*b + b*a = 0. We defined n + 2 and n as k^2 and j^2, respectively, and 2 = n + 2 - n, so thus we have

2 = (j + k)(j - k)

 

[ZBR]

So what's the most effective way to study for math? I'm currently in a Pre-cal/Trig class that's 5 credit hours and the teacher is just blowing through everything. I did pretty well on the first exam but I was wondering if there was another way to study for them. My current method consists of just staring at my notes and trying to memorize as much as I can. I do all the homework for the class and during the homework I can figure it all out but when it comes to testing, I have trouble remembering things. Any effective ways that you guys have learned to be able to soak in the knowledge instead of just memorizing and forgetting?

 

[Therion]

So what's the most effective way to study for math? I'm currently in a Pre-cal/Trig class that's 5 credit hours and the teacher is just blowing through everything. I did pretty well on the first exam but I was wondering if there was another way to study for them. My current method consists of just staring at my notes and trying to memorize as much as I can. I do all the homework for the class and during the homework I can figure it all out but when it comes to testing, I have trouble remembering things. Any effective ways that you guys have learned to be able to soak in the knowledge instead of just memorizing and forgetting?

Spend some time looking at the reasoning behind what you're studying. If it isn't showing up during class, it should be in the textbook. Then instead of trying to memorize seemingly random formulas, you'll be memorizing things that actually make sense, so you can more easily fill in any gaps where you do happen to forget.

 

[kgtrep]

So what's the most effective way to study for math? I'm currently in a Pre-cal/Trig class that's 5 credit hours and the teacher is just blowing through everything. I did pretty well on the first exam but I was wondering if there was another way to study for them. My current method consists of just staring at my notes and trying to memorize as much as I can. I do all the homework for the class and during the homework I can figure it all out but when it comes to testing, I have trouble remembering things. Any effective ways that you guys have learned to be able to soak in the knowledge instead of just memorizing and forgetting?

Tell yourself a story, think about why what you're studying would matter and where it can be applied. You can go online (or ask us) if your textbook doesn't explain these.

 

[Aikidoka]

So what's the most effective way to study for math? I'm currently in a Pre-cal/Trig class that's 5 credit hours and the teacher is just blowing through everything. I did pretty well on the first exam but I was wondering if there was another way to study for them. My current method consists of just staring at my notes and trying to memorize as much as I can. I do all the homework for the class and during the homework I can figure it all out but when it comes to testing, I have trouble remembering things. Any effective ways that you guys have learned to be able to soak in the knowledge instead of just memorizing and forgetting?

You should also do more problems. If you have a textbook then try to do all the problems for each chapter.

 

[ZBR]

Thank you guys! We had our first test last week in which I got a B on so I didn't do so bad but it's still the beginning. I guess we have another test next week so if I have any questions I will definitely ask. The teacher is nice and I can tell that she knows what she's doing but I also think teaching this class is her second job while teaching in a middle or high school is her first so she is always rushing to get done early. She doesn't have office hours and the only time we really get to answer questions is after class. We can email her but it's kind of tough communicating that way.

 

[M.D]

Can anyone help me with

x=vt
v=v0+at


I'm missing V and T
I can say that v=x/t and equate that to x/t=v0+at, then if I multiply by t I get at^2+v0t-x but I'm not sure how to exprees t1,2 with paramaters, or if it's the right direction in the first place

Any help will be much apprrciated

 

[XenodudeX]

So I'm having a little trouble with a Mathematical Induction problem:

Let P be the statement that 1^3 +2^3 +···+n^3 = (n(n+1)/2)^2 for the positive integer n.

I can figure out the basis step okay, but the real problem comes with the induction part.

I basically have to prove that 1^3+ 2^3+...+k^3+(k+1)^3 = ((k+1)(k+2)/2)^2

How do I do this?

edit: I managed to get (k(k+1)/2)^2 + (k+1)^3 , but I'm having a really hard time simplifying this further.

 

[surjective]

So I'm having a little trouble with a Mathematical Induction problem:

edit: I managed to get (k(k+1)/2)^2 + (k+1)^3 , but I'm having a really hard time simplifying this further.

There is a (k+1)^2 term that shows up twice in that last sum.

 

[XenodudeX]

There is a (k+1)^2 term that shows up twice in that last sum.

huh?

 

[Koren]

huh?

Well... you want to do something like this:

1^3+ 2^3+...+k^3+(k+1)^3

= 1^3+ 2^3+...+k^3 + (k+1)^3

= ((k)(k+1)/2)^2 + (k+1)^3

= (missing part)

= ((k+1)(k+2)/2)^2


In this situation, one solution is to take the two elements that are really similar, and find how you go from one to the other: ((k)(k+1)/2)^2 to ((k+1)(k+2)/2)^2

Then, the idea is to find common pieces, and differences. You want to go fro

((k+1)/2)^2 * k^2 to ((k+1)/2)^2 * (k+2)^2

((k+1)/2)^2 * k^2 to ((k+1)/2)^2 * (k^2 + 4k + 4)

((k+1)/2)^2 * k^2 to ((k+1)/2)^2 * k^2 + ((k+1)/2)^2 * (4k + 4)


Then, the issue is to link the difference, ((k+1)/2)^2 * (4k + 4), and (k+1)^3.

You then just have to put all pieces togethers

 

[Wollan]

I need help with some basic Polynomial division:

My calculation:

The answer is supposed to be:

I have no idea how they got 13 at that term.

 

[Hypertrooper]

I need help with some basic Polynomial division:

My calculation:

The answer is supposed to be:

I have no idea how they got 13 at that term.

Are you doing the polynomial division in a finite field/ring? If not, your mistake is already in the first line. You are supposed to subtract -(4x^4-16x^2) from 4X^4-5X^3-3X^2+X-9, so you get -5X^3+13X^2+X-9.

You continue with -5X. So your second subtracting would be with -(-5X^3+20X), and then you get 13X^2+21X-9.

 

[Wollan]

Are you doing the polynomial division in a finite field/ring? If not, your mistake is already in the first line.

Cheers. This concept hasn't been brought up in the book so far. It's one of the optional extra exercises for the chapter so I guess a teacher (or private trial/error/research) was supposed to fill in the blanks here.

 

[crimsondynamics]

Halp please!

1) A wooden cuboid of volume 135cm3 is put into a rectangular water tank. One third of the wooden cuboi is lying above the water level. If the water level has risen by 3cm, find the base area of the water tank.

2) Some marbles are immersed in water in a rectangular vessel measuring 5cm x 4cm (l x w). If 10 more marbles each of volume 4cm3 are put into the vessel and no water overflows, find the rise in water level.

Spoiler

lolwut

 

[Koren]

Halp please!

1) A wooden cuboid of volume 135cm3 is put into a rectangular water tank. One third of the wooden cuboi is lying above the water level. If the water level has risen by 3cm, find the base area of the water tank.

2) Some marbles are immersed in water in a rectangular vessel measuring 5cm x 4cm (l x w). If 10 more marbles each of volume 4cm3 are put into the vessel and no water overflows, find the rise in water level.

Spoiler

lolwut

1) water is incompressible, so its volume doesn't change.

Let's call x the surface of the base.

In the first case, the volume of water istimes h

In the second case, the volume is (x-s) times (h+3) where s is the area of a side of the cuboid.

(computations done in centimeters)

We'll need h, but the exercise hint at how much is h+3...

2) It's the same idea...

The volume of water in the first case is (4 times 5 times h1) minus V1 where h1 is the height level of water and V1 the volume occupied by marbles.

In the second case, it's (4 times 5 times h2) minus (V1 + V2) where V2 is the volume of the additional marbles.

Since no water have been added/removed, it's the same volume in both cases.

V1 will disappear in calculations, and you're after something involving v2 and v1...

 

[Link1110]

How do I differentiate the power series: (&#8722;(4n&#8722;7)x^n) / (6n+7)

I've been at this for over an hour, and I'm really stuck! The lecture just said to differentite that, but none of the choices have (6n+7)^2 in the denominator. Rather stuck here.

 

[ibyea]

How do I differentiate the power series: (&#8722;(4n&#8722;7)x^n) / (6n+7)

I've been at this for over an hour, and I'm really stuck! The lecture just said to differentite that, but none of the choices have (6n+7)^2 in the denominator. Rather stuck here.

Use the power rule. Remember you are differentiating with respect to x, so it's not like anything else matters. All the other stuff are just constants.

 

[Link1110]

Use the power rule. Remember you are differentiating with respect to x, so it's not like anything else matters. All the other stuff are just constants.

I need a derivitive power series, probably should've said that. So can't just do n(4n-7)*x^n-1


Trying to work backward, I save scummed the answer out of the multiple choices, and itr has a 6n+13 on the bottom. I figured that I have to differentiate, distribute the n, and then change all the ns in the equation to n+1s. Not sure why I have to do that